TSTP Solution File: ITP263^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP263^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 03:28:11 EDT 2023
% Result : Timeout 299.74s 300.17s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.44/2.50 % Problem : ITP263^3 : TPTP v8.1.2. Released v8.1.0.
% 2.44/2.51 % Command : do_cvc5 %s %d
% 2.50/2.72 % Computer : n021.cluster.edu
% 2.50/2.72 % Model : x86_64 x86_64
% 2.50/2.72 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.50/2.72 % Memory : 8042.1875MB
% 2.50/2.72 % OS : Linux 3.10.0-693.el7.x86_64
% 2.50/2.72 % CPULimit : 300
% 2.50/2.72 % WCLimit : 300
% 2.50/2.72 % DateTime : Sun Aug 27 11:18:00 EDT 2023
% 2.50/2.72 % CPUTime :
% 5.05/5.22 %----Proving TH0
% 5.05/5.22 %------------------------------------------------------------------------------
% 5.05/5.22 % File : ITP263^3 : TPTP v8.1.2. Released v8.1.0.
% 5.05/5.22 % Domain : Interactive Theorem Proving
% 5.05/5.22 % Problem : Sledgehammer problem VEBT_DeleteCorrectness 00648_039539
% 5.05/5.22 % Version : [Des22] axioms.
% 5.05/5.22 % English :
% 5.05/5.22
% 5.05/5.22 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.05/5.22 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.05/5.22 % Source : [Des22]
% 5.05/5.22 % Names : 0073_VEBT_DeleteCorrectness_00648_039539 [Des22]
% 5.05/5.22
% 5.05/5.22 % Status : Theorem
% 5.05/5.22 % Rating : 1.00 v8.1.0
% 5.05/5.22 % Syntax : Number of formulae : 11279 (5676 unt;1040 typ; 0 def)
% 5.05/5.22 % Number of atoms : 28262 (12153 equ; 0 cnn)
% 5.05/5.22 % Maximal formula atoms : 71 ( 2 avg)
% 5.05/5.22 % Number of connectives : 120711 (2833 ~; 535 |;1826 &;104831 @)
% 5.05/5.22 % ( 0 <=>;10686 =>; 0 <=; 0 <~>)
% 5.05/5.22 % Maximal formula depth : 39 ( 6 avg)
% 5.05/5.22 % Number of types : 101 ( 100 usr)
% 5.05/5.22 % Number of type conns : 4300 (4300 >; 0 *; 0 +; 0 <<)
% 5.05/5.22 % Number of symbols : 943 ( 940 usr; 64 con; 0-8 aty)
% 5.05/5.22 % Number of variables : 26550 (2592 ^;23216 !; 742 ?;26550 :)
% 5.05/5.22 % SPC : TH0_THM_EQU_NAR
% 5.05/5.22
% 5.05/5.22 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.05/5.22 % from the van Emde Boas Trees session in the Archive of Formal
% 5.05/5.22 % proofs -
% 5.05/5.22 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.05/5.22 % 2022-02-18 08:36:02.987
% 5.05/5.22 %------------------------------------------------------------------------------
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% 5.05/5.23 thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
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% 5.05/5.23 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
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% 5.05/5.23 thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
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% 5.05/5.23 thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
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% 5.05/5.23 thf(ty_n_t__Set__Oset_It__Num__Onum_J,type,
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% 5.05/5.23 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
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% 5.05/5.23 thf(ty_n_t__List__Olist_I_Eo_J,type,
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% 5.05/5.23 thf(ty_n_t__Set__Oset_I_Eo_J,type,
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% 5.05/5.23 thf(ty_n_t__Real__Oreal,type,
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% 5.05/5.23 thf(ty_n_t__Rat__Orat,type,
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% 5.05/5.23 thf(ty_n_t__Num__Onum,type,
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% 5.05/5.23 thf(ty_n_t__Nat__Onat,type,
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% 5.05/5.23 thf(ty_n_t__Int__Oint,type,
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% 5.05/5.23 thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
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% 5.05/5.23 thf(sy_c_Bit__Operations_Oand__int__rel,type,
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% 5.05/5.23 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
% 5.05/5.23 unique5052692396658037445od_int: num > num > product_prod_int_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 5.05/5.23 unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 5.05/5.23 unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Code____Numeral__Ointeger,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Complex__Ocomplex,type,
% 5.05/5.23 comm_s2602460028002588243omplex: complex > nat > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Int__Oint,type,
% 5.05/5.23 comm_s4660882817536571857er_int: int > nat > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Nat__Onat,type,
% 5.05/5.23 comm_s4663373288045622133er_nat: nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Rat__Orat,type,
% 5.05/5.23 comm_s4028243227959126397er_rat: rat > nat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Real__Oreal,type,
% 5.05/5.23 comm_s7457072308508201937r_real: real > nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 semiri3624122377584611663nteger: nat > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex,type,
% 5.05/5.23 semiri5044797733671781792omplex: nat > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Int__Oint,type,
% 5.05/5.23 semiri1406184849735516958ct_int: nat > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 5.05/5.23 semiri1408675320244567234ct_nat: nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Rat__Orat,type,
% 5.05/5.23 semiri773545260158071498ct_rat: nat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 5.05/5.23 semiri2265585572941072030t_real: nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 5.05/5.23 invers8013647133539491842omplex: complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 5.05/5.23 inverse_inverse_rat: rat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 5.05/5.23 inverse_inverse_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 5.05/5.23 at_bot_real: filter_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 5.05/5.23 at_top_nat: filter_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 5.05/5.23 at_top_real: filter_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 5.05/5.23 eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.05/5.23 eventu5826381225784669381omplex: ( produc4411394909380815293omplex > $o ) > filter6041513312241820739omplex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.05/5.23 eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.05/5.23 eventu3244425730907250241l_real: ( produc2422161461964618553l_real > $o ) > filter2146258269922977983l_real > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 5.05/5.23 eventually_real: ( real > $o ) > filter_real > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.05/5.23 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.05/5.23 filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.05/5.23 filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.05/5.23 princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.05/5.23 princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Filter_Oprod__filter_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 5.05/5.23 finite_card_o: set_o > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 5.05/5.23 finite_card_complex: set_complex > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 5.05/5.23 finite_card_int: set_int > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 5.05/5.23 finite_card_nat: set_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 5.05/5.23 finite410649719033368117t_unit: set_Product_unit > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 finite_card_set_nat: set_set_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 5.05/5.23 finite_card_char: set_char > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
% 5.05/5.23 finite_finite_o: set_o > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 5.05/5.23 finite3207457112153483333omplex: set_complex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 5.05/5.23 finite_finite_int: set_int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
% 5.05/5.23 finite_finite_list_o: set_list_o > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.05/5.23 finite8712137658972009173omplex: set_list_complex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Int__Oint_J,type,
% 5.05/5.23 finite3922522038869484883st_int: set_list_int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
% 5.05/5.23 finite8100373058378681591st_nat: set_list_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.05/5.23 finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 5.05/5.23 finite_finite_nat: set_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__Num__Onum,type,
% 5.05/5.23 finite_finite_num: set_num > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
% 5.05/5.23 finite_finite_rat: set_rat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 5.05/5.23 finite_finite_real: set_real > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.05/5.23 finite6551019134538273531omplex: set_set_complex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
% 5.05/5.23 finite6197958912794628473et_int: set_set_int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 finite1152437895449049373et_nat: set_set_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Finite__Set_Ofinite_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.05/5.23 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.05/5.23 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.05/5.23 comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 5.05/5.23 comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 5.05/5.23 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 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 ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.05/5.23 the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 5.05/5.23 gcd_Gcd_int: set_int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 5.05/5.23 gcd_Gcd_nat: set_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_GCD_Obezw,type,
% 5.05/5.23 bezw: nat > nat > product_prod_int_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_GCD_Obezw__rel,type,
% 5.05/5.23 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 5.05/5.23 gcd_gcd_int: int > int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 5.05/5.23 gcd_gcd_nat: nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_GCD_Ogcd__nat__rel,type,
% 5.05/5.23 gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 abs_abs_Code_integer: code_integer > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex,type,
% 5.05/5.23 abs_abs_complex: complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 5.05/5.23 abs_abs_int: int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 5.05/5.23 abs_abs_rat: rat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 5.05/5.23 abs_abs_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 5.05/5.23 minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Int__Oint_M_Eo_J,type,
% 5.05/5.23 minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Nat__Onat_M_Eo_J,type,
% 5.05/5.23 minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 5.05/5.23 minus_711738161318947805_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Real__Oreal_M_Eo_J,type,
% 5.05/5.23 minus_minus_real_o: ( real > $o ) > ( real > $o ) > real > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
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% 5.05/5.23 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Nat__Onat_J_001t__Real__Oreal,type,
% 5.05/5.23 groups5107569545109728110t_real: ( set_nat > real ) > set_set_nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Int__Oint,type,
% 5.05/5.23 groups1705073143266064639nt_int: ( int > int ) > set_int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.05/5.23 groups6464643781859351333omplex: ( nat > complex ) > set_nat > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Int__Oint,type,
% 5.05/5.23 groups705719431365010083at_int: ( nat > int ) > set_nat > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.05/5.23 groups73079841787564623at_rat: ( nat > rat ) > set_nat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.05/5.23 groups129246275422532515t_real: ( nat > real ) > set_nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Groups__List_Ocomm__semiring__0__class_Ohorner__sum_001_Eo_001t__Int__Oint,type,
% 5.05/5.23 groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_HOL_OThe_001t__Int__Oint,type,
% 5.05/5.23 the_int: ( int > $o ) > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_HOL_OThe_001t__Real__Oreal,type,
% 5.05/5.23 the_real: ( real > $o ) > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 if_Code_integer: $o > code_integer > code_integer > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Complex__Ocomplex,type,
% 5.05/5.23 if_complex: $o > complex > complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Extended____Nat__Oenat,type,
% 5.05/5.23 if_Extended_enat: $o > extended_enat > extended_enat > extended_enat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Int__Oint,type,
% 5.05/5.23 if_int: $o > int > int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__List__Olist_It__Int__Oint_J,type,
% 5.05/5.23 if_list_int: $o > list_int > list_int > list_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Nat__Onat,type,
% 5.05/5.23 if_nat: $o > nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Num__Onum,type,
% 5.05/5.23 if_num: $o > num > num > num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.05/5.23 if_option_nat: $o > option_nat > option_nat > option_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.05/5.23 if_option_num: $o > option_num > option_num > option_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.05/5.23 if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.05/5.23 if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.05/5.23 if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.05/5.23 if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Rat__Orat,type,
% 5.05/5.23 if_rat: $o > rat > rat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Real__Oreal,type,
% 5.05/5.23 if_real: $o > real > real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 5.05/5.23 if_set_int: $o > set_int > set_int > set_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Int_OAbs__Integ,type,
% 5.05/5.23 abs_Integ: product_prod_nat_nat > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Int_ORep__Integ,type,
% 5.05/5.23 rep_Integ: int > product_prod_nat_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Int_Oint__ge__less__than,type,
% 5.05/5.23 int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Int_Oint__ge__less__than2,type,
% 5.05/5.23 int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Int_Onat,type,
% 5.05/5.23 nat2: int > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 5.05/5.23 ring_1_Ints_real: set_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 5.05/5.23 ring_1_of_int_rat: int > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 5.05/5.23 ring_1_of_int_real: int > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 5.05/5.23 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 5.05/5.23 sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 5.05/5.23 sup_sup_int: int > int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 5.05/5.23 sup_sup_nat: nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
% 5.05/5.23 sup_sup_set_set_o: set_set_o > set_set_o > set_set_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 5.05/5.23 sup_sup_set_set_int: set_set_int > set_set_int > set_set_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.05/5.23 sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 5.05/5.23 lattic8263393255366662781ax_int: set_int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.05/5.23 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.05/5.23 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 5.05/5.23 at_infinity_real: filter_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 5.05/5.23 append_int: list_int > list_int > list_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 5.05/5.23 append_nat: list_nat > list_nat > list_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 5.05/5.23 distinct_int: list_int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.05/5.23 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.05/5.23 cons_int: int > list_int > list_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.05/5.23 cons_nat: nat > list_nat > list_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 5.05/5.23 nil_int: list_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.05/5.23 nil_nat: list_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.05/5.23 set_o2: list_o > set_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.05/5.23 set_complex2: list_complex > set_complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.05/5.23 set_int2: list_int > set_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.05/5.23 set_nat2: list_nat > set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.05/5.23 set_real2: list_real > set_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 set_set_nat2: list_set_nat > set_set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.05/5.23 list_update_o: list_o > nat > $o > list_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 5.05/5.23 list_update_complex: list_complex > nat > complex > list_complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.05/5.23 list_update_int: list_int > nat > int > list_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.05/5.23 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.05/5.23 list_update_real: list_real > nat > real > list_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001_Eo,type,
% 5.05/5.23 nth_o: list_o > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.05/5.23 nth_complex: list_complex > nat > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.05/5.23 nth_int: list_int > nat > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.05/5.23 nth_nat: list_nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.05/5.23 nth_num: list_num > nat > num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.05/5.23 nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 5.05/5.23 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 5.05/5.23 nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.05/5.23 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.05/5.23 nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.05/5.23 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.05/5.23 nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.05/5.23 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.05/5.23 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.05/5.23 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.05/5.23 nth_real: list_real > nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 nth_set_nat: list_set_nat > nat > set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.05/5.23 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.05/5.23 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.05/5.23 produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__Int__Oint_001_Eo,type,
% 5.05/5.23 product_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 5.05/5.23 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 produc662631939642741121T_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.05/5.23 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Int__Oint,type,
% 5.05/5.23 product_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 product_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Num__Onum,type,
% 5.05/5.23 product_nat_num: list_nat > list_num > list_P1726324292696863441at_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 5.05/5.23 product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.05/5.23 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.05/5.23 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.05/5.23 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.05/5.23 replicate_o: nat > $o > list_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.05/5.23 replicate_complex: nat > complex > list_complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.05/5.23 replicate_int: nat > int > list_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.05/5.23 replicate_nat: nat > nat > list_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.05/5.23 replicate_real: nat > real > list_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 replicate_set_nat: nat > set_nat > list_set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oupto,type,
% 5.05/5.23 upto: int > int > list_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oupto__aux,type,
% 5.05/5.23 upto_aux: int > int > list_int > list_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_List_Oupto__rel,type,
% 5.05/5.23 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_OSuc,type,
% 5.05/5.23 suc: nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.05/5.23 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.05/5.23 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.05/5.23 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.05/5.23 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Onat_Opred,type,
% 5.05/5.23 pred: nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 semiri4939895301339042750nteger: nat > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.05/5.23 semiri8010041392384452111omplex: nat > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.05/5.23 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.05/5.23 semiri1314217659103216013at_int: nat > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.05/5.23 semiri1316708129612266289at_nat: nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.05/5.23 semiri681578069525770553at_rat: nat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.05/5.23 semiri5074537144036343181t_real: nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 semiri4055485073559036834nteger: ( code_integer > code_integer ) > nat > code_integer > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 5.05/5.23 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 5.05/5.23 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 5.05/5.23 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 5.05/5.23 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 5.05/5.23 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.05/5.23 size_size_list_o: list_o > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 5.05/5.23 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.05/5.23 size_s3451745648224563538omplex: list_complex > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.05/5.23 size_size_list_int: list_int > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.05/5.23 size_size_list_nat: list_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 5.05/5.23 size_size_list_num: list_num > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.05/5.23 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.05/5.23 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.05/5.23 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_M_Eo_J_J,type,
% 5.05/5.23 size_s4246224855604898693_int_o: list_P5087981734274514673_int_o > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.05/5.23 size_s5157815400016825771nt_int: list_P5707943133018811711nt_int > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.05/5.23 size_s6639371672096860321T_VEBT: list_P7524865323317820941T_VEBT > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.05/5.23 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 5.05/5.23 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.05/5.23 size_size_list_real: list_real > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.05/5.23 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.05/5.23 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.05/5.23 size_size_num: num > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.05/5.23 size_size_option_nat: option_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.05/5.23 size_size_option_num: option_num > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.05/5.23 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 5.05/5.23 size_size_char: char > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.05/5.23 nat_list_encode: list_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.05/5.23 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.05/5.23 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.05/5.23 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.05/5.23 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.05/5.23 nat_set_decode: nat > set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.05/5.23 nat_set_encode: set_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.05/5.23 nat_triangle: nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_NthRoot_Oroot,type,
% 5.05/5.23 root: nat > real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_NthRoot_Osqrt,type,
% 5.05/5.23 sqrt: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_OBitM,type,
% 5.05/5.23 bitM: num > num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oinc,type,
% 5.05/5.23 inc: num > num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.05/5.23 neg_nu7009210354673126013omplex: complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.05/5.23 neg_numeral_dbl_int: int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.05/5.23 neg_numeral_dbl_rat: rat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.05/5.23 neg_numeral_dbl_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.05/5.23 neg_nu6511756317524482435omplex: complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 5.05/5.23 neg_nu3811975205180677377ec_int: int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.05/5.23 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.05/5.23 neg_nu6075765906172075777c_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.05/5.23 neg_nu8557863876264182079omplex: complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 5.05/5.23 neg_nu5851722552734809277nc_int: int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.05/5.23 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 5.05/5.23 neg_nu8295874005876285629c_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.05/5.23 neg_numeral_sub_int: num > num > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Onum_OBit0,type,
% 5.05/5.23 bit0: num > num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Onum_OBit1,type,
% 5.05/5.23 bit1: num > num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Onum_OOne,type,
% 5.05/5.23 one: num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.05/5.23 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Onum_Osize__num,type,
% 5.05/5.23 size_num: num > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Onum__of__nat,type,
% 5.05/5.23 num_of_nat: nat > num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 numera6620942414471956472nteger: num > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 5.05/5.23 numera6690914467698888265omplex: num > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 5.05/5.23 numera1916890842035813515d_enat: num > extended_enat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
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% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 5.05/5.23 ord_less_eq_num: num > num > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
% 5.05/5.23 ord_less_eq_rat: rat > rat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 5.05/5.23 ord_less_eq_real: real > real > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 5.05/5.23 ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.05/5.23 ord_le211207098394363844omplex: set_complex > set_complex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Num__Onum_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
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% 5.05/5.23
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% 5.05/5.23
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% 5.05/5.23
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Rat__Orat_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Omax_001t__Extended____Nat__Oenat,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
% 5.05/5.23 ord_max_int: int > int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
% 5.05/5.23 ord_max_nat: nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Omax_001t__Num__Onum,type,
% 5.05/5.23 ord_max_num: num > num > num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
% 5.05/5.23 ord_max_rat: rat > rat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
% 5.05/5.23 ord_max_real: real > real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Int__Oint_J,type,
% 5.05/5.23 ord_max_set_int: set_int > set_int > set_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 ord_max_set_nat: set_nat > set_nat > set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.05/5.23 ord_max_set_real: set_real > set_real > set_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 5.05/5.23 order_Greatest_nat: ( nat > $o ) > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.05/5.23 order_9091379641038594480t_real: ( nat > real ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 order_mono_nat_nat: ( nat > nat ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.05/5.23 order_mono_nat_real: ( nat > real ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 5.05/5.23 top_top_set_o: set_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Int__Oint_J,type,
% 5.05/5.23 top_top_set_int: set_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 top_top_set_nat: set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 5.05/5.23 top_to1996260823553986621t_unit: set_Product_unit ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.05/5.23 top_top_set_real: set_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__String__Ochar_J,type,
% 5.05/5.23 top_top_set_char: set_char ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 power_8256067586552552935nteger: code_integer > nat > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
% 5.05/5.23 power_power_complex: complex > nat > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 5.05/5.23 power_power_int: int > nat > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 5.05/5.23 power_power_nat: nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 5.05/5.23 power_power_rat: rat > nat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 5.05/5.23 power_power_real: real > nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 5.05/5.23 produc4035269172776083154on_nat: ( nat > nat > $o ) > produc4953844613479565601on_nat > produc2233624965454879586on_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.05/5.23 produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
% 5.05/5.23 produc8929957630744042906on_nat: ( nat > nat > nat ) > produc4953844613479565601on_nat > produc8306885398267862888on_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Num__Onum_Mt__Num__Onum_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 5.05/5.23 produc3576312749637752826on_num: ( num > num > $o ) > produc3447558737645232053on_num > produc7036089656553540234on_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
% 5.05/5.23 produc5778274026573060048on_num: ( num > num > num ) > produc3447558737645232053on_num > produc1193250871479095198on_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.05/5.23 produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.05/5.23 produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.05/5.23 produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
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% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 5.05/5.23 product_Pair_int_int: int > int > product_prod_int_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001_Eo,type,
% 5.05/5.23 product_Pair_nat_o: nat > $o > product_prod_nat_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Int__Oint,type,
% 5.05/5.23 product_Pair_nat_int: nat > int > product_prod_nat_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 5.05/5.23 product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.05/5.23 produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.05/5.23 produc1195630363706982562at_num: nat > product_prod_nat_num > produc2963631642982155120at_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.05/5.23 produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.05/5.23 produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.05/5.23 produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
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% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 5.05/5.23 produc7828578312038201481er_o_o: ( code_integer > $o > $o ) > produc6271795597528267376eger_o > $o ).
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% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.05/5.23 produc1043322548047392435omplex: ( code_integer > $o > set_complex ) > produc6271795597528267376eger_o > set_complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.05/5.23 produc242741666403216561t_real: ( code_integer > $o > set_real ) > produc6271795597528267376eger_o > set_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__String__Ochar,type,
% 5.05/5.23 produc4188289175737317920o_char: ( code_integer > $o > char ) > produc6271795597528267376eger_o > char ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.05/5.23 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.05/5.23 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.05/5.23 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 5.05/5.23 produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.05/5.23 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.05/5.23 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.05/5.23 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 produc1830744345554046123nteger: ( nat > nat > code_integer ) > product_prod_nat_nat > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.05/5.23 produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 5.05/5.23 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.05/5.23
% 5.05/5.23 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,
% 5.05/5.23 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.05/5.23 produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.05/5.23 produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001_Eo,type,
% 5.05/5.23 produc4927758841916487424_num_o: ( nat > num > $o ) > product_prod_nat_num > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.05/5.23 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.05/5.23 produc6231982587499038204omplex: ( nat > num > set_complex ) > product_prod_nat_num > set_complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.05/5.23 produc1435849484188172666t_real: ( nat > num > set_real ) > product_prod_nat_num > set_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001_Eo,type,
% 5.05/5.23 produc5703948589228662326_num_o: ( num > num > $o ) > product_prod_num_num > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.05/5.23 produc2866383454006189126omplex: ( num > num > set_complex ) > product_prod_num_num > set_complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Int__Oint_J,type,
% 5.05/5.23 produc6406642877701697732et_int: ( num > num > set_int ) > product_prod_num_num > set_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.23 produc1361121860356118632et_nat: ( num > num > set_nat ) > product_prod_num_num > set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.05/5.23 produc8296048397933160132t_real: ( num > num > set_real ) > product_prod_num_num > set_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 5.05/5.23 produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.05/5.23 product_fst_int_int: product_prod_int_int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.05/5.23 product_snd_int_int: product_prod_int_int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.05/5.23 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rat_OFract,type,
% 5.05/5.23 fract: int > int > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rat_OFrct,type,
% 5.05/5.23 frct: product_prod_int_int > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rat_Onormalize,type,
% 5.05/5.23 normalize: product_prod_int_int > product_prod_int_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rat_Oquotient__of,type,
% 5.05/5.23 quotient_of: rat > product_prod_int_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.05/5.23 real_V2521375963428798218omplex: set_complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.05/5.23 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 5.05/5.23 real_V3694042436643373181omplex: complex > complex > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 5.05/5.23 real_V975177566351809787t_real: real > real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.05/5.23 real_V1022390504157884413omplex: complex > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.05/5.23 real_V7735802525324610683m_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.05/5.23 real_V4546457046886955230omplex: real > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 5.05/5.23 real_V2046097035970521341omplex: real > complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 5.05/5.23 real_V1485227260804924795R_real: real > real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.05/5.23 divide1717551699836669952omplex: complex > complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 5.05/5.23 divide_divide_int: int > int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.05/5.23 divide_divide_nat: nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.05/5.23 divide_divide_rat: rat > rat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.05/5.23 divide_divide_real: real > real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.05/5.23 dvd_dvd_complex: complex > complex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.05/5.23 dvd_dvd_int: int > int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.05/5.23 dvd_dvd_nat: nat > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.05/5.23 dvd_dvd_rat: rat > rat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.05/5.23 dvd_dvd_real: real > real > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.05/5.23 modulo_modulo_int: int > int > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.05/5.23 modulo_modulo_nat: nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 zero_n356916108424825756nteger: $o > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 5.05/5.23 zero_n1201886186963655149omplex: $o > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.05/5.23 zero_n2684676970156552555ol_int: $o > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.05/5.23 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.05/5.23 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.05/5.23 zero_n3304061248610475627l_real: $o > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 5.05/5.23 suminf_complex: ( nat > complex ) > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 5.05/5.23 suminf_int: ( nat > int ) > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 5.05/5.23 suminf_nat: ( nat > nat ) > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.05/5.23 suminf_real: ( nat > real ) > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 5.05/5.23 summable_complex: ( nat > complex ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 5.05/5.23 summable_int: ( nat > int ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 5.05/5.23 summable_nat: ( nat > nat ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.05/5.23 summable_real: ( nat > real ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
% 5.05/5.23 sums_complex: ( nat > complex ) > complex > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osums_001t__Int__Oint,type,
% 5.05/5.23 sums_int: ( nat > int ) > int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
% 5.05/5.23 sums_nat: ( nat > nat ) > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.05/5.23 sums_real: ( nat > real ) > real > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Set_OCollect_001_Eo,type,
% 5.05/5.23 collect_o: ( $o > $o ) > set_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.05/5.23 collect_complex: ( complex > $o ) > set_complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 5.05/5.23 collect_int: ( int > $o ) > set_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
% 5.05/5.23 collect_list_o: ( list_o > $o ) > set_list_o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.05/5.23 collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
% 5.05/5.23 collect_list_int: ( list_int > $o ) > set_list_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 5.05/5.23 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
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% 5.05/5.23 topolo4860482606490270245n_real: set_real > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.05/5.23 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.05/5.23 topolo2815343760600316023s_real: real > filter_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Complex__Ocomplex,type,
% 5.05/5.23 topolo6517432010174082258omplex: ( nat > complex ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.05/5.23 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 5.05/5.23 topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 5.05/5.23 topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Oarccos,type,
% 5.05/5.23 arccos: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.05/5.23 arcosh_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Oarcsin,type,
% 5.05/5.23 arcsin: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Oarctan,type,
% 5.05/5.23 arctan: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.05/5.23 arsinh_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.05/5.23 artanh_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.05/5.23 cos_complex: complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.05/5.23 cos_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.05/5.23 cos_coeff: nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.05/5.23 cosh_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.05/5.23 cot_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Odiffs_001t__Code____Numeral__Ointeger,type,
% 5.05/5.23 diffs_Code_integer: ( nat > code_integer ) > nat > code_integer ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.05/5.23 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 5.05/5.23 diffs_int: ( nat > int ) > nat > int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Odiffs_001t__Rat__Orat,type,
% 5.05/5.23 diffs_rat: ( nat > rat ) > nat > rat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.05/5.23 diffs_real: ( nat > real ) > nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.05/5.23 exp_complex: complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.05/5.23 exp_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.05/5.23 ln_ln_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Olog,type,
% 5.05/5.23 log: real > real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Opi,type,
% 5.05/5.23 pi: real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.05/5.23 powr_real: real > real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.05/5.23 sin_complex: complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.05/5.23 sin_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.05/5.23 sin_coeff: nat > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.05/5.23 sinh_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.05/5.23 tan_complex: complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.05/5.23 tan_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.05/5.23 tanh_complex: complex > complex ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.05/5.23 tanh_real: real > real ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.05/5.23 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.05/5.23 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.05/5.23 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.05/5.23 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.05/5.23 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.05/5.23 vEBT_VEBT_high: nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.05/5.23 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.05/5.23 vEBT_VEBT_low: nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.05/5.23 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.05/5.23 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.05/5.23 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.05/5.23 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.05/5.23 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.05/5.23 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.05/5.23 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.05/5.23 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.05/5.23 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.05/5.23 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 5.05/5.23 vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 5.05/5.23 vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.05/5.23 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.05/5.23 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.05/5.23 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.05/5.23 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.05/5.23 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.05/5.23 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.05/5.23 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.05/5.23 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.05/5.23 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.05/5.23 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.05/5.23 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.05/5.23 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.05/5.23 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.05/5.23 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.05/5.23 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.05/5.23 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 5.05/5.23 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.05/5.23 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift__rel_001t__Nat__Onat,type,
% 5.05/5.23 vEBT_V3895251965096974666el_nat: produc8306885398267862888on_nat > produc8306885398267862888on_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift__rel_001t__Num__Onum,type,
% 5.05/5.23 vEBT_V452583751252753300el_num: produc1193250871479095198on_num > produc1193250871479095198on_num > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift__rel_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.05/5.23 vEBT_V7235779383477046023at_nat: produc5542196010084753463at_nat > produc5542196010084753463at_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 5.05/5.23 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 5.05/5.23 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.05/5.23 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.05/5.23 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.05/5.23 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 5.05/5.23 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 5.05/5.23 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 5.05/5.23 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 5.05/5.23 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 5.05/5.23 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 5.05/5.23 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.05/5.23 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.05/5.23 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.05/5.23 accp_P6019419558468335806at_nat: ( produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o ) > produc4471711990508489141at_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 5.05/5.23 accp_P5496254298877145759on_nat: ( produc8306885398267862888on_nat > produc8306885398267862888on_nat > $o ) > produc8306885398267862888on_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J_J,type,
% 5.05/5.23 accp_P4916641582247091100at_num: ( produc3368934014287244435at_num > produc3368934014287244435at_num > $o ) > produc3368934014287244435at_num > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 5.05/5.23 accp_P7605991808943153877on_num: ( produc1193250871479095198on_num > produc1193250871479095198on_num > $o ) > produc1193250871479095198on_num > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 5.05/5.23 accp_P3267385326087170368at_nat: ( produc5542196010084753463at_nat > produc5542196010084753463at_nat > $o ) > produc5542196010084753463at_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.05/5.23 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.05/5.23 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.05/5.23 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.05/5.23 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.23 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Omeasure_001t__Int__Oint,type,
% 5.05/5.23 measure_int: ( int > nat ) > set_Pr958786334691620121nt_int ).
% 5.05/5.23
% 5.05/5.23 thf(sy_c_Wellfounded_Omeasure_001t__Nat__Onat,type,
% 5.05/5.23 measure_nat: ( nat > nat ) > set_Pr1261947904930325089at_nat ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_Wellfounded_Omeasure_001t__Num__Onum,type,
% 5.05/5.24 measure_num: ( num > nat ) > set_Pr8218934625190621173um_num ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.05/5.24 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.05/5.24 fChoice_real: ( real > $o ) > real ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001_Eo,type,
% 5.05/5.24 member_o: $o > set_o > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.05/5.24 member_complex: complex > set_complex > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Int__Oint,type,
% 5.05/5.24 member_int: int > set_int > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.05/5.24 member_list_o: list_o > set_list_o > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 5.05/5.24 member_list_int: list_int > set_list_int > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.05/5.24 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Nat__Onat,type,
% 5.05/5.24 member_nat: nat > set_nat > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Num__Onum,type,
% 5.05/5.24 member_num: num > set_num > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.05/5.24 member1379723562493234055eger_o: produc6271795597528267376eger_o > set_Pr448751882837621926eger_o > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.05/5.24 member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.05/5.24 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.05/5.24 member9148766508732265716at_num: product_prod_nat_num > set_Pr6200539531224447659at_num > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.05/5.24 member7279096912039735102um_num: product_prod_num_num > set_Pr8218934625190621173um_num > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Rat__Orat,type,
% 5.05/5.24 member_rat: rat > set_rat > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Real__Oreal,type,
% 5.05/5.24 member_real: real > set_real > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 5.05/5.24 member_set_int: set_int > set_set_int > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.05/5.24 member_set_nat: set_nat > set_set_nat > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.05/5.24 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.05/5.24
% 5.05/5.24 thf(sy_v_deg____,type,
% 5.05/5.24 deg: nat ).
% 5.05/5.24
% 5.05/5.24 thf(sy_v_lx____,type,
% 5.05/5.24 lx: nat ).
% 5.05/5.24
% 5.05/5.24 thf(sy_v_m____,type,
% 5.05/5.24 m: nat ).
% 5.05/5.24
% 5.05/5.24 thf(sy_v_ma____,type,
% 5.05/5.24 ma: nat ).
% 5.05/5.24
% 5.05/5.24 thf(sy_v_mi____,type,
% 5.05/5.24 mi: nat ).
% 5.05/5.24
% 5.05/5.24 thf(sy_v_na____,type,
% 5.05/5.24 na: nat ).
% 5.05/5.24
% 5.05/5.24 thf(sy_v_summary____,type,
% 5.05/5.24 summary: vEBT_VEBT ).
% 5.05/5.24
% 5.05/5.24 thf(sy_v_summin____,type,
% 5.05/5.24 summin: nat ).
% 5.05/5.24
% 5.05/5.24 thf(sy_v_treeList____,type,
% 5.05/5.24 treeList: list_VEBT_VEBT ).
% 5.05/5.24
% 5.05/5.24 thf(sy_v_xa____,type,
% 5.05/5.24 xa: nat ).
% 5.05/5.24
% 5.05/5.24 % Relevant facts (10202)
% 5.05/5.24 thf(fact_0_False,axiom,
% 5.05/5.24 xa = mi ).
% 5.05/5.24
% 5.05/5.24 % False
% 5.05/5.24 thf(fact_1_bit__split__inv,axiom,
% 5.05/5.24 ! [X: nat,D: nat] :
% 5.05/5.24 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 5.05/5.24 = X ) ).
% 5.05/5.24
% 5.05/5.24 % bit_split_inv
% 5.05/5.24 thf(fact_2_xmi,axiom,
% 5.05/5.24 xa = mi ).
% 5.05/5.24
% 5.05/5.24 % xmi
% 5.05/5.24 thf(fact_3_pow__sum,axiom,
% 5.05/5.24 ! [A: nat,B: nat] :
% 5.05/5.24 ( ( 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 ) )
% 5.05/5.24 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.05/5.24
% 5.05/5.24 % pow_sum
% 5.05/5.24 thf(fact_4__092_060open_062x_A_092_060noteq_062_Ami_A_092_060or_062_Ax_A_092_060noteq_062_Ama_092_060close_062,axiom,
% 5.05/5.24 ( ( xa != mi )
% 5.05/5.24 | ( xa != ma ) ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>x \<noteq> mi \<or> x \<noteq> ma\<close>
% 5.05/5.24 thf(fact_5_high__def,axiom,
% 5.05/5.24 ( vEBT_VEBT_high
% 5.05/5.24 = ( ^ [X2: nat,N: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % high_def
% 5.05/5.24 thf(fact_6__C9_C,axiom,
% 5.05/5.24 ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.24 = na ) ).
% 5.05/5.24
% 5.05/5.24 % "9"
% 5.05/5.24 thf(fact_7_bit__concat__def,axiom,
% 5.05/5.24 ( vEBT_VEBT_bit_concat
% 5.05/5.24 = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % bit_concat_def
% 5.05/5.24 thf(fact_8__C3_C,axiom,
% 5.05/5.24 ( deg
% 5.05/5.24 = ( plus_plus_nat @ na @ m ) ) ).
% 5.05/5.24
% 5.05/5.24 % "3"
% 5.05/5.24 thf(fact_9__C4_Ohyps_C_I7_J,axiom,
% 5.05/5.24 ord_less_eq_nat @ mi @ ma ).
% 5.05/5.24
% 5.05/5.24 % "4.hyps"(7)
% 5.05/5.24 thf(fact_10_hprolist,axiom,
% 5.05/5.24 ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) )
% 5.05/5.24 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % hprolist
% 5.05/5.24 thf(fact_11__C4_Ohyps_C_I8_J,axiom,
% 5.05/5.24 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.05/5.24
% 5.05/5.24 % "4.hyps"(8)
% 5.05/5.24 thf(fact_12_ninNullc,axiom,
% 5.05/5.24 vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ).
% 5.05/5.24
% 5.05/5.24 % ninNullc
% 5.05/5.24 thf(fact_13__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_061_A_Iif_Ax_A_061_Ami_Athen_Athe_A_Ivebt__mint_Asummary_J_A_K_A2_A_094_A_Ideg_Adiv_A2_J_A_L_Athe_A_Ivebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__mint_Asummary_J_J_J_Aelse_Ax_J_092_060close_062,axiom,
% 5.05/5.24 ( ( ( xa = mi )
% 5.05/5.24 => ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.05/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ ( the_nat @ ( vEBT_vebt_mint @ summary ) ) ) ) ) ) ) )
% 5.05/5.24 & ( ( xa != mi )
% 5.05/5.24 => ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.05/5.24 = xa ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>summin * 2 ^ n + lx = (if x = mi then the (vebt_mint summary) * 2 ^ (deg div 2) + the (vebt_mint (treeList ! the (vebt_mint summary))) else x)\<close>
% 5.05/5.24 thf(fact_14_xnin,axiom,
% 5.05/5.24 vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) ).
% 5.05/5.24
% 5.05/5.24 % xnin
% 5.05/5.24 thf(fact_15__092_060open_062length_AtreeList_A_061_Alength_A_ItreeList_A_091high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_A_Ilow_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_093_J_092_060close_062,axiom,
% 5.05/5.24 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.05/5.24 = ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>length treeList = length (treeList [high (summin * 2 ^ n + lx) n := vebt_delete (treeList ! high (summin * 2 ^ n + lx) n) (low (summin * 2 ^ n + lx) n)])\<close>
% 5.05/5.24 thf(fact_16_add__self__div__2,axiom,
% 5.05/5.24 ! [M: nat] :
% 5.05/5.24 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.24 = M ) ).
% 5.05/5.24
% 5.05/5.24 % add_self_div_2
% 5.05/5.24 thf(fact_17__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_060_A2_A_094_Adeg_092_060close_062,axiom,
% 5.05/5.24 ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>summin * 2 ^ n + lx < 2 ^ deg\<close>
% 5.05/5.24 thf(fact_18_nnvalid,axiom,
% 5.05/5.24 vEBT_invar_vebt @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ na ).
% 5.05/5.24
% 5.05/5.24 % nnvalid
% 5.05/5.24 thf(fact_19__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062,axiom,
% 5.05/5.24 ( ( mi != ma )
% 5.05/5.24 & ( ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>mi \<noteq> ma \<and> x < 2 ^ deg\<close>
% 5.05/5.24 thf(fact_20_option_Ocollapse,axiom,
% 5.05/5.24 ! [Option: option4927543243414619207at_nat] :
% 5.05/5.24 ( ( Option != none_P5556105721700978146at_nat )
% 5.05/5.24 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.05/5.24 = Option ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.collapse
% 5.05/5.24 thf(fact_21_option_Ocollapse,axiom,
% 5.05/5.24 ! [Option: option_nat] :
% 5.05/5.24 ( ( Option != none_nat )
% 5.05/5.24 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.05/5.24 = Option ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.collapse
% 5.05/5.24 thf(fact_22_option_Ocollapse,axiom,
% 5.05/5.24 ! [Option: option_num] :
% 5.05/5.24 ( ( Option != none_num )
% 5.05/5.24 => ( ( some_num @ ( the_num @ Option ) )
% 5.05/5.24 = Option ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.collapse
% 5.05/5.24 thf(fact_23__C10_C,axiom,
% 5.05/5.24 vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ deg ).
% 5.05/5.24
% 5.05/5.24 % "10"
% 5.05/5.24 thf(fact_24_distrib__left__numeral,axiom,
% 5.05/5.24 ! [V: num,B: complex,C: complex] :
% 5.05/5.24 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.05/5.24 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % distrib_left_numeral
% 5.05/5.24 thf(fact_25_distrib__left__numeral,axiom,
% 5.05/5.24 ! [V: num,B: real,C: real] :
% 5.05/5.24 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.05/5.24 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % distrib_left_numeral
% 5.05/5.24 thf(fact_26_distrib__left__numeral,axiom,
% 5.05/5.24 ! [V: num,B: rat,C: rat] :
% 5.05/5.24 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.05/5.24 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % distrib_left_numeral
% 5.05/5.24 thf(fact_27_distrib__left__numeral,axiom,
% 5.05/5.24 ! [V: num,B: nat,C: nat] :
% 5.05/5.24 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.05/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % distrib_left_numeral
% 5.05/5.24 thf(fact_28_distrib__left__numeral,axiom,
% 5.05/5.24 ! [V: num,B: int,C: int] :
% 5.05/5.24 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.05/5.24 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % distrib_left_numeral
% 5.05/5.24 thf(fact_29_distrib__right__numeral,axiom,
% 5.05/5.24 ! [A: complex,B: complex,V: num] :
% 5.05/5.24 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.05/5.24 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % distrib_right_numeral
% 5.05/5.24 thf(fact_30_distrib__right__numeral,axiom,
% 5.05/5.24 ! [A: real,B: real,V: num] :
% 5.05/5.24 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.05/5.24 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % distrib_right_numeral
% 5.05/5.24 thf(fact_31_distrib__right__numeral,axiom,
% 5.05/5.24 ! [A: rat,B: rat,V: num] :
% 5.05/5.24 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.05/5.24 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % distrib_right_numeral
% 5.05/5.24 thf(fact_32_distrib__right__numeral,axiom,
% 5.05/5.24 ! [A: nat,B: nat,V: num] :
% 5.05/5.24 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.05/5.24 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % distrib_right_numeral
% 5.05/5.24 thf(fact_33_distrib__right__numeral,axiom,
% 5.05/5.24 ! [A: int,B: int,V: num] :
% 5.05/5.24 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.05/5.24 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % distrib_right_numeral
% 5.05/5.24 thf(fact_34__092_060open_062vebt__member_Asummary_A_Ihigh_Ama_An_J_092_060close_062,axiom,
% 5.05/5.24 vEBT_vebt_member @ summary @ ( vEBT_VEBT_high @ ma @ na ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>vebt_member summary (high ma n)\<close>
% 5.05/5.24 thf(fact_35_power__shift,axiom,
% 5.05/5.24 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.24 ( ( ( power_power_nat @ X @ Y )
% 5.05/5.24 = Z )
% 5.05/5.24 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.05/5.24 = ( some_nat @ Z ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % power_shift
% 5.05/5.24 thf(fact_36_deg__deg__n,axiom,
% 5.05/5.24 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N2 )
% 5.05/5.24 => ( Deg = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % deg_deg_n
% 5.05/5.24 thf(fact_37_maxbmo,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,X: nat] :
% 5.05/5.24 ( ( ( vEBT_vebt_maxt @ T )
% 5.05/5.24 = ( some_nat @ X ) )
% 5.05/5.24 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 5.05/5.24
% 5.05/5.24 % maxbmo
% 5.05/5.24 thf(fact_38_not__min__Null__member,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT] :
% 5.05/5.24 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.05/5.24 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.05/5.24
% 5.05/5.24 % not_min_Null_member
% 5.05/5.24 thf(fact_39_min__Null__member,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,X: nat] :
% 5.05/5.24 ( ( vEBT_VEBT_minNull @ T )
% 5.05/5.24 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 5.05/5.24
% 5.05/5.24 % min_Null_member
% 5.05/5.24 thf(fact_40__092_060open_062Some_Asummin_A_061_Avebt__mint_Asummary_092_060close_062,axiom,
% 5.05/5.24 ( ( some_nat @ summin )
% 5.05/5.24 = ( vEBT_vebt_mint @ summary ) ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>Some summin = vebt_mint summary\<close>
% 5.05/5.24 thf(fact_41__C1_C,axiom,
% 5.05/5.24 vEBT_invar_vebt @ summary @ m ).
% 5.05/5.24
% 5.05/5.24 % "1"
% 5.05/5.24 thf(fact_42__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062summin_O_ASome_Asummin_A_061_Avebt__mint_Asummary_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.05/5.24 ~ ! [Summin: nat] :
% 5.05/5.24 ( ( some_nat @ Summin )
% 5.05/5.24 != ( vEBT_vebt_mint @ summary ) ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>\<And>thesis. (\<And>summin. Some summin = vebt_mint summary \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.05/5.24 thf(fact_43_dele__bmo__cont__corr,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 5.05/5.24 = ( ( X != Y )
% 5.05/5.24 & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % dele_bmo_cont_corr
% 5.05/5.24 thf(fact_44_both__member__options__equiv__member,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.05/5.24 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % both_member_options_equiv_member
% 5.05/5.24 thf(fact_45_valid__member__both__member__options,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.05/5.24 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % valid_member_both_member_options
% 5.05/5.24 thf(fact_46_max__in__set__def,axiom,
% 5.05/5.24 ( vEBT_VEBT_max_in_set
% 5.05/5.24 = ( ^ [Xs: set_nat,X2: nat] :
% 5.05/5.24 ( ( member_nat @ X2 @ Xs )
% 5.05/5.24 & ! [Y2: nat] :
% 5.05/5.24 ( ( member_nat @ Y2 @ Xs )
% 5.05/5.24 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % max_in_set_def
% 5.05/5.24 thf(fact_47_min__in__set__def,axiom,
% 5.05/5.24 ( vEBT_VEBT_min_in_set
% 5.05/5.24 = ( ^ [Xs: set_nat,X2: nat] :
% 5.05/5.24 ( ( member_nat @ X2 @ Xs )
% 5.05/5.24 & ! [Y2: nat] :
% 5.05/5.24 ( ( member_nat @ Y2 @ Xs )
% 5.05/5.24 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % min_in_set_def
% 5.05/5.24 thf(fact_48_mint__member,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,Maxi: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( vEBT_vebt_mint @ T )
% 5.05/5.24 = ( some_nat @ Maxi ) )
% 5.05/5.24 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % mint_member
% 5.05/5.24 thf(fact_49_minminNull,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT] :
% 5.05/5.24 ( ( ( vEBT_vebt_mint @ T )
% 5.05/5.24 = none_nat )
% 5.05/5.24 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.05/5.24
% 5.05/5.24 % minminNull
% 5.05/5.24 thf(fact_50_minNullmin,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT] :
% 5.05/5.24 ( ( vEBT_VEBT_minNull @ T )
% 5.05/5.24 => ( ( vEBT_vebt_mint @ T )
% 5.05/5.24 = none_nat ) ) ).
% 5.05/5.24
% 5.05/5.24 % minNullmin
% 5.05/5.24 thf(fact_51_maxt__member,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,Maxi: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( vEBT_vebt_maxt @ T )
% 5.05/5.24 = ( some_nat @ Maxi ) )
% 5.05/5.24 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % maxt_member
% 5.05/5.24 thf(fact_52__C8_C,axiom,
% 5.05/5.24 na = m ).
% 5.05/5.24
% 5.05/5.24 % "8"
% 5.05/5.24 thf(fact_53__092_060open_062Some_Alx_A_061_Avebt__mint_A_ItreeList_A_B_Asummin_J_092_060close_062,axiom,
% 5.05/5.24 ( ( some_nat @ lx )
% 5.05/5.24 = ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ summin ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>Some lx = vebt_mint (treeList ! summin)\<close>
% 5.05/5.24 thf(fact_54_mint__corr__help,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,Mini: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( vEBT_vebt_mint @ T )
% 5.05/5.24 = ( some_nat @ Mini ) )
% 5.05/5.24 => ( ( vEBT_vebt_member @ T @ X )
% 5.05/5.24 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % mint_corr_help
% 5.05/5.24 thf(fact_55_mem__Collect__eq,axiom,
% 5.05/5.24 ! [A: real,P: real > $o] :
% 5.05/5.24 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.05/5.24 = ( P @ A ) ) ).
% 5.05/5.24
% 5.05/5.24 % mem_Collect_eq
% 5.05/5.24 thf(fact_56_mem__Collect__eq,axiom,
% 5.05/5.24 ! [A: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.05/5.24 ( ( member5262025264175285858nt_int @ A @ ( collec213857154873943460nt_int @ P ) )
% 5.05/5.24 = ( P @ A ) ) ).
% 5.05/5.24
% 5.05/5.24 % mem_Collect_eq
% 5.05/5.24 thf(fact_57_mem__Collect__eq,axiom,
% 5.05/5.24 ! [A: complex,P: complex > $o] :
% 5.05/5.24 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.05/5.24 = ( P @ A ) ) ).
% 5.05/5.24
% 5.05/5.24 % mem_Collect_eq
% 5.05/5.24 thf(fact_58_mem__Collect__eq,axiom,
% 5.05/5.24 ! [A: set_nat,P: set_nat > $o] :
% 5.05/5.24 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 5.05/5.24 = ( P @ A ) ) ).
% 5.05/5.24
% 5.05/5.24 % mem_Collect_eq
% 5.05/5.24 thf(fact_59_mem__Collect__eq,axiom,
% 5.05/5.24 ! [A: nat,P: nat > $o] :
% 5.05/5.24 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.05/5.24 = ( P @ A ) ) ).
% 5.05/5.24
% 5.05/5.24 % mem_Collect_eq
% 5.05/5.24 thf(fact_60_mem__Collect__eq,axiom,
% 5.05/5.24 ! [A: int,P: int > $o] :
% 5.05/5.24 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.05/5.24 = ( P @ A ) ) ).
% 5.05/5.24
% 5.05/5.24 % mem_Collect_eq
% 5.05/5.24 thf(fact_61_Collect__mem__eq,axiom,
% 5.05/5.24 ! [A2: set_real] :
% 5.05/5.24 ( ( collect_real
% 5.05/5.24 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 5.05/5.24 = A2 ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_mem_eq
% 5.05/5.24 thf(fact_62_Collect__mem__eq,axiom,
% 5.05/5.24 ! [A2: set_Pr958786334691620121nt_int] :
% 5.05/5.24 ( ( collec213857154873943460nt_int
% 5.05/5.24 @ ^ [X2: product_prod_int_int] : ( member5262025264175285858nt_int @ X2 @ A2 ) )
% 5.05/5.24 = A2 ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_mem_eq
% 5.05/5.24 thf(fact_63_Collect__mem__eq,axiom,
% 5.05/5.24 ! [A2: set_complex] :
% 5.05/5.24 ( ( collect_complex
% 5.05/5.24 @ ^ [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 5.05/5.24 = A2 ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_mem_eq
% 5.05/5.24 thf(fact_64_Collect__mem__eq,axiom,
% 5.05/5.24 ! [A2: set_set_nat] :
% 5.05/5.24 ( ( collect_set_nat
% 5.05/5.24 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A2 ) )
% 5.05/5.24 = A2 ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_mem_eq
% 5.05/5.24 thf(fact_65_Collect__mem__eq,axiom,
% 5.05/5.24 ! [A2: set_nat] :
% 5.05/5.24 ( ( collect_nat
% 5.05/5.24 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 5.05/5.24 = A2 ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_mem_eq
% 5.05/5.24 thf(fact_66_Collect__mem__eq,axiom,
% 5.05/5.24 ! [A2: set_int] :
% 5.05/5.24 ( ( collect_int
% 5.05/5.24 @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 5.05/5.24 = A2 ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_mem_eq
% 5.05/5.24 thf(fact_67_Collect__cong,axiom,
% 5.05/5.24 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.05/5.24 ( ! [X3: product_prod_int_int] :
% 5.05/5.24 ( ( P @ X3 )
% 5.05/5.24 = ( Q @ X3 ) )
% 5.05/5.24 => ( ( collec213857154873943460nt_int @ P )
% 5.05/5.24 = ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_cong
% 5.05/5.24 thf(fact_68_Collect__cong,axiom,
% 5.05/5.24 ! [P: complex > $o,Q: complex > $o] :
% 5.05/5.24 ( ! [X3: complex] :
% 5.05/5.24 ( ( P @ X3 )
% 5.05/5.24 = ( Q @ X3 ) )
% 5.05/5.24 => ( ( collect_complex @ P )
% 5.05/5.24 = ( collect_complex @ Q ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_cong
% 5.05/5.24 thf(fact_69_Collect__cong,axiom,
% 5.05/5.24 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.05/5.24 ( ! [X3: set_nat] :
% 5.05/5.24 ( ( P @ X3 )
% 5.05/5.24 = ( Q @ X3 ) )
% 5.05/5.24 => ( ( collect_set_nat @ P )
% 5.05/5.24 = ( collect_set_nat @ Q ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_cong
% 5.05/5.24 thf(fact_70_Collect__cong,axiom,
% 5.05/5.24 ! [P: nat > $o,Q: nat > $o] :
% 5.05/5.24 ( ! [X3: nat] :
% 5.05/5.24 ( ( P @ X3 )
% 5.05/5.24 = ( Q @ X3 ) )
% 5.05/5.24 => ( ( collect_nat @ P )
% 5.05/5.24 = ( collect_nat @ Q ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_cong
% 5.05/5.24 thf(fact_71_Collect__cong,axiom,
% 5.05/5.24 ! [P: int > $o,Q: int > $o] :
% 5.05/5.24 ( ! [X3: int] :
% 5.05/5.24 ( ( P @ X3 )
% 5.05/5.24 = ( Q @ X3 ) )
% 5.05/5.24 => ( ( collect_int @ P )
% 5.05/5.24 = ( collect_int @ Q ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % Collect_cong
% 5.05/5.24 thf(fact_72_maxt__corr__help,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,Maxi: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( vEBT_vebt_maxt @ T )
% 5.05/5.24 = ( some_nat @ Maxi ) )
% 5.05/5.24 => ( ( vEBT_vebt_member @ T @ X )
% 5.05/5.24 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % maxt_corr_help
% 5.05/5.24 thf(fact_73__C2_C,axiom,
% 5.05/5.24 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.05/5.24 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.05/5.24
% 5.05/5.24 % "2"
% 5.05/5.24 thf(fact_74_numeral__eq__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ( numera6690914467698888265omplex @ M )
% 5.05/5.24 = ( numera6690914467698888265omplex @ N2 ) )
% 5.05/5.24 = ( M = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_eq_iff
% 5.05/5.24 thf(fact_75_numeral__eq__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ( numeral_numeral_real @ M )
% 5.05/5.24 = ( numeral_numeral_real @ N2 ) )
% 5.05/5.24 = ( M = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_eq_iff
% 5.05/5.24 thf(fact_76_numeral__eq__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ( numeral_numeral_rat @ M )
% 5.05/5.24 = ( numeral_numeral_rat @ N2 ) )
% 5.05/5.24 = ( M = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_eq_iff
% 5.05/5.24 thf(fact_77_numeral__eq__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ( numeral_numeral_nat @ M )
% 5.05/5.24 = ( numeral_numeral_nat @ N2 ) )
% 5.05/5.24 = ( M = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_eq_iff
% 5.05/5.24 thf(fact_78_numeral__eq__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ( numeral_numeral_int @ M )
% 5.05/5.24 = ( numeral_numeral_int @ N2 ) )
% 5.05/5.24 = ( M = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_eq_iff
% 5.05/5.24 thf(fact_79_option_Oinject,axiom,
% 5.05/5.24 ! [X22: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 5.05/5.24 ( ( ( some_P7363390416028606310at_nat @ X22 )
% 5.05/5.24 = ( some_P7363390416028606310at_nat @ Y22 ) )
% 5.05/5.24 = ( X22 = Y22 ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.inject
% 5.05/5.24 thf(fact_80_option_Oinject,axiom,
% 5.05/5.24 ! [X22: nat,Y22: nat] :
% 5.05/5.24 ( ( ( some_nat @ X22 )
% 5.05/5.24 = ( some_nat @ Y22 ) )
% 5.05/5.24 = ( X22 = Y22 ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.inject
% 5.05/5.24 thf(fact_81_option_Oinject,axiom,
% 5.05/5.24 ! [X22: num,Y22: num] :
% 5.05/5.24 ( ( ( some_num @ X22 )
% 5.05/5.24 = ( some_num @ Y22 ) )
% 5.05/5.24 = ( X22 = Y22 ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.inject
% 5.05/5.24 thf(fact_82__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062,axiom,
% 5.05/5.24 ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ X_1 ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>\<exists>z. both_member_options (treeList ! summin) z\<close>
% 5.05/5.24 thf(fact_83__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lx_O_ASome_Alx_A_061_Avebt__mint_A_ItreeList_A_B_Asummin_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.05/5.24 ~ ! [Lx: nat] :
% 5.05/5.24 ( ( some_nat @ Lx )
% 5.05/5.24 != ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ treeList @ summin ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>\<And>thesis. (\<And>lx. Some lx = vebt_mint (treeList ! summin) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.05/5.24 thf(fact_84__C12_C,axiom,
% 5.05/5.24 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.05/5.24
% 5.05/5.24 % "12"
% 5.05/5.24 thf(fact_85__C4_OIH_C_I2_J,axiom,
% 5.05/5.24 ! [X: nat] : ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ summary @ X ) @ m ) ).
% 5.05/5.24
% 5.05/5.24 % "4.IH"(2)
% 5.05/5.24 thf(fact_86__C4_C,axiom,
% 5.05/5.24 ! [I: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.05/5.24 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X4 ) )
% 5.05/5.24 = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % "4"
% 5.05/5.24 thf(fact_87_high__bound__aux,axiom,
% 5.05/5.24 ! [Ma: nat,N2: nat,M: nat] :
% 5.05/5.24 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 5.05/5.24 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % high_bound_aux
% 5.05/5.24 thf(fact_88_inrg,axiom,
% 5.05/5.24 ( ( ord_less_eq_nat @ mi @ xa )
% 5.05/5.24 & ( ord_less_eq_nat @ xa @ ma ) ) ).
% 5.05/5.24
% 5.05/5.24 % inrg
% 5.05/5.24 thf(fact_89_misiz,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,M: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( some_nat @ M )
% 5.05/5.24 = ( vEBT_vebt_mint @ T ) )
% 5.05/5.24 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % misiz
% 5.05/5.24 thf(fact_90_member__bound,axiom,
% 5.05/5.24 ! [Tree: vEBT_VEBT,X: nat,N2: nat] :
% 5.05/5.24 ( ( vEBT_vebt_member @ Tree @ X )
% 5.05/5.24 => ( ( vEBT_invar_vebt @ Tree @ N2 )
% 5.05/5.24 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % member_bound
% 5.05/5.24 thf(fact_91__092_060open_062invar__vebt_A_ItreeList_A_B_Asummin_J_An_092_060close_062,axiom,
% 5.05/5.24 vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ summin ) @ na ).
% 5.05/5.24
% 5.05/5.24 % \<open>invar_vebt (treeList ! summin) n\<close>
% 5.05/5.24 thf(fact_92__092_060open_062vebt__member_A_ItreeList_A_B_Asummin_J_Alx_092_060close_062,axiom,
% 5.05/5.24 vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ summin ) @ lx ).
% 5.05/5.24
% 5.05/5.24 % \<open>vebt_member (treeList ! summin) lx\<close>
% 5.05/5.24 thf(fact_93__092_060open_062both__member__options_Asummary_A_Ihigh_Ama_An_J_092_060close_062,axiom,
% 5.05/5.24 vEBT_V8194947554948674370ptions @ summary @ ( vEBT_VEBT_high @ ma @ na ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>both_member_options summary (high ma n)\<close>
% 5.05/5.24 thf(fact_94_numeral__le__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.05/5.24 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_le_iff
% 5.05/5.24 thf(fact_95_numeral__le__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.05/5.24 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_le_iff
% 5.05/5.24 thf(fact_96_numeral__le__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.24 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_le_iff
% 5.05/5.24 thf(fact_97_numeral__le__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.05/5.24 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_le_iff
% 5.05/5.24 thf(fact_98_numeral__less__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.05/5.24 = ( ord_less_num @ M @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_less_iff
% 5.05/5.24 thf(fact_99_numeral__less__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.05/5.24 = ( ord_less_num @ M @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_less_iff
% 5.05/5.24 thf(fact_100_numeral__less__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.24 = ( ord_less_num @ M @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_less_iff
% 5.05/5.24 thf(fact_101_numeral__less__iff,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.05/5.24 = ( ord_less_num @ M @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_less_iff
% 5.05/5.24 thf(fact_102_high__inv,axiom,
% 5.05/5.24 ! [X: nat,N2: nat,Y: nat] :
% 5.05/5.24 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.24 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
% 5.05/5.24 = Y ) ) ).
% 5.05/5.24
% 5.05/5.24 % high_inv
% 5.05/5.24 thf(fact_103_low__inv,axiom,
% 5.05/5.24 ! [X: nat,N2: nat,Y: nat] :
% 5.05/5.24 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.24 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
% 5.05/5.24 = X ) ) ).
% 5.05/5.24
% 5.05/5.24 % low_inv
% 5.05/5.24 thf(fact_104_mult__numeral__left__semiring__numeral,axiom,
% 5.05/5.24 ! [V: num,W: num,Z: complex] :
% 5.05/5.24 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.05/5.24 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_left_semiring_numeral
% 5.05/5.24 thf(fact_105_mult__numeral__left__semiring__numeral,axiom,
% 5.05/5.24 ! [V: num,W: num,Z: real] :
% 5.05/5.24 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.05/5.24 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_left_semiring_numeral
% 5.05/5.24 thf(fact_106_mult__numeral__left__semiring__numeral,axiom,
% 5.05/5.24 ! [V: num,W: num,Z: rat] :
% 5.05/5.24 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.05/5.24 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_left_semiring_numeral
% 5.05/5.24 thf(fact_107_mult__numeral__left__semiring__numeral,axiom,
% 5.05/5.24 ! [V: num,W: num,Z: nat] :
% 5.05/5.24 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.05/5.24 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_left_semiring_numeral
% 5.05/5.24 thf(fact_108_mult__numeral__left__semiring__numeral,axiom,
% 5.05/5.24 ! [V: num,W: num,Z: int] :
% 5.05/5.24 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.05/5.24 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_left_semiring_numeral
% 5.05/5.24 thf(fact_109_numeral__times__numeral,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.05/5.24 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_times_numeral
% 5.05/5.24 thf(fact_110_numeral__times__numeral,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_times_numeral
% 5.05/5.24 thf(fact_111_numeral__times__numeral,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_times_numeral
% 5.05/5.24 thf(fact_112_numeral__times__numeral,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_times_numeral
% 5.05/5.24 thf(fact_113_numeral__times__numeral,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_times_numeral
% 5.05/5.24 thf(fact_114_add__numeral__left,axiom,
% 5.05/5.24 ! [V: num,W: num,Z: complex] :
% 5.05/5.24 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.05/5.24 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % add_numeral_left
% 5.05/5.24 thf(fact_115_add__numeral__left,axiom,
% 5.05/5.24 ! [V: num,W: num,Z: real] :
% 5.05/5.24 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.05/5.24 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % add_numeral_left
% 5.05/5.24 thf(fact_116_add__numeral__left,axiom,
% 5.05/5.24 ! [V: num,W: num,Z: rat] :
% 5.05/5.24 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.05/5.24 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % add_numeral_left
% 5.05/5.24 thf(fact_117_add__numeral__left,axiom,
% 5.05/5.24 ! [V: num,W: num,Z: nat] :
% 5.05/5.24 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.05/5.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % add_numeral_left
% 5.05/5.24 thf(fact_118_add__numeral__left,axiom,
% 5.05/5.24 ! [V: num,W: num,Z: int] :
% 5.05/5.24 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.05/5.24 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % add_numeral_left
% 5.05/5.24 thf(fact_119_numeral__plus__numeral,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.05/5.24 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_plus_numeral
% 5.05/5.24 thf(fact_120_numeral__plus__numeral,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_plus_numeral
% 5.05/5.24 thf(fact_121_numeral__plus__numeral,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_plus_numeral
% 5.05/5.24 thf(fact_122_numeral__plus__numeral,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_plus_numeral
% 5.05/5.24 thf(fact_123_numeral__plus__numeral,axiom,
% 5.05/5.24 ! [M: num,N2: num] :
% 5.05/5.24 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_plus_numeral
% 5.05/5.24 thf(fact_124_num__double,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( times_times_num @ ( bit0 @ one ) @ N2 )
% 5.05/5.24 = ( bit0 @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % num_double
% 5.05/5.24 thf(fact_125_del__single__cont,axiom,
% 5.05/5.24 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ( X = Mi )
% 5.05/5.24 & ( X = Ma ) )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_single_cont
% 5.05/5.24 thf(fact_126_not__Some__eq,axiom,
% 5.05/5.24 ! [X: option4927543243414619207at_nat] :
% 5.05/5.24 ( ( ! [Y2: product_prod_nat_nat] :
% 5.05/5.24 ( X
% 5.05/5.24 != ( some_P7363390416028606310at_nat @ Y2 ) ) )
% 5.05/5.24 = ( X = none_P5556105721700978146at_nat ) ) ).
% 5.05/5.24
% 5.05/5.24 % not_Some_eq
% 5.05/5.24 thf(fact_127_not__Some__eq,axiom,
% 5.05/5.24 ! [X: option_nat] :
% 5.05/5.24 ( ( ! [Y2: nat] :
% 5.05/5.24 ( X
% 5.05/5.24 != ( some_nat @ Y2 ) ) )
% 5.05/5.24 = ( X = none_nat ) ) ).
% 5.05/5.24
% 5.05/5.24 % not_Some_eq
% 5.05/5.24 thf(fact_128_not__Some__eq,axiom,
% 5.05/5.24 ! [X: option_num] :
% 5.05/5.24 ( ( ! [Y2: num] :
% 5.05/5.24 ( X
% 5.05/5.24 != ( some_num @ Y2 ) ) )
% 5.05/5.24 = ( X = none_num ) ) ).
% 5.05/5.24
% 5.05/5.24 % not_Some_eq
% 5.05/5.24 thf(fact_129_not__None__eq,axiom,
% 5.05/5.24 ! [X: option4927543243414619207at_nat] :
% 5.05/5.24 ( ( X != none_P5556105721700978146at_nat )
% 5.05/5.24 = ( ? [Y2: product_prod_nat_nat] :
% 5.05/5.24 ( X
% 5.05/5.24 = ( some_P7363390416028606310at_nat @ Y2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % not_None_eq
% 5.05/5.24 thf(fact_130_not__None__eq,axiom,
% 5.05/5.24 ! [X: option_nat] :
% 5.05/5.24 ( ( X != none_nat )
% 5.05/5.24 = ( ? [Y2: nat] :
% 5.05/5.24 ( X
% 5.05/5.24 = ( some_nat @ Y2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % not_None_eq
% 5.05/5.24 thf(fact_131_not__None__eq,axiom,
% 5.05/5.24 ! [X: option_num] :
% 5.05/5.24 ( ( X != none_num )
% 5.05/5.24 = ( ? [Y2: num] :
% 5.05/5.24 ( X
% 5.05/5.24 = ( some_num @ Y2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % not_None_eq
% 5.05/5.24 thf(fact_132_member__correct,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( vEBT_vebt_member @ T @ X )
% 5.05/5.24 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % member_correct
% 5.05/5.24 thf(fact_133__092_060open_062summin_A_060_A2_A_094_Am_092_060close_062,axiom,
% 5.05/5.24 ord_less_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>summin < 2 ^ m\<close>
% 5.05/5.24 thf(fact_134_delt__out__of__range,axiom,
% 5.05/5.24 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ( ord_less_nat @ X @ Mi )
% 5.05/5.24 | ( ord_less_nat @ Ma @ X ) )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % delt_out_of_range
% 5.05/5.24 thf(fact_135__092_060open_062both__member__options_A_ItreeList_A_B_Ahigh_Ama_An_J_A_Ilow_Ama_An_J_092_060close_062,axiom,
% 5.05/5.24 vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ma @ na ) ) @ ( vEBT_VEBT_low @ ma @ na ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>both_member_options (treeList ! high ma n) (low ma n)\<close>
% 5.05/5.24 thf(fact_136_lesseq__shift,axiom,
% 5.05/5.24 ( ord_less_eq_nat
% 5.05/5.24 = ( ^ [X2: nat,Y2: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % lesseq_shift
% 5.05/5.24 thf(fact_137__C7_C,axiom,
% 5.05/5.24 ( ( mi != ma )
% 5.05/5.24 => ! [I: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.05/5.24 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.05/5.24 = I )
% 5.05/5.24 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.05/5.24 & ! [Y3: nat] :
% 5.05/5.24 ( ( ( ( vEBT_VEBT_high @ Y3 @ na )
% 5.05/5.24 = I )
% 5.05/5.24 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ Y3 @ na ) ) )
% 5.05/5.24 => ( ( ord_less_nat @ mi @ Y3 )
% 5.05/5.24 & ( ord_less_eq_nat @ Y3 @ ma ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % "7"
% 5.05/5.24 thf(fact_138_mi__ma__2__deg,axiom,
% 5.05/5.24 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N2 )
% 5.05/5.24 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.05/5.24 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % mi_ma_2_deg
% 5.05/5.24 thf(fact_139_summaxma,axiom,
% 5.05/5.24 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.05/5.24 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % summaxma
% 5.05/5.24 thf(fact_140__C6_C,axiom,
% 5.05/5.24 ( ( ord_less_eq_nat @ mi @ ma )
% 5.05/5.24 & ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % "6"
% 5.05/5.24 thf(fact_141_both__member__options__ding,axiom,
% 5.05/5.24 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N2 )
% 5.05/5.24 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.05/5.24 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.24 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % both_member_options_ding
% 5.05/5.24 thf(fact_142_member__inv,axiom,
% 5.05/5.24 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.05/5.24 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 & ( ( X = Mi )
% 5.05/5.24 | ( X = Ma )
% 5.05/5.24 | ( ( ord_less_nat @ X @ Ma )
% 5.05/5.24 & ( ord_less_nat @ Mi @ X )
% 5.05/5.24 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % member_inv
% 5.05/5.24 thf(fact_143_le__divide__eq__numeral1_I1_J,axiom,
% 5.05/5.24 ! [A: real,B: real,W: num] :
% 5.05/5.24 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.05/5.24 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.05/5.24
% 5.05/5.24 % le_divide_eq_numeral1(1)
% 5.05/5.24 thf(fact_144_le__divide__eq__numeral1_I1_J,axiom,
% 5.05/5.24 ! [A: rat,B: rat,W: num] :
% 5.05/5.24 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.05/5.24 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.05/5.24
% 5.05/5.24 % le_divide_eq_numeral1(1)
% 5.05/5.24 thf(fact_145_divide__le__eq__numeral1_I1_J,axiom,
% 5.05/5.24 ! [B: real,W: num,A: real] :
% 5.05/5.24 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.05/5.24 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % divide_le_eq_numeral1(1)
% 5.05/5.24 thf(fact_146_divide__le__eq__numeral1_I1_J,axiom,
% 5.05/5.24 ! [B: rat,W: num,A: rat] :
% 5.05/5.24 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.05/5.24 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % divide_le_eq_numeral1(1)
% 5.05/5.24 thf(fact_147_less__divide__eq__numeral1_I1_J,axiom,
% 5.05/5.24 ! [A: real,B: real,W: num] :
% 5.05/5.24 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.05/5.24 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.05/5.24
% 5.05/5.24 % less_divide_eq_numeral1(1)
% 5.05/5.24 thf(fact_148_less__divide__eq__numeral1_I1_J,axiom,
% 5.05/5.24 ! [A: rat,B: rat,W: num] :
% 5.05/5.24 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.05/5.24 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.05/5.24
% 5.05/5.24 % less_divide_eq_numeral1(1)
% 5.05/5.24 thf(fact_149_divide__less__eq__numeral1_I1_J,axiom,
% 5.05/5.24 ! [B: real,W: num,A: real] :
% 5.05/5.24 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.05/5.24 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % divide_less_eq_numeral1(1)
% 5.05/5.24 thf(fact_150_divide__less__eq__numeral1_I1_J,axiom,
% 5.05/5.24 ! [B: rat,W: num,A: rat] :
% 5.05/5.24 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.05/5.24 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % divide_less_eq_numeral1(1)
% 5.05/5.24 thf(fact_151__092_060open_062high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_060_Alength_AtreeList_092_060close_062,axiom,
% 5.05/5.24 ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ).
% 5.05/5.24
% 5.05/5.24 % \<open>high (summin * 2 ^ n + lx) n < length treeList\<close>
% 5.05/5.24 thf(fact_152_hlbound,axiom,
% 5.05/5.24 ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.05/5.24 & ( ord_less_nat @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % hlbound
% 5.05/5.24 thf(fact_153_yhelper,axiom,
% 5.05/5.24 ! [Y: nat] :
% 5.05/5.24 ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ Y @ na ) ) @ ( vEBT_VEBT_low @ Y @ na ) )
% 5.05/5.24 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Y @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.05/5.24 => ( ( ord_less_nat @ mi @ Y )
% 5.05/5.24 & ( ord_less_eq_nat @ Y @ ma )
% 5.05/5.24 & ( ord_less_nat @ ( vEBT_VEBT_low @ Y @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % yhelper
% 5.05/5.24 thf(fact_154__C7b_C,axiom,
% 5.05/5.24 ! [I: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.05/5.24 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.05/5.24 = I )
% 5.05/5.24 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.05/5.24 & ! [Y3: nat] :
% 5.05/5.24 ( ( ( ( vEBT_VEBT_high @ Y3 @ na )
% 5.05/5.24 = I )
% 5.05/5.24 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ Y3 @ na ) ) )
% 5.05/5.24 => ( ( ord_less_nat @ mi @ Y3 )
% 5.05/5.24 & ( ord_less_eq_nat @ Y3 @ ma ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % "7b"
% 5.05/5.24 thf(fact_155_nothprolist,axiom,
% 5.05/5.24 ! [I2: nat] :
% 5.05/5.24 ( ( ( I2
% 5.05/5.24 != ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) )
% 5.05/5.24 & ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
% 5.05/5.24 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ I2 )
% 5.05/5.24 = ( nth_VEBT_VEBT @ treeList @ I2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % nothprolist
% 5.05/5.24 thf(fact_156_newlistlength,axiom,
% 5.05/5.24 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) )
% 5.05/5.24 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.05/5.24
% 5.05/5.24 % newlistlength
% 5.05/5.24 thf(fact_157_del__x__not__mi__newnode__not__nil,axiom,
% 5.05/5.24 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ( ord_less_nat @ Mi @ X )
% 5.05/5.24 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = H2 )
% 5.05/5.24 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = L2 )
% 5.05/5.24 => ( ( Newnode
% 5.05/5.24 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 5.05/5.24 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.05/5.24 => ( ( Newlist
% 5.05/5.24 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.05/5.24 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_x_not_mi_newnode_not_nil
% 5.05/5.24 thf(fact_158_del__x__mi__lets__in__not__minNull,axiom,
% 5.05/5.24 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.05/5.24 ( ( ( X = Mi )
% 5.05/5.24 & ( ord_less_nat @ X @ Ma ) )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = H2 )
% 5.05/5.24 => ( ( Xn
% 5.05/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.05/5.24 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = L2 )
% 5.05/5.24 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 => ( ( Newnode
% 5.05/5.24 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 5.05/5.24 => ( ( Newlist
% 5.05/5.24 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.05/5.24 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_x_mi_lets_in_not_minNull
% 5.05/5.24 thf(fact_159_del__x__not__mia,axiom,
% 5.05/5.24 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ( ord_less_nat @ Mi @ X )
% 5.05/5.24 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = H2 )
% 5.05/5.24 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = L2 )
% 5.05/5.24 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 5.05/5.24 @ ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ Mi
% 5.05/5.24 @ ( if_nat @ ( X = Ma )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.05/5.24 = none_nat )
% 5.05/5.24 @ Mi
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ Deg
% 5.05/5.24 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 5.05/5.24 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.05/5.24 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_x_not_mia
% 5.05/5.24 thf(fact_160_del__x__not__mi__new__node__nil,axiom,
% 5.05/5.24 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.05/5.24 ( ( ( ord_less_nat @ Mi @ X )
% 5.05/5.24 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = H2 )
% 5.05/5.24 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = L2 )
% 5.05/5.24 => ( ( Newnode
% 5.05/5.24 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 5.05/5.24 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.05/5.24 => ( ( Sn
% 5.05/5.24 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.05/5.24 => ( ( Newlist
% 5.05/5.24 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.05/5.24 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ Mi
% 5.05/5.24 @ ( if_nat @ ( X = Ma )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.05/5.24 = none_nat )
% 5.05/5.24 @ Mi
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ Deg
% 5.05/5.24 @ Newlist
% 5.05/5.24 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_x_not_mi_new_node_nil
% 5.05/5.24 thf(fact_161_del__x__not__mi,axiom,
% 5.05/5.24 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ( ord_less_nat @ Mi @ X )
% 5.05/5.24 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = H2 )
% 5.05/5.24 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = L2 )
% 5.05/5.24 => ( ( Newnode
% 5.05/5.24 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 5.05/5.24 => ( ( Newlist
% 5.05/5.24 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.05/5.24 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ Mi
% 5.05/5.24 @ ( if_nat @ ( X = Ma )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.05/5.24 = none_nat )
% 5.05/5.24 @ Mi
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ Deg
% 5.05/5.24 @ Newlist
% 5.05/5.24 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 5.05/5.24 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_x_not_mi
% 5.05/5.24 thf(fact_162_del__x__mia,axiom,
% 5.05/5.24 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ( X = Mi )
% 5.05/5.24 & ( ord_less_nat @ X @ Ma ) )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.05/5.24 = Ma )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 = none_nat )
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ Deg
% 5.05/5.24 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.05/5.24 = Ma )
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ Deg
% 5.05/5.24 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ Summary ) )
% 5.05/5.24 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_x_mia
% 5.05/5.24 thf(fact_163_del__x__mi__lets__in__minNull,axiom,
% 5.05/5.24 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 5.05/5.24 ( ( ( X = Mi )
% 5.05/5.24 & ( ord_less_nat @ X @ Ma ) )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = H2 )
% 5.05/5.24 => ( ( Xn
% 5.05/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.05/5.24 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = L2 )
% 5.05/5.24 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 => ( ( Newnode
% 5.05/5.24 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 5.05/5.24 => ( ( Newlist
% 5.05/5.24 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.05/5.24 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.05/5.24 => ( ( Sn
% 5.05/5.24 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ Xn
% 5.05/5.24 @ ( if_nat @ ( Xn = Ma )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.05/5.24 = none_nat )
% 5.05/5.24 @ Xn
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ Deg
% 5.05/5.24 @ Newlist
% 5.05/5.24 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_x_mi_lets_in_minNull
% 5.05/5.24 thf(fact_164_del__x__mi__lets__in,axiom,
% 5.05/5.24 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.05/5.24 ( ( ( X = Mi )
% 5.05/5.24 & ( ord_less_nat @ X @ Ma ) )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = H2 )
% 5.05/5.24 => ( ( Xn
% 5.05/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.05/5.24 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = L2 )
% 5.05/5.24 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 => ( ( Newnode
% 5.05/5.24 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 5.05/5.24 => ( ( Newlist
% 5.05/5.24 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 5.05/5.24 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ Xn
% 5.05/5.24 @ ( if_nat @ ( Xn = Ma )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.05/5.24 = none_nat )
% 5.05/5.24 @ Xn
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ Deg
% 5.05/5.24 @ Newlist
% 5.05/5.24 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 5.05/5.24 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_x_mi_lets_in
% 5.05/5.24 thf(fact_165_del__x__mi,axiom,
% 5.05/5.24 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L2: nat] :
% 5.05/5.24 ( ( ( X = Mi )
% 5.05/5.24 & ( ord_less_nat @ X @ Ma ) )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = H2 )
% 5.05/5.24 => ( ( Xn
% 5.05/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.05/5.24 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.24 = L2 )
% 5.05/5.24 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 5.05/5.24 @ ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ Xn
% 5.05/5.24 @ ( if_nat @ ( Xn = Ma )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.05/5.24 = none_nat )
% 5.05/5.24 @ Xn
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ Deg
% 5.05/5.24 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) )
% 5.05/5.24 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.05/5.24 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_x_mi
% 5.05/5.24 thf(fact_166_del__in__range,axiom,
% 5.05/5.24 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ( ord_less_eq_nat @ Mi @ X )
% 5.05/5.24 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.05/5.24 => ( ( Mi != Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( ( X = Mi )
% 5.05/5.24 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.05/5.24 = Ma ) )
% 5.05/5.24 & ( ( X != Mi )
% 5.05/5.24 => ( X = Ma ) ) )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 = none_nat )
% 5.05/5.24 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ Deg
% 5.05/5.24 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( ( X = Mi )
% 5.05/5.24 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.05/5.24 = Ma ) )
% 5.05/5.24 & ( ( X != Mi )
% 5.05/5.24 => ( X = Ma ) ) )
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ Deg
% 5.05/5.24 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ Summary ) )
% 5.05/5.24 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % del_in_range
% 5.05/5.24 thf(fact_167__C4_OIH_C_I1_J,axiom,
% 5.05/5.24 ! [X5: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.05/5.24 => ( ( vEBT_invar_vebt @ X5 @ na )
% 5.05/5.24 & ! [Xa: nat] : ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ X5 @ Xa ) @ na ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % "4.IH"(1)
% 5.05/5.24 thf(fact_168__C5_C,axiom,
% 5.05/5.24 ( ( mi = ma )
% 5.05/5.24 => ! [X5: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.05/5.24 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % "5"
% 5.05/5.24 thf(fact_169_add__One__commute,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_num @ one @ N2 )
% 5.05/5.24 = ( plus_plus_num @ N2 @ one ) ) ).
% 5.05/5.24
% 5.05/5.24 % add_One_commute
% 5.05/5.24 thf(fact_170_div__le__dividend,axiom,
% 5.05/5.24 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 5.05/5.24
% 5.05/5.24 % div_le_dividend
% 5.05/5.24 thf(fact_171_div__le__mono,axiom,
% 5.05/5.24 ! [M: nat,N2: nat,K: nat] :
% 5.05/5.24 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.24 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % div_le_mono
% 5.05/5.24 thf(fact_172_div__mult2__numeral__eq,axiom,
% 5.05/5.24 ! [A: nat,K: num,L2: num] :
% 5.05/5.24 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 5.05/5.24 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % div_mult2_numeral_eq
% 5.05/5.24 thf(fact_173_div__mult2__numeral__eq,axiom,
% 5.05/5.24 ! [A: int,K: num,L2: num] :
% 5.05/5.24 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 5.05/5.24 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % div_mult2_numeral_eq
% 5.05/5.24 thf(fact_174_less__mult__imp__div__less,axiom,
% 5.05/5.24 ! [M: nat,I2: nat,N2: nat] :
% 5.05/5.24 ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N2 ) )
% 5.05/5.24 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % less_mult_imp_div_less
% 5.05/5.24 thf(fact_175_times__div__less__eq__dividend,axiom,
% 5.05/5.24 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 5.05/5.24
% 5.05/5.24 % times_div_less_eq_dividend
% 5.05/5.24 thf(fact_176_div__times__less__eq__dividend,axiom,
% 5.05/5.24 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 5.05/5.24
% 5.05/5.24 % div_times_less_eq_dividend
% 5.05/5.24 thf(fact_177_is__num__normalize_I1_J,axiom,
% 5.05/5.24 ! [A: real,B: real,C: real] :
% 5.05/5.24 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.05/5.24 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % is_num_normalize(1)
% 5.05/5.24 thf(fact_178_is__num__normalize_I1_J,axiom,
% 5.05/5.24 ! [A: rat,B: rat,C: rat] :
% 5.05/5.24 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.05/5.24 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % is_num_normalize(1)
% 5.05/5.24 thf(fact_179_is__num__normalize_I1_J,axiom,
% 5.05/5.24 ! [A: int,B: int,C: int] :
% 5.05/5.24 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.05/5.24 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % is_num_normalize(1)
% 5.05/5.24 thf(fact_180_combine__options__cases,axiom,
% 5.05/5.24 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.05/5.24 ( ( ( X = none_P5556105721700978146at_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ! [A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.05/5.24 ( ( X
% 5.05/5.24 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.05/5.24 => ( ( Y
% 5.05/5.24 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.05/5.24 => ( P @ X @ Y ) ) )
% 5.05/5.24 => ( P @ X @ Y ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % combine_options_cases
% 5.05/5.24 thf(fact_181_combine__options__cases,axiom,
% 5.05/5.24 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y: option_nat] :
% 5.05/5.24 ( ( ( X = none_P5556105721700978146at_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ( ( Y = none_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ! [A3: product_prod_nat_nat,B2: nat] :
% 5.05/5.24 ( ( X
% 5.05/5.24 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.05/5.24 => ( ( Y
% 5.05/5.24 = ( some_nat @ B2 ) )
% 5.05/5.24 => ( P @ X @ Y ) ) )
% 5.05/5.24 => ( P @ X @ Y ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % combine_options_cases
% 5.05/5.24 thf(fact_182_combine__options__cases,axiom,
% 5.05/5.24 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 5.05/5.24 ( ( ( X = none_P5556105721700978146at_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ( ( Y = none_num )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ! [A3: product_prod_nat_nat,B2: num] :
% 5.05/5.24 ( ( X
% 5.05/5.24 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.05/5.24 => ( ( Y
% 5.05/5.24 = ( some_num @ B2 ) )
% 5.05/5.24 => ( P @ X @ Y ) ) )
% 5.05/5.24 => ( P @ X @ Y ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % combine_options_cases
% 5.05/5.24 thf(fact_183_combine__options__cases,axiom,
% 5.05/5.24 ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.05/5.24 ( ( ( X = none_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ! [A3: nat,B2: product_prod_nat_nat] :
% 5.05/5.24 ( ( X
% 5.05/5.24 = ( some_nat @ A3 ) )
% 5.05/5.24 => ( ( Y
% 5.05/5.24 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.05/5.24 => ( P @ X @ Y ) ) )
% 5.05/5.24 => ( P @ X @ Y ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % combine_options_cases
% 5.05/5.24 thf(fact_184_combine__options__cases,axiom,
% 5.05/5.24 ! [X: option_nat,P: option_nat > option_nat > $o,Y: option_nat] :
% 5.05/5.24 ( ( ( X = none_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ( ( Y = none_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ! [A3: nat,B2: nat] :
% 5.05/5.24 ( ( X
% 5.05/5.24 = ( some_nat @ A3 ) )
% 5.05/5.24 => ( ( Y
% 5.05/5.24 = ( some_nat @ B2 ) )
% 5.05/5.24 => ( P @ X @ Y ) ) )
% 5.05/5.24 => ( P @ X @ Y ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % combine_options_cases
% 5.05/5.24 thf(fact_185_combine__options__cases,axiom,
% 5.05/5.24 ! [X: option_nat,P: option_nat > option_num > $o,Y: option_num] :
% 5.05/5.24 ( ( ( X = none_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ( ( Y = none_num )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ! [A3: nat,B2: num] :
% 5.05/5.24 ( ( X
% 5.05/5.24 = ( some_nat @ A3 ) )
% 5.05/5.24 => ( ( Y
% 5.05/5.24 = ( some_num @ B2 ) )
% 5.05/5.24 => ( P @ X @ Y ) ) )
% 5.05/5.24 => ( P @ X @ Y ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % combine_options_cases
% 5.05/5.24 thf(fact_186_combine__options__cases,axiom,
% 5.05/5.24 ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.05/5.24 ( ( ( X = none_num )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ! [A3: num,B2: product_prod_nat_nat] :
% 5.05/5.24 ( ( X
% 5.05/5.24 = ( some_num @ A3 ) )
% 5.05/5.24 => ( ( Y
% 5.05/5.24 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.05/5.24 => ( P @ X @ Y ) ) )
% 5.05/5.24 => ( P @ X @ Y ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % combine_options_cases
% 5.05/5.24 thf(fact_187_combine__options__cases,axiom,
% 5.05/5.24 ! [X: option_num,P: option_num > option_nat > $o,Y: option_nat] :
% 5.05/5.24 ( ( ( X = none_num )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ( ( Y = none_nat )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ! [A3: num,B2: nat] :
% 5.05/5.24 ( ( X
% 5.05/5.24 = ( some_num @ A3 ) )
% 5.05/5.24 => ( ( Y
% 5.05/5.24 = ( some_nat @ B2 ) )
% 5.05/5.24 => ( P @ X @ Y ) ) )
% 5.05/5.24 => ( P @ X @ Y ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % combine_options_cases
% 5.05/5.24 thf(fact_188_combine__options__cases,axiom,
% 5.05/5.24 ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 5.05/5.24 ( ( ( X = none_num )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ( ( Y = none_num )
% 5.05/5.24 => ( P @ X @ Y ) )
% 5.05/5.24 => ( ! [A3: num,B2: num] :
% 5.05/5.24 ( ( X
% 5.05/5.24 = ( some_num @ A3 ) )
% 5.05/5.24 => ( ( Y
% 5.05/5.24 = ( some_num @ B2 ) )
% 5.05/5.24 => ( P @ X @ Y ) ) )
% 5.05/5.24 => ( P @ X @ Y ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % combine_options_cases
% 5.05/5.24 thf(fact_189_split__option__all,axiom,
% 5.05/5.24 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.05/5.24 ! [X6: option4927543243414619207at_nat] : ( P2 @ X6 ) )
% 5.05/5.24 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.05/5.24 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.05/5.24 & ! [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % split_option_all
% 5.05/5.24 thf(fact_190_split__option__all,axiom,
% 5.05/5.24 ( ( ^ [P2: option_nat > $o] :
% 5.05/5.24 ! [X6: option_nat] : ( P2 @ X6 ) )
% 5.05/5.24 = ( ^ [P3: option_nat > $o] :
% 5.05/5.24 ( ( P3 @ none_nat )
% 5.05/5.24 & ! [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % split_option_all
% 5.05/5.24 thf(fact_191_split__option__all,axiom,
% 5.05/5.24 ( ( ^ [P2: option_num > $o] :
% 5.05/5.24 ! [X6: option_num] : ( P2 @ X6 ) )
% 5.05/5.24 = ( ^ [P3: option_num > $o] :
% 5.05/5.24 ( ( P3 @ none_num )
% 5.05/5.24 & ! [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % split_option_all
% 5.05/5.24 thf(fact_192_split__option__ex,axiom,
% 5.05/5.24 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 5.05/5.24 ? [X6: option4927543243414619207at_nat] : ( P2 @ X6 ) )
% 5.05/5.24 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.05/5.24 ( ( P3 @ none_P5556105721700978146at_nat )
% 5.05/5.24 | ? [X2: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % split_option_ex
% 5.05/5.24 thf(fact_193_split__option__ex,axiom,
% 5.05/5.24 ( ( ^ [P2: option_nat > $o] :
% 5.05/5.24 ? [X6: option_nat] : ( P2 @ X6 ) )
% 5.05/5.24 = ( ^ [P3: option_nat > $o] :
% 5.05/5.24 ( ( P3 @ none_nat )
% 5.05/5.24 | ? [X2: nat] : ( P3 @ ( some_nat @ X2 ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % split_option_ex
% 5.05/5.24 thf(fact_194_split__option__ex,axiom,
% 5.05/5.24 ( ( ^ [P2: option_num > $o] :
% 5.05/5.24 ? [X6: option_num] : ( P2 @ X6 ) )
% 5.05/5.24 = ( ^ [P3: option_num > $o] :
% 5.05/5.24 ( ( P3 @ none_num )
% 5.05/5.24 | ? [X2: num] : ( P3 @ ( some_num @ X2 ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % split_option_ex
% 5.05/5.24 thf(fact_195_option_Oexhaust,axiom,
% 5.05/5.24 ! [Y: option4927543243414619207at_nat] :
% 5.05/5.24 ( ( Y != none_P5556105721700978146at_nat )
% 5.05/5.24 => ~ ! [X23: product_prod_nat_nat] :
% 5.05/5.24 ( Y
% 5.05/5.24 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.exhaust
% 5.05/5.24 thf(fact_196_option_Oexhaust,axiom,
% 5.05/5.24 ! [Y: option_nat] :
% 5.05/5.24 ( ( Y != none_nat )
% 5.05/5.24 => ~ ! [X23: nat] :
% 5.05/5.24 ( Y
% 5.05/5.24 != ( some_nat @ X23 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.exhaust
% 5.05/5.24 thf(fact_197_option_Oexhaust,axiom,
% 5.05/5.24 ! [Y: option_num] :
% 5.05/5.24 ( ( Y != none_num )
% 5.05/5.24 => ~ ! [X23: num] :
% 5.05/5.24 ( Y
% 5.05/5.24 != ( some_num @ X23 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.exhaust
% 5.05/5.24 thf(fact_198_option_OdiscI,axiom,
% 5.05/5.24 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 5.05/5.24 ( ( Option
% 5.05/5.24 = ( some_P7363390416028606310at_nat @ X22 ) )
% 5.05/5.24 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.discI
% 5.05/5.24 thf(fact_199_option_OdiscI,axiom,
% 5.05/5.24 ! [Option: option_nat,X22: nat] :
% 5.05/5.24 ( ( Option
% 5.05/5.24 = ( some_nat @ X22 ) )
% 5.05/5.24 => ( Option != none_nat ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.discI
% 5.05/5.24 thf(fact_200_option_OdiscI,axiom,
% 5.05/5.24 ! [Option: option_num,X22: num] :
% 5.05/5.24 ( ( Option
% 5.05/5.24 = ( some_num @ X22 ) )
% 5.05/5.24 => ( Option != none_num ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.discI
% 5.05/5.24 thf(fact_201_option_Odistinct_I1_J,axiom,
% 5.05/5.24 ! [X22: product_prod_nat_nat] :
% 5.05/5.24 ( none_P5556105721700978146at_nat
% 5.05/5.24 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.distinct(1)
% 5.05/5.24 thf(fact_202_option_Odistinct_I1_J,axiom,
% 5.05/5.24 ! [X22: nat] :
% 5.05/5.24 ( none_nat
% 5.05/5.24 != ( some_nat @ X22 ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.distinct(1)
% 5.05/5.24 thf(fact_203_option_Odistinct_I1_J,axiom,
% 5.05/5.24 ! [X22: num] :
% 5.05/5.24 ( none_num
% 5.05/5.24 != ( some_num @ X22 ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.distinct(1)
% 5.05/5.24 thf(fact_204_div__mult2__eq,axiom,
% 5.05/5.24 ! [M: nat,N2: nat,Q2: nat] :
% 5.05/5.24 ( ( divide_divide_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
% 5.05/5.24 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % div_mult2_eq
% 5.05/5.24 thf(fact_205_option_Osel,axiom,
% 5.05/5.24 ! [X22: product_prod_nat_nat] :
% 5.05/5.24 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.05/5.24 = X22 ) ).
% 5.05/5.24
% 5.05/5.24 % option.sel
% 5.05/5.24 thf(fact_206_option_Osel,axiom,
% 5.05/5.24 ! [X22: nat] :
% 5.05/5.24 ( ( the_nat @ ( some_nat @ X22 ) )
% 5.05/5.24 = X22 ) ).
% 5.05/5.24
% 5.05/5.24 % option.sel
% 5.05/5.24 thf(fact_207_option_Osel,axiom,
% 5.05/5.24 ! [X22: num] :
% 5.05/5.24 ( ( the_num @ ( some_num @ X22 ) )
% 5.05/5.24 = X22 ) ).
% 5.05/5.24
% 5.05/5.24 % option.sel
% 5.05/5.24 thf(fact_208_option_Oexpand,axiom,
% 5.05/5.24 ! [Option: option_nat,Option2: option_nat] :
% 5.05/5.24 ( ( ( Option = none_nat )
% 5.05/5.24 = ( Option2 = none_nat ) )
% 5.05/5.24 => ( ( ( Option != none_nat )
% 5.05/5.24 => ( ( Option2 != none_nat )
% 5.05/5.24 => ( ( the_nat @ Option )
% 5.05/5.24 = ( the_nat @ Option2 ) ) ) )
% 5.05/5.24 => ( Option = Option2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.expand
% 5.05/5.24 thf(fact_209_option_Oexpand,axiom,
% 5.05/5.24 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 5.05/5.24 ( ( ( Option = none_P5556105721700978146at_nat )
% 5.05/5.24 = ( Option2 = none_P5556105721700978146at_nat ) )
% 5.05/5.24 => ( ( ( Option != none_P5556105721700978146at_nat )
% 5.05/5.24 => ( ( Option2 != none_P5556105721700978146at_nat )
% 5.05/5.24 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 5.05/5.24 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 5.05/5.24 => ( Option = Option2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.expand
% 5.05/5.24 thf(fact_210_option_Oexpand,axiom,
% 5.05/5.24 ! [Option: option_num,Option2: option_num] :
% 5.05/5.24 ( ( ( Option = none_num )
% 5.05/5.24 = ( Option2 = none_num ) )
% 5.05/5.24 => ( ( ( Option != none_num )
% 5.05/5.24 => ( ( Option2 != none_num )
% 5.05/5.24 => ( ( the_num @ Option )
% 5.05/5.24 = ( the_num @ Option2 ) ) ) )
% 5.05/5.24 => ( Option = Option2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.expand
% 5.05/5.24 thf(fact_211_mult__numeral__1__right,axiom,
% 5.05/5.24 ! [A: complex] :
% 5.05/5.24 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_1_right
% 5.05/5.24 thf(fact_212_mult__numeral__1__right,axiom,
% 5.05/5.24 ! [A: real] :
% 5.05/5.24 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_1_right
% 5.05/5.24 thf(fact_213_mult__numeral__1__right,axiom,
% 5.05/5.24 ! [A: rat] :
% 5.05/5.24 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_1_right
% 5.05/5.24 thf(fact_214_mult__numeral__1__right,axiom,
% 5.05/5.24 ! [A: nat] :
% 5.05/5.24 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_1_right
% 5.05/5.24 thf(fact_215_mult__numeral__1__right,axiom,
% 5.05/5.24 ! [A: int] :
% 5.05/5.24 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_1_right
% 5.05/5.24 thf(fact_216_mult__numeral__1,axiom,
% 5.05/5.24 ! [A: complex] :
% 5.05/5.24 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_1
% 5.05/5.24 thf(fact_217_mult__numeral__1,axiom,
% 5.05/5.24 ! [A: real] :
% 5.05/5.24 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_1
% 5.05/5.24 thf(fact_218_mult__numeral__1,axiom,
% 5.05/5.24 ! [A: rat] :
% 5.05/5.24 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_1
% 5.05/5.24 thf(fact_219_mult__numeral__1,axiom,
% 5.05/5.24 ! [A: nat] :
% 5.05/5.24 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_1
% 5.05/5.24 thf(fact_220_mult__numeral__1,axiom,
% 5.05/5.24 ! [A: int] :
% 5.05/5.24 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % mult_numeral_1
% 5.05/5.24 thf(fact_221_numeral__Bit0,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 5.05/5.24 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_Bit0
% 5.05/5.24 thf(fact_222_numeral__Bit0,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 5.05/5.24 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_Bit0
% 5.05/5.24 thf(fact_223_numeral__Bit0,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 5.05/5.24 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_Bit0
% 5.05/5.24 thf(fact_224_numeral__Bit0,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.05/5.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_Bit0
% 5.05/5.24 thf(fact_225_numeral__Bit0,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 5.05/5.24 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_Bit0
% 5.05/5.24 thf(fact_226_divide__numeral__1,axiom,
% 5.05/5.24 ! [A: complex] :
% 5.05/5.24 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % divide_numeral_1
% 5.05/5.24 thf(fact_227_divide__numeral__1,axiom,
% 5.05/5.24 ! [A: real] :
% 5.05/5.24 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % divide_numeral_1
% 5.05/5.24 thf(fact_228_divide__numeral__1,axiom,
% 5.05/5.24 ! [A: rat] :
% 5.05/5.24 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.05/5.24 = A ) ).
% 5.05/5.24
% 5.05/5.24 % divide_numeral_1
% 5.05/5.24 thf(fact_229_option_Oexhaust__sel,axiom,
% 5.05/5.24 ! [Option: option4927543243414619207at_nat] :
% 5.05/5.24 ( ( Option != none_P5556105721700978146at_nat )
% 5.05/5.24 => ( Option
% 5.05/5.24 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.exhaust_sel
% 5.05/5.24 thf(fact_230_option_Oexhaust__sel,axiom,
% 5.05/5.24 ! [Option: option_nat] :
% 5.05/5.24 ( ( Option != none_nat )
% 5.05/5.24 => ( Option
% 5.05/5.24 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.exhaust_sel
% 5.05/5.24 thf(fact_231_option_Oexhaust__sel,axiom,
% 5.05/5.24 ! [Option: option_num] :
% 5.05/5.24 ( ( Option != none_num )
% 5.05/5.24 => ( Option
% 5.05/5.24 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % option.exhaust_sel
% 5.05/5.24 thf(fact_232_numeral__code_I2_J,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 5.05/5.24 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_code(2)
% 5.05/5.24 thf(fact_233_numeral__code_I2_J,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 5.05/5.24 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_code(2)
% 5.05/5.24 thf(fact_234_numeral__code_I2_J,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 5.05/5.24 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_code(2)
% 5.05/5.24 thf(fact_235_numeral__code_I2_J,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.05/5.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_code(2)
% 5.05/5.24 thf(fact_236_numeral__code_I2_J,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 5.05/5.24 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_code(2)
% 5.05/5.24 thf(fact_237_numeral__Bit0__div__2,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.24 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_Bit0_div_2
% 5.05/5.24 thf(fact_238_numeral__Bit0__div__2,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.05/5.24 = ( numeral_numeral_int @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_Bit0_div_2
% 5.05/5.24 thf(fact_239_left__add__twice,axiom,
% 5.05/5.24 ! [A: complex,B: complex] :
% 5.05/5.24 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.05/5.24 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.05/5.24
% 5.05/5.24 % left_add_twice
% 5.05/5.24 thf(fact_240_left__add__twice,axiom,
% 5.05/5.24 ! [A: real,B: real] :
% 5.05/5.24 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.05/5.24 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.05/5.24
% 5.05/5.24 % left_add_twice
% 5.05/5.24 thf(fact_241_left__add__twice,axiom,
% 5.05/5.24 ! [A: rat,B: rat] :
% 5.05/5.24 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.05/5.24 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.05/5.24
% 5.05/5.24 % left_add_twice
% 5.05/5.24 thf(fact_242_left__add__twice,axiom,
% 5.05/5.24 ! [A: nat,B: nat] :
% 5.05/5.24 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.05/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.05/5.24
% 5.05/5.24 % left_add_twice
% 5.05/5.24 thf(fact_243_left__add__twice,axiom,
% 5.05/5.24 ! [A: int,B: int] :
% 5.05/5.24 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.05/5.24 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.05/5.24
% 5.05/5.24 % left_add_twice
% 5.05/5.24 thf(fact_244_mult__2__right,axiom,
% 5.05/5.24 ! [Z: complex] :
% 5.05/5.24 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.05/5.24 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_2_right
% 5.05/5.24 thf(fact_245_mult__2__right,axiom,
% 5.05/5.24 ! [Z: real] :
% 5.05/5.24 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.05/5.24 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_2_right
% 5.05/5.24 thf(fact_246_mult__2__right,axiom,
% 5.05/5.24 ! [Z: rat] :
% 5.05/5.24 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.05/5.24 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_2_right
% 5.05/5.24 thf(fact_247_mult__2__right,axiom,
% 5.05/5.24 ! [Z: nat] :
% 5.05/5.24 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.24 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_2_right
% 5.05/5.24 thf(fact_248_mult__2__right,axiom,
% 5.05/5.24 ! [Z: int] :
% 5.05/5.24 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.05/5.24 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_2_right
% 5.05/5.24 thf(fact_249_mult__2,axiom,
% 5.05/5.24 ! [Z: complex] :
% 5.05/5.24 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.05/5.24 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_2
% 5.05/5.24 thf(fact_250_mult__2,axiom,
% 5.05/5.24 ! [Z: real] :
% 5.05/5.24 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.05/5.24 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_2
% 5.05/5.24 thf(fact_251_mult__2,axiom,
% 5.05/5.24 ! [Z: rat] :
% 5.05/5.24 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.05/5.24 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_2
% 5.05/5.24 thf(fact_252_mult__2,axiom,
% 5.05/5.24 ! [Z: nat] :
% 5.05/5.24 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.05/5.24 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_2
% 5.05/5.24 thf(fact_253_mult__2,axiom,
% 5.05/5.24 ! [Z: int] :
% 5.05/5.24 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.05/5.24 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.05/5.24
% 5.05/5.24 % mult_2
% 5.05/5.24 thf(fact_254_in__children__def,axiom,
% 5.05/5.24 ( vEBT_V5917875025757280293ildren
% 5.05/5.24 = ( ^ [N: nat,TreeList2: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X2 @ N ) ) @ ( vEBT_VEBT_low @ X2 @ N ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % in_children_def
% 5.05/5.24 thf(fact_255_succ__list__to__short,axiom,
% 5.05/5.24 ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.24 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = none_nat ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % succ_list_to_short
% 5.05/5.24 thf(fact_256_pred__list__to__short,axiom,
% 5.05/5.24 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.24 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = none_nat ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % pred_list_to_short
% 5.05/5.24 thf(fact_257_allvalidinlist,axiom,
% 5.05/5.24 ! [X5: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
% 5.05/5.24 => ( vEBT_invar_vebt @ X5 @ na ) ) ).
% 5.05/5.24
% 5.05/5.24 % allvalidinlist
% 5.05/5.24 thf(fact_258_post__member__pre__member,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.24 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.24 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 5.05/5.24 => ( ( vEBT_vebt_member @ T @ Y )
% 5.05/5.24 | ( X = Y ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % post_member_pre_member
% 5.05/5.24 thf(fact_259_nested__mint,axiom,
% 5.05/5.24 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,Va: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N2 )
% 5.05/5.24 => ( ( N2
% 5.05/5.24 = ( suc @ ( suc @ Va ) ) )
% 5.05/5.24 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.05/5.24 => ( ( Ma != Mi )
% 5.05/5.24 => ( 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 ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % nested_mint
% 5.05/5.24 thf(fact_260_valid__insert__both__member__options__pres,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.24 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.24 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.05/5.24 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % valid_insert_both_member_options_pres
% 5.05/5.24 thf(fact_261_valid__insert__both__member__options__add,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.24 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % valid_insert_both_member_options_add
% 5.05/5.24 thf(fact_262_insert__simp__mima,axiom,
% 5.05/5.24 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ( X = Mi )
% 5.05/5.24 | ( X = Ma ) )
% 5.05/5.24 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % insert_simp_mima
% 5.05/5.24 thf(fact_263_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.05/5.24 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.05/5.24 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.24 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % both_member_options_from_chilf_to_complete_tree
% 5.05/5.24 thf(fact_264_succ__min,axiom,
% 5.05/5.24 ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ord_less_nat @ X @ Mi )
% 5.05/5.24 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( some_nat @ Mi ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % succ_min
% 5.05/5.24 thf(fact_265_pred__max,axiom,
% 5.05/5.24 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.24 => ( ( ord_less_nat @ Ma @ X )
% 5.05/5.24 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( some_nat @ Ma ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % pred_max
% 5.05/5.24 thf(fact_266_even__odd__cases,axiom,
% 5.05/5.24 ! [X: nat] :
% 5.05/5.24 ( ! [N3: nat] :
% 5.05/5.24 ( X
% 5.05/5.24 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.05/5.24 => ~ ! [N3: nat] :
% 5.05/5.24 ( X
% 5.05/5.24 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % even_odd_cases
% 5.05/5.24 thf(fact_267_deg__SUcn__Node,axiom,
% 5.05/5.24 ! [Tree: vEBT_VEBT,N2: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N2 ) ) )
% 5.05/5.24 => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.05/5.24 ( Tree
% 5.05/5.24 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N2 ) ) @ TreeList3 @ S ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % deg_SUcn_Node
% 5.05/5.24 thf(fact_268__C11_C,axiom,
% 5.05/5.24 ord_less_eq_nat @ one_one_nat @ na ).
% 5.05/5.24
% 5.05/5.24 % "11"
% 5.05/5.24 thf(fact_269_inthall,axiom,
% 5.05/5.24 ! [Xs2: list_complex,P: complex > $o,N2: nat] :
% 5.05/5.24 ( ! [X3: complex] :
% 5.05/5.24 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 5.05/5.24 => ( P @ X3 ) )
% 5.05/5.24 => ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.05/5.24 => ( P @ ( nth_complex @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % inthall
% 5.05/5.24 thf(fact_270_inthall,axiom,
% 5.05/5.24 ! [Xs2: list_real,P: real > $o,N2: nat] :
% 5.05/5.24 ( ! [X3: real] :
% 5.05/5.24 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 5.05/5.24 => ( P @ X3 ) )
% 5.05/5.24 => ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs2 ) )
% 5.05/5.24 => ( P @ ( nth_real @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % inthall
% 5.05/5.24 thf(fact_271_inthall,axiom,
% 5.05/5.24 ! [Xs2: list_set_nat,P: set_nat > $o,N2: nat] :
% 5.05/5.24 ( ! [X3: set_nat] :
% 5.05/5.24 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 5.05/5.24 => ( P @ X3 ) )
% 5.05/5.24 => ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.05/5.24 => ( P @ ( nth_set_nat @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % inthall
% 5.05/5.24 thf(fact_272_inthall,axiom,
% 5.05/5.24 ! [Xs2: list_nat,P: nat > $o,N2: nat] :
% 5.05/5.24 ( ! [X3: nat] :
% 5.05/5.24 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.05/5.24 => ( P @ X3 ) )
% 5.05/5.24 => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.24 => ( P @ ( nth_nat @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % inthall
% 5.05/5.24 thf(fact_273_inthall,axiom,
% 5.05/5.24 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N2: nat] :
% 5.05/5.24 ( ! [X3: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.05/5.24 => ( P @ X3 ) )
% 5.05/5.24 => ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.24 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % inthall
% 5.05/5.24 thf(fact_274_inthall,axiom,
% 5.05/5.24 ! [Xs2: list_o,P: $o > $o,N2: nat] :
% 5.05/5.24 ( ! [X3: $o] :
% 5.05/5.24 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.05/5.24 => ( P @ X3 ) )
% 5.05/5.24 => ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.24 => ( P @ ( nth_o @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % inthall
% 5.05/5.24 thf(fact_275_inthall,axiom,
% 5.05/5.24 ! [Xs2: list_int,P: int > $o,N2: nat] :
% 5.05/5.24 ( ! [X3: int] :
% 5.05/5.24 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.05/5.24 => ( P @ X3 ) )
% 5.05/5.24 => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.24 => ( P @ ( nth_int @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % inthall
% 5.05/5.24 thf(fact_276__C0_C,axiom,
% 5.05/5.24 ! [X5: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.05/5.24 => ( vEBT_invar_vebt @ X5 @ na ) ) ).
% 5.05/5.24
% 5.05/5.24 % "0"
% 5.05/5.24 thf(fact_277_mi__eq__ma__no__ch,axiom,
% 5.05/5.24 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.05/5.24 => ( ( Mi = Ma )
% 5.05/5.24 => ( ! [X5: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.05/5.24 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 5.05/5.24 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % mi_eq_ma_no_ch
% 5.05/5.24 thf(fact_278_geqmaxNone,axiom,
% 5.05/5.24 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N2 )
% 5.05/5.24 => ( ( ord_less_eq_nat @ Ma @ X )
% 5.05/5.24 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 = none_nat ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % geqmaxNone
% 5.05/5.24 thf(fact_279_helpyd,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.05/5.24 = ( some_nat @ Y ) )
% 5.05/5.24 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % helpyd
% 5.05/5.24 thf(fact_280_helpypredd,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat,Y: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.05/5.24 = ( some_nat @ Y ) )
% 5.05/5.24 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % helpypredd
% 5.05/5.24 thf(fact_281_set__n__deg__not__0,axiom,
% 5.05/5.24 ! [TreeList: list_VEBT_VEBT,N2: nat,M: nat] :
% 5.05/5.24 ( ! [X3: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.05/5.24 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.05/5.24 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.05/5.24 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.05/5.24 => ( ord_less_eq_nat @ one_one_nat @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % set_n_deg_not_0
% 5.05/5.24 thf(fact_282_numeral__eq__one__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ( numera6690914467698888265omplex @ N2 )
% 5.05/5.24 = one_one_complex )
% 5.05/5.24 = ( N2 = one ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_eq_one_iff
% 5.05/5.24 thf(fact_283_numeral__eq__one__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ( numeral_numeral_real @ N2 )
% 5.05/5.24 = one_one_real )
% 5.05/5.24 = ( N2 = one ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_eq_one_iff
% 5.05/5.24 thf(fact_284_numeral__eq__one__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ( numeral_numeral_rat @ N2 )
% 5.05/5.24 = one_one_rat )
% 5.05/5.24 = ( N2 = one ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_eq_one_iff
% 5.05/5.24 thf(fact_285_numeral__eq__one__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ( numeral_numeral_nat @ N2 )
% 5.05/5.24 = one_one_nat )
% 5.05/5.24 = ( N2 = one ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_eq_one_iff
% 5.05/5.24 thf(fact_286_numeral__eq__one__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ( numeral_numeral_int @ N2 )
% 5.05/5.24 = one_one_int )
% 5.05/5.24 = ( N2 = one ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_eq_one_iff
% 5.05/5.24 thf(fact_287_one__eq__numeral__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( one_one_complex
% 5.05/5.24 = ( numera6690914467698888265omplex @ N2 ) )
% 5.05/5.24 = ( one = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_eq_numeral_iff
% 5.05/5.24 thf(fact_288_one__eq__numeral__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( one_one_real
% 5.05/5.24 = ( numeral_numeral_real @ N2 ) )
% 5.05/5.24 = ( one = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_eq_numeral_iff
% 5.05/5.24 thf(fact_289_one__eq__numeral__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( one_one_rat
% 5.05/5.24 = ( numeral_numeral_rat @ N2 ) )
% 5.05/5.24 = ( one = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_eq_numeral_iff
% 5.05/5.24 thf(fact_290_one__eq__numeral__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( one_one_nat
% 5.05/5.24 = ( numeral_numeral_nat @ N2 ) )
% 5.05/5.24 = ( one = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_eq_numeral_iff
% 5.05/5.24 thf(fact_291_one__eq__numeral__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( one_one_int
% 5.05/5.24 = ( numeral_numeral_int @ N2 ) )
% 5.05/5.24 = ( one = N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_eq_numeral_iff
% 5.05/5.24 thf(fact_292_both__member__options__from__complete__tree__to__child,axiom,
% 5.05/5.24 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.05/5.24 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.05/5.24 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.24 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.24 | ( X = Mi )
% 5.05/5.24 | ( X = Ma ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % both_member_options_from_complete_tree_to_child
% 5.05/5.24 thf(fact_293_Suc__numeral,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % Suc_numeral
% 5.05/5.24 thf(fact_294_one__add__one,axiom,
% 5.05/5.24 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.05/5.24 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_add_one
% 5.05/5.24 thf(fact_295_one__add__one,axiom,
% 5.05/5.24 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.05/5.24 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_add_one
% 5.05/5.24 thf(fact_296_one__add__one,axiom,
% 5.05/5.24 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.05/5.24 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_add_one
% 5.05/5.24 thf(fact_297_one__add__one,axiom,
% 5.05/5.24 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.05/5.24 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_add_one
% 5.05/5.24 thf(fact_298_one__add__one,axiom,
% 5.05/5.24 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.05/5.24 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_add_one
% 5.05/5.24 thf(fact_299_add__2__eq__Suc,axiom,
% 5.05/5.24 ! [N2: nat] :
% 5.05/5.24 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.05/5.24 = ( suc @ ( suc @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % add_2_eq_Suc
% 5.05/5.24 thf(fact_300_add__2__eq__Suc_H,axiom,
% 5.05/5.24 ! [N2: nat] :
% 5.05/5.24 ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.24 = ( suc @ ( suc @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % add_2_eq_Suc'
% 5.05/5.24 thf(fact_301_div2__Suc__Suc,axiom,
% 5.05/5.24 ! [M: nat] :
% 5.05/5.24 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.24 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % div2_Suc_Suc
% 5.05/5.24 thf(fact_302_Suc__1,axiom,
% 5.05/5.24 ( ( suc @ one_one_nat )
% 5.05/5.24 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % Suc_1
% 5.05/5.24 thf(fact_303_numeral__plus__one,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ one_one_complex )
% 5.05/5.24 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_plus_one
% 5.05/5.24 thf(fact_304_numeral__plus__one,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 5.05/5.24 = ( numeral_numeral_real @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_plus_one
% 5.05/5.24 thf(fact_305_numeral__plus__one,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 5.05/5.24 = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_plus_one
% 5.05/5.24 thf(fact_306_numeral__plus__one,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 5.05/5.24 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_plus_one
% 5.05/5.24 thf(fact_307_numeral__plus__one,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 5.05/5.24 = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_plus_one
% 5.05/5.24 thf(fact_308_one__plus__numeral,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N2 ) )
% 5.05/5.24 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_plus_numeral
% 5.05/5.24 thf(fact_309_one__plus__numeral,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_plus_numeral
% 5.05/5.24 thf(fact_310_one__plus__numeral,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_plus_numeral
% 5.05/5.24 thf(fact_311_one__plus__numeral,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_plus_numeral
% 5.05/5.24 thf(fact_312_one__plus__numeral,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 5.05/5.24 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_plus_numeral
% 5.05/5.24 thf(fact_313_numeral__le__one__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 5.05/5.24 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_le_one_iff
% 5.05/5.24 thf(fact_314_numeral__le__one__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 5.05/5.24 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_le_one_iff
% 5.05/5.24 thf(fact_315_numeral__le__one__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 5.05/5.24 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_le_one_iff
% 5.05/5.24 thf(fact_316_numeral__le__one__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 5.05/5.24 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_le_one_iff
% 5.05/5.24 thf(fact_317_one__less__numeral__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 5.05/5.24 = ( ord_less_num @ one @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_less_numeral_iff
% 5.05/5.24 thf(fact_318_one__less__numeral__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.05/5.24 = ( ord_less_num @ one @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_less_numeral_iff
% 5.05/5.24 thf(fact_319_one__less__numeral__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.24 = ( ord_less_num @ one @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_less_numeral_iff
% 5.05/5.24 thf(fact_320_one__less__numeral__iff,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 5.05/5.24 = ( ord_less_num @ one @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_less_numeral_iff
% 5.05/5.24 thf(fact_321_succ__correct,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat,Sx: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.05/5.24 = ( some_nat @ Sx ) )
% 5.05/5.24 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % succ_correct
% 5.05/5.24 thf(fact_322_pred__correct,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat,Sx: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.05/5.24 = ( some_nat @ Sx ) )
% 5.05/5.24 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % pred_correct
% 5.05/5.24 thf(fact_323_local_Opower__def,axiom,
% 5.05/5.24 ( vEBT_VEBT_power
% 5.05/5.24 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.05/5.24
% 5.05/5.24 % local.power_def
% 5.05/5.24 thf(fact_324_le__num__One__iff,axiom,
% 5.05/5.24 ! [X: num] :
% 5.05/5.24 ( ( ord_less_eq_num @ X @ one )
% 5.05/5.24 = ( X = one ) ) ).
% 5.05/5.24
% 5.05/5.24 % le_num_One_iff
% 5.05/5.24 thf(fact_325_le__numeral__extra_I4_J,axiom,
% 5.05/5.24 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.05/5.24
% 5.05/5.24 % le_numeral_extra(4)
% 5.05/5.24 thf(fact_326_le__numeral__extra_I4_J,axiom,
% 5.05/5.24 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.05/5.24
% 5.05/5.24 % le_numeral_extra(4)
% 5.05/5.24 thf(fact_327_le__numeral__extra_I4_J,axiom,
% 5.05/5.24 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.05/5.24
% 5.05/5.24 % le_numeral_extra(4)
% 5.05/5.24 thf(fact_328_le__numeral__extra_I4_J,axiom,
% 5.05/5.24 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.05/5.24
% 5.05/5.24 % le_numeral_extra(4)
% 5.05/5.24 thf(fact_329_less__numeral__extra_I4_J,axiom,
% 5.05/5.24 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.05/5.24
% 5.05/5.24 % less_numeral_extra(4)
% 5.05/5.24 thf(fact_330_less__numeral__extra_I4_J,axiom,
% 5.05/5.24 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.05/5.24
% 5.05/5.24 % less_numeral_extra(4)
% 5.05/5.24 thf(fact_331_less__numeral__extra_I4_J,axiom,
% 5.05/5.24 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.05/5.24
% 5.05/5.24 % less_numeral_extra(4)
% 5.05/5.24 thf(fact_332_less__numeral__extra_I4_J,axiom,
% 5.05/5.24 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.05/5.24
% 5.05/5.24 % less_numeral_extra(4)
% 5.05/5.24 thf(fact_333_one__le__numeral,axiom,
% 5.05/5.24 ! [N2: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_le_numeral
% 5.05/5.24 thf(fact_334_one__le__numeral,axiom,
% 5.05/5.24 ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_le_numeral
% 5.05/5.24 thf(fact_335_one__le__numeral,axiom,
% 5.05/5.24 ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_le_numeral
% 5.05/5.24 thf(fact_336_one__le__numeral,axiom,
% 5.05/5.24 ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_le_numeral
% 5.05/5.24 thf(fact_337_not__numeral__less__one,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ one_one_real ) ).
% 5.05/5.24
% 5.05/5.24 % not_numeral_less_one
% 5.05/5.24 thf(fact_338_not__numeral__less__one,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 5.05/5.24
% 5.05/5.24 % not_numeral_less_one
% 5.05/5.24 thf(fact_339_not__numeral__less__one,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 5.05/5.24
% 5.05/5.24 % not_numeral_less_one
% 5.05/5.24 thf(fact_340_not__numeral__less__one,axiom,
% 5.05/5.24 ! [N2: num] :
% 5.05/5.24 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 5.05/5.24
% 5.05/5.24 % not_numeral_less_one
% 5.05/5.24 thf(fact_341_one__plus__numeral__commute,axiom,
% 5.05/5.24 ! [X: num] :
% 5.05/5.24 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 5.05/5.24 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_plus_numeral_commute
% 5.05/5.24 thf(fact_342_one__plus__numeral__commute,axiom,
% 5.05/5.24 ! [X: num] :
% 5.05/5.24 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.05/5.24 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_plus_numeral_commute
% 5.05/5.24 thf(fact_343_one__plus__numeral__commute,axiom,
% 5.05/5.24 ! [X: num] :
% 5.05/5.24 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.05/5.24 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_plus_numeral_commute
% 5.05/5.24 thf(fact_344_one__plus__numeral__commute,axiom,
% 5.05/5.24 ! [X: num] :
% 5.05/5.24 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.05/5.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_plus_numeral_commute
% 5.05/5.24 thf(fact_345_one__plus__numeral__commute,axiom,
% 5.05/5.24 ! [X: num] :
% 5.05/5.24 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.05/5.24 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.05/5.24
% 5.05/5.24 % one_plus_numeral_commute
% 5.05/5.24 thf(fact_346_numeral__One,axiom,
% 5.05/5.24 ( ( numera6690914467698888265omplex @ one )
% 5.05/5.24 = one_one_complex ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_One
% 5.05/5.24 thf(fact_347_numeral__One,axiom,
% 5.05/5.24 ( ( numeral_numeral_real @ one )
% 5.05/5.24 = one_one_real ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_One
% 5.05/5.24 thf(fact_348_numeral__One,axiom,
% 5.05/5.24 ( ( numeral_numeral_rat @ one )
% 5.05/5.24 = one_one_rat ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_One
% 5.05/5.24 thf(fact_349_numeral__One,axiom,
% 5.05/5.24 ( ( numeral_numeral_nat @ one )
% 5.05/5.24 = one_one_nat ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_One
% 5.05/5.24 thf(fact_350_numeral__One,axiom,
% 5.05/5.24 ( ( numeral_numeral_int @ one )
% 5.05/5.24 = one_one_int ) ).
% 5.05/5.24
% 5.05/5.24 % numeral_One
% 5.05/5.24 thf(fact_351_Suc__div__le__mono,axiom,
% 5.05/5.24 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % Suc_div_le_mono
% 5.05/5.24 thf(fact_352_numerals_I1_J,axiom,
% 5.05/5.24 ( ( numeral_numeral_nat @ one )
% 5.05/5.24 = one_one_nat ) ).
% 5.05/5.24
% 5.05/5.24 % numerals(1)
% 5.05/5.24 thf(fact_353_Suc__nat__number__of__add,axiom,
% 5.05/5.24 ! [V: num,N2: nat] :
% 5.05/5.24 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 5.05/5.24 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 5.05/5.24
% 5.05/5.24 % Suc_nat_number_of_add
% 5.05/5.24 thf(fact_354_div__nat__eqI,axiom,
% 5.05/5.24 ! [N2: nat,Q2: nat,M: nat] :
% 5.05/5.24 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q2 ) @ M )
% 5.05/5.24 => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q2 ) ) )
% 5.05/5.24 => ( ( divide_divide_nat @ M @ N2 )
% 5.05/5.24 = Q2 ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % div_nat_eqI
% 5.05/5.24 thf(fact_355_nat__1__add__1,axiom,
% 5.05/5.24 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.05/5.24 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % nat_1_add_1
% 5.05/5.24 thf(fact_356_maxt__corr,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( vEBT_vebt_maxt @ T )
% 5.05/5.24 = ( some_nat @ X ) )
% 5.05/5.24 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % maxt_corr
% 5.05/5.24 thf(fact_357_maxt__sound,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.05/5.24 => ( ( vEBT_vebt_maxt @ T )
% 5.05/5.24 = ( some_nat @ X ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % maxt_sound
% 5.05/5.24 thf(fact_358_mint__sound,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.05/5.24 => ( ( vEBT_vebt_mint @ T )
% 5.05/5.24 = ( some_nat @ X ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % mint_sound
% 5.05/5.24 thf(fact_359_mint__corr,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( ( vEBT_vebt_mint @ T )
% 5.05/5.24 = ( some_nat @ X ) )
% 5.05/5.24 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % mint_corr
% 5.05/5.24 thf(fact_360_vebt__delete_Osimps_I7_J,axiom,
% 5.05/5.24 ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.24 ( ( ( ( ord_less_nat @ X @ Mi )
% 5.05/5.24 | ( ord_less_nat @ Ma @ X ) )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) )
% 5.05/5.24 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 5.05/5.24 | ( ord_less_nat @ Ma @ X ) )
% 5.05/5.24 => ( ( ( ( X = Mi )
% 5.05/5.24 & ( X = Ma ) )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) )
% 5.05/5.24 & ( ~ ( ( X = Mi )
% 5.05/5.24 & ( X = Ma ) )
% 5.05/5.24 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( ( X = Mi )
% 5.05/5.24 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.05/5.24 = Ma ) )
% 5.05/5.24 & ( ( X != Mi )
% 5.05/5.24 => ( X = Ma ) ) )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 = none_nat )
% 5.05/5.24 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ ( suc @ ( suc @ Va ) )
% 5.05/5.24 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ ( vEBT_Node
% 5.05/5.24 @ ( some_P7363390416028606310at_nat
% 5.05/5.24 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.05/5.24 @ ( if_nat
% 5.05/5.24 @ ( ( ( X = Mi )
% 5.05/5.24 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.05/5.24 = Ma ) )
% 5.05/5.24 & ( ( X != Mi )
% 5.05/5.24 => ( X = Ma ) ) )
% 5.05/5.24 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.24 @ Ma ) ) )
% 5.05/5.24 @ ( suc @ ( suc @ Va ) )
% 5.05/5.24 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 @ Summary ) )
% 5.05/5.24 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % vebt_delete.simps(7)
% 5.05/5.24 thf(fact_361_invar__vebt_Ointros_I5_J,axiom,
% 5.05/5.24 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.05/5.24 ( ! [X3: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.05/5.24 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.05/5.24 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.05/5.24 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.05/5.24 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.05/5.24 => ( ( M
% 5.05/5.24 = ( suc @ N2 ) )
% 5.05/5.24 => ( ( Deg
% 5.05/5.24 = ( plus_plus_nat @ N2 @ M ) )
% 5.05/5.24 => ( ! [I3: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.05/5.24 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X4 ) )
% 5.05/5.24 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.05/5.24 => ( ( ( Mi = Ma )
% 5.05/5.24 => ! [X3: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.05/5.24 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.05/5.24 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.05/5.24 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.05/5.24 => ( ( ( Mi != Ma )
% 5.05/5.24 => ! [I3: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.05/5.24 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 5.05/5.24 = I3 )
% 5.05/5.24 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 5.05/5.24 & ! [X3: nat] :
% 5.05/5.24 ( ( ( ( vEBT_VEBT_high @ X3 @ N2 )
% 5.05/5.24 = I3 )
% 5.05/5.24 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) )
% 5.05/5.24 => ( ( ord_less_nat @ Mi @ X3 )
% 5.05/5.24 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.05/5.24 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % invar_vebt.intros(5)
% 5.05/5.24 thf(fact_362_invar__vebt_Ointros_I4_J,axiom,
% 5.05/5.24 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.05/5.24 ( ! [X3: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.05/5.24 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.05/5.24 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.05/5.24 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.05/5.24 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.05/5.24 => ( ( M = N2 )
% 5.05/5.24 => ( ( Deg
% 5.05/5.24 = ( plus_plus_nat @ N2 @ M ) )
% 5.05/5.24 => ( ! [I3: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.05/5.24 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X4 ) )
% 5.05/5.24 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.05/5.24 => ( ( ( Mi = Ma )
% 5.05/5.24 => ! [X3: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.05/5.24 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.05/5.24 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.05/5.24 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.05/5.24 => ( ( ( Mi != Ma )
% 5.05/5.24 => ! [I3: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.05/5.24 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 5.05/5.24 = I3 )
% 5.05/5.24 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 5.05/5.24 & ! [X3: nat] :
% 5.05/5.24 ( ( ( ( vEBT_VEBT_high @ X3 @ N2 )
% 5.05/5.24 = I3 )
% 5.05/5.24 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) )
% 5.05/5.24 => ( ( ord_less_nat @ Mi @ X3 )
% 5.05/5.24 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 5.05/5.24 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % invar_vebt.intros(4)
% 5.05/5.24 thf(fact_363_set__vebt__set__vebt_H__valid,axiom,
% 5.05/5.24 ! [T: vEBT_VEBT,N2: nat] :
% 5.05/5.24 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.24 => ( ( vEBT_set_vebt @ T )
% 5.05/5.24 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % set_vebt_set_vebt'_valid
% 5.05/5.24 thf(fact_364_vebt__member_Osimps_I5_J,axiom,
% 5.05/5.24 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.05/5.24 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.05/5.24 = ( ( X != Mi )
% 5.05/5.24 => ( ( X != Ma )
% 5.05/5.24 => ( ~ ( ord_less_nat @ X @ Mi )
% 5.05/5.24 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.05/5.24 => ( ~ ( ord_less_nat @ Ma @ X )
% 5.05/5.24 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.05/5.24 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.24 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.24 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % vebt_member.simps(5)
% 5.05/5.24 thf(fact_365_set__swap,axiom,
% 5.05/5.24 ! [I2: nat,Xs2: list_nat,J: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.24 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.24 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I2 ) ) )
% 5.05/5.24 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % set_swap
% 5.05/5.24 thf(fact_366_set__swap,axiom,
% 5.05/5.24 ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.24 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.24 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 5.05/5.24 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % set_swap
% 5.05/5.24 thf(fact_367_set__swap,axiom,
% 5.05/5.24 ! [I2: nat,Xs2: list_o,J: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.24 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.24 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I2 ) ) )
% 5.05/5.24 = ( set_o2 @ Xs2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % set_swap
% 5.05/5.24 thf(fact_368_set__swap,axiom,
% 5.05/5.24 ! [I2: nat,Xs2: list_int,J: nat] :
% 5.05/5.24 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.24 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.24 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I2 ) ) )
% 5.05/5.24 = ( set_int2 @ Xs2 ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % set_swap
% 5.05/5.24 thf(fact_369_invar__vebt_Ointros_I3_J,axiom,
% 5.05/5.24 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.05/5.24 ( ! [X3: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.05/5.24 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.05/5.24 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.05/5.24 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.05/5.24 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.05/5.24 => ( ( M
% 5.05/5.24 = ( suc @ N2 ) )
% 5.05/5.24 => ( ( Deg
% 5.05/5.24 = ( plus_plus_nat @ N2 @ M ) )
% 5.05/5.24 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.05/5.24 => ( ! [X3: vEBT_VEBT] :
% 5.05/5.24 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.05/5.24 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.05/5.24 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.05/5.24
% 5.05/5.24 % invar_vebt.intros(3)
% 5.05/5.24 thf(fact_370_power__increasing__iff,axiom,
% 5.05/5.24 ! [B: real,X: nat,Y: nat] :
% 5.05/5.24 ( ( ord_less_real @ one_one_real @ B )
% 5.05/5.24 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.05/5.25 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_increasing_iff
% 5.05/5.25 thf(fact_371_power__increasing__iff,axiom,
% 5.05/5.25 ! [B: rat,X: nat,Y: nat] :
% 5.05/5.25 ( ( ord_less_rat @ one_one_rat @ B )
% 5.05/5.25 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.05/5.25 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_increasing_iff
% 5.05/5.25 thf(fact_372_power__increasing__iff,axiom,
% 5.05/5.25 ! [B: nat,X: nat,Y: nat] :
% 5.05/5.25 ( ( ord_less_nat @ one_one_nat @ B )
% 5.05/5.25 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.05/5.25 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_increasing_iff
% 5.05/5.25 thf(fact_373_power__increasing__iff,axiom,
% 5.05/5.25 ! [B: int,X: nat,Y: nat] :
% 5.05/5.25 ( ( ord_less_int @ one_one_int @ B )
% 5.05/5.25 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.05/5.25 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_increasing_iff
% 5.05/5.25 thf(fact_374_set__vebt_H__def,axiom,
% 5.05/5.25 ( vEBT_VEBT_set_vebt
% 5.05/5.25 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_vebt'_def
% 5.05/5.25 thf(fact_375_VEBT_Oinject_I1_J,axiom,
% 5.05/5.25 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.05/5.25 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.05/5.25 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.05/5.25 = ( ( X11 = Y11 )
% 5.05/5.25 & ( X12 = Y12 )
% 5.05/5.25 & ( X13 = Y13 )
% 5.05/5.25 & ( X14 = Y14 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % VEBT.inject(1)
% 5.05/5.25 thf(fact_376_list__update__overwrite,axiom,
% 5.05/5.25 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.05/5.25 ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 @ Y )
% 5.05/5.25 = ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ Y ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_overwrite
% 5.05/5.25 thf(fact_377_pred__member,axiom,
% 5.05/5.25 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 5.05/5.25 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 5.05/5.25 = ( ( vEBT_vebt_member @ T @ Y )
% 5.05/5.25 & ( ord_less_nat @ Y @ X )
% 5.05/5.25 & ! [Z2: nat] :
% 5.05/5.25 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 5.05/5.25 & ( ord_less_nat @ Z2 @ X ) )
% 5.05/5.25 => ( ord_less_eq_nat @ Z2 @ Y ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % pred_member
% 5.05/5.25 thf(fact_378_succ__member,axiom,
% 5.05/5.25 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 5.05/5.25 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 5.05/5.25 = ( ( vEBT_vebt_member @ T @ Y )
% 5.05/5.25 & ( ord_less_nat @ X @ Y )
% 5.05/5.25 & ! [Z2: nat] :
% 5.05/5.25 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 5.05/5.25 & ( ord_less_nat @ X @ Z2 ) )
% 5.05/5.25 => ( ord_less_eq_nat @ Y @ Z2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % succ_member
% 5.05/5.25 thf(fact_379_pred__corr,axiom,
% 5.05/5.25 ! [T: vEBT_VEBT,N2: nat,X: nat,Px: nat] :
% 5.05/5.25 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.25 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.05/5.25 = ( some_nat @ Px ) )
% 5.05/5.25 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % pred_corr
% 5.05/5.25 thf(fact_380_succ__corr,axiom,
% 5.05/5.25 ! [T: vEBT_VEBT,N2: nat,X: nat,Sx: nat] :
% 5.05/5.25 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.25 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.05/5.25 = ( some_nat @ Sx ) )
% 5.05/5.25 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % succ_corr
% 5.05/5.25 thf(fact_381_power__one,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ( ( power_power_rat @ one_one_rat @ N2 )
% 5.05/5.25 = one_one_rat ) ).
% 5.05/5.25
% 5.05/5.25 % power_one
% 5.05/5.25 thf(fact_382_power__one,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ( ( power_power_nat @ one_one_nat @ N2 )
% 5.05/5.25 = one_one_nat ) ).
% 5.05/5.25
% 5.05/5.25 % power_one
% 5.05/5.25 thf(fact_383_power__one,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ( ( power_power_real @ one_one_real @ N2 )
% 5.05/5.25 = one_one_real ) ).
% 5.05/5.25
% 5.05/5.25 % power_one
% 5.05/5.25 thf(fact_384_power__one,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ( ( power_power_int @ one_one_int @ N2 )
% 5.05/5.25 = one_one_int ) ).
% 5.05/5.25
% 5.05/5.25 % power_one
% 5.05/5.25 thf(fact_385_power__one,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ( ( power_power_complex @ one_one_complex @ N2 )
% 5.05/5.25 = one_one_complex ) ).
% 5.05/5.25
% 5.05/5.25 % power_one
% 5.05/5.25 thf(fact_386_power__one__right,axiom,
% 5.05/5.25 ! [A: nat] :
% 5.05/5.25 ( ( power_power_nat @ A @ one_one_nat )
% 5.05/5.25 = A ) ).
% 5.05/5.25
% 5.05/5.25 % power_one_right
% 5.05/5.25 thf(fact_387_power__one__right,axiom,
% 5.05/5.25 ! [A: real] :
% 5.05/5.25 ( ( power_power_real @ A @ one_one_nat )
% 5.05/5.25 = A ) ).
% 5.05/5.25
% 5.05/5.25 % power_one_right
% 5.05/5.25 thf(fact_388_power__one__right,axiom,
% 5.05/5.25 ! [A: int] :
% 5.05/5.25 ( ( power_power_int @ A @ one_one_nat )
% 5.05/5.25 = A ) ).
% 5.05/5.25
% 5.05/5.25 % power_one_right
% 5.05/5.25 thf(fact_389_power__one__right,axiom,
% 5.05/5.25 ! [A: complex] :
% 5.05/5.25 ( ( power_power_complex @ A @ one_one_nat )
% 5.05/5.25 = A ) ).
% 5.05/5.25
% 5.05/5.25 % power_one_right
% 5.05/5.25 thf(fact_390_length__list__update,axiom,
% 5.05/5.25 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 5.05/5.25 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) )
% 5.05/5.25 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % length_list_update
% 5.05/5.25 thf(fact_391_length__list__update,axiom,
% 5.05/5.25 ! [Xs2: list_o,I2: nat,X: $o] :
% 5.05/5.25 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I2 @ X ) )
% 5.05/5.25 = ( size_size_list_o @ Xs2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % length_list_update
% 5.05/5.25 thf(fact_392_length__list__update,axiom,
% 5.05/5.25 ! [Xs2: list_int,I2: nat,X: int] :
% 5.05/5.25 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I2 @ X ) )
% 5.05/5.25 = ( size_size_list_int @ Xs2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % length_list_update
% 5.05/5.25 thf(fact_393_nth__list__update__neq,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,Xs2: list_nat,X: nat] :
% 5.05/5.25 ( ( I2 != J )
% 5.05/5.25 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.05/5.25 = ( nth_nat @ Xs2 @ J ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update_neq
% 5.05/5.25 thf(fact_394_nth__list__update__neq,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,Xs2: list_int,X: int] :
% 5.05/5.25 ( ( I2 != J )
% 5.05/5.25 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.05/5.25 = ( nth_int @ Xs2 @ J ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update_neq
% 5.05/5.25 thf(fact_395_nth__list__update__neq,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.05/5.25 ( ( I2 != J )
% 5.05/5.25 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.05/5.25 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update_neq
% 5.05/5.25 thf(fact_396_list__update__id,axiom,
% 5.05/5.25 ! [Xs2: list_nat,I2: nat] :
% 5.05/5.25 ( ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ I2 ) )
% 5.05/5.25 = Xs2 ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_id
% 5.05/5.25 thf(fact_397_list__update__id,axiom,
% 5.05/5.25 ! [Xs2: list_int,I2: nat] :
% 5.05/5.25 ( ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ I2 ) )
% 5.05/5.25 = Xs2 ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_id
% 5.05/5.25 thf(fact_398_list__update__id,axiom,
% 5.05/5.25 ! [Xs2: list_VEBT_VEBT,I2: nat] :
% 5.05/5.25 ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) )
% 5.05/5.25 = Xs2 ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_id
% 5.05/5.25 thf(fact_399_power__inject__exp,axiom,
% 5.05/5.25 ! [A: real,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_real @ one_one_real @ A )
% 5.05/5.25 => ( ( ( power_power_real @ A @ M )
% 5.05/5.25 = ( power_power_real @ A @ N2 ) )
% 5.05/5.25 = ( M = N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_inject_exp
% 5.05/5.25 thf(fact_400_power__inject__exp,axiom,
% 5.05/5.25 ! [A: rat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_rat @ one_one_rat @ A )
% 5.05/5.25 => ( ( ( power_power_rat @ A @ M )
% 5.05/5.25 = ( power_power_rat @ A @ N2 ) )
% 5.05/5.25 = ( M = N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_inject_exp
% 5.05/5.25 thf(fact_401_power__inject__exp,axiom,
% 5.05/5.25 ! [A: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ one_one_nat @ A )
% 5.05/5.25 => ( ( ( power_power_nat @ A @ M )
% 5.05/5.25 = ( power_power_nat @ A @ N2 ) )
% 5.05/5.25 = ( M = N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_inject_exp
% 5.05/5.25 thf(fact_402_power__inject__exp,axiom,
% 5.05/5.25 ! [A: int,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_int @ one_one_int @ A )
% 5.05/5.25 => ( ( ( power_power_int @ A @ M )
% 5.05/5.25 = ( power_power_int @ A @ N2 ) )
% 5.05/5.25 = ( M = N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_inject_exp
% 5.05/5.25 thf(fact_403_list__update__beyond,axiom,
% 5.05/5.25 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I2 )
% 5.05/5.25 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 5.05/5.25 = Xs2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_beyond
% 5.05/5.25 thf(fact_404_list__update__beyond,axiom,
% 5.05/5.25 ! [Xs2: list_o,I2: nat,X: $o] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I2 )
% 5.05/5.25 => ( ( list_update_o @ Xs2 @ I2 @ X )
% 5.05/5.25 = Xs2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_beyond
% 5.05/5.25 thf(fact_405_list__update__beyond,axiom,
% 5.05/5.25 ! [Xs2: list_int,I2: nat,X: int] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I2 )
% 5.05/5.25 => ( ( list_update_int @ Xs2 @ I2 @ X )
% 5.05/5.25 = Xs2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_beyond
% 5.05/5.25 thf(fact_406_power__mult__numeral,axiom,
% 5.05/5.25 ! [A: nat,M: num,N2: num] :
% 5.05/5.25 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.25 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult_numeral
% 5.05/5.25 thf(fact_407_power__mult__numeral,axiom,
% 5.05/5.25 ! [A: real,M: num,N2: num] :
% 5.05/5.25 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.25 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult_numeral
% 5.05/5.25 thf(fact_408_power__mult__numeral,axiom,
% 5.05/5.25 ! [A: int,M: num,N2: num] :
% 5.05/5.25 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.25 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult_numeral
% 5.05/5.25 thf(fact_409_power__mult__numeral,axiom,
% 5.05/5.25 ! [A: complex,M: num,N2: num] :
% 5.05/5.25 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.05/5.25 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult_numeral
% 5.05/5.25 thf(fact_410_power__strict__increasing__iff,axiom,
% 5.05/5.25 ! [B: real,X: nat,Y: nat] :
% 5.05/5.25 ( ( ord_less_real @ one_one_real @ B )
% 5.05/5.25 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.05/5.25 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_strict_increasing_iff
% 5.05/5.25 thf(fact_411_power__strict__increasing__iff,axiom,
% 5.05/5.25 ! [B: rat,X: nat,Y: nat] :
% 5.05/5.25 ( ( ord_less_rat @ one_one_rat @ B )
% 5.05/5.25 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.05/5.25 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_strict_increasing_iff
% 5.05/5.25 thf(fact_412_power__strict__increasing__iff,axiom,
% 5.05/5.25 ! [B: nat,X: nat,Y: nat] :
% 5.05/5.25 ( ( ord_less_nat @ one_one_nat @ B )
% 5.05/5.25 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.05/5.25 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_strict_increasing_iff
% 5.05/5.25 thf(fact_413_power__strict__increasing__iff,axiom,
% 5.05/5.25 ! [B: int,X: nat,Y: nat] :
% 5.05/5.25 ( ( ord_less_int @ one_one_int @ B )
% 5.05/5.25 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.05/5.25 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_strict_increasing_iff
% 5.05/5.25 thf(fact_414_power__add__numeral2,axiom,
% 5.05/5.25 ! [A: complex,M: num,N2: num,B: complex] :
% 5.05/5.25 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.05/5.25 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add_numeral2
% 5.05/5.25 thf(fact_415_power__add__numeral2,axiom,
% 5.05/5.25 ! [A: real,M: num,N2: num,B: real] :
% 5.05/5.25 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.05/5.25 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add_numeral2
% 5.05/5.25 thf(fact_416_power__add__numeral2,axiom,
% 5.05/5.25 ! [A: rat,M: num,N2: num,B: rat] :
% 5.05/5.25 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.05/5.25 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add_numeral2
% 5.05/5.25 thf(fact_417_power__add__numeral2,axiom,
% 5.05/5.25 ! [A: nat,M: num,N2: num,B: nat] :
% 5.05/5.25 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.05/5.25 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add_numeral2
% 5.05/5.25 thf(fact_418_power__add__numeral2,axiom,
% 5.05/5.25 ! [A: int,M: num,N2: num,B: int] :
% 5.05/5.25 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.05/5.25 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add_numeral2
% 5.05/5.25 thf(fact_419_power__add__numeral,axiom,
% 5.05/5.25 ! [A: complex,M: num,N2: num] :
% 5.05/5.25 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.05/5.25 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add_numeral
% 5.05/5.25 thf(fact_420_power__add__numeral,axiom,
% 5.05/5.25 ! [A: real,M: num,N2: num] :
% 5.05/5.25 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.05/5.25 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add_numeral
% 5.05/5.25 thf(fact_421_power__add__numeral,axiom,
% 5.05/5.25 ! [A: rat,M: num,N2: num] :
% 5.05/5.25 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.05/5.25 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add_numeral
% 5.05/5.25 thf(fact_422_power__add__numeral,axiom,
% 5.05/5.25 ! [A: nat,M: num,N2: num] :
% 5.05/5.25 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.05/5.25 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add_numeral
% 5.05/5.25 thf(fact_423_power__add__numeral,axiom,
% 5.05/5.25 ! [A: int,M: num,N2: num] :
% 5.05/5.25 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.05/5.25 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add_numeral
% 5.05/5.25 thf(fact_424_nth__list__update__eq,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_nat,X: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.25 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ I2 )
% 5.05/5.25 = X ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update_eq
% 5.05/5.25 thf(fact_425_nth__list__update__eq,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.25 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 )
% 5.05/5.25 = X ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update_eq
% 5.05/5.25 thf(fact_426_nth__list__update__eq,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_o,X: $o] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.25 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ I2 )
% 5.05/5.25 = X ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update_eq
% 5.05/5.25 thf(fact_427_nth__list__update__eq,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_int,X: int] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.25 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ I2 )
% 5.05/5.25 = X ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update_eq
% 5.05/5.25 thf(fact_428_subset__code_I1_J,axiom,
% 5.05/5.25 ! [Xs2: list_complex,B3: set_complex] :
% 5.05/5.25 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ B3 )
% 5.05/5.25 = ( ! [X2: complex] :
% 5.05/5.25 ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.05/5.25 => ( member_complex @ X2 @ B3 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % subset_code(1)
% 5.05/5.25 thf(fact_429_subset__code_I1_J,axiom,
% 5.05/5.25 ! [Xs2: list_real,B3: set_real] :
% 5.05/5.25 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ B3 )
% 5.05/5.25 = ( ! [X2: real] :
% 5.05/5.25 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.05/5.25 => ( member_real @ X2 @ B3 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % subset_code(1)
% 5.05/5.25 thf(fact_430_subset__code_I1_J,axiom,
% 5.05/5.25 ! [Xs2: list_set_nat,B3: set_set_nat] :
% 5.05/5.25 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs2 ) @ B3 )
% 5.05/5.25 = ( ! [X2: set_nat] :
% 5.05/5.25 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs2 ) )
% 5.05/5.25 => ( member_set_nat @ X2 @ B3 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % subset_code(1)
% 5.05/5.25 thf(fact_431_subset__code_I1_J,axiom,
% 5.05/5.25 ! [Xs2: list_nat,B3: set_nat] :
% 5.05/5.25 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ B3 )
% 5.05/5.25 = ( ! [X2: nat] :
% 5.05/5.25 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.05/5.25 => ( member_nat @ X2 @ B3 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % subset_code(1)
% 5.05/5.25 thf(fact_432_subset__code_I1_J,axiom,
% 5.05/5.25 ! [Xs2: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.05/5.25 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ B3 )
% 5.05/5.25 = ( ! [X2: vEBT_VEBT] :
% 5.05/5.25 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.05/5.25 => ( member_VEBT_VEBT @ X2 @ B3 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % subset_code(1)
% 5.05/5.25 thf(fact_433_subset__code_I1_J,axiom,
% 5.05/5.25 ! [Xs2: list_int,B3: set_int] :
% 5.05/5.25 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ B3 )
% 5.05/5.25 = ( ! [X2: int] :
% 5.05/5.25 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.05/5.25 => ( member_int @ X2 @ B3 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % subset_code(1)
% 5.05/5.25 thf(fact_434_Ex__list__of__length,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ? [Xs3: list_VEBT_VEBT] :
% 5.05/5.25 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.05/5.25 = N2 ) ).
% 5.05/5.25
% 5.05/5.25 % Ex_list_of_length
% 5.05/5.25 thf(fact_435_Ex__list__of__length,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ? [Xs3: list_o] :
% 5.05/5.25 ( ( size_size_list_o @ Xs3 )
% 5.05/5.25 = N2 ) ).
% 5.05/5.25
% 5.05/5.25 % Ex_list_of_length
% 5.05/5.25 thf(fact_436_Ex__list__of__length,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ? [Xs3: list_int] :
% 5.05/5.25 ( ( size_size_list_int @ Xs3 )
% 5.05/5.25 = N2 ) ).
% 5.05/5.25
% 5.05/5.25 % Ex_list_of_length
% 5.05/5.25 thf(fact_437_neq__if__length__neq,axiom,
% 5.05/5.25 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.05/5.25 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.05/5.25 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.05/5.25 => ( Xs2 != Ys ) ) ).
% 5.05/5.25
% 5.05/5.25 % neq_if_length_neq
% 5.05/5.25 thf(fact_438_neq__if__length__neq,axiom,
% 5.05/5.25 ! [Xs2: list_o,Ys: list_o] :
% 5.05/5.25 ( ( ( size_size_list_o @ Xs2 )
% 5.05/5.25 != ( size_size_list_o @ Ys ) )
% 5.05/5.25 => ( Xs2 != Ys ) ) ).
% 5.05/5.25
% 5.05/5.25 % neq_if_length_neq
% 5.05/5.25 thf(fact_439_neq__if__length__neq,axiom,
% 5.05/5.25 ! [Xs2: list_int,Ys: list_int] :
% 5.05/5.25 ( ( ( size_size_list_int @ Xs2 )
% 5.05/5.25 != ( size_size_list_int @ Ys ) )
% 5.05/5.25 => ( Xs2 != Ys ) ) ).
% 5.05/5.25
% 5.05/5.25 % neq_if_length_neq
% 5.05/5.25 thf(fact_440_list__update__swap,axiom,
% 5.05/5.25 ! [I2: nat,I4: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT,X7: vEBT_VEBT] :
% 5.05/5.25 ( ( I2 != I4 )
% 5.05/5.25 => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I4 @ X7 )
% 5.05/5.25 = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I4 @ X7 ) @ I2 @ X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_swap
% 5.05/5.25 thf(fact_441_power__commuting__commutes,axiom,
% 5.05/5.25 ! [X: complex,Y: complex,N2: nat] :
% 5.05/5.25 ( ( ( times_times_complex @ X @ Y )
% 5.05/5.25 = ( times_times_complex @ Y @ X ) )
% 5.05/5.25 => ( ( times_times_complex @ ( power_power_complex @ X @ N2 ) @ Y )
% 5.05/5.25 = ( times_times_complex @ Y @ ( power_power_complex @ X @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_commuting_commutes
% 5.05/5.25 thf(fact_442_power__commuting__commutes,axiom,
% 5.05/5.25 ! [X: real,Y: real,N2: nat] :
% 5.05/5.25 ( ( ( times_times_real @ X @ Y )
% 5.05/5.25 = ( times_times_real @ Y @ X ) )
% 5.05/5.25 => ( ( times_times_real @ ( power_power_real @ X @ N2 ) @ Y )
% 5.05/5.25 = ( times_times_real @ Y @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_commuting_commutes
% 5.05/5.25 thf(fact_443_power__commuting__commutes,axiom,
% 5.05/5.25 ! [X: rat,Y: rat,N2: nat] :
% 5.05/5.25 ( ( ( times_times_rat @ X @ Y )
% 5.05/5.25 = ( times_times_rat @ Y @ X ) )
% 5.05/5.25 => ( ( times_times_rat @ ( power_power_rat @ X @ N2 ) @ Y )
% 5.05/5.25 = ( times_times_rat @ Y @ ( power_power_rat @ X @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_commuting_commutes
% 5.05/5.25 thf(fact_444_power__commuting__commutes,axiom,
% 5.05/5.25 ! [X: nat,Y: nat,N2: nat] :
% 5.05/5.25 ( ( ( times_times_nat @ X @ Y )
% 5.05/5.25 = ( times_times_nat @ Y @ X ) )
% 5.05/5.25 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ Y )
% 5.05/5.25 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_commuting_commutes
% 5.05/5.25 thf(fact_445_power__commuting__commutes,axiom,
% 5.05/5.25 ! [X: int,Y: int,N2: nat] :
% 5.05/5.25 ( ( ( times_times_int @ X @ Y )
% 5.05/5.25 = ( times_times_int @ Y @ X ) )
% 5.05/5.25 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ Y )
% 5.05/5.25 = ( times_times_int @ Y @ ( power_power_int @ X @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_commuting_commutes
% 5.05/5.25 thf(fact_446_power__mult__distrib,axiom,
% 5.05/5.25 ! [A: complex,B: complex,N2: nat] :
% 5.05/5.25 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N2 )
% 5.05/5.25 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult_distrib
% 5.05/5.25 thf(fact_447_power__mult__distrib,axiom,
% 5.05/5.25 ! [A: real,B: real,N2: nat] :
% 5.05/5.25 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N2 )
% 5.05/5.25 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult_distrib
% 5.05/5.25 thf(fact_448_power__mult__distrib,axiom,
% 5.05/5.25 ! [A: rat,B: rat,N2: nat] :
% 5.05/5.25 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N2 )
% 5.05/5.25 = ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult_distrib
% 5.05/5.25 thf(fact_449_power__mult__distrib,axiom,
% 5.05/5.25 ! [A: nat,B: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
% 5.05/5.25 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult_distrib
% 5.05/5.25 thf(fact_450_power__mult__distrib,axiom,
% 5.05/5.25 ! [A: int,B: int,N2: nat] :
% 5.05/5.25 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N2 )
% 5.05/5.25 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult_distrib
% 5.05/5.25 thf(fact_451_power__commutes,axiom,
% 5.05/5.25 ! [A: complex,N2: nat] :
% 5.05/5.25 ( ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A )
% 5.05/5.25 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_commutes
% 5.05/5.25 thf(fact_452_power__commutes,axiom,
% 5.05/5.25 ! [A: real,N2: nat] :
% 5.05/5.25 ( ( times_times_real @ ( power_power_real @ A @ N2 ) @ A )
% 5.05/5.25 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_commutes
% 5.05/5.25 thf(fact_453_power__commutes,axiom,
% 5.05/5.25 ! [A: rat,N2: nat] :
% 5.05/5.25 ( ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ A )
% 5.05/5.25 = ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_commutes
% 5.05/5.25 thf(fact_454_power__commutes,axiom,
% 5.05/5.25 ! [A: nat,N2: nat] :
% 5.05/5.25 ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
% 5.05/5.25 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_commutes
% 5.05/5.25 thf(fact_455_power__commutes,axiom,
% 5.05/5.25 ! [A: int,N2: nat] :
% 5.05/5.25 ( ( times_times_int @ ( power_power_int @ A @ N2 ) @ A )
% 5.05/5.25 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_commutes
% 5.05/5.25 thf(fact_456_power__divide,axiom,
% 5.05/5.25 ! [A: complex,B: complex,N2: nat] :
% 5.05/5.25 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N2 )
% 5.05/5.25 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_divide
% 5.05/5.25 thf(fact_457_power__divide,axiom,
% 5.05/5.25 ! [A: real,B: real,N2: nat] :
% 5.05/5.25 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N2 )
% 5.05/5.25 = ( divide_divide_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_divide
% 5.05/5.25 thf(fact_458_power__divide,axiom,
% 5.05/5.25 ! [A: rat,B: rat,N2: nat] :
% 5.05/5.25 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N2 )
% 5.05/5.25 = ( divide_divide_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_divide
% 5.05/5.25 thf(fact_459_length__induct,axiom,
% 5.05/5.25 ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.05/5.25 ( ! [Xs3: list_VEBT_VEBT] :
% 5.05/5.25 ( ! [Ys2: list_VEBT_VEBT] :
% 5.05/5.25 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.05/5.25 => ( P @ Ys2 ) )
% 5.05/5.25 => ( P @ Xs3 ) )
% 5.05/5.25 => ( P @ Xs2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % length_induct
% 5.05/5.25 thf(fact_460_length__induct,axiom,
% 5.05/5.25 ! [P: list_o > $o,Xs2: list_o] :
% 5.05/5.25 ( ! [Xs3: list_o] :
% 5.05/5.25 ( ! [Ys2: list_o] :
% 5.05/5.25 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.05/5.25 => ( P @ Ys2 ) )
% 5.05/5.25 => ( P @ Xs3 ) )
% 5.05/5.25 => ( P @ Xs2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % length_induct
% 5.05/5.25 thf(fact_461_length__induct,axiom,
% 5.05/5.25 ! [P: list_int > $o,Xs2: list_int] :
% 5.05/5.25 ( ! [Xs3: list_int] :
% 5.05/5.25 ( ! [Ys2: list_int] :
% 5.05/5.25 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 5.05/5.25 => ( P @ Ys2 ) )
% 5.05/5.25 => ( P @ Xs3 ) )
% 5.05/5.25 => ( P @ Xs2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % length_induct
% 5.05/5.25 thf(fact_462_power__mult,axiom,
% 5.05/5.25 ! [A: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N2 ) )
% 5.05/5.25 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult
% 5.05/5.25 thf(fact_463_power__mult,axiom,
% 5.05/5.25 ! [A: real,M: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_real @ A @ ( times_times_nat @ M @ N2 ) )
% 5.05/5.25 = ( power_power_real @ ( power_power_real @ A @ M ) @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult
% 5.05/5.25 thf(fact_464_power__mult,axiom,
% 5.05/5.25 ! [A: int,M: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_int @ A @ ( times_times_nat @ M @ N2 ) )
% 5.05/5.25 = ( power_power_int @ ( power_power_int @ A @ M ) @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult
% 5.05/5.25 thf(fact_465_power__mult,axiom,
% 5.05/5.25 ! [A: complex,M: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N2 ) )
% 5.05/5.25 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_mult
% 5.05/5.25 thf(fact_466_set__update__subsetI,axiom,
% 5.05/5.25 ! [Xs2: list_complex,A2: set_complex,X: complex,I2: nat] :
% 5.05/5.25 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 5.05/5.25 => ( ( member_complex @ X @ A2 )
% 5.05/5.25 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_subsetI
% 5.05/5.25 thf(fact_467_set__update__subsetI,axiom,
% 5.05/5.25 ! [Xs2: list_real,A2: set_real,X: real,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A2 )
% 5.05/5.25 => ( ( member_real @ X @ A2 )
% 5.05/5.25 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_subsetI
% 5.05/5.25 thf(fact_468_set__update__subsetI,axiom,
% 5.05/5.25 ! [Xs2: list_set_nat,A2: set_set_nat,X: set_nat,I2: nat] :
% 5.05/5.25 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs2 ) @ A2 )
% 5.05/5.25 => ( ( member_set_nat @ X @ A2 )
% 5.05/5.25 => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_subsetI
% 5.05/5.25 thf(fact_469_set__update__subsetI,axiom,
% 5.05/5.25 ! [Xs2: list_nat,A2: set_nat,X: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 5.05/5.25 => ( ( member_nat @ X @ A2 )
% 5.05/5.25 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_subsetI
% 5.05/5.25 thf(fact_470_set__update__subsetI,axiom,
% 5.05/5.25 ! [Xs2: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I2: nat] :
% 5.05/5.25 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 5.05/5.25 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.05/5.25 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_subsetI
% 5.05/5.25 thf(fact_471_set__update__subsetI,axiom,
% 5.05/5.25 ! [Xs2: list_int,A2: set_int,X: int,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 5.05/5.25 => ( ( member_int @ X @ A2 )
% 5.05/5.25 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I2 @ X ) ) @ A2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_subsetI
% 5.05/5.25 thf(fact_472_one__le__power,axiom,
% 5.05/5.25 ! [A: real,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.05/5.25 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % one_le_power
% 5.05/5.25 thf(fact_473_one__le__power,axiom,
% 5.05/5.25 ! [A: rat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.05/5.25 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % one_le_power
% 5.05/5.25 thf(fact_474_one__le__power,axiom,
% 5.05/5.25 ! [A: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.05/5.25 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % one_le_power
% 5.05/5.25 thf(fact_475_one__le__power,axiom,
% 5.05/5.25 ! [A: int,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.05/5.25 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % one_le_power
% 5.05/5.25 thf(fact_476_left__right__inverse__power,axiom,
% 5.05/5.25 ! [X: complex,Y: complex,N2: nat] :
% 5.05/5.25 ( ( ( times_times_complex @ X @ Y )
% 5.05/5.25 = one_one_complex )
% 5.05/5.25 => ( ( times_times_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 5.05/5.25 = one_one_complex ) ) ).
% 5.05/5.25
% 5.05/5.25 % left_right_inverse_power
% 5.05/5.25 thf(fact_477_left__right__inverse__power,axiom,
% 5.05/5.25 ! [X: real,Y: real,N2: nat] :
% 5.05/5.25 ( ( ( times_times_real @ X @ Y )
% 5.05/5.25 = one_one_real )
% 5.05/5.25 => ( ( times_times_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 5.05/5.25 = one_one_real ) ) ).
% 5.05/5.25
% 5.05/5.25 % left_right_inverse_power
% 5.05/5.25 thf(fact_478_left__right__inverse__power,axiom,
% 5.05/5.25 ! [X: rat,Y: rat,N2: nat] :
% 5.05/5.25 ( ( ( times_times_rat @ X @ Y )
% 5.05/5.25 = one_one_rat )
% 5.05/5.25 => ( ( times_times_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 5.05/5.25 = one_one_rat ) ) ).
% 5.05/5.25
% 5.05/5.25 % left_right_inverse_power
% 5.05/5.25 thf(fact_479_left__right__inverse__power,axiom,
% 5.05/5.25 ! [X: nat,Y: nat,N2: nat] :
% 5.05/5.25 ( ( ( times_times_nat @ X @ Y )
% 5.05/5.25 = one_one_nat )
% 5.05/5.25 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 5.05/5.25 = one_one_nat ) ) ).
% 5.05/5.25
% 5.05/5.25 % left_right_inverse_power
% 5.05/5.25 thf(fact_480_left__right__inverse__power,axiom,
% 5.05/5.25 ! [X: int,Y: int,N2: nat] :
% 5.05/5.25 ( ( ( times_times_int @ X @ Y )
% 5.05/5.25 = one_one_int )
% 5.05/5.25 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.05/5.25 = one_one_int ) ) ).
% 5.05/5.25
% 5.05/5.25 % left_right_inverse_power
% 5.05/5.25 thf(fact_481_power__Suc2,axiom,
% 5.05/5.25 ! [A: complex,N2: nat] :
% 5.05/5.25 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 5.05/5.25 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_Suc2
% 5.05/5.25 thf(fact_482_power__Suc2,axiom,
% 5.05/5.25 ! [A: real,N2: nat] :
% 5.05/5.25 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.05/5.25 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ A ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_Suc2
% 5.05/5.25 thf(fact_483_power__Suc2,axiom,
% 5.05/5.25 ! [A: rat,N2: nat] :
% 5.05/5.25 ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 5.05/5.25 = ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ A ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_Suc2
% 5.05/5.25 thf(fact_484_power__Suc2,axiom,
% 5.05/5.25 ! [A: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.05/5.25 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_Suc2
% 5.05/5.25 thf(fact_485_power__Suc2,axiom,
% 5.05/5.25 ! [A: int,N2: nat] :
% 5.05/5.25 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.05/5.25 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ A ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_Suc2
% 5.05/5.25 thf(fact_486_power__Suc,axiom,
% 5.05/5.25 ! [A: complex,N2: nat] :
% 5.05/5.25 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 5.05/5.25 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_Suc
% 5.05/5.25 thf(fact_487_power__Suc,axiom,
% 5.05/5.25 ! [A: real,N2: nat] :
% 5.05/5.25 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.05/5.25 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_Suc
% 5.05/5.25 thf(fact_488_power__Suc,axiom,
% 5.05/5.25 ! [A: rat,N2: nat] :
% 5.05/5.25 ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 5.05/5.25 = ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_Suc
% 5.05/5.25 thf(fact_489_power__Suc,axiom,
% 5.05/5.25 ! [A: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.05/5.25 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_Suc
% 5.05/5.25 thf(fact_490_power__Suc,axiom,
% 5.05/5.25 ! [A: int,N2: nat] :
% 5.05/5.25 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.05/5.25 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_Suc
% 5.05/5.25 thf(fact_491_power__one__over,axiom,
% 5.05/5.25 ! [A: complex,N2: nat] :
% 5.05/5.25 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N2 )
% 5.05/5.25 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_one_over
% 5.05/5.25 thf(fact_492_power__one__over,axiom,
% 5.05/5.25 ! [A: real,N2: nat] :
% 5.05/5.25 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N2 )
% 5.05/5.25 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_one_over
% 5.05/5.25 thf(fact_493_power__one__over,axiom,
% 5.05/5.25 ! [A: rat,N2: nat] :
% 5.05/5.25 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N2 )
% 5.05/5.25 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_one_over
% 5.05/5.25 thf(fact_494_power__add,axiom,
% 5.05/5.25 ! [A: complex,M: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.05/5.25 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add
% 5.05/5.25 thf(fact_495_power__add,axiom,
% 5.05/5.25 ! [A: real,M: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.05/5.25 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add
% 5.05/5.25 thf(fact_496_power__add,axiom,
% 5.05/5.25 ! [A: rat,M: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.05/5.25 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add
% 5.05/5.25 thf(fact_497_power__add,axiom,
% 5.05/5.25 ! [A: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.05/5.25 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add
% 5.05/5.25 thf(fact_498_power__add,axiom,
% 5.05/5.25 ! [A: int,M: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.05/5.25 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_add
% 5.05/5.25 thf(fact_499_nth__equalityI,axiom,
% 5.05/5.25 ! [Xs2: list_nat,Ys: list_nat] :
% 5.05/5.25 ( ( ( size_size_list_nat @ Xs2 )
% 5.05/5.25 = ( size_size_list_nat @ Ys ) )
% 5.05/5.25 => ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.25 => ( ( nth_nat @ Xs2 @ I3 )
% 5.05/5.25 = ( nth_nat @ Ys @ I3 ) ) )
% 5.05/5.25 => ( Xs2 = Ys ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_equalityI
% 5.05/5.25 thf(fact_500_nth__equalityI,axiom,
% 5.05/5.25 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.05/5.25 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.05/5.25 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.05/5.25 => ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.25 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 5.05/5.25 = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 5.05/5.25 => ( Xs2 = Ys ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_equalityI
% 5.05/5.25 thf(fact_501_nth__equalityI,axiom,
% 5.05/5.25 ! [Xs2: list_o,Ys: list_o] :
% 5.05/5.25 ( ( ( size_size_list_o @ Xs2 )
% 5.05/5.25 = ( size_size_list_o @ Ys ) )
% 5.05/5.25 => ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.25 => ( ( nth_o @ Xs2 @ I3 )
% 5.05/5.25 = ( nth_o @ Ys @ I3 ) ) )
% 5.05/5.25 => ( Xs2 = Ys ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_equalityI
% 5.05/5.25 thf(fact_502_nth__equalityI,axiom,
% 5.05/5.25 ! [Xs2: list_int,Ys: list_int] :
% 5.05/5.25 ( ( ( size_size_list_int @ Xs2 )
% 5.05/5.25 = ( size_size_list_int @ Ys ) )
% 5.05/5.25 => ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.25 => ( ( nth_int @ Xs2 @ I3 )
% 5.05/5.25 = ( nth_int @ Ys @ I3 ) ) )
% 5.05/5.25 => ( Xs2 = Ys ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_equalityI
% 5.05/5.25 thf(fact_503_Skolem__list__nth,axiom,
% 5.05/5.25 ! [K: nat,P: nat > nat > $o] :
% 5.05/5.25 ( ( ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ K )
% 5.05/5.25 => ? [X4: nat] : ( P @ I5 @ X4 ) ) )
% 5.05/5.25 = ( ? [Xs: list_nat] :
% 5.05/5.25 ( ( ( size_size_list_nat @ Xs )
% 5.05/5.25 = K )
% 5.05/5.25 & ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ K )
% 5.05/5.25 => ( P @ I5 @ ( nth_nat @ Xs @ I5 ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Skolem_list_nth
% 5.05/5.25 thf(fact_504_Skolem__list__nth,axiom,
% 5.05/5.25 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.05/5.25 ( ( ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ K )
% 5.05/5.25 => ? [X4: vEBT_VEBT] : ( P @ I5 @ X4 ) ) )
% 5.05/5.25 = ( ? [Xs: list_VEBT_VEBT] :
% 5.05/5.25 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.05/5.25 = K )
% 5.05/5.25 & ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ K )
% 5.05/5.25 => ( P @ I5 @ ( nth_VEBT_VEBT @ Xs @ I5 ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Skolem_list_nth
% 5.05/5.25 thf(fact_505_Skolem__list__nth,axiom,
% 5.05/5.25 ! [K: nat,P: nat > $o > $o] :
% 5.05/5.25 ( ( ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ K )
% 5.05/5.25 => ? [X4: $o] : ( P @ I5 @ X4 ) ) )
% 5.05/5.25 = ( ? [Xs: list_o] :
% 5.05/5.25 ( ( ( size_size_list_o @ Xs )
% 5.05/5.25 = K )
% 5.05/5.25 & ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ K )
% 5.05/5.25 => ( P @ I5 @ ( nth_o @ Xs @ I5 ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Skolem_list_nth
% 5.05/5.25 thf(fact_506_Skolem__list__nth,axiom,
% 5.05/5.25 ! [K: nat,P: nat > int > $o] :
% 5.05/5.25 ( ( ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ K )
% 5.05/5.25 => ? [X4: int] : ( P @ I5 @ X4 ) ) )
% 5.05/5.25 = ( ? [Xs: list_int] :
% 5.05/5.25 ( ( ( size_size_list_int @ Xs )
% 5.05/5.25 = K )
% 5.05/5.25 & ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ K )
% 5.05/5.25 => ( P @ I5 @ ( nth_int @ Xs @ I5 ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Skolem_list_nth
% 5.05/5.25 thf(fact_507_list__eq__iff__nth__eq,axiom,
% 5.05/5.25 ( ( ^ [Y4: list_nat,Z3: list_nat] : ( Y4 = Z3 ) )
% 5.05/5.25 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 5.05/5.25 ( ( ( size_size_list_nat @ Xs )
% 5.05/5.25 = ( size_size_list_nat @ Ys3 ) )
% 5.05/5.25 & ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 5.05/5.25 => ( ( nth_nat @ Xs @ I5 )
% 5.05/5.25 = ( nth_nat @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_eq_iff_nth_eq
% 5.05/5.25 thf(fact_508_list__eq__iff__nth__eq,axiom,
% 5.05/5.25 ( ( ^ [Y4: list_VEBT_VEBT,Z3: list_VEBT_VEBT] : ( Y4 = Z3 ) )
% 5.05/5.25 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.05/5.25 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.05/5.25 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.05/5.25 & ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.05/5.25 => ( ( nth_VEBT_VEBT @ Xs @ I5 )
% 5.05/5.25 = ( nth_VEBT_VEBT @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_eq_iff_nth_eq
% 5.05/5.25 thf(fact_509_list__eq__iff__nth__eq,axiom,
% 5.05/5.25 ( ( ^ [Y4: list_o,Z3: list_o] : ( Y4 = Z3 ) )
% 5.05/5.25 = ( ^ [Xs: list_o,Ys3: list_o] :
% 5.05/5.25 ( ( ( size_size_list_o @ Xs )
% 5.05/5.25 = ( size_size_list_o @ Ys3 ) )
% 5.05/5.25 & ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 5.05/5.25 => ( ( nth_o @ Xs @ I5 )
% 5.05/5.25 = ( nth_o @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_eq_iff_nth_eq
% 5.05/5.25 thf(fact_510_list__eq__iff__nth__eq,axiom,
% 5.05/5.25 ( ( ^ [Y4: list_int,Z3: list_int] : ( Y4 = Z3 ) )
% 5.05/5.25 = ( ^ [Xs: list_int,Ys3: list_int] :
% 5.05/5.25 ( ( ( size_size_list_int @ Xs )
% 5.05/5.25 = ( size_size_list_int @ Ys3 ) )
% 5.05/5.25 & ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 5.05/5.25 => ( ( nth_int @ Xs @ I5 )
% 5.05/5.25 = ( nth_int @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_eq_iff_nth_eq
% 5.05/5.25 thf(fact_511_set__vebt__def,axiom,
% 5.05/5.25 ( vEBT_set_vebt
% 5.05/5.25 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_vebt_def
% 5.05/5.25 thf(fact_512_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.05/5.25 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.05/5.25 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.05/5.25
% 5.05/5.25 % VEBT_internal.minNull.simps(5)
% 5.05/5.25 thf(fact_513_vebt__delete_Osimps_I4_J,axiom,
% 5.05/5.25 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 5.05/5.25 ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 5.05/5.25 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ).
% 5.05/5.25
% 5.05/5.25 % vebt_delete.simps(4)
% 5.05/5.25 thf(fact_514_vebt__member_Osimps_I2_J,axiom,
% 5.05/5.25 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 5.05/5.25 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 5.05/5.25
% 5.05/5.25 % vebt_member.simps(2)
% 5.05/5.25 thf(fact_515_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.05/5.25 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 5.05/5.25
% 5.05/5.25 % VEBT_internal.minNull.simps(4)
% 5.05/5.25 thf(fact_516_power__less__power__Suc,axiom,
% 5.05/5.25 ! [A: real,N2: nat] :
% 5.05/5.25 ( ( ord_less_real @ one_one_real @ A )
% 5.05/5.25 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_less_power_Suc
% 5.05/5.25 thf(fact_517_power__less__power__Suc,axiom,
% 5.05/5.25 ! [A: rat,N2: nat] :
% 5.05/5.25 ( ( ord_less_rat @ one_one_rat @ A )
% 5.05/5.25 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_less_power_Suc
% 5.05/5.25 thf(fact_518_power__less__power__Suc,axiom,
% 5.05/5.25 ! [A: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ one_one_nat @ A )
% 5.05/5.25 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_less_power_Suc
% 5.05/5.25 thf(fact_519_power__less__power__Suc,axiom,
% 5.05/5.25 ! [A: int,N2: nat] :
% 5.05/5.25 ( ( ord_less_int @ one_one_int @ A )
% 5.05/5.25 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_less_power_Suc
% 5.05/5.25 thf(fact_520_power__gt1__lemma,axiom,
% 5.05/5.25 ! [A: real,N2: nat] :
% 5.05/5.25 ( ( ord_less_real @ one_one_real @ A )
% 5.05/5.25 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_gt1_lemma
% 5.05/5.25 thf(fact_521_power__gt1__lemma,axiom,
% 5.05/5.25 ! [A: rat,N2: nat] :
% 5.05/5.25 ( ( ord_less_rat @ one_one_rat @ A )
% 5.05/5.25 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_gt1_lemma
% 5.05/5.25 thf(fact_522_power__gt1__lemma,axiom,
% 5.05/5.25 ! [A: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ one_one_nat @ A )
% 5.05/5.25 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_gt1_lemma
% 5.05/5.25 thf(fact_523_power__gt1__lemma,axiom,
% 5.05/5.25 ! [A: int,N2: nat] :
% 5.05/5.25 ( ( ord_less_int @ one_one_int @ A )
% 5.05/5.25 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_gt1_lemma
% 5.05/5.25 thf(fact_524_power__gt1,axiom,
% 5.05/5.25 ! [A: real,N2: nat] :
% 5.05/5.25 ( ( ord_less_real @ one_one_real @ A )
% 5.05/5.25 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_gt1
% 5.05/5.25 thf(fact_525_power__gt1,axiom,
% 5.05/5.25 ! [A: rat,N2: nat] :
% 5.05/5.25 ( ( ord_less_rat @ one_one_rat @ A )
% 5.05/5.25 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_gt1
% 5.05/5.25 thf(fact_526_power__gt1,axiom,
% 5.05/5.25 ! [A: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ one_one_nat @ A )
% 5.05/5.25 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_gt1
% 5.05/5.25 thf(fact_527_power__gt1,axiom,
% 5.05/5.25 ! [A: int,N2: nat] :
% 5.05/5.25 ( ( ord_less_int @ one_one_int @ A )
% 5.05/5.25 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_gt1
% 5.05/5.25 thf(fact_528_power__less__imp__less__exp,axiom,
% 5.05/5.25 ! [A: real,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_real @ one_one_real @ A )
% 5.05/5.25 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 5.05/5.25 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_less_imp_less_exp
% 5.05/5.25 thf(fact_529_power__less__imp__less__exp,axiom,
% 5.05/5.25 ! [A: rat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_rat @ one_one_rat @ A )
% 5.05/5.25 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 5.05/5.25 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_less_imp_less_exp
% 5.05/5.25 thf(fact_530_power__less__imp__less__exp,axiom,
% 5.05/5.25 ! [A: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ one_one_nat @ A )
% 5.05/5.25 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.05/5.25 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_less_imp_less_exp
% 5.05/5.25 thf(fact_531_power__less__imp__less__exp,axiom,
% 5.05/5.25 ! [A: int,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_int @ one_one_int @ A )
% 5.05/5.25 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.05/5.25 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_less_imp_less_exp
% 5.05/5.25 thf(fact_532_power__strict__increasing,axiom,
% 5.05/5.25 ! [N2: nat,N4: nat,A: real] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ N4 )
% 5.05/5.25 => ( ( ord_less_real @ one_one_real @ A )
% 5.05/5.25 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_strict_increasing
% 5.05/5.25 thf(fact_533_power__strict__increasing,axiom,
% 5.05/5.25 ! [N2: nat,N4: nat,A: rat] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ N4 )
% 5.05/5.25 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.05/5.25 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_strict_increasing
% 5.05/5.25 thf(fact_534_power__strict__increasing,axiom,
% 5.05/5.25 ! [N2: nat,N4: nat,A: nat] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ N4 )
% 5.05/5.25 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.05/5.25 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_strict_increasing
% 5.05/5.25 thf(fact_535_power__strict__increasing,axiom,
% 5.05/5.25 ! [N2: nat,N4: nat,A: int] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ N4 )
% 5.05/5.25 => ( ( ord_less_int @ one_one_int @ A )
% 5.05/5.25 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_strict_increasing
% 5.05/5.25 thf(fact_536_power__increasing,axiom,
% 5.05/5.25 ! [N2: nat,N4: nat,A: real] :
% 5.05/5.25 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.05/5.25 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.05/5.25 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_increasing
% 5.05/5.25 thf(fact_537_power__increasing,axiom,
% 5.05/5.25 ! [N2: nat,N4: nat,A: rat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.05/5.25 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.05/5.25 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_increasing
% 5.05/5.25 thf(fact_538_power__increasing,axiom,
% 5.05/5.25 ! [N2: nat,N4: nat,A: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.05/5.25 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.05/5.25 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_increasing
% 5.05/5.25 thf(fact_539_power__increasing,axiom,
% 5.05/5.25 ! [N2: nat,N4: nat,A: int] :
% 5.05/5.25 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.05/5.25 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.05/5.25 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_increasing
% 5.05/5.25 thf(fact_540_nth__mem,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_complex] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.05/5.25 => ( member_complex @ ( nth_complex @ Xs2 @ N2 ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_mem
% 5.05/5.25 thf(fact_541_nth__mem,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_real] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs2 ) )
% 5.05/5.25 => ( member_real @ ( nth_real @ Xs2 @ N2 ) @ ( set_real2 @ Xs2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_mem
% 5.05/5.25 thf(fact_542_nth__mem,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_set_nat] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.05/5.25 => ( member_set_nat @ ( nth_set_nat @ Xs2 @ N2 ) @ ( set_set_nat2 @ Xs2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_mem
% 5.05/5.25 thf(fact_543_nth__mem,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_nat] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.25 => ( member_nat @ ( nth_nat @ Xs2 @ N2 ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_mem
% 5.05/5.25 thf(fact_544_nth__mem,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_VEBT_VEBT] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.25 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N2 ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_mem
% 5.05/5.25 thf(fact_545_nth__mem,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_o] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.25 => ( member_o @ ( nth_o @ Xs2 @ N2 ) @ ( set_o2 @ Xs2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_mem
% 5.05/5.25 thf(fact_546_nth__mem,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_int] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.25 => ( member_int @ ( nth_int @ Xs2 @ N2 ) @ ( set_int2 @ Xs2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_mem
% 5.05/5.25 thf(fact_547_list__ball__nth,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_nat,P: nat > $o] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.25 => ( ! [X3: nat] :
% 5.05/5.25 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X3 ) )
% 5.05/5.25 => ( P @ ( nth_nat @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_ball_nth
% 5.05/5.25 thf(fact_548_list__ball__nth,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.25 => ( ! [X3: vEBT_VEBT] :
% 5.05/5.25 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X3 ) )
% 5.05/5.25 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_ball_nth
% 5.05/5.25 thf(fact_549_list__ball__nth,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_o,P: $o > $o] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.25 => ( ! [X3: $o] :
% 5.05/5.25 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X3 ) )
% 5.05/5.25 => ( P @ ( nth_o @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_ball_nth
% 5.05/5.25 thf(fact_550_list__ball__nth,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_int,P: int > $o] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.25 => ( ! [X3: int] :
% 5.05/5.25 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X3 ) )
% 5.05/5.25 => ( P @ ( nth_int @ Xs2 @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_ball_nth
% 5.05/5.25 thf(fact_551_in__set__conv__nth,axiom,
% 5.05/5.25 ! [X: complex,Xs2: list_complex] :
% 5.05/5.25 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.05/5.25 = ( ? [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.05/5.25 & ( ( nth_complex @ Xs2 @ I5 )
% 5.05/5.25 = X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % in_set_conv_nth
% 5.05/5.25 thf(fact_552_in__set__conv__nth,axiom,
% 5.05/5.25 ! [X: real,Xs2: list_real] :
% 5.05/5.25 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.05/5.25 = ( ? [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_size_list_real @ Xs2 ) )
% 5.05/5.25 & ( ( nth_real @ Xs2 @ I5 )
% 5.05/5.25 = X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % in_set_conv_nth
% 5.05/5.25 thf(fact_553_in__set__conv__nth,axiom,
% 5.05/5.25 ! [X: set_nat,Xs2: list_set_nat] :
% 5.05/5.25 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.05/5.25 = ( ? [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.05/5.25 & ( ( nth_set_nat @ Xs2 @ I5 )
% 5.05/5.25 = X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % in_set_conv_nth
% 5.05/5.25 thf(fact_554_in__set__conv__nth,axiom,
% 5.05/5.25 ! [X: nat,Xs2: list_nat] :
% 5.05/5.25 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.05/5.25 = ( ? [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.25 & ( ( nth_nat @ Xs2 @ I5 )
% 5.05/5.25 = X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % in_set_conv_nth
% 5.05/5.25 thf(fact_555_in__set__conv__nth,axiom,
% 5.05/5.25 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.05/5.25 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.05/5.25 = ( ? [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.25 & ( ( nth_VEBT_VEBT @ Xs2 @ I5 )
% 5.05/5.25 = X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % in_set_conv_nth
% 5.05/5.25 thf(fact_556_in__set__conv__nth,axiom,
% 5.05/5.25 ! [X: $o,Xs2: list_o] :
% 5.05/5.25 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.05/5.25 = ( ? [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.25 & ( ( nth_o @ Xs2 @ I5 )
% 5.05/5.25 = X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % in_set_conv_nth
% 5.05/5.25 thf(fact_557_in__set__conv__nth,axiom,
% 5.05/5.25 ! [X: int,Xs2: list_int] :
% 5.05/5.25 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.05/5.25 = ( ? [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.25 & ( ( nth_int @ Xs2 @ I5 )
% 5.05/5.25 = X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % in_set_conv_nth
% 5.05/5.25 thf(fact_558_all__nth__imp__all__set,axiom,
% 5.05/5.25 ! [Xs2: list_complex,P: complex > $o,X: complex] :
% 5.05/5.25 ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_complex @ Xs2 @ I3 ) ) )
% 5.05/5.25 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_nth_imp_all_set
% 5.05/5.25 thf(fact_559_all__nth__imp__all__set,axiom,
% 5.05/5.25 ! [Xs2: list_real,P: real > $o,X: real] :
% 5.05/5.25 ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_real @ Xs2 @ I3 ) ) )
% 5.05/5.25 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_nth_imp_all_set
% 5.05/5.25 thf(fact_560_all__nth__imp__all__set,axiom,
% 5.05/5.25 ! [Xs2: list_set_nat,P: set_nat > $o,X: set_nat] :
% 5.05/5.25 ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_set_nat @ Xs2 @ I3 ) ) )
% 5.05/5.25 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_nth_imp_all_set
% 5.05/5.25 thf(fact_561_all__nth__imp__all__set,axiom,
% 5.05/5.25 ! [Xs2: list_nat,P: nat > $o,X: nat] :
% 5.05/5.25 ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_nat @ Xs2 @ I3 ) ) )
% 5.05/5.25 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_nth_imp_all_set
% 5.05/5.25 thf(fact_562_all__nth__imp__all__set,axiom,
% 5.05/5.25 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.05/5.25 ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) )
% 5.05/5.25 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_nth_imp_all_set
% 5.05/5.25 thf(fact_563_all__nth__imp__all__set,axiom,
% 5.05/5.25 ! [Xs2: list_o,P: $o > $o,X: $o] :
% 5.05/5.25 ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_o @ Xs2 @ I3 ) ) )
% 5.05/5.25 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_nth_imp_all_set
% 5.05/5.25 thf(fact_564_all__nth__imp__all__set,axiom,
% 5.05/5.25 ! [Xs2: list_int,P: int > $o,X: int] :
% 5.05/5.25 ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_int @ Xs2 @ I3 ) ) )
% 5.05/5.25 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_nth_imp_all_set
% 5.05/5.25 thf(fact_565_all__set__conv__all__nth,axiom,
% 5.05/5.25 ! [Xs2: list_nat,P: nat > $o] :
% 5.05/5.25 ( ( ! [X2: nat] :
% 5.05/5.25 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X2 ) ) )
% 5.05/5.25 = ( ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_nat @ Xs2 @ I5 ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_set_conv_all_nth
% 5.05/5.25 thf(fact_566_all__set__conv__all__nth,axiom,
% 5.05/5.25 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.05/5.25 ( ( ! [X2: vEBT_VEBT] :
% 5.05/5.25 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X2 ) ) )
% 5.05/5.25 = ( ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I5 ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_set_conv_all_nth
% 5.05/5.25 thf(fact_567_all__set__conv__all__nth,axiom,
% 5.05/5.25 ! [Xs2: list_o,P: $o > $o] :
% 5.05/5.25 ( ( ! [X2: $o] :
% 5.05/5.25 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X2 ) ) )
% 5.05/5.25 = ( ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_o @ Xs2 @ I5 ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_set_conv_all_nth
% 5.05/5.25 thf(fact_568_all__set__conv__all__nth,axiom,
% 5.05/5.25 ! [Xs2: list_int,P: int > $o] :
% 5.05/5.25 ( ( ! [X2: int] :
% 5.05/5.25 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.05/5.25 => ( P @ X2 ) ) )
% 5.05/5.25 = ( ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.25 => ( P @ ( nth_int @ Xs2 @ I5 ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % all_set_conv_all_nth
% 5.05/5.25 thf(fact_569_set__update__memI,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_complex,X: complex] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.05/5.25 => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_memI
% 5.05/5.25 thf(fact_570_set__update__memI,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_real,X: real] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs2 ) )
% 5.05/5.25 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_memI
% 5.05/5.25 thf(fact_571_set__update__memI,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_set_nat,X: set_nat] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 5.05/5.25 => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_memI
% 5.05/5.25 thf(fact_572_set__update__memI,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_nat,X: nat] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.25 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_memI
% 5.05/5.25 thf(fact_573_set__update__memI,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.25 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_memI
% 5.05/5.25 thf(fact_574_set__update__memI,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_o,X: $o] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.25 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_memI
% 5.05/5.25 thf(fact_575_set__update__memI,axiom,
% 5.05/5.25 ! [N2: nat,Xs2: list_int,X: int] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.25 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N2 @ X ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % set_update_memI
% 5.05/5.25 thf(fact_576_list__update__same__conv,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_nat,X: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.25 => ( ( ( list_update_nat @ Xs2 @ I2 @ X )
% 5.05/5.25 = Xs2 )
% 5.05/5.25 = ( ( nth_nat @ Xs2 @ I2 )
% 5.05/5.25 = X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_same_conv
% 5.05/5.25 thf(fact_577_list__update__same__conv,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.25 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 5.05/5.25 = Xs2 )
% 5.05/5.25 = ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 5.05/5.25 = X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_same_conv
% 5.05/5.25 thf(fact_578_list__update__same__conv,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_o,X: $o] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.25 => ( ( ( list_update_o @ Xs2 @ I2 @ X )
% 5.05/5.25 = Xs2 )
% 5.05/5.25 = ( ( nth_o @ Xs2 @ I2 )
% 5.05/5.25 = X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_same_conv
% 5.05/5.25 thf(fact_579_list__update__same__conv,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_int,X: int] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.25 => ( ( ( list_update_int @ Xs2 @ I2 @ X )
% 5.05/5.25 = Xs2 )
% 5.05/5.25 = ( ( nth_int @ Xs2 @ I2 )
% 5.05/5.25 = X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % list_update_same_conv
% 5.05/5.25 thf(fact_580_nth__list__update,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_nat,J: nat,X: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 5.05/5.25 => ( ( ( I2 = J )
% 5.05/5.25 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.05/5.25 = X ) )
% 5.05/5.25 & ( ( I2 != J )
% 5.05/5.25 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J )
% 5.05/5.25 = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update
% 5.05/5.25 thf(fact_581_nth__list__update,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.05/5.25 => ( ( ( I2 = J )
% 5.05/5.25 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.05/5.25 = X ) )
% 5.05/5.25 & ( ( I2 != J )
% 5.05/5.25 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J )
% 5.05/5.25 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update
% 5.05/5.25 thf(fact_582_nth__list__update,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_o,X: $o,J: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 5.05/5.25 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ J )
% 5.05/5.25 = ( ( ( I2 = J )
% 5.05/5.25 => X )
% 5.05/5.25 & ( ( I2 != J )
% 5.05/5.25 => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update
% 5.05/5.25 thf(fact_583_nth__list__update,axiom,
% 5.05/5.25 ! [I2: nat,Xs2: list_int,J: nat,X: int] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 5.05/5.25 => ( ( ( I2 = J )
% 5.05/5.25 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.05/5.25 = X ) )
% 5.05/5.25 & ( ( I2 != J )
% 5.05/5.25 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J )
% 5.05/5.25 = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nth_list_update
% 5.05/5.25 thf(fact_584_power__numeral__even,axiom,
% 5.05/5.25 ! [Z: complex,W: num] :
% 5.05/5.25 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.05/5.25 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_numeral_even
% 5.05/5.25 thf(fact_585_power__numeral__even,axiom,
% 5.05/5.25 ! [Z: real,W: num] :
% 5.05/5.25 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.05/5.25 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_numeral_even
% 5.05/5.25 thf(fact_586_power__numeral__even,axiom,
% 5.05/5.25 ! [Z: rat,W: num] :
% 5.05/5.25 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.05/5.25 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_numeral_even
% 5.05/5.25 thf(fact_587_power__numeral__even,axiom,
% 5.05/5.25 ! [Z: nat,W: num] :
% 5.05/5.25 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.05/5.25 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_numeral_even
% 5.05/5.25 thf(fact_588_power__numeral__even,axiom,
% 5.05/5.25 ! [Z: int,W: num] :
% 5.05/5.25 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.05/5.25 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_numeral_even
% 5.05/5.25 thf(fact_589_power__le__imp__le__exp,axiom,
% 5.05/5.25 ! [A: real,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_real @ one_one_real @ A )
% 5.05/5.25 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 5.05/5.25 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_le_imp_le_exp
% 5.05/5.25 thf(fact_590_power__le__imp__le__exp,axiom,
% 5.05/5.25 ! [A: rat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_rat @ one_one_rat @ A )
% 5.05/5.25 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 5.05/5.25 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_le_imp_le_exp
% 5.05/5.25 thf(fact_591_power__le__imp__le__exp,axiom,
% 5.05/5.25 ! [A: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ one_one_nat @ A )
% 5.05/5.25 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.05/5.25 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_le_imp_le_exp
% 5.05/5.25 thf(fact_592_power__le__imp__le__exp,axiom,
% 5.05/5.25 ! [A: int,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_int @ one_one_int @ A )
% 5.05/5.25 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.05/5.25 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_le_imp_le_exp
% 5.05/5.25 thf(fact_593_power2__eq__square,axiom,
% 5.05/5.25 ! [A: complex] :
% 5.05/5.25 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( times_times_complex @ A @ A ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_eq_square
% 5.05/5.25 thf(fact_594_power2__eq__square,axiom,
% 5.05/5.25 ! [A: real] :
% 5.05/5.25 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( times_times_real @ A @ A ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_eq_square
% 5.05/5.25 thf(fact_595_power2__eq__square,axiom,
% 5.05/5.25 ! [A: rat] :
% 5.05/5.25 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( times_times_rat @ A @ A ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_eq_square
% 5.05/5.25 thf(fact_596_power2__eq__square,axiom,
% 5.05/5.25 ! [A: nat] :
% 5.05/5.25 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( times_times_nat @ A @ A ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_eq_square
% 5.05/5.25 thf(fact_597_power2__eq__square,axiom,
% 5.05/5.25 ! [A: int] :
% 5.05/5.25 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( times_times_int @ A @ A ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_eq_square
% 5.05/5.25 thf(fact_598_power4__eq__xxxx,axiom,
% 5.05/5.25 ! [X: complex] :
% 5.05/5.25 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.05/5.25 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % power4_eq_xxxx
% 5.05/5.25 thf(fact_599_power4__eq__xxxx,axiom,
% 5.05/5.25 ! [X: real] :
% 5.05/5.25 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.05/5.25 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % power4_eq_xxxx
% 5.05/5.25 thf(fact_600_power4__eq__xxxx,axiom,
% 5.05/5.25 ! [X: rat] :
% 5.05/5.25 ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.05/5.25 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % power4_eq_xxxx
% 5.05/5.25 thf(fact_601_power4__eq__xxxx,axiom,
% 5.05/5.25 ! [X: nat] :
% 5.05/5.25 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.05/5.25 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % power4_eq_xxxx
% 5.05/5.25 thf(fact_602_power4__eq__xxxx,axiom,
% 5.05/5.25 ! [X: int] :
% 5.05/5.25 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.05/5.25 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % power4_eq_xxxx
% 5.05/5.25 thf(fact_603_one__power2,axiom,
% 5.05/5.25 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = one_one_rat ) ).
% 5.05/5.25
% 5.05/5.25 % one_power2
% 5.05/5.25 thf(fact_604_one__power2,axiom,
% 5.05/5.25 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = one_one_nat ) ).
% 5.05/5.25
% 5.05/5.25 % one_power2
% 5.05/5.25 thf(fact_605_one__power2,axiom,
% 5.05/5.25 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = one_one_real ) ).
% 5.05/5.25
% 5.05/5.25 % one_power2
% 5.05/5.25 thf(fact_606_one__power2,axiom,
% 5.05/5.25 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = one_one_int ) ).
% 5.05/5.25
% 5.05/5.25 % one_power2
% 5.05/5.25 thf(fact_607_one__power2,axiom,
% 5.05/5.25 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = one_one_complex ) ).
% 5.05/5.25
% 5.05/5.25 % one_power2
% 5.05/5.25 thf(fact_608_power__even__eq,axiom,
% 5.05/5.25 ! [A: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.25 = ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_even_eq
% 5.05/5.25 thf(fact_609_power__even__eq,axiom,
% 5.05/5.25 ! [A: real,N2: nat] :
% 5.05/5.25 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.25 = ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_even_eq
% 5.05/5.25 thf(fact_610_power__even__eq,axiom,
% 5.05/5.25 ! [A: int,N2: nat] :
% 5.05/5.25 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.25 = ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_even_eq
% 5.05/5.25 thf(fact_611_power__even__eq,axiom,
% 5.05/5.25 ! [A: complex,N2: nat] :
% 5.05/5.25 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.25 = ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_even_eq
% 5.05/5.25 thf(fact_612_less__exp,axiom,
% 5.05/5.25 ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_exp
% 5.05/5.25 thf(fact_613_power2__nat__le__imp__le,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 5.05/5.25 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_nat_le_imp_le
% 5.05/5.25 thf(fact_614_power2__nat__le__eq__le,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.25 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_nat_le_eq_le
% 5.05/5.25 thf(fact_615_self__le__ge2__pow,axiom,
% 5.05/5.25 ! [K: nat,M: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.05/5.25 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % self_le_ge2_pow
% 5.05/5.25 thf(fact_616_power2__sum,axiom,
% 5.05/5.25 ! [X: complex,Y: complex] :
% 5.05/5.25 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_sum
% 5.05/5.25 thf(fact_617_power2__sum,axiom,
% 5.05/5.25 ! [X: real,Y: real] :
% 5.05/5.25 ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_sum
% 5.05/5.25 thf(fact_618_power2__sum,axiom,
% 5.05/5.25 ! [X: rat,Y: rat] :
% 5.05/5.25 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_sum
% 5.05/5.25 thf(fact_619_power2__sum,axiom,
% 5.05/5.25 ! [X: nat,Y: nat] :
% 5.05/5.25 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_sum
% 5.05/5.25 thf(fact_620_power2__sum,axiom,
% 5.05/5.25 ! [X: int,Y: int] :
% 5.05/5.25 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_sum
% 5.05/5.25 thf(fact_621_power__odd__eq,axiom,
% 5.05/5.25 ! [A: complex,N2: nat] :
% 5.05/5.25 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.05/5.25 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_odd_eq
% 5.05/5.25 thf(fact_622_power__odd__eq,axiom,
% 5.05/5.25 ! [A: real,N2: nat] :
% 5.05/5.25 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.05/5.25 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_odd_eq
% 5.05/5.25 thf(fact_623_power__odd__eq,axiom,
% 5.05/5.25 ! [A: rat,N2: nat] :
% 5.05/5.25 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.05/5.25 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_odd_eq
% 5.05/5.25 thf(fact_624_power__odd__eq,axiom,
% 5.05/5.25 ! [A: nat,N2: nat] :
% 5.05/5.25 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.05/5.25 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_odd_eq
% 5.05/5.25 thf(fact_625_power__odd__eq,axiom,
% 5.05/5.25 ! [A: int,N2: nat] :
% 5.05/5.25 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.05/5.25 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_odd_eq
% 5.05/5.25 thf(fact_626_ex__power__ivl2,axiom,
% 5.05/5.25 ! [B: nat,K: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.05/5.25 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.05/5.25 => ? [N3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.05/5.25 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % ex_power_ivl2
% 5.05/5.25 thf(fact_627_ex__power__ivl1,axiom,
% 5.05/5.25 ! [B: nat,K: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.05/5.25 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.05/5.25 => ? [N3: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.05/5.25 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % ex_power_ivl1
% 5.05/5.25 thf(fact_628_invar__vebt_Ointros_I2_J,axiom,
% 5.05/5.25 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.05/5.25 ( ! [X3: vEBT_VEBT] :
% 5.05/5.25 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.05/5.25 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.05/5.25 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.05/5.25 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.05/5.25 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.05/5.25 => ( ( M = N2 )
% 5.05/5.25 => ( ( Deg
% 5.05/5.25 = ( plus_plus_nat @ N2 @ M ) )
% 5.05/5.25 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.05/5.25 => ( ! [X3: vEBT_VEBT] :
% 5.05/5.25 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.05/5.25 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.05/5.25 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % invar_vebt.intros(2)
% 5.05/5.25 thf(fact_629_greater__shift,axiom,
% 5.05/5.25 ( ord_less_nat
% 5.05/5.25 = ( ^ [Y2: nat,X2: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % greater_shift
% 5.05/5.25 thf(fact_630_less__shift,axiom,
% 5.05/5.25 ( ord_less_nat
% 5.05/5.25 = ( ^ [X2: nat,Y2: nat] : ( vEBT_VEBT_less @ ( some_nat @ X2 ) @ ( some_nat @ Y2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_shift
% 5.05/5.25 thf(fact_631_insert__simp__norm,axiom,
% 5.05/5.25 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.05/5.25 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.25 => ( ( ord_less_nat @ Mi @ X )
% 5.05/5.25 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.25 => ( ( X != Ma )
% 5.05/5.25 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.25 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % insert_simp_norm
% 5.05/5.25 thf(fact_632_insert__simp__excp,axiom,
% 5.05/5.25 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.05/5.25 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.25 => ( ( ord_less_nat @ X @ Mi )
% 5.05/5.25 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.25 => ( ( X != Ma )
% 5.05/5.25 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.25 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % insert_simp_excp
% 5.05/5.25 thf(fact_633_mintlistlength,axiom,
% 5.05/5.25 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.05/5.25 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N2 )
% 5.05/5.25 => ( ( Mi != Ma )
% 5.05/5.25 => ( ( ord_less_nat @ Mi @ Ma )
% 5.05/5.25 & ? [M2: nat] :
% 5.05/5.25 ( ( ( some_nat @ M2 )
% 5.05/5.25 = ( vEBT_vebt_mint @ Summary ) )
% 5.05/5.25 & ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % mintlistlength
% 5.05/5.25 thf(fact_634_semiring__norm_I69_J,axiom,
% 5.05/5.25 ! [M: num] :
% 5.05/5.25 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(69)
% 5.05/5.25 thf(fact_635_semiring__norm_I76_J,axiom,
% 5.05/5.25 ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(76)
% 5.05/5.25 thf(fact_636_sum__squares__bound,axiom,
% 5.05/5.25 ! [X: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % sum_squares_bound
% 5.05/5.25 thf(fact_637_sum__squares__bound,axiom,
% 5.05/5.25 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % sum_squares_bound
% 5.05/5.25 thf(fact_638_semiring__norm_I2_J,axiom,
% 5.05/5.25 ( ( plus_plus_num @ one @ one )
% 5.05/5.25 = ( bit0 @ one ) ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(2)
% 5.05/5.25 thf(fact_639_mult__Suc__right,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 5.05/5.25 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % mult_Suc_right
% 5.05/5.25 thf(fact_640_vebt__insert_Osimps_I4_J,axiom,
% 5.05/5.25 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.05/5.25 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 5.05/5.25 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 5.05/5.25
% 5.05/5.25 % vebt_insert.simps(4)
% 5.05/5.25 thf(fact_641_semiring__norm_I87_J,axiom,
% 5.05/5.25 ! [M: num,N2: num] :
% 5.05/5.25 ( ( ( bit0 @ M )
% 5.05/5.25 = ( bit0 @ N2 ) )
% 5.05/5.25 = ( M = N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(87)
% 5.05/5.25 thf(fact_642_old_Onat_Oinject,axiom,
% 5.05/5.25 ! [Nat: nat,Nat2: nat] :
% 5.05/5.25 ( ( ( suc @ Nat )
% 5.05/5.25 = ( suc @ Nat2 ) )
% 5.05/5.25 = ( Nat = Nat2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % old.nat.inject
% 5.05/5.25 thf(fact_643_nat_Oinject,axiom,
% 5.05/5.25 ! [X22: nat,Y22: nat] :
% 5.05/5.25 ( ( ( suc @ X22 )
% 5.05/5.25 = ( suc @ Y22 ) )
% 5.05/5.25 = ( X22 = Y22 ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat.inject
% 5.05/5.25 thf(fact_644_power__minus__is__div,axiom,
% 5.05/5.25 ! [B: nat,A: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.25 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 5.05/5.25 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power_minus_is_div
% 5.05/5.25 thf(fact_645_semiring__norm_I85_J,axiom,
% 5.05/5.25 ! [M: num] :
% 5.05/5.25 ( ( bit0 @ M )
% 5.05/5.25 != one ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(85)
% 5.05/5.25 thf(fact_646_semiring__norm_I83_J,axiom,
% 5.05/5.25 ! [N2: num] :
% 5.05/5.25 ( one
% 5.05/5.25 != ( bit0 @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(83)
% 5.05/5.25 thf(fact_647_Suc__less__eq,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.05/5.25 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_less_eq
% 5.05/5.25 thf(fact_648_Suc__mono,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ M @ N2 )
% 5.05/5.25 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_mono
% 5.05/5.25 thf(fact_649_lessI,axiom,
% 5.05/5.25 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % lessI
% 5.05/5.25 thf(fact_650_Suc__le__mono,axiom,
% 5.05/5.25 ! [N2: nat,M: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 5.05/5.25 = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_le_mono
% 5.05/5.25 thf(fact_651_add__Suc__right,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 5.05/5.25 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % add_Suc_right
% 5.05/5.25 thf(fact_652_nat__add__left__cancel__less,axiom,
% 5.05/5.25 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.05/5.25 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_add_left_cancel_less
% 5.05/5.25 thf(fact_653_Suc__diff__diff,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,K: nat] :
% 5.05/5.25 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 5.05/5.25 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_diff_diff
% 5.05/5.25 thf(fact_654_diff__Suc__Suc,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.05/5.25 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_Suc_Suc
% 5.05/5.25 thf(fact_655_nat__add__left__cancel__le,axiom,
% 5.05/5.25 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.05/5.25 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_add_left_cancel_le
% 5.05/5.25 thf(fact_656_diff__diff__cancel,axiom,
% 5.05/5.25 ! [I2: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ I2 @ N2 )
% 5.05/5.25 => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I2 ) )
% 5.05/5.25 = I2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_diff_cancel
% 5.05/5.25 thf(fact_657_diff__diff__left,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.25 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.05/5.25 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_diff_left
% 5.05/5.25 thf(fact_658_nat__1__eq__mult__iff,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( one_one_nat
% 5.05/5.25 = ( times_times_nat @ M @ N2 ) )
% 5.05/5.25 = ( ( M = one_one_nat )
% 5.05/5.25 & ( N2 = one_one_nat ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_1_eq_mult_iff
% 5.05/5.25 thf(fact_659_nat__mult__eq__1__iff,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ( times_times_nat @ M @ N2 )
% 5.05/5.25 = one_one_nat )
% 5.05/5.25 = ( ( M = one_one_nat )
% 5.05/5.25 & ( N2 = one_one_nat ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_mult_eq_1_iff
% 5.05/5.25 thf(fact_660_semiring__norm_I6_J,axiom,
% 5.05/5.25 ! [M: num,N2: num] :
% 5.05/5.25 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.05/5.25 = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(6)
% 5.05/5.25 thf(fact_661_max__Suc__Suc,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.05/5.25 = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_Suc_Suc
% 5.05/5.25 thf(fact_662_semiring__norm_I13_J,axiom,
% 5.05/5.25 ! [M: num,N2: num] :
% 5.05/5.25 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.05/5.25 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(13)
% 5.05/5.25 thf(fact_663_semiring__norm_I12_J,axiom,
% 5.05/5.25 ! [N2: num] :
% 5.05/5.25 ( ( times_times_num @ one @ N2 )
% 5.05/5.25 = N2 ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(12)
% 5.05/5.25 thf(fact_664_semiring__norm_I11_J,axiom,
% 5.05/5.25 ! [M: num] :
% 5.05/5.25 ( ( times_times_num @ M @ one )
% 5.05/5.25 = M ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(11)
% 5.05/5.25 thf(fact_665_semiring__norm_I78_J,axiom,
% 5.05/5.25 ! [M: num,N2: num] :
% 5.05/5.25 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.05/5.25 = ( ord_less_num @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(78)
% 5.05/5.25 thf(fact_666_semiring__norm_I71_J,axiom,
% 5.05/5.25 ! [M: num,N2: num] :
% 5.05/5.25 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.05/5.25 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(71)
% 5.05/5.25 thf(fact_667_semiring__norm_I75_J,axiom,
% 5.05/5.25 ! [M: num] :
% 5.05/5.25 ~ ( ord_less_num @ M @ one ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(75)
% 5.05/5.25 thf(fact_668_semiring__norm_I68_J,axiom,
% 5.05/5.25 ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) ).
% 5.05/5.25
% 5.05/5.25 % semiring_norm(68)
% 5.05/5.25 thf(fact_669_left__diff__distrib__numeral,axiom,
% 5.05/5.25 ! [A: complex,B: complex,V: num] :
% 5.05/5.25 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.05/5.25 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % left_diff_distrib_numeral
% 5.05/5.25 thf(fact_670_left__diff__distrib__numeral,axiom,
% 5.05/5.25 ! [A: real,B: real,V: num] :
% 5.05/5.25 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.05/5.25 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % left_diff_distrib_numeral
% 5.05/5.25 thf(fact_671_left__diff__distrib__numeral,axiom,
% 5.05/5.25 ! [A: rat,B: rat,V: num] :
% 5.05/5.25 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.05/5.25 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % left_diff_distrib_numeral
% 5.05/5.25 thf(fact_672_left__diff__distrib__numeral,axiom,
% 5.05/5.25 ! [A: int,B: int,V: num] :
% 5.05/5.25 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.05/5.25 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % left_diff_distrib_numeral
% 5.05/5.25 thf(fact_673_right__diff__distrib__numeral,axiom,
% 5.05/5.25 ! [V: num,B: complex,C: complex] :
% 5.05/5.25 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.05/5.25 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % right_diff_distrib_numeral
% 5.05/5.25 thf(fact_674_right__diff__distrib__numeral,axiom,
% 5.05/5.25 ! [V: num,B: real,C: real] :
% 5.05/5.25 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.05/5.25 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % right_diff_distrib_numeral
% 5.05/5.25 thf(fact_675_right__diff__distrib__numeral,axiom,
% 5.05/5.25 ! [V: num,B: rat,C: rat] :
% 5.05/5.25 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.05/5.25 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % right_diff_distrib_numeral
% 5.05/5.25 thf(fact_676_right__diff__distrib__numeral,axiom,
% 5.05/5.25 ! [V: num,B: int,C: int] :
% 5.05/5.25 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.05/5.25 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % right_diff_distrib_numeral
% 5.05/5.25 thf(fact_677_max__number__of_I1_J,axiom,
% 5.05/5.25 ! [U: num,V: num] :
% 5.05/5.25 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.05/5.25 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.05/5.25 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.05/5.25 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.05/5.25 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.05/5.25 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_number_of(1)
% 5.05/5.25 thf(fact_678_max__number__of_I1_J,axiom,
% 5.05/5.25 ! [U: num,V: num] :
% 5.05/5.25 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.05/5.25 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.05/5.25 = ( numera6620942414471956472nteger @ V ) ) )
% 5.05/5.25 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.05/5.25 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.05/5.25 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_number_of(1)
% 5.05/5.25 thf(fact_679_max__number__of_I1_J,axiom,
% 5.05/5.25 ! [U: num,V: num] :
% 5.05/5.25 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.05/5.25 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.05/5.25 = ( numeral_numeral_real @ V ) ) )
% 5.05/5.25 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.05/5.25 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.05/5.25 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_number_of(1)
% 5.05/5.25 thf(fact_680_max__number__of_I1_J,axiom,
% 5.05/5.25 ! [U: num,V: num] :
% 5.05/5.25 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.05/5.25 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.05/5.25 = ( numeral_numeral_rat @ V ) ) )
% 5.05/5.25 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.05/5.25 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.05/5.25 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_number_of(1)
% 5.05/5.25 thf(fact_681_max__number__of_I1_J,axiom,
% 5.05/5.25 ! [U: num,V: num] :
% 5.05/5.25 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.05/5.25 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.05/5.25 = ( numeral_numeral_nat @ V ) ) )
% 5.05/5.25 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.05/5.25 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.05/5.25 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_number_of(1)
% 5.05/5.25 thf(fact_682_max__number__of_I1_J,axiom,
% 5.05/5.25 ! [U: num,V: num] :
% 5.05/5.25 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.05/5.25 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.05/5.25 = ( numeral_numeral_int @ V ) ) )
% 5.05/5.25 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.05/5.25 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.05/5.25 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_number_of(1)
% 5.05/5.25 thf(fact_683_max__0__1_I5_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.05/5.25 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(5)
% 5.05/5.25 thf(fact_684_max__0__1_I5_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 5.05/5.25 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(5)
% 5.05/5.25 thf(fact_685_max__0__1_I5_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.05/5.25 = ( numeral_numeral_real @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(5)
% 5.05/5.25 thf(fact_686_max__0__1_I5_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.05/5.25 = ( numeral_numeral_rat @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(5)
% 5.05/5.25 thf(fact_687_max__0__1_I5_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.05/5.25 = ( numeral_numeral_nat @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(5)
% 5.05/5.25 thf(fact_688_max__0__1_I5_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.05/5.25 = ( numeral_numeral_int @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(5)
% 5.05/5.25 thf(fact_689_max__0__1_I6_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 5.05/5.25 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(6)
% 5.05/5.25 thf(fact_690_max__0__1_I6_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 5.05/5.25 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(6)
% 5.05/5.25 thf(fact_691_max__0__1_I6_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 5.05/5.25 = ( numeral_numeral_real @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(6)
% 5.05/5.25 thf(fact_692_max__0__1_I6_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 5.05/5.25 = ( numeral_numeral_rat @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(6)
% 5.05/5.25 thf(fact_693_max__0__1_I6_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 5.05/5.25 = ( numeral_numeral_nat @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(6)
% 5.05/5.25 thf(fact_694_max__0__1_I6_J,axiom,
% 5.05/5.25 ! [X: num] :
% 5.05/5.25 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 5.05/5.25 = ( numeral_numeral_int @ X ) ) ).
% 5.05/5.25
% 5.05/5.25 % max_0_1(6)
% 5.05/5.25 thf(fact_695_Nat_Odiff__diff__right,axiom,
% 5.05/5.25 ! [K: nat,J: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ J )
% 5.05/5.25 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.05/5.25 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.diff_diff_right
% 5.05/5.25 thf(fact_696_Nat_Oadd__diff__assoc2,axiom,
% 5.05/5.25 ! [K: nat,J: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ J )
% 5.05/5.25 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.05/5.25 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.add_diff_assoc2
% 5.05/5.25 thf(fact_697_Nat_Oadd__diff__assoc,axiom,
% 5.05/5.25 ! [K: nat,J: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ J )
% 5.05/5.25 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.05/5.25 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.add_diff_assoc
% 5.05/5.25 thf(fact_698_diff__Suc__1,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 5.05/5.25 = N2 ) ).
% 5.05/5.25
% 5.05/5.25 % diff_Suc_1
% 5.05/5.25 thf(fact_699_diff__Suc__diff__eq2,axiom,
% 5.05/5.25 ! [K: nat,J: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ J )
% 5.05/5.25 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 5.05/5.25 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_Suc_diff_eq2
% 5.05/5.25 thf(fact_700_diff__Suc__diff__eq1,axiom,
% 5.05/5.25 ! [K: nat,J: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ J )
% 5.05/5.25 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.05/5.25 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_Suc_diff_eq1
% 5.05/5.25 thf(fact_701_diff__commute,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.25 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.05/5.25 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_commute
% 5.05/5.25 thf(fact_702_nat__minus__add__max,axiom,
% 5.05/5.25 ! [N2: nat,M: nat] :
% 5.05/5.25 ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 5.05/5.25 = ( ord_max_nat @ N2 @ M ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_minus_add_max
% 5.05/5.25 thf(fact_703_nat__add__max__left,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,Q2: nat] :
% 5.05/5.25 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
% 5.05/5.25 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N2 @ Q2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_add_max_left
% 5.05/5.25 thf(fact_704_nat__add__max__right,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,Q2: nat] :
% 5.05/5.25 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
% 5.05/5.25 = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_add_max_right
% 5.05/5.25 thf(fact_705_nat__mult__max__left,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,Q2: nat] :
% 5.05/5.25 ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
% 5.05/5.25 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_mult_max_left
% 5.05/5.25 thf(fact_706_nat__mult__max__right,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,Q2: nat] :
% 5.05/5.25 ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
% 5.05/5.25 = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_mult_max_right
% 5.05/5.25 thf(fact_707_zero__induct__lemma,axiom,
% 5.05/5.25 ! [P: nat > $o,K: nat,I2: nat] :
% 5.05/5.25 ( ( P @ K )
% 5.05/5.25 => ( ! [N3: nat] :
% 5.05/5.25 ( ( P @ ( suc @ N3 ) )
% 5.05/5.25 => ( P @ N3 ) )
% 5.05/5.25 => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % zero_induct_lemma
% 5.05/5.25 thf(fact_708_less__imp__diff__less,axiom,
% 5.05/5.25 ! [J: nat,K: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ J @ K )
% 5.05/5.25 => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_imp_diff_less
% 5.05/5.25 thf(fact_709_diff__less__mono2,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,L2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ M @ N2 )
% 5.05/5.25 => ( ( ord_less_nat @ M @ L2 )
% 5.05/5.25 => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N2 ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_less_mono2
% 5.05/5.25 thf(fact_710_diff__le__mono2,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,L2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.25 => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N2 ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_le_mono2
% 5.05/5.25 thf(fact_711_le__diff__iff_H,axiom,
% 5.05/5.25 ! [A: nat,C: nat,B: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ A @ C )
% 5.05/5.25 => ( ( ord_less_eq_nat @ B @ C )
% 5.05/5.25 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.05/5.25 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % le_diff_iff'
% 5.05/5.25 thf(fact_712_diff__le__self,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 5.05/5.25
% 5.05/5.25 % diff_le_self
% 5.05/5.25 thf(fact_713_diff__le__mono,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,L2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.25 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N2 @ L2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_le_mono
% 5.05/5.25 thf(fact_714_Nat_Odiff__diff__eq,axiom,
% 5.05/5.25 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ M )
% 5.05/5.25 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.05/5.25 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.05/5.25 = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.diff_diff_eq
% 5.05/5.25 thf(fact_715_le__diff__iff,axiom,
% 5.05/5.25 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ M )
% 5.05/5.25 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.05/5.25 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.05/5.25 = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % le_diff_iff
% 5.05/5.25 thf(fact_716_eq__diff__iff,axiom,
% 5.05/5.25 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ M )
% 5.05/5.25 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.05/5.25 => ( ( ( minus_minus_nat @ M @ K )
% 5.05/5.25 = ( minus_minus_nat @ N2 @ K ) )
% 5.05/5.25 = ( M = N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % eq_diff_iff
% 5.05/5.25 thf(fact_717_Nat_Odiff__cancel,axiom,
% 5.05/5.25 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.05/5.25 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.diff_cancel
% 5.05/5.25 thf(fact_718_diff__cancel2,axiom,
% 5.05/5.25 ! [M: nat,K: nat,N2: nat] :
% 5.05/5.25 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.05/5.25 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_cancel2
% 5.05/5.25 thf(fact_719_diff__add__inverse,axiom,
% 5.05/5.25 ! [N2: nat,M: nat] :
% 5.05/5.25 ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 5.05/5.25 = M ) ).
% 5.05/5.25
% 5.05/5.25 % diff_add_inverse
% 5.05/5.25 thf(fact_720_diff__add__inverse2,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 5.05/5.25 = M ) ).
% 5.05/5.25
% 5.05/5.25 % diff_add_inverse2
% 5.05/5.25 thf(fact_721_diff__mult__distrib,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,K: nat] :
% 5.05/5.25 ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
% 5.05/5.25 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_mult_distrib
% 5.05/5.25 thf(fact_722_diff__mult__distrib2,axiom,
% 5.05/5.25 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.05/5.25 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_mult_distrib2
% 5.05/5.25 thf(fact_723_Suc__diff__Suc,axiom,
% 5.05/5.25 ! [N2: nat,M: nat] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ M )
% 5.05/5.25 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 5.05/5.25 = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_diff_Suc
% 5.05/5.25 thf(fact_724_diff__less__Suc,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_less_Suc
% 5.05/5.25 thf(fact_725_Suc__diff__le,axiom,
% 5.05/5.25 ! [N2: nat,M: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ N2 @ M )
% 5.05/5.25 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.05/5.25 = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_diff_le
% 5.05/5.25 thf(fact_726_diff__less__mono,axiom,
% 5.05/5.25 ! [A: nat,B: nat,C: nat] :
% 5.05/5.25 ( ( ord_less_nat @ A @ B )
% 5.05/5.25 => ( ( ord_less_eq_nat @ C @ A )
% 5.05/5.25 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_less_mono
% 5.05/5.25 thf(fact_727_less__diff__iff,axiom,
% 5.05/5.25 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ M )
% 5.05/5.25 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.05/5.25 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.05/5.25 = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_diff_iff
% 5.05/5.25 thf(fact_728_add__diff__inverse__nat,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ~ ( ord_less_nat @ M @ N2 )
% 5.05/5.25 => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 5.05/5.25 = M ) ) ).
% 5.05/5.25
% 5.05/5.25 % add_diff_inverse_nat
% 5.05/5.25 thf(fact_729_less__diff__conv,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.05/5.25 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_diff_conv
% 5.05/5.25 thf(fact_730_Nat_Ole__imp__diff__is__add,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.25 => ( ( ( minus_minus_nat @ J @ I2 )
% 5.05/5.25 = K )
% 5.05/5.25 = ( J
% 5.05/5.25 = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.le_imp_diff_is_add
% 5.05/5.25 thf(fact_731_Nat_Odiff__add__assoc2,axiom,
% 5.05/5.25 ! [K: nat,J: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ J )
% 5.05/5.25 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 5.05/5.25 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.diff_add_assoc2
% 5.05/5.25 thf(fact_732_Nat_Odiff__add__assoc,axiom,
% 5.05/5.25 ! [K: nat,J: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ J )
% 5.05/5.25 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.05/5.25 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.diff_add_assoc
% 5.05/5.25 thf(fact_733_Nat_Ole__diff__conv2,axiom,
% 5.05/5.25 ! [K: nat,J: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ J )
% 5.05/5.25 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.05/5.25 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.le_diff_conv2
% 5.05/5.25 thf(fact_734_le__diff__conv,axiom,
% 5.05/5.25 ! [J: nat,K: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.05/5.25 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % le_diff_conv
% 5.05/5.25 thf(fact_735_diff__Suc__eq__diff__pred,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.05/5.25 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_Suc_eq_diff_pred
% 5.05/5.25 thf(fact_736_less__diff__conv2,axiom,
% 5.05/5.25 ! [K: nat,J: nat,I2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ K @ J )
% 5.05/5.25 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.05/5.25 = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_diff_conv2
% 5.05/5.25 thf(fact_737_nat__eq__add__iff1,axiom,
% 5.05/5.25 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ J @ I2 )
% 5.05/5.25 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.05/5.25 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.05/5.25 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
% 5.05/5.25 = N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_eq_add_iff1
% 5.05/5.25 thf(fact_738_nat__eq__add__iff2,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.25 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.05/5.25 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.05/5.25 = ( M
% 5.05/5.25 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_eq_add_iff2
% 5.05/5.25 thf(fact_739_nat__le__add__iff1,axiom,
% 5.05/5.25 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ J @ I2 )
% 5.05/5.25 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.05/5.25 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_le_add_iff1
% 5.05/5.25 thf(fact_740_nat__le__add__iff2,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.25 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.05/5.25 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_le_add_iff2
% 5.05/5.25 thf(fact_741_nat__diff__add__eq1,axiom,
% 5.05/5.25 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ J @ I2 )
% 5.05/5.25 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.05/5.25 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_diff_add_eq1
% 5.05/5.25 thf(fact_742_nat__diff__add__eq2,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.25 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.05/5.25 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_diff_add_eq2
% 5.05/5.25 thf(fact_743_nat__less__add__iff1,axiom,
% 5.05/5.25 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ J @ I2 )
% 5.05/5.25 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.05/5.25 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_less_add_iff1
% 5.05/5.25 thf(fact_744_nat__less__add__iff2,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.25 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.05/5.25 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_less_add_iff2
% 5.05/5.25 thf(fact_745_n__not__Suc__n,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ( N2
% 5.05/5.25 != ( suc @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % n_not_Suc_n
% 5.05/5.25 thf(fact_746_Suc__inject,axiom,
% 5.05/5.25 ! [X: nat,Y: nat] :
% 5.05/5.25 ( ( ( suc @ X )
% 5.05/5.25 = ( suc @ Y ) )
% 5.05/5.25 => ( X = Y ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_inject
% 5.05/5.25 thf(fact_747_linorder__neqE__nat,axiom,
% 5.05/5.25 ! [X: nat,Y: nat] :
% 5.05/5.25 ( ( X != Y )
% 5.05/5.25 => ( ~ ( ord_less_nat @ X @ Y )
% 5.05/5.25 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % linorder_neqE_nat
% 5.05/5.25 thf(fact_748_infinite__descent,axiom,
% 5.05/5.25 ! [P: nat > $o,N2: nat] :
% 5.05/5.25 ( ! [N3: nat] :
% 5.05/5.25 ( ~ ( P @ N3 )
% 5.05/5.25 => ? [M3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ M3 @ N3 )
% 5.05/5.25 & ~ ( P @ M3 ) ) )
% 5.05/5.25 => ( P @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % infinite_descent
% 5.05/5.25 thf(fact_749_nat__less__induct,axiom,
% 5.05/5.25 ! [P: nat > $o,N2: nat] :
% 5.05/5.25 ( ! [N3: nat] :
% 5.05/5.25 ( ! [M3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ M3 @ N3 )
% 5.05/5.25 => ( P @ M3 ) )
% 5.05/5.25 => ( P @ N3 ) )
% 5.05/5.25 => ( P @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_less_induct
% 5.05/5.25 thf(fact_750_less__irrefl__nat,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 5.05/5.25
% 5.05/5.25 % less_irrefl_nat
% 5.05/5.25 thf(fact_751_less__not__refl3,axiom,
% 5.05/5.25 ! [S2: nat,T: nat] :
% 5.05/5.25 ( ( ord_less_nat @ S2 @ T )
% 5.05/5.25 => ( S2 != T ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_not_refl3
% 5.05/5.25 thf(fact_752_less__not__refl2,axiom,
% 5.05/5.25 ! [N2: nat,M: nat] :
% 5.05/5.25 ( ( ord_less_nat @ N2 @ M )
% 5.05/5.25 => ( M != N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_not_refl2
% 5.05/5.25 thf(fact_753_less__not__refl,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 5.05/5.25
% 5.05/5.25 % less_not_refl
% 5.05/5.25 thf(fact_754_nat__neq__iff,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( M != N2 )
% 5.05/5.25 = ( ( ord_less_nat @ M @ N2 )
% 5.05/5.25 | ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_neq_iff
% 5.05/5.25 thf(fact_755_Nat_Oex__has__greatest__nat,axiom,
% 5.05/5.25 ! [P: nat > $o,K: nat,B: nat] :
% 5.05/5.25 ( ( P @ K )
% 5.05/5.25 => ( ! [Y5: nat] :
% 5.05/5.25 ( ( P @ Y5 )
% 5.05/5.25 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.05/5.25 => ? [X3: nat] :
% 5.05/5.25 ( ( P @ X3 )
% 5.05/5.25 & ! [Y3: nat] :
% 5.05/5.25 ( ( P @ Y3 )
% 5.05/5.25 => ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.ex_has_greatest_nat
% 5.05/5.25 thf(fact_756_nat__le__linear,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.25 | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_le_linear
% 5.05/5.25 thf(fact_757_le__antisym,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.25 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.05/5.25 => ( M = N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % le_antisym
% 5.05/5.25 thf(fact_758_eq__imp__le,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( M = N2 )
% 5.05/5.25 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % eq_imp_le
% 5.05/5.25 thf(fact_759_le__trans,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.25 => ( ( ord_less_eq_nat @ J @ K )
% 5.05/5.25 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % le_trans
% 5.05/5.25 thf(fact_760_le__refl,axiom,
% 5.05/5.25 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 5.05/5.25
% 5.05/5.25 % le_refl
% 5.05/5.25 thf(fact_761_size__neq__size__imp__neq,axiom,
% 5.05/5.25 ! [X: char,Y: char] :
% 5.05/5.25 ( ( ( size_size_char @ X )
% 5.05/5.25 != ( size_size_char @ Y ) )
% 5.05/5.25 => ( X != Y ) ) ).
% 5.05/5.25
% 5.05/5.25 % size_neq_size_imp_neq
% 5.05/5.25 thf(fact_762_size__neq__size__imp__neq,axiom,
% 5.05/5.25 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 5.05/5.25 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 5.05/5.25 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 5.05/5.25 => ( X != Y ) ) ).
% 5.05/5.25
% 5.05/5.25 % size_neq_size_imp_neq
% 5.05/5.25 thf(fact_763_size__neq__size__imp__neq,axiom,
% 5.05/5.25 ! [X: list_o,Y: list_o] :
% 5.05/5.25 ( ( ( size_size_list_o @ X )
% 5.05/5.25 != ( size_size_list_o @ Y ) )
% 5.05/5.25 => ( X != Y ) ) ).
% 5.05/5.25
% 5.05/5.25 % size_neq_size_imp_neq
% 5.05/5.25 thf(fact_764_size__neq__size__imp__neq,axiom,
% 5.05/5.25 ! [X: list_int,Y: list_int] :
% 5.05/5.25 ( ( ( size_size_list_int @ X )
% 5.05/5.25 != ( size_size_list_int @ Y ) )
% 5.05/5.25 => ( X != Y ) ) ).
% 5.05/5.25
% 5.05/5.25 % size_neq_size_imp_neq
% 5.05/5.25 thf(fact_765_size__neq__size__imp__neq,axiom,
% 5.05/5.25 ! [X: num,Y: num] :
% 5.05/5.25 ( ( ( size_size_num @ X )
% 5.05/5.25 != ( size_size_num @ Y ) )
% 5.05/5.25 => ( X != Y ) ) ).
% 5.05/5.25
% 5.05/5.25 % size_neq_size_imp_neq
% 5.05/5.25 thf(fact_766_power2__commute,axiom,
% 5.05/5.25 ! [X: complex,Y: complex] :
% 5.05/5.25 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( power_power_complex @ ( minus_minus_complex @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_commute
% 5.05/5.25 thf(fact_767_power2__commute,axiom,
% 5.05/5.25 ! [X: real,Y: real] :
% 5.05/5.25 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( power_power_real @ ( minus_minus_real @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_commute
% 5.05/5.25 thf(fact_768_power2__commute,axiom,
% 5.05/5.25 ! [X: rat,Y: rat] :
% 5.05/5.25 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( power_power_rat @ ( minus_minus_rat @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_commute
% 5.05/5.25 thf(fact_769_power2__commute,axiom,
% 5.05/5.25 ! [X: int,Y: int] :
% 5.05/5.25 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( power_power_int @ ( minus_minus_int @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_commute
% 5.05/5.25 thf(fact_770_diff__le__diff__pow,axiom,
% 5.05/5.25 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.05/5.25 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % diff_le_diff_pow
% 5.05/5.25 thf(fact_771_not__less__less__Suc__eq,axiom,
% 5.05/5.25 ! [N2: nat,M: nat] :
% 5.05/5.25 ( ~ ( ord_less_nat @ N2 @ M )
% 5.05/5.25 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.05/5.25 = ( N2 = M ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % not_less_less_Suc_eq
% 5.05/5.25 thf(fact_772_strict__inc__induct,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,P: nat > $o] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ J )
% 5.05/5.25 => ( ! [I3: nat] :
% 5.05/5.25 ( ( J
% 5.05/5.25 = ( suc @ I3 ) )
% 5.05/5.25 => ( P @ I3 ) )
% 5.05/5.25 => ( ! [I3: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ J )
% 5.05/5.25 => ( ( P @ ( suc @ I3 ) )
% 5.05/5.25 => ( P @ I3 ) ) )
% 5.05/5.25 => ( P @ I2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % strict_inc_induct
% 5.05/5.25 thf(fact_773_less__Suc__induct,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,P: nat > nat > $o] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ J )
% 5.05/5.25 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 5.05/5.25 => ( ! [I3: nat,J2: nat,K2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ J2 )
% 5.05/5.25 => ( ( ord_less_nat @ J2 @ K2 )
% 5.05/5.25 => ( ( P @ I3 @ J2 )
% 5.05/5.25 => ( ( P @ J2 @ K2 )
% 5.05/5.25 => ( P @ I3 @ K2 ) ) ) ) )
% 5.05/5.25 => ( P @ I2 @ J ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_Suc_induct
% 5.05/5.25 thf(fact_774_less__trans__Suc,axiom,
% 5.05/5.25 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ J )
% 5.05/5.25 => ( ( ord_less_nat @ J @ K )
% 5.05/5.25 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_trans_Suc
% 5.05/5.25 thf(fact_775_Suc__less__SucD,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.05/5.25 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_less_SucD
% 5.05/5.25 thf(fact_776_less__antisym,axiom,
% 5.05/5.25 ! [N2: nat,M: nat] :
% 5.05/5.25 ( ~ ( ord_less_nat @ N2 @ M )
% 5.05/5.25 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.05/5.25 => ( M = N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_antisym
% 5.05/5.25 thf(fact_777_Suc__less__eq2,axiom,
% 5.05/5.25 ! [N2: nat,M: nat] :
% 5.05/5.25 ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.05/5.25 = ( ? [M4: nat] :
% 5.05/5.25 ( ( M
% 5.05/5.25 = ( suc @ M4 ) )
% 5.05/5.25 & ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_less_eq2
% 5.05/5.25 thf(fact_778_All__less__Suc,axiom,
% 5.05/5.25 ! [N2: nat,P: nat > $o] :
% 5.05/5.25 ( ( ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 5.05/5.25 => ( P @ I5 ) ) )
% 5.05/5.25 = ( ( P @ N2 )
% 5.05/5.25 & ! [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ N2 )
% 5.05/5.25 => ( P @ I5 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % All_less_Suc
% 5.05/5.25 thf(fact_779_not__less__eq,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 5.05/5.25 = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % not_less_eq
% 5.05/5.25 thf(fact_780_less__Suc__eq,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.05/5.25 = ( ( ord_less_nat @ M @ N2 )
% 5.05/5.25 | ( M = N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_Suc_eq
% 5.05/5.25 thf(fact_781_Ex__less__Suc,axiom,
% 5.05/5.25 ! [N2: nat,P: nat > $o] :
% 5.05/5.25 ( ( ? [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 5.05/5.25 & ( P @ I5 ) ) )
% 5.05/5.25 = ( ( P @ N2 )
% 5.05/5.25 | ? [I5: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I5 @ N2 )
% 5.05/5.25 & ( P @ I5 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Ex_less_Suc
% 5.05/5.25 thf(fact_782_less__SucI,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ M @ N2 )
% 5.05/5.25 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_SucI
% 5.05/5.25 thf(fact_783_less__SucE,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.05/5.25 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.05/5.25 => ( M = N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_SucE
% 5.05/5.25 thf(fact_784_Suc__lessI,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ M @ N2 )
% 5.05/5.25 => ( ( ( suc @ M )
% 5.05/5.25 != N2 )
% 5.05/5.25 => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_lessI
% 5.05/5.25 thf(fact_785_Suc__lessE,axiom,
% 5.05/5.25 ! [I2: nat,K: nat] :
% 5.05/5.25 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 5.05/5.25 => ~ ! [J2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ J2 )
% 5.05/5.25 => ( K
% 5.05/5.25 != ( suc @ J2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_lessE
% 5.05/5.25 thf(fact_786_Suc__lessD,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 5.05/5.25 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_lessD
% 5.05/5.25 thf(fact_787_Nat_OlessE,axiom,
% 5.05/5.25 ! [I2: nat,K: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ K )
% 5.05/5.25 => ( ( K
% 5.05/5.25 != ( suc @ I2 ) )
% 5.05/5.25 => ~ ! [J2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I2 @ J2 )
% 5.05/5.25 => ( K
% 5.05/5.25 != ( suc @ J2 ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Nat.lessE
% 5.05/5.25 thf(fact_788_power2__diff,axiom,
% 5.05/5.25 ! [X: complex,Y: complex] :
% 5.05/5.25 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_diff
% 5.05/5.25 thf(fact_789_power2__diff,axiom,
% 5.05/5.25 ! [X: real,Y: real] :
% 5.05/5.25 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_diff
% 5.05/5.25 thf(fact_790_power2__diff,axiom,
% 5.05/5.25 ! [X: rat,Y: rat] :
% 5.05/5.25 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_diff
% 5.05/5.25 thf(fact_791_power2__diff,axiom,
% 5.05/5.25 ! [X: int,Y: int] :
% 5.05/5.25 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.05/5.25 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % power2_diff
% 5.05/5.25 thf(fact_792_transitive__stepwise__le,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,R: nat > nat > $o] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.25 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 5.05/5.25 => ( ! [X3: nat,Y5: nat,Z4: nat] :
% 5.05/5.25 ( ( R @ X3 @ Y5 )
% 5.05/5.25 => ( ( R @ Y5 @ Z4 )
% 5.05/5.25 => ( R @ X3 @ Z4 ) ) )
% 5.05/5.25 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 5.05/5.25 => ( R @ M @ N2 ) ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % transitive_stepwise_le
% 5.05/5.25 thf(fact_793_nat__induct__at__least,axiom,
% 5.05/5.25 ! [M: nat,N2: nat,P: nat > $o] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.25 => ( ( P @ M )
% 5.05/5.25 => ( ! [N3: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ N3 )
% 5.05/5.25 => ( ( P @ N3 )
% 5.05/5.25 => ( P @ ( suc @ N3 ) ) ) )
% 5.05/5.25 => ( P @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_induct_at_least
% 5.05/5.25 thf(fact_794_full__nat__induct,axiom,
% 5.05/5.25 ! [P: nat > $o,N2: nat] :
% 5.05/5.25 ( ! [N3: nat] :
% 5.05/5.25 ( ! [M3: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N3 )
% 5.05/5.25 => ( P @ M3 ) )
% 5.05/5.25 => ( P @ N3 ) )
% 5.05/5.25 => ( P @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % full_nat_induct
% 5.05/5.25 thf(fact_795_not__less__eq__eq,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 5.05/5.25 = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 5.05/5.25
% 5.05/5.25 % not_less_eq_eq
% 5.05/5.25 thf(fact_796_Suc__n__not__le__n,axiom,
% 5.05/5.25 ! [N2: nat] :
% 5.05/5.25 ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_n_not_le_n
% 5.05/5.25 thf(fact_797_le__Suc__eq,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.05/5.25 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.25 | ( M
% 5.05/5.25 = ( suc @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % le_Suc_eq
% 5.05/5.25 thf(fact_798_Suc__le__D,axiom,
% 5.05/5.25 ! [N2: nat,M5: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M5 )
% 5.05/5.25 => ? [M2: nat] :
% 5.05/5.25 ( M5
% 5.05/5.25 = ( suc @ M2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_le_D
% 5.05/5.25 thf(fact_799_le__SucI,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.25 => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % le_SucI
% 5.05/5.25 thf(fact_800_le__SucE,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.05/5.25 => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.25 => ( M
% 5.05/5.25 = ( suc @ N2 ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % le_SucE
% 5.05/5.25 thf(fact_801_Suc__leD,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.05/5.25 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.05/5.25
% 5.05/5.25 % Suc_leD
% 5.05/5.25 thf(fact_802_nat__arith_Osuc1,axiom,
% 5.05/5.25 ! [A2: nat,K: nat,A: nat] :
% 5.05/5.25 ( ( A2
% 5.05/5.25 = ( plus_plus_nat @ K @ A ) )
% 5.05/5.25 => ( ( suc @ A2 )
% 5.05/5.25 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % nat_arith.suc1
% 5.05/5.25 thf(fact_803_add__Suc,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 5.05/5.25 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % add_Suc
% 5.05/5.25 thf(fact_804_add__Suc__shift,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 5.05/5.25 = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % add_Suc_shift
% 5.05/5.25 thf(fact_805_less__mono__imp__le__mono,axiom,
% 5.05/5.25 ! [F: nat > nat,I2: nat,J: nat] :
% 5.05/5.25 ( ! [I3: nat,J2: nat] :
% 5.05/5.25 ( ( ord_less_nat @ I3 @ J2 )
% 5.05/5.25 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 5.05/5.25 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.25 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 5.05/5.25
% 5.05/5.25 % less_mono_imp_le_mono
% 5.05/5.25 thf(fact_806_le__neq__implies__less,axiom,
% 5.05/5.25 ! [M: nat,N2: nat] :
% 5.05/5.25 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.25 => ( ( M != N2 )
% 5.05/5.25 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_neq_implies_less
% 5.05/5.26 thf(fact_807_less__or__eq__imp__le,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ( ord_less_nat @ M @ N2 )
% 5.05/5.26 | ( M = N2 ) )
% 5.05/5.26 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_or_eq_imp_le
% 5.05/5.26 thf(fact_808_le__eq__less__or__eq,axiom,
% 5.05/5.26 ( ord_less_eq_nat
% 5.05/5.26 = ( ^ [M6: nat,N: nat] :
% 5.05/5.26 ( ( ord_less_nat @ M6 @ N )
% 5.05/5.26 | ( M6 = N ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_eq_less_or_eq
% 5.05/5.26 thf(fact_809_less__imp__le__nat,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_nat @ M @ N2 )
% 5.05/5.26 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_imp_le_nat
% 5.05/5.26 thf(fact_810_nat__less__le,axiom,
% 5.05/5.26 ( ord_less_nat
% 5.05/5.26 = ( ^ [M6: nat,N: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ M6 @ N )
% 5.05/5.26 & ( M6 != N ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % nat_less_le
% 5.05/5.26 thf(fact_811_add__lessD1,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.26 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.05/5.26 => ( ord_less_nat @ I2 @ K ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_lessD1
% 5.05/5.26 thf(fact_812_add__less__mono,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.26 ( ( ord_less_nat @ I2 @ J )
% 5.05/5.26 => ( ( ord_less_nat @ K @ L2 )
% 5.05/5.26 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_less_mono
% 5.05/5.26 thf(fact_813_not__add__less1,axiom,
% 5.05/5.26 ! [I2: nat,J: nat] :
% 5.05/5.26 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 5.05/5.26
% 5.05/5.26 % not_add_less1
% 5.05/5.26 thf(fact_814_not__add__less2,axiom,
% 5.05/5.26 ! [J: nat,I2: nat] :
% 5.05/5.26 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 5.05/5.26
% 5.05/5.26 % not_add_less2
% 5.05/5.26 thf(fact_815_add__less__mono1,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.26 ( ( ord_less_nat @ I2 @ J )
% 5.05/5.26 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_less_mono1
% 5.05/5.26 thf(fact_816_trans__less__add1,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,M: nat] :
% 5.05/5.26 ( ( ord_less_nat @ I2 @ J )
% 5.05/5.26 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % trans_less_add1
% 5.05/5.26 thf(fact_817_trans__less__add2,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,M: nat] :
% 5.05/5.26 ( ( ord_less_nat @ I2 @ J )
% 5.05/5.26 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % trans_less_add2
% 5.05/5.26 thf(fact_818_less__add__eq__less,axiom,
% 5.05/5.26 ! [K: nat,L2: nat,M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_nat @ K @ L2 )
% 5.05/5.26 => ( ( ( plus_plus_nat @ M @ L2 )
% 5.05/5.26 = ( plus_plus_nat @ K @ N2 ) )
% 5.05/5.26 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_eq_less
% 5.05/5.26 thf(fact_819_Suc__mult__cancel1,axiom,
% 5.05/5.26 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.26 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.05/5.26 = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.05/5.26 = ( M = N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % Suc_mult_cancel1
% 5.05/5.26 thf(fact_820_add__leE,axiom,
% 5.05/5.26 ! [M: nat,K: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.05/5.26 => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.26 => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_leE
% 5.05/5.26 thf(fact_821_le__add1,axiom,
% 5.05/5.26 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_add1
% 5.05/5.26 thf(fact_822_le__add2,axiom,
% 5.05/5.26 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_add2
% 5.05/5.26 thf(fact_823_add__leD1,axiom,
% 5.05/5.26 ! [M: nat,K: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.05/5.26 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_leD1
% 5.05/5.26 thf(fact_824_add__leD2,axiom,
% 5.05/5.26 ! [M: nat,K: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.05/5.26 => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_leD2
% 5.05/5.26 thf(fact_825_le__Suc__ex,axiom,
% 5.05/5.26 ! [K: nat,L2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ K @ L2 )
% 5.05/5.26 => ? [N3: nat] :
% 5.05/5.26 ( L2
% 5.05/5.26 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_Suc_ex
% 5.05/5.26 thf(fact_826_add__le__mono,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.26 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.05/5.26 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_le_mono
% 5.05/5.26 thf(fact_827_add__le__mono1,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.26 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_le_mono1
% 5.05/5.26 thf(fact_828_trans__le__add1,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,M: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.26 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % trans_le_add1
% 5.05/5.26 thf(fact_829_trans__le__add2,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,M: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.26 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % trans_le_add2
% 5.05/5.26 thf(fact_830_nat__le__iff__add,axiom,
% 5.05/5.26 ( ord_less_eq_nat
% 5.05/5.26 = ( ^ [M6: nat,N: nat] :
% 5.05/5.26 ? [K3: nat] :
% 5.05/5.26 ( N
% 5.05/5.26 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % nat_le_iff_add
% 5.05/5.26 thf(fact_831_le__cube,axiom,
% 5.05/5.26 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_cube
% 5.05/5.26 thf(fact_832_le__square,axiom,
% 5.05/5.26 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_square
% 5.05/5.26 thf(fact_833_mult__le__mono,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.26 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.05/5.26 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_le_mono
% 5.05/5.26 thf(fact_834_mult__le__mono1,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.26 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_le_mono1
% 5.05/5.26 thf(fact_835_mult__le__mono2,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,K: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.26 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_le_mono2
% 5.05/5.26 thf(fact_836_add__mult__distrib,axiom,
% 5.05/5.26 ! [M: nat,N2: nat,K: nat] :
% 5.05/5.26 ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
% 5.05/5.26 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_mult_distrib
% 5.05/5.26 thf(fact_837_add__mult__distrib2,axiom,
% 5.05/5.26 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.26 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
% 5.05/5.26 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_mult_distrib2
% 5.05/5.26 thf(fact_838_left__add__mult__distrib,axiom,
% 5.05/5.26 ! [I2: nat,U: nat,J: nat,K: nat] :
% 5.05/5.26 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.05/5.26 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) ).
% 5.05/5.26
% 5.05/5.26 % left_add_mult_distrib
% 5.05/5.26 thf(fact_839_nat__mult__1,axiom,
% 5.05/5.26 ! [N2: nat] :
% 5.05/5.26 ( ( times_times_nat @ one_one_nat @ N2 )
% 5.05/5.26 = N2 ) ).
% 5.05/5.26
% 5.05/5.26 % nat_mult_1
% 5.05/5.26 thf(fact_840_nat__mult__1__right,axiom,
% 5.05/5.26 ! [N2: nat] :
% 5.05/5.26 ( ( times_times_nat @ N2 @ one_one_nat )
% 5.05/5.26 = N2 ) ).
% 5.05/5.26
% 5.05/5.26 % nat_mult_1_right
% 5.05/5.26 thf(fact_841_L2__set__mult__ineq__lemma,axiom,
% 5.05/5.26 ! [A: real,C: real,B: real,D: 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 @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % L2_set_mult_ineq_lemma
% 5.05/5.26 thf(fact_842_four__x__squared,axiom,
% 5.05/5.26 ! [X: real] :
% 5.05/5.26 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.05/5.26 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % four_x_squared
% 5.05/5.26 thf(fact_843_lift__Suc__mono__less__iff,axiom,
% 5.05/5.26 ! [F: nat > real,N2: nat,M: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_real @ ( F @ N2 ) @ ( F @ M ) )
% 5.05/5.26 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_less_iff
% 5.05/5.26 thf(fact_844_lift__Suc__mono__less__iff,axiom,
% 5.05/5.26 ! [F: nat > rat,N2: nat,M: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_rat @ ( F @ N2 ) @ ( F @ M ) )
% 5.05/5.26 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_less_iff
% 5.05/5.26 thf(fact_845_lift__Suc__mono__less__iff,axiom,
% 5.05/5.26 ! [F: nat > num,N2: nat,M: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 5.05/5.26 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_less_iff
% 5.05/5.26 thf(fact_846_lift__Suc__mono__less__iff,axiom,
% 5.05/5.26 ! [F: nat > nat,N2: nat,M: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 5.05/5.26 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_less_iff
% 5.05/5.26 thf(fact_847_lift__Suc__mono__less__iff,axiom,
% 5.05/5.26 ! [F: nat > int,N2: nat,M: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 5.05/5.26 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_less_iff
% 5.05/5.26 thf(fact_848_lift__Suc__mono__less,axiom,
% 5.05/5.26 ! [F: nat > real,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_real @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_less
% 5.05/5.26 thf(fact_849_lift__Suc__mono__less,axiom,
% 5.05/5.26 ! [F: nat > rat,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_rat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_less
% 5.05/5.26 thf(fact_850_lift__Suc__mono__less,axiom,
% 5.05/5.26 ! [F: nat > num,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_less
% 5.05/5.26 thf(fact_851_lift__Suc__mono__less,axiom,
% 5.05/5.26 ! [F: nat > nat,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_less
% 5.05/5.26 thf(fact_852_lift__Suc__mono__less,axiom,
% 5.05/5.26 ! [F: nat > int,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_less
% 5.05/5.26 thf(fact_853_lift__Suc__antimono__le,axiom,
% 5.05/5.26 ! [F: nat > set_int,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_eq_set_int @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_antimono_le
% 5.05/5.26 thf(fact_854_lift__Suc__antimono__le,axiom,
% 5.05/5.26 ! [F: nat > rat,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_antimono_le
% 5.05/5.26 thf(fact_855_lift__Suc__antimono__le,axiom,
% 5.05/5.26 ! [F: nat > num,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_antimono_le
% 5.05/5.26 thf(fact_856_lift__Suc__antimono__le,axiom,
% 5.05/5.26 ! [F: nat > nat,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_antimono_le
% 5.05/5.26 thf(fact_857_lift__Suc__antimono__le,axiom,
% 5.05/5.26 ! [F: nat > int,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_antimono_le
% 5.05/5.26 thf(fact_858_lift__Suc__mono__le,axiom,
% 5.05/5.26 ! [F: nat > set_int,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_le
% 5.05/5.26 thf(fact_859_lift__Suc__mono__le,axiom,
% 5.05/5.26 ! [F: nat > rat,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_le
% 5.05/5.26 thf(fact_860_lift__Suc__mono__le,axiom,
% 5.05/5.26 ! [F: nat > num,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_le
% 5.05/5.26 thf(fact_861_lift__Suc__mono__le,axiom,
% 5.05/5.26 ! [F: nat > nat,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_le
% 5.05/5.26 thf(fact_862_lift__Suc__mono__le,axiom,
% 5.05/5.26 ! [F: nat > int,N2: nat,N5: nat] :
% 5.05/5.26 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.05/5.26 => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % lift_Suc_mono_le
% 5.05/5.26 thf(fact_863_le__imp__less__Suc,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.26 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_imp_less_Suc
% 5.05/5.26 thf(fact_864_less__eq__Suc__le,axiom,
% 5.05/5.26 ( ord_less_nat
% 5.05/5.26 = ( ^ [N: nat] : ( ord_less_eq_nat @ ( suc @ N ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_eq_Suc_le
% 5.05/5.26 thf(fact_865_less__Suc__eq__le,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.05/5.26 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_Suc_eq_le
% 5.05/5.26 thf(fact_866_le__less__Suc__eq,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ M @ N2 )
% 5.05/5.26 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.05/5.26 = ( N2 = M ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_less_Suc_eq
% 5.05/5.26 thf(fact_867_Suc__le__lessD,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.05/5.26 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % Suc_le_lessD
% 5.05/5.26 thf(fact_868_inc__induct,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,P: nat > $o] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.26 => ( ( P @ J )
% 5.05/5.26 => ( ! [N3: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.05/5.26 => ( ( ord_less_nat @ N3 @ J )
% 5.05/5.26 => ( ( P @ ( suc @ N3 ) )
% 5.05/5.26 => ( P @ N3 ) ) ) )
% 5.05/5.26 => ( P @ I2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % inc_induct
% 5.05/5.26 thf(fact_869_dec__induct,axiom,
% 5.05/5.26 ! [I2: nat,J: nat,P: nat > $o] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.26 => ( ( P @ I2 )
% 5.05/5.26 => ( ! [N3: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.05/5.26 => ( ( ord_less_nat @ N3 @ J )
% 5.05/5.26 => ( ( P @ N3 )
% 5.05/5.26 => ( P @ ( suc @ N3 ) ) ) ) )
% 5.05/5.26 => ( P @ J ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % dec_induct
% 5.05/5.26 thf(fact_870_Suc__le__eq,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.05/5.26 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % Suc_le_eq
% 5.05/5.26 thf(fact_871_Suc__leI,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_nat @ M @ N2 )
% 5.05/5.26 => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % Suc_leI
% 5.05/5.26 thf(fact_872_less__imp__Suc__add,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_nat @ M @ N2 )
% 5.05/5.26 => ? [K2: nat] :
% 5.05/5.26 ( N2
% 5.05/5.26 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_imp_Suc_add
% 5.05/5.26 thf(fact_873_less__iff__Suc__add,axiom,
% 5.05/5.26 ( ord_less_nat
% 5.05/5.26 = ( ^ [M6: nat,N: nat] :
% 5.05/5.26 ? [K3: nat] :
% 5.05/5.26 ( N
% 5.05/5.26 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_iff_Suc_add
% 5.05/5.26 thf(fact_874_less__add__Suc2,axiom,
% 5.05/5.26 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_Suc2
% 5.05/5.26 thf(fact_875_less__add__Suc1,axiom,
% 5.05/5.26 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_Suc1
% 5.05/5.26 thf(fact_876_less__natE,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_nat @ M @ N2 )
% 5.05/5.26 => ~ ! [Q3: nat] :
% 5.05/5.26 ( N2
% 5.05/5.26 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_natE
% 5.05/5.26 thf(fact_877_Suc__mult__less__cancel1,axiom,
% 5.05/5.26 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.05/5.26 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % Suc_mult_less_cancel1
% 5.05/5.26 thf(fact_878_mono__nat__linear__lb,axiom,
% 5.05/5.26 ! [F: nat > nat,M: nat,K: nat] :
% 5.05/5.26 ( ! [M2: nat,N3: nat] :
% 5.05/5.26 ( ( ord_less_nat @ M2 @ N3 )
% 5.05/5.26 => ( ord_less_nat @ ( F @ M2 ) @ ( F @ N3 ) ) )
% 5.05/5.26 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % mono_nat_linear_lb
% 5.05/5.26 thf(fact_879_Suc__mult__le__cancel1,axiom,
% 5.05/5.26 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.05/5.26 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % Suc_mult_le_cancel1
% 5.05/5.26 thf(fact_880_mult__Suc,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 5.05/5.26 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_Suc
% 5.05/5.26 thf(fact_881_Suc__eq__plus1,axiom,
% 5.05/5.26 ( suc
% 5.05/5.26 = ( ^ [N: nat] : ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % Suc_eq_plus1
% 5.05/5.26 thf(fact_882_plus__1__eq__Suc,axiom,
% 5.05/5.26 ( ( plus_plus_nat @ one_one_nat )
% 5.05/5.26 = suc ) ).
% 5.05/5.26
% 5.05/5.26 % plus_1_eq_Suc
% 5.05/5.26 thf(fact_883_Suc__eq__plus1__left,axiom,
% 5.05/5.26 ( suc
% 5.05/5.26 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.05/5.26
% 5.05/5.26 % Suc_eq_plus1_left
% 5.05/5.26 thf(fact_884_vebt__insert_Osimps_I5_J,axiom,
% 5.05/5.26 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.05/5.26 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.05/5.26 = ( if_VEBT_VEBT
% 5.05/5.26 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.26 & ~ ( ( X = Mi )
% 5.05/5.26 | ( X = Ma ) ) )
% 5.05/5.26 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( 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 @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( 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 @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.05/5.26 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % vebt_insert.simps(5)
% 5.05/5.26 thf(fact_885_le__add__diff__inverse2,axiom,
% 5.05/5.26 ! [B: real,A: real] :
% 5.05/5.26 ( ( ord_less_eq_real @ B @ A )
% 5.05/5.26 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_add_diff_inverse2
% 5.05/5.26 thf(fact_886_le__add__diff__inverse2,axiom,
% 5.05/5.26 ! [B: rat,A: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.26 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_add_diff_inverse2
% 5.05/5.26 thf(fact_887_le__add__diff__inverse2,axiom,
% 5.05/5.26 ! [B: nat,A: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.26 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_add_diff_inverse2
% 5.05/5.26 thf(fact_888_le__add__diff__inverse2,axiom,
% 5.05/5.26 ! [B: int,A: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ B @ A )
% 5.05/5.26 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_add_diff_inverse2
% 5.05/5.26 thf(fact_889_le__add__diff__inverse,axiom,
% 5.05/5.26 ! [B: real,A: real] :
% 5.05/5.26 ( ( ord_less_eq_real @ B @ A )
% 5.05/5.26 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_add_diff_inverse
% 5.05/5.26 thf(fact_890_le__add__diff__inverse,axiom,
% 5.05/5.26 ! [B: rat,A: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.26 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_add_diff_inverse
% 5.05/5.26 thf(fact_891_le__add__diff__inverse,axiom,
% 5.05/5.26 ! [B: nat,A: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.26 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_add_diff_inverse
% 5.05/5.26 thf(fact_892_le__add__diff__inverse,axiom,
% 5.05/5.26 ! [B: int,A: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ B @ A )
% 5.05/5.26 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_add_diff_inverse
% 5.05/5.26 thf(fact_893_pred__less__length__list,axiom,
% 5.05/5.26 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.26 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.05/5.26 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.26 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.26 = ( if_option_nat
% 5.05/5.26 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 != none_nat )
% 5.05/5.26 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.26 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 @ ( if_option_nat
% 5.05/5.26 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.26 = none_nat )
% 5.05/5.26 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.05/5.26 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % pred_less_length_list
% 5.05/5.26 thf(fact_894_pred__lesseq__max,axiom,
% 5.05/5.26 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.26 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.05/5.26 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.26 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.26 @ ( if_option_nat
% 5.05/5.26 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 != none_nat )
% 5.05/5.26 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.26 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 @ ( if_option_nat
% 5.05/5.26 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.26 = none_nat )
% 5.05/5.26 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.05/5.26 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.05/5.26 @ none_nat ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % pred_lesseq_max
% 5.05/5.26 thf(fact_895_succ__greatereq__min,axiom,
% 5.05/5.26 ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.26 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.05/5.26 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.26 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.26 @ ( if_option_nat
% 5.05/5.26 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 != none_nat )
% 5.05/5.26 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.26 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 @ ( if_option_nat
% 5.05/5.26 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.26 = none_nat )
% 5.05/5.26 @ none_nat
% 5.05/5.26 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.05/5.26 @ none_nat ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % succ_greatereq_min
% 5.05/5.26 thf(fact_896_succ__less__length__list,axiom,
% 5.05/5.26 ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.05/5.26 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.05/5.26 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.26 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.05/5.26 = ( if_option_nat
% 5.05/5.26 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 != none_nat )
% 5.05/5.26 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.26 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 @ ( if_option_nat
% 5.05/5.26 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.26 = none_nat )
% 5.05/5.26 @ none_nat
% 5.05/5.26 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % succ_less_length_list
% 5.05/5.26 thf(fact_897_mul__def,axiom,
% 5.05/5.26 ( vEBT_VEBT_mul
% 5.05/5.26 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.05/5.26
% 5.05/5.26 % mul_def
% 5.05/5.26 thf(fact_898_add__def,axiom,
% 5.05/5.26 ( vEBT_VEBT_add
% 5.05/5.26 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_def
% 5.05/5.26 thf(fact_899_div__exp__eq,axiom,
% 5.05/5.26 ! [A: nat,M: nat,N2: nat] :
% 5.05/5.26 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.26 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % div_exp_eq
% 5.05/5.26 thf(fact_900_div__exp__eq,axiom,
% 5.05/5.26 ! [A: int,M: nat,N2: nat] :
% 5.05/5.26 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.05/5.26 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % div_exp_eq
% 5.05/5.26 thf(fact_901_field__less__half__sum,axiom,
% 5.05/5.26 ! [X: real,Y: real] :
% 5.05/5.26 ( ( ord_less_real @ X @ Y )
% 5.05/5.26 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % field_less_half_sum
% 5.05/5.26 thf(fact_902_field__less__half__sum,axiom,
% 5.05/5.26 ! [X: rat,Y: rat] :
% 5.05/5.26 ( ( ord_less_rat @ X @ Y )
% 5.05/5.26 => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % field_less_half_sum
% 5.05/5.26 thf(fact_903_vebt__maxt_Osimps_I3_J,axiom,
% 5.05/5.26 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.05/5.26 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.05/5.26 = ( some_nat @ Ma ) ) ).
% 5.05/5.26
% 5.05/5.26 % vebt_maxt.simps(3)
% 5.05/5.26 thf(fact_904_add__shift,axiom,
% 5.05/5.26 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.26 ( ( ( plus_plus_nat @ X @ Y )
% 5.05/5.26 = Z )
% 5.05/5.26 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.05/5.26 = ( some_nat @ Z ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_shift
% 5.05/5.26 thf(fact_905_mul__shift,axiom,
% 5.05/5.26 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.26 ( ( ( times_times_nat @ X @ Y )
% 5.05/5.26 = Z )
% 5.05/5.26 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.05/5.26 = ( some_nat @ Z ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % mul_shift
% 5.05/5.26 thf(fact_906_real__divide__square__eq,axiom,
% 5.05/5.26 ! [R2: real,A: real] :
% 5.05/5.26 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 5.05/5.26 = ( divide_divide_real @ A @ R2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % real_divide_square_eq
% 5.05/5.26 thf(fact_907_bits__div__by__1,axiom,
% 5.05/5.26 ! [A: nat] :
% 5.05/5.26 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % bits_div_by_1
% 5.05/5.26 thf(fact_908_bits__div__by__1,axiom,
% 5.05/5.26 ! [A: int] :
% 5.05/5.26 ( ( divide_divide_int @ A @ one_one_int )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % bits_div_by_1
% 5.05/5.26 thf(fact_909_div__by__1,axiom,
% 5.05/5.26 ! [A: complex] :
% 5.05/5.26 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % div_by_1
% 5.05/5.26 thf(fact_910_div__by__1,axiom,
% 5.05/5.26 ! [A: real] :
% 5.05/5.26 ( ( divide_divide_real @ A @ one_one_real )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % div_by_1
% 5.05/5.26 thf(fact_911_div__by__1,axiom,
% 5.05/5.26 ! [A: rat] :
% 5.05/5.26 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % div_by_1
% 5.05/5.26 thf(fact_912_div__by__1,axiom,
% 5.05/5.26 ! [A: nat] :
% 5.05/5.26 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % div_by_1
% 5.05/5.26 thf(fact_913_div__by__1,axiom,
% 5.05/5.26 ! [A: int] :
% 5.05/5.26 ( ( divide_divide_int @ A @ one_one_int )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % div_by_1
% 5.05/5.26 thf(fact_914_less__eq__real__def,axiom,
% 5.05/5.26 ( ord_less_eq_real
% 5.05/5.26 = ( ^ [X2: real,Y2: real] :
% 5.05/5.26 ( ( ord_less_real @ X2 @ Y2 )
% 5.05/5.26 | ( X2 = Y2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_eq_real_def
% 5.05/5.26 thf(fact_915_complete__real,axiom,
% 5.05/5.26 ! [S3: set_real] :
% 5.05/5.26 ( ? [X5: real] : ( member_real @ X5 @ S3 )
% 5.05/5.26 => ( ? [Z5: real] :
% 5.05/5.26 ! [X3: real] :
% 5.05/5.26 ( ( member_real @ X3 @ S3 )
% 5.05/5.26 => ( ord_less_eq_real @ X3 @ Z5 ) )
% 5.05/5.26 => ? [Y5: real] :
% 5.05/5.26 ( ! [X5: real] :
% 5.05/5.26 ( ( member_real @ X5 @ S3 )
% 5.05/5.26 => ( ord_less_eq_real @ X5 @ Y5 ) )
% 5.05/5.26 & ! [Z5: real] :
% 5.05/5.26 ( ! [X3: real] :
% 5.05/5.26 ( ( member_real @ X3 @ S3 )
% 5.05/5.26 => ( ord_less_eq_real @ X3 @ Z5 ) )
% 5.05/5.26 => ( ord_less_eq_real @ Y5 @ Z5 ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % complete_real
% 5.05/5.26 thf(fact_916_real__arch__pow,axiom,
% 5.05/5.26 ! [X: real,Y: real] :
% 5.05/5.26 ( ( ord_less_real @ one_one_real @ X )
% 5.05/5.26 => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N3 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % real_arch_pow
% 5.05/5.26 thf(fact_917_linorder__neqE__linordered__idom,axiom,
% 5.05/5.26 ! [X: real,Y: real] :
% 5.05/5.26 ( ( X != Y )
% 5.05/5.26 => ( ~ ( ord_less_real @ X @ Y )
% 5.05/5.26 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % linorder_neqE_linordered_idom
% 5.05/5.26 thf(fact_918_linorder__neqE__linordered__idom,axiom,
% 5.05/5.26 ! [X: rat,Y: rat] :
% 5.05/5.26 ( ( X != Y )
% 5.05/5.26 => ( ~ ( ord_less_rat @ X @ Y )
% 5.05/5.26 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % linorder_neqE_linordered_idom
% 5.05/5.26 thf(fact_919_linorder__neqE__linordered__idom,axiom,
% 5.05/5.26 ! [X: int,Y: int] :
% 5.05/5.26 ( ( X != Y )
% 5.05/5.26 => ( ~ ( ord_less_int @ X @ Y )
% 5.05/5.26 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % linorder_neqE_linordered_idom
% 5.05/5.26 thf(fact_920_combine__common__factor,axiom,
% 5.05/5.26 ! [A: real,E: real,B: real,C: real] :
% 5.05/5.26 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 5.05/5.26 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 5.05/5.26
% 5.05/5.26 % combine_common_factor
% 5.05/5.26 thf(fact_921_combine__common__factor,axiom,
% 5.05/5.26 ! [A: rat,E: rat,B: rat,C: rat] :
% 5.05/5.26 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 5.05/5.26 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 5.05/5.26
% 5.05/5.26 % combine_common_factor
% 5.05/5.26 thf(fact_922_combine__common__factor,axiom,
% 5.05/5.26 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.05/5.26 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.05/5.26 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.05/5.26
% 5.05/5.26 % combine_common_factor
% 5.05/5.26 thf(fact_923_combine__common__factor,axiom,
% 5.05/5.26 ! [A: int,E: int,B: int,C: int] :
% 5.05/5.26 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.05/5.26 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.05/5.26
% 5.05/5.26 % combine_common_factor
% 5.05/5.26 thf(fact_924_distrib__right,axiom,
% 5.05/5.26 ! [A: real,B: real,C: real] :
% 5.05/5.26 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % distrib_right
% 5.05/5.26 thf(fact_925_distrib__right,axiom,
% 5.05/5.26 ! [A: rat,B: rat,C: rat] :
% 5.05/5.26 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % distrib_right
% 5.05/5.26 thf(fact_926_distrib__right,axiom,
% 5.05/5.26 ! [A: nat,B: nat,C: nat] :
% 5.05/5.26 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % distrib_right
% 5.05/5.26 thf(fact_927_distrib__right,axiom,
% 5.05/5.26 ! [A: int,B: int,C: int] :
% 5.05/5.26 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % distrib_right
% 5.05/5.26 thf(fact_928_distrib__left,axiom,
% 5.05/5.26 ! [A: real,B: real,C: real] :
% 5.05/5.26 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.05/5.26 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % distrib_left
% 5.05/5.26 thf(fact_929_distrib__left,axiom,
% 5.05/5.26 ! [A: rat,B: rat,C: rat] :
% 5.05/5.26 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.05/5.26 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % distrib_left
% 5.05/5.26 thf(fact_930_distrib__left,axiom,
% 5.05/5.26 ! [A: nat,B: nat,C: nat] :
% 5.05/5.26 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.05/5.26 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % distrib_left
% 5.05/5.26 thf(fact_931_distrib__left,axiom,
% 5.05/5.26 ! [A: int,B: int,C: int] :
% 5.05/5.26 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.05/5.26 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % distrib_left
% 5.05/5.26 thf(fact_932_comm__semiring__class_Odistrib,axiom,
% 5.05/5.26 ! [A: real,B: real,C: real] :
% 5.05/5.26 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % comm_semiring_class.distrib
% 5.05/5.26 thf(fact_933_comm__semiring__class_Odistrib,axiom,
% 5.05/5.26 ! [A: rat,B: rat,C: rat] :
% 5.05/5.26 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % comm_semiring_class.distrib
% 5.05/5.26 thf(fact_934_comm__semiring__class_Odistrib,axiom,
% 5.05/5.26 ! [A: nat,B: nat,C: nat] :
% 5.05/5.26 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % comm_semiring_class.distrib
% 5.05/5.26 thf(fact_935_comm__semiring__class_Odistrib,axiom,
% 5.05/5.26 ! [A: int,B: int,C: int] :
% 5.05/5.26 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % comm_semiring_class.distrib
% 5.05/5.26 thf(fact_936_ring__class_Oring__distribs_I1_J,axiom,
% 5.05/5.26 ! [A: real,B: real,C: real] :
% 5.05/5.26 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.05/5.26 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % ring_class.ring_distribs(1)
% 5.05/5.26 thf(fact_937_ring__class_Oring__distribs_I1_J,axiom,
% 5.05/5.26 ! [A: rat,B: rat,C: rat] :
% 5.05/5.26 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.05/5.26 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % ring_class.ring_distribs(1)
% 5.05/5.26 thf(fact_938_ring__class_Oring__distribs_I1_J,axiom,
% 5.05/5.26 ! [A: int,B: int,C: int] :
% 5.05/5.26 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.05/5.26 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % ring_class.ring_distribs(1)
% 5.05/5.26 thf(fact_939_ring__class_Oring__distribs_I2_J,axiom,
% 5.05/5.26 ! [A: real,B: real,C: real] :
% 5.05/5.26 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % ring_class.ring_distribs(2)
% 5.05/5.26 thf(fact_940_ring__class_Oring__distribs_I2_J,axiom,
% 5.05/5.26 ! [A: rat,B: rat,C: rat] :
% 5.05/5.26 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % ring_class.ring_distribs(2)
% 5.05/5.26 thf(fact_941_ring__class_Oring__distribs_I2_J,axiom,
% 5.05/5.26 ! [A: int,B: int,C: int] :
% 5.05/5.26 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.05/5.26 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % ring_class.ring_distribs(2)
% 5.05/5.26 thf(fact_942_two__realpow__ge__one,axiom,
% 5.05/5.26 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % two_realpow_ge_one
% 5.05/5.26 thf(fact_943_right__diff__distrib_H,axiom,
% 5.05/5.26 ! [A: real,B: real,C: real] :
% 5.05/5.26 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.05/5.26 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % right_diff_distrib'
% 5.05/5.26 thf(fact_944_right__diff__distrib_H,axiom,
% 5.05/5.26 ! [A: rat,B: rat,C: rat] :
% 5.05/5.26 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.05/5.26 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % right_diff_distrib'
% 5.05/5.26 thf(fact_945_right__diff__distrib_H,axiom,
% 5.05/5.26 ! [A: nat,B: nat,C: nat] :
% 5.05/5.26 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.05/5.26 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % right_diff_distrib'
% 5.05/5.26 thf(fact_946_right__diff__distrib_H,axiom,
% 5.05/5.26 ! [A: int,B: int,C: int] :
% 5.05/5.26 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.05/5.26 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % right_diff_distrib'
% 5.05/5.26 thf(fact_947_left__diff__distrib_H,axiom,
% 5.05/5.26 ! [B: real,C: real,A: real] :
% 5.05/5.26 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.05/5.26 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % left_diff_distrib'
% 5.05/5.26 thf(fact_948_left__diff__distrib_H,axiom,
% 5.05/5.26 ! [B: rat,C: rat,A: rat] :
% 5.05/5.26 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.05/5.26 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % left_diff_distrib'
% 5.05/5.26 thf(fact_949_left__diff__distrib_H,axiom,
% 5.05/5.26 ! [B: nat,C: nat,A: nat] :
% 5.05/5.26 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.05/5.26 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % left_diff_distrib'
% 5.05/5.26 thf(fact_950_left__diff__distrib_H,axiom,
% 5.05/5.26 ! [B: int,C: int,A: int] :
% 5.05/5.26 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.05/5.26 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % left_diff_distrib'
% 5.05/5.26 thf(fact_951_right__diff__distrib,axiom,
% 5.05/5.26 ! [A: real,B: real,C: real] :
% 5.05/5.26 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.05/5.26 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % right_diff_distrib
% 5.05/5.26 thf(fact_952_right__diff__distrib,axiom,
% 5.05/5.26 ! [A: rat,B: rat,C: rat] :
% 5.05/5.26 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.05/5.26 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % right_diff_distrib
% 5.05/5.26 thf(fact_953_right__diff__distrib,axiom,
% 5.05/5.26 ! [A: int,B: int,C: int] :
% 5.05/5.26 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.05/5.26 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % right_diff_distrib
% 5.05/5.26 thf(fact_954_left__diff__distrib,axiom,
% 5.05/5.26 ! [A: real,B: real,C: real] :
% 5.05/5.26 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.05/5.26 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % left_diff_distrib
% 5.05/5.26 thf(fact_955_left__diff__distrib,axiom,
% 5.05/5.26 ! [A: rat,B: rat,C: rat] :
% 5.05/5.26 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.05/5.26 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % left_diff_distrib
% 5.05/5.26 thf(fact_956_left__diff__distrib,axiom,
% 5.05/5.26 ! [A: int,B: int,C: int] :
% 5.05/5.26 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.05/5.26 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % left_diff_distrib
% 5.05/5.26 thf(fact_957_add__diff__add,axiom,
% 5.05/5.26 ! [A: real,C: real,B: real,D: real] :
% 5.05/5.26 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.05/5.26 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_diff_add
% 5.05/5.26 thf(fact_958_add__diff__add,axiom,
% 5.05/5.26 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.05/5.26 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 5.05/5.26 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_diff_add
% 5.05/5.26 thf(fact_959_add__diff__add,axiom,
% 5.05/5.26 ! [A: int,C: int,B: int,D: int] :
% 5.05/5.26 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.05/5.26 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_diff_add
% 5.05/5.26 thf(fact_960_lambda__one,axiom,
% 5.05/5.26 ( ( ^ [X2: complex] : X2 )
% 5.05/5.26 = ( times_times_complex @ one_one_complex ) ) ).
% 5.05/5.26
% 5.05/5.26 % lambda_one
% 5.05/5.26 thf(fact_961_lambda__one,axiom,
% 5.05/5.26 ( ( ^ [X2: real] : X2 )
% 5.05/5.26 = ( times_times_real @ one_one_real ) ) ).
% 5.05/5.26
% 5.05/5.26 % lambda_one
% 5.05/5.26 thf(fact_962_lambda__one,axiom,
% 5.05/5.26 ( ( ^ [X2: rat] : X2 )
% 5.05/5.26 = ( times_times_rat @ one_one_rat ) ) ).
% 5.05/5.26
% 5.05/5.26 % lambda_one
% 5.05/5.26 thf(fact_963_lambda__one,axiom,
% 5.05/5.26 ( ( ^ [X2: nat] : X2 )
% 5.05/5.26 = ( times_times_nat @ one_one_nat ) ) ).
% 5.05/5.26
% 5.05/5.26 % lambda_one
% 5.05/5.26 thf(fact_964_lambda__one,axiom,
% 5.05/5.26 ( ( ^ [X2: int] : X2 )
% 5.05/5.26 = ( times_times_int @ one_one_int ) ) ).
% 5.05/5.26
% 5.05/5.26 % lambda_one
% 5.05/5.26 thf(fact_965_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.05/5.26 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.05/5.26 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 5.05/5.26 = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.simps(3)
% 5.05/5.26 thf(fact_966_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.05/5.26 ! [F: num > num > num,A: num,B: num] :
% 5.05/5.26 ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.05/5.26 = ( some_num @ ( F @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.simps(3)
% 5.05/5.26 thf(fact_967_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.05/5.26 ! [F: nat > nat > nat,A: nat,B: nat] :
% 5.05/5.26 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 5.05/5.26 = ( some_nat @ ( F @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.simps(3)
% 5.05/5.26 thf(fact_968_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.05/5.26 ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 5.05/5.26 ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 5.05/5.26 = none_P5556105721700978146at_nat ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.simps(1)
% 5.05/5.26 thf(fact_969_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.05/5.26 ! [Uu: num > num > num,Uv: option_num] :
% 5.05/5.26 ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 5.05/5.26 = none_num ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.simps(1)
% 5.05/5.26 thf(fact_970_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.05/5.26 ! [Uu: nat > nat > nat,Uv: option_nat] :
% 5.05/5.26 ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 5.05/5.26 = none_nat ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.simps(1)
% 5.05/5.26 thf(fact_971_less__1__mult,axiom,
% 5.05/5.26 ! [M: real,N2: real] :
% 5.05/5.26 ( ( ord_less_real @ one_one_real @ M )
% 5.05/5.26 => ( ( ord_less_real @ one_one_real @ N2 )
% 5.05/5.26 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_1_mult
% 5.05/5.26 thf(fact_972_less__1__mult,axiom,
% 5.05/5.26 ! [M: rat,N2: rat] :
% 5.05/5.26 ( ( ord_less_rat @ one_one_rat @ M )
% 5.05/5.26 => ( ( ord_less_rat @ one_one_rat @ N2 )
% 5.05/5.26 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_1_mult
% 5.05/5.26 thf(fact_973_less__1__mult,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_nat @ one_one_nat @ M )
% 5.05/5.26 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.05/5.26 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_1_mult
% 5.05/5.26 thf(fact_974_less__1__mult,axiom,
% 5.05/5.26 ! [M: int,N2: int] :
% 5.05/5.26 ( ( ord_less_int @ one_one_int @ M )
% 5.05/5.26 => ( ( ord_less_int @ one_one_int @ N2 )
% 5.05/5.26 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_1_mult
% 5.05/5.26 thf(fact_975_less__add__one,axiom,
% 5.05/5.26 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_one
% 5.05/5.26 thf(fact_976_less__add__one,axiom,
% 5.05/5.26 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_one
% 5.05/5.26 thf(fact_977_less__add__one,axiom,
% 5.05/5.26 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_one
% 5.05/5.26 thf(fact_978_less__add__one,axiom,
% 5.05/5.26 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_one
% 5.05/5.26 thf(fact_979_add__mono1,axiom,
% 5.05/5.26 ! [A: real,B: real] :
% 5.05/5.26 ( ( ord_less_real @ A @ B )
% 5.05/5.26 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_mono1
% 5.05/5.26 thf(fact_980_add__mono1,axiom,
% 5.05/5.26 ! [A: rat,B: rat] :
% 5.05/5.26 ( ( ord_less_rat @ A @ B )
% 5.05/5.26 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_mono1
% 5.05/5.26 thf(fact_981_add__mono1,axiom,
% 5.05/5.26 ! [A: nat,B: nat] :
% 5.05/5.26 ( ( ord_less_nat @ A @ B )
% 5.05/5.26 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_mono1
% 5.05/5.26 thf(fact_982_add__mono1,axiom,
% 5.05/5.26 ! [A: int,B: int] :
% 5.05/5.26 ( ( ord_less_int @ A @ B )
% 5.05/5.26 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_mono1
% 5.05/5.26 thf(fact_983_add__le__imp__le__diff,axiom,
% 5.05/5.26 ! [I2: real,K: real,N2: real] :
% 5.05/5.26 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N2 @ K ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_le_imp_le_diff
% 5.05/5.26 thf(fact_984_add__le__imp__le__diff,axiom,
% 5.05/5.26 ! [I2: rat,K: rat,N2: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_le_imp_le_diff
% 5.05/5.26 thf(fact_985_add__le__imp__le__diff,axiom,
% 5.05/5.26 ! [I2: nat,K: nat,N2: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_le_imp_le_diff
% 5.05/5.26 thf(fact_986_add__le__imp__le__diff,axiom,
% 5.05/5.26 ! [I2: int,K: int,N2: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_le_imp_le_diff
% 5.05/5.26 thf(fact_987_add__le__add__imp__diff__le,axiom,
% 5.05/5.26 ! [I2: real,K: real,N2: real,J: real] :
% 5.05/5.26 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 5.05/5.26 => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 5.05/5.26 => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_le_add_imp_diff_le
% 5.05/5.26 thf(fact_988_add__le__add__imp__diff__le,axiom,
% 5.05/5.26 ! [I2: rat,K: rat,N2: rat,J: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 5.05/5.26 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 5.05/5.26 => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_le_add_imp_diff_le
% 5.05/5.26 thf(fact_989_add__le__add__imp__diff__le,axiom,
% 5.05/5.26 ! [I2: nat,K: nat,N2: nat,J: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 5.05/5.26 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 5.05/5.26 => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_le_add_imp_diff_le
% 5.05/5.26 thf(fact_990_add__le__add__imp__diff__le,axiom,
% 5.05/5.26 ! [I2: int,K: int,N2: int,J: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 5.05/5.26 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.05/5.26 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 5.05/5.26 => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % add_le_add_imp_diff_le
% 5.05/5.26 thf(fact_991_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.05/5.26 ! [A: real,B: real] :
% 5.05/5.26 ( ~ ( ord_less_real @ A @ B )
% 5.05/5.26 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % linordered_semidom_class.add_diff_inverse
% 5.05/5.26 thf(fact_992_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.05/5.26 ! [A: rat,B: rat] :
% 5.05/5.26 ( ~ ( ord_less_rat @ A @ B )
% 5.05/5.26 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % linordered_semidom_class.add_diff_inverse
% 5.05/5.26 thf(fact_993_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.05/5.26 ! [A: nat,B: nat] :
% 5.05/5.26 ( ~ ( ord_less_nat @ A @ B )
% 5.05/5.26 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % linordered_semidom_class.add_diff_inverse
% 5.05/5.26 thf(fact_994_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.05/5.26 ! [A: int,B: int] :
% 5.05/5.26 ( ~ ( ord_less_int @ A @ B )
% 5.05/5.26 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % linordered_semidom_class.add_diff_inverse
% 5.05/5.26 thf(fact_995_mult__diff__mult,axiom,
% 5.05/5.26 ! [X: real,Y: real,A: real,B: real] :
% 5.05/5.26 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 5.05/5.26 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_diff_mult
% 5.05/5.26 thf(fact_996_mult__diff__mult,axiom,
% 5.05/5.26 ! [X: rat,Y: rat,A: rat,B: rat] :
% 5.05/5.26 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 5.05/5.26 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_diff_mult
% 5.05/5.26 thf(fact_997_mult__diff__mult,axiom,
% 5.05/5.26 ! [X: int,Y: int,A: int,B: int] :
% 5.05/5.26 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 5.05/5.26 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_diff_mult
% 5.05/5.26 thf(fact_998_square__diff__square__factored,axiom,
% 5.05/5.26 ! [X: real,Y: real] :
% 5.05/5.26 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.05/5.26 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % square_diff_square_factored
% 5.05/5.26 thf(fact_999_square__diff__square__factored,axiom,
% 5.05/5.26 ! [X: rat,Y: rat] :
% 5.05/5.26 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.05/5.26 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % square_diff_square_factored
% 5.05/5.26 thf(fact_1000_square__diff__square__factored,axiom,
% 5.05/5.26 ! [X: int,Y: int] :
% 5.05/5.26 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.05/5.26 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % square_diff_square_factored
% 5.05/5.26 thf(fact_1001_eq__add__iff2,axiom,
% 5.05/5.26 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.05/5.26 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.05/5.26 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.05/5.26 = ( C
% 5.05/5.26 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % eq_add_iff2
% 5.05/5.26 thf(fact_1002_eq__add__iff2,axiom,
% 5.05/5.26 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.05/5.26 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.05/5.26 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.05/5.26 = ( C
% 5.05/5.26 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % eq_add_iff2
% 5.05/5.26 thf(fact_1003_eq__add__iff2,axiom,
% 5.05/5.26 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.05/5.26 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.05/5.26 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.05/5.26 = ( C
% 5.05/5.26 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % eq_add_iff2
% 5.05/5.26 thf(fact_1004_eq__add__iff1,axiom,
% 5.05/5.26 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.05/5.26 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.05/5.26 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.05/5.26 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 5.05/5.26 = D ) ) ).
% 5.05/5.26
% 5.05/5.26 % eq_add_iff1
% 5.05/5.26 thf(fact_1005_eq__add__iff1,axiom,
% 5.05/5.26 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.05/5.26 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.05/5.26 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.05/5.26 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 5.05/5.26 = D ) ) ).
% 5.05/5.26
% 5.05/5.26 % eq_add_iff1
% 5.05/5.26 thf(fact_1006_eq__add__iff1,axiom,
% 5.05/5.26 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.05/5.26 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.05/5.26 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.05/5.26 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.05/5.26 = D ) ) ).
% 5.05/5.26
% 5.05/5.26 % eq_add_iff1
% 5.05/5.26 thf(fact_1007_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.05/5.26 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 5.05/5.26 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb )
% 5.05/5.26 = Y )
% 5.05/5.26 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.05/5.26 => ( Y != none_P5556105721700978146at_nat ) )
% 5.05/5.26 => ( ( ? [V2: product_prod_nat_nat] :
% 5.05/5.26 ( Xa2
% 5.05/5.26 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.05/5.26 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.05/5.26 => ( Y != none_P5556105721700978146at_nat ) ) )
% 5.05/5.26 => ~ ! [A3: product_prod_nat_nat] :
% 5.05/5.26 ( ( Xa2
% 5.05/5.26 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.05/5.26 => ! [B2: product_prod_nat_nat] :
% 5.05/5.26 ( ( Xb
% 5.05/5.26 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.05/5.26 => ( Y
% 5.05/5.26 != ( some_P7363390416028606310at_nat @ ( X @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.elims
% 5.05/5.26 thf(fact_1008_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.05/5.26 ! [X: num > num > num,Xa2: option_num,Xb: option_num,Y: option_num] :
% 5.05/5.26 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb )
% 5.05/5.26 = Y )
% 5.05/5.26 => ( ( ( Xa2 = none_num )
% 5.05/5.26 => ( Y != none_num ) )
% 5.05/5.26 => ( ( ? [V2: num] :
% 5.05/5.26 ( Xa2
% 5.05/5.26 = ( some_num @ V2 ) )
% 5.05/5.26 => ( ( Xb = none_num )
% 5.05/5.26 => ( Y != none_num ) ) )
% 5.05/5.26 => ~ ! [A3: num] :
% 5.05/5.26 ( ( Xa2
% 5.05/5.26 = ( some_num @ A3 ) )
% 5.05/5.26 => ! [B2: num] :
% 5.05/5.26 ( ( Xb
% 5.05/5.26 = ( some_num @ B2 ) )
% 5.05/5.26 => ( Y
% 5.05/5.26 != ( some_num @ ( X @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.elims
% 5.05/5.26 thf(fact_1009_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.05/5.26 ! [X: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y: option_nat] :
% 5.05/5.26 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb )
% 5.05/5.26 = Y )
% 5.05/5.26 => ( ( ( Xa2 = none_nat )
% 5.05/5.26 => ( Y != none_nat ) )
% 5.05/5.26 => ( ( ? [V2: nat] :
% 5.05/5.26 ( Xa2
% 5.05/5.26 = ( some_nat @ V2 ) )
% 5.05/5.26 => ( ( Xb = none_nat )
% 5.05/5.26 => ( Y != none_nat ) ) )
% 5.05/5.26 => ~ ! [A3: nat] :
% 5.05/5.26 ( ( Xa2
% 5.05/5.26 = ( some_nat @ A3 ) )
% 5.05/5.26 => ! [B2: nat] :
% 5.05/5.26 ( ( Xb
% 5.05/5.26 = ( some_nat @ B2 ) )
% 5.05/5.26 => ( Y
% 5.05/5.26 != ( some_nat @ ( X @ A3 @ B2 ) ) ) ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.elims
% 5.05/5.26 thf(fact_1010_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.05/5.26 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.05/5.26 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.05/5.26 = none_P5556105721700978146at_nat ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.simps(2)
% 5.05/5.26 thf(fact_1011_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.05/5.26 ! [Uw: num > num > num,V: num] :
% 5.05/5.26 ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 5.05/5.26 = none_num ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.simps(2)
% 5.05/5.26 thf(fact_1012_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.05/5.26 ! [Uw: nat > nat > nat,V: nat] :
% 5.05/5.26 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 5.05/5.26 = none_nat ) ).
% 5.05/5.26
% 5.05/5.26 % VEBT_internal.option_shift.simps(2)
% 5.05/5.26 thf(fact_1013_ordered__ring__class_Ole__add__iff2,axiom,
% 5.05/5.26 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.05/5.26 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % ordered_ring_class.le_add_iff2
% 5.05/5.26 thf(fact_1014_ordered__ring__class_Ole__add__iff2,axiom,
% 5.05/5.26 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % ordered_ring_class.le_add_iff2
% 5.05/5.26 thf(fact_1015_ordered__ring__class_Ole__add__iff2,axiom,
% 5.05/5.26 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % ordered_ring_class.le_add_iff2
% 5.05/5.26 thf(fact_1016_ordered__ring__class_Ole__add__iff1,axiom,
% 5.05/5.26 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.05/5.26 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.05/5.26
% 5.05/5.26 % ordered_ring_class.le_add_iff1
% 5.05/5.26 thf(fact_1017_ordered__ring__class_Ole__add__iff1,axiom,
% 5.05/5.26 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.05/5.26
% 5.05/5.26 % ordered_ring_class.le_add_iff1
% 5.05/5.26 thf(fact_1018_ordered__ring__class_Ole__add__iff1,axiom,
% 5.05/5.26 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.05/5.26
% 5.05/5.26 % ordered_ring_class.le_add_iff1
% 5.05/5.26 thf(fact_1019_less__add__iff2,axiom,
% 5.05/5.26 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.05/5.26 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_iff2
% 5.05/5.26 thf(fact_1020_less__add__iff2,axiom,
% 5.05/5.26 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.05/5.26 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_iff2
% 5.05/5.26 thf(fact_1021_less__add__iff2,axiom,
% 5.05/5.26 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.05/5.26 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_iff2
% 5.05/5.26 thf(fact_1022_less__add__iff1,axiom,
% 5.05/5.26 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.05/5.26 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_iff1
% 5.05/5.26 thf(fact_1023_less__add__iff1,axiom,
% 5.05/5.26 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.05/5.26 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_iff1
% 5.05/5.26 thf(fact_1024_less__add__iff1,axiom,
% 5.05/5.26 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.05/5.26 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.05/5.26 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_add_iff1
% 5.05/5.26 thf(fact_1025_square__diff__one__factored,axiom,
% 5.05/5.26 ! [X: complex] :
% 5.05/5.26 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 5.05/5.26 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % square_diff_one_factored
% 5.05/5.26 thf(fact_1026_square__diff__one__factored,axiom,
% 5.05/5.26 ! [X: real] :
% 5.05/5.26 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 5.05/5.26 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % square_diff_one_factored
% 5.05/5.26 thf(fact_1027_square__diff__one__factored,axiom,
% 5.05/5.26 ! [X: rat] :
% 5.05/5.26 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 5.05/5.26 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % square_diff_one_factored
% 5.05/5.26 thf(fact_1028_square__diff__one__factored,axiom,
% 5.05/5.26 ! [X: int] :
% 5.05/5.26 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 5.05/5.26 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % square_diff_one_factored
% 5.05/5.26 thf(fact_1029_vebt__mint_Osimps_I2_J,axiom,
% 5.05/5.26 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.05/5.26 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.05/5.26 = none_nat ) ).
% 5.05/5.26
% 5.05/5.26 % vebt_mint.simps(2)
% 5.05/5.26 thf(fact_1030_vebt__maxt_Osimps_I2_J,axiom,
% 5.05/5.26 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.05/5.26 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.05/5.26 = none_nat ) ).
% 5.05/5.26
% 5.05/5.26 % vebt_maxt.simps(2)
% 5.05/5.26 thf(fact_1031_field__sum__of__halves,axiom,
% 5.05/5.26 ! [X: real] :
% 5.05/5.26 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % field_sum_of_halves
% 5.05/5.26 thf(fact_1032_field__sum__of__halves,axiom,
% 5.05/5.26 ! [X: rat] :
% 5.05/5.26 ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % field_sum_of_halves
% 5.05/5.26 thf(fact_1033_vebt__mint_Osimps_I3_J,axiom,
% 5.05/5.26 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.05/5.26 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.05/5.26 = ( some_nat @ Mi ) ) ).
% 5.05/5.26
% 5.05/5.26 % vebt_mint.simps(3)
% 5.05/5.26 thf(fact_1034_vebt__succ_Osimps_I6_J,axiom,
% 5.05/5.26 ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.26 ( ( ( ord_less_nat @ X @ Mi )
% 5.05/5.26 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.05/5.26 = ( some_nat @ Mi ) ) )
% 5.05/5.26 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.05/5.26 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.05/5.26 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.26 @ ( if_option_nat
% 5.05/5.26 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 != none_nat )
% 5.05/5.26 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.26 @ ( 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 @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 @ ( if_option_nat
% 5.05/5.26 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.26 = none_nat )
% 5.05/5.26 @ none_nat
% 5.05/5.26 @ ( 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 @ X @ ( 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 @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.05/5.26 @ none_nat ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % vebt_succ.simps(6)
% 5.05/5.26 thf(fact_1035_vebt__pred_Osimps_I7_J,axiom,
% 5.05/5.26 ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.05/5.26 ( ( ( ord_less_nat @ Ma @ X )
% 5.05/5.26 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.05/5.26 = ( some_nat @ Ma ) ) )
% 5.05/5.26 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.05/5.26 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X )
% 5.05/5.26 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.26 @ ( if_option_nat
% 5.05/5.26 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 != none_nat )
% 5.05/5.26 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.26 @ ( 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 @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.26 @ ( if_option_nat
% 5.05/5.26 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.26 = none_nat )
% 5.05/5.26 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.05/5.26 @ ( 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 @ X @ ( 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 @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.05/5.26 @ none_nat ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % vebt_pred.simps(7)
% 5.05/5.26 thf(fact_1036_real__average__minus__first,axiom,
% 5.05/5.26 ! [A: real,B: real] :
% 5.05/5.26 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.05/5.26 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % real_average_minus_first
% 5.05/5.26 thf(fact_1037_real__average__minus__second,axiom,
% 5.05/5.26 ! [B: real,A: real] :
% 5.05/5.26 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.05/5.26 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % real_average_minus_second
% 5.05/5.26 thf(fact_1038_pred__empty,axiom,
% 5.05/5.26 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.26 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.26 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.05/5.26 = none_nat )
% 5.05/5.26 = ( ( collect_nat
% 5.05/5.26 @ ^ [Y2: nat] :
% 5.05/5.26 ( ( vEBT_vebt_member @ T @ Y2 )
% 5.05/5.26 & ( ord_less_nat @ Y2 @ X ) ) )
% 5.05/5.26 = bot_bot_set_nat ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % pred_empty
% 5.05/5.26 thf(fact_1039_succ__empty,axiom,
% 5.05/5.26 ! [T: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.26 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.26 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.05/5.26 = none_nat )
% 5.05/5.26 = ( ( collect_nat
% 5.05/5.26 @ ^ [Y2: nat] :
% 5.05/5.26 ( ( vEBT_vebt_member @ T @ Y2 )
% 5.05/5.26 & ( ord_less_nat @ X @ Y2 ) ) )
% 5.05/5.26 = bot_bot_set_nat ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % succ_empty
% 5.05/5.26 thf(fact_1040_max_Oabsorb3,axiom,
% 5.05/5.26 ! [B: extended_enat,A: extended_enat] :
% 5.05/5.26 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.05/5.26 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb3
% 5.05/5.26 thf(fact_1041_max_Oabsorb3,axiom,
% 5.05/5.26 ! [B: code_integer,A: code_integer] :
% 5.05/5.26 ( ( ord_le6747313008572928689nteger @ B @ A )
% 5.05/5.26 => ( ( ord_max_Code_integer @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb3
% 5.05/5.26 thf(fact_1042_max_Oabsorb3,axiom,
% 5.05/5.26 ! [B: real,A: real] :
% 5.05/5.26 ( ( ord_less_real @ B @ A )
% 5.05/5.26 => ( ( ord_max_real @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb3
% 5.05/5.26 thf(fact_1043_max_Oabsorb3,axiom,
% 5.05/5.26 ! [B: rat,A: rat] :
% 5.05/5.26 ( ( ord_less_rat @ B @ A )
% 5.05/5.26 => ( ( ord_max_rat @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb3
% 5.05/5.26 thf(fact_1044_max_Oabsorb3,axiom,
% 5.05/5.26 ! [B: num,A: num] :
% 5.05/5.26 ( ( ord_less_num @ B @ A )
% 5.05/5.26 => ( ( ord_max_num @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb3
% 5.05/5.26 thf(fact_1045_max_Oabsorb3,axiom,
% 5.05/5.26 ! [B: nat,A: nat] :
% 5.05/5.26 ( ( ord_less_nat @ B @ A )
% 5.05/5.26 => ( ( ord_max_nat @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb3
% 5.05/5.26 thf(fact_1046_max_Oabsorb3,axiom,
% 5.05/5.26 ! [B: int,A: int] :
% 5.05/5.26 ( ( ord_less_int @ B @ A )
% 5.05/5.26 => ( ( ord_max_int @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb3
% 5.05/5.26 thf(fact_1047_max_Oabsorb4,axiom,
% 5.05/5.26 ! [A: extended_enat,B: extended_enat] :
% 5.05/5.26 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.05/5.26 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb4
% 5.05/5.26 thf(fact_1048_max_Oabsorb4,axiom,
% 5.05/5.26 ! [A: code_integer,B: code_integer] :
% 5.05/5.26 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.05/5.26 => ( ( ord_max_Code_integer @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb4
% 5.05/5.26 thf(fact_1049_max_Oabsorb4,axiom,
% 5.05/5.26 ! [A: real,B: real] :
% 5.05/5.26 ( ( ord_less_real @ A @ B )
% 5.05/5.26 => ( ( ord_max_real @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb4
% 5.05/5.26 thf(fact_1050_max_Oabsorb4,axiom,
% 5.05/5.26 ! [A: rat,B: rat] :
% 5.05/5.26 ( ( ord_less_rat @ A @ B )
% 5.05/5.26 => ( ( ord_max_rat @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb4
% 5.05/5.26 thf(fact_1051_max_Oabsorb4,axiom,
% 5.05/5.26 ! [A: num,B: num] :
% 5.05/5.26 ( ( ord_less_num @ A @ B )
% 5.05/5.26 => ( ( ord_max_num @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb4
% 5.05/5.26 thf(fact_1052_max_Oabsorb4,axiom,
% 5.05/5.26 ! [A: nat,B: nat] :
% 5.05/5.26 ( ( ord_less_nat @ A @ B )
% 5.05/5.26 => ( ( ord_max_nat @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb4
% 5.05/5.26 thf(fact_1053_max_Oabsorb4,axiom,
% 5.05/5.26 ! [A: int,B: int] :
% 5.05/5.26 ( ( ord_less_int @ A @ B )
% 5.05/5.26 => ( ( ord_max_int @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb4
% 5.05/5.26 thf(fact_1054_max__less__iff__conj,axiom,
% 5.05/5.26 ! [X: extended_enat,Y: extended_enat,Z: extended_enat] :
% 5.05/5.26 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y ) @ Z )
% 5.05/5.26 = ( ( ord_le72135733267957522d_enat @ X @ Z )
% 5.05/5.26 & ( ord_le72135733267957522d_enat @ Y @ Z ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max_less_iff_conj
% 5.05/5.26 thf(fact_1055_max__less__iff__conj,axiom,
% 5.05/5.26 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.05/5.26 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 5.05/5.26 = ( ( ord_le6747313008572928689nteger @ X @ Z )
% 5.05/5.26 & ( ord_le6747313008572928689nteger @ Y @ Z ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max_less_iff_conj
% 5.05/5.26 thf(fact_1056_max__less__iff__conj,axiom,
% 5.05/5.26 ! [X: real,Y: real,Z: real] :
% 5.05/5.26 ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.05/5.26 = ( ( ord_less_real @ X @ Z )
% 5.05/5.26 & ( ord_less_real @ Y @ Z ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max_less_iff_conj
% 5.05/5.26 thf(fact_1057_max__less__iff__conj,axiom,
% 5.05/5.26 ! [X: rat,Y: rat,Z: rat] :
% 5.05/5.26 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 5.05/5.26 = ( ( ord_less_rat @ X @ Z )
% 5.05/5.26 & ( ord_less_rat @ Y @ Z ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max_less_iff_conj
% 5.05/5.26 thf(fact_1058_max__less__iff__conj,axiom,
% 5.05/5.26 ! [X: num,Y: num,Z: num] :
% 5.05/5.26 ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
% 5.05/5.26 = ( ( ord_less_num @ X @ Z )
% 5.05/5.26 & ( ord_less_num @ Y @ Z ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max_less_iff_conj
% 5.05/5.26 thf(fact_1059_max__less__iff__conj,axiom,
% 5.05/5.26 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.26 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 5.05/5.26 = ( ( ord_less_nat @ X @ Z )
% 5.05/5.26 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max_less_iff_conj
% 5.05/5.26 thf(fact_1060_max__less__iff__conj,axiom,
% 5.05/5.26 ! [X: int,Y: int,Z: int] :
% 5.05/5.26 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.05/5.26 = ( ( ord_less_int @ X @ Z )
% 5.05/5.26 & ( ord_less_int @ Y @ Z ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max_less_iff_conj
% 5.05/5.26 thf(fact_1061_max_Oabsorb1,axiom,
% 5.05/5.26 ! [B: extended_enat,A: extended_enat] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.05/5.26 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb1
% 5.05/5.26 thf(fact_1062_max_Oabsorb1,axiom,
% 5.05/5.26 ! [B: code_integer,A: code_integer] :
% 5.05/5.26 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.05/5.26 => ( ( ord_max_Code_integer @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb1
% 5.05/5.26 thf(fact_1063_max_Oabsorb1,axiom,
% 5.05/5.26 ! [B: rat,A: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.26 => ( ( ord_max_rat @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb1
% 5.05/5.26 thf(fact_1064_max_Oabsorb1,axiom,
% 5.05/5.26 ! [B: num,A: num] :
% 5.05/5.26 ( ( ord_less_eq_num @ B @ A )
% 5.05/5.26 => ( ( ord_max_num @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb1
% 5.05/5.26 thf(fact_1065_max_Oabsorb1,axiom,
% 5.05/5.26 ! [B: nat,A: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.26 => ( ( ord_max_nat @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb1
% 5.05/5.26 thf(fact_1066_max_Oabsorb1,axiom,
% 5.05/5.26 ! [B: int,A: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ B @ A )
% 5.05/5.26 => ( ( ord_max_int @ A @ B )
% 5.05/5.26 = A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb1
% 5.05/5.26 thf(fact_1067_max_Oright__idem,axiom,
% 5.05/5.26 ! [A: nat,B: nat] :
% 5.05/5.26 ( ( ord_max_nat @ ( ord_max_nat @ A @ B ) @ B )
% 5.05/5.26 = ( ord_max_nat @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.right_idem
% 5.05/5.26 thf(fact_1068_max_Oright__idem,axiom,
% 5.05/5.26 ! [A: extended_enat,B: extended_enat] :
% 5.05/5.26 ( ( ord_ma741700101516333627d_enat @ ( ord_ma741700101516333627d_enat @ A @ B ) @ B )
% 5.05/5.26 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.right_idem
% 5.05/5.26 thf(fact_1069_max_Oright__idem,axiom,
% 5.05/5.26 ! [A: int,B: int] :
% 5.05/5.26 ( ( ord_max_int @ ( ord_max_int @ A @ B ) @ B )
% 5.05/5.26 = ( ord_max_int @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.right_idem
% 5.05/5.26 thf(fact_1070_max_Oright__idem,axiom,
% 5.05/5.26 ! [A: code_integer,B: code_integer] :
% 5.05/5.26 ( ( ord_max_Code_integer @ ( ord_max_Code_integer @ A @ B ) @ B )
% 5.05/5.26 = ( ord_max_Code_integer @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.right_idem
% 5.05/5.26 thf(fact_1071_max_Oleft__idem,axiom,
% 5.05/5.26 ! [A: nat,B: nat] :
% 5.05/5.26 ( ( ord_max_nat @ A @ ( ord_max_nat @ A @ B ) )
% 5.05/5.26 = ( ord_max_nat @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.left_idem
% 5.05/5.26 thf(fact_1072_max_Oleft__idem,axiom,
% 5.05/5.26 ! [A: extended_enat,B: extended_enat] :
% 5.05/5.26 ( ( ord_ma741700101516333627d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.05/5.26 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.left_idem
% 5.05/5.26 thf(fact_1073_max_Oleft__idem,axiom,
% 5.05/5.26 ! [A: int,B: int] :
% 5.05/5.26 ( ( ord_max_int @ A @ ( ord_max_int @ A @ B ) )
% 5.05/5.26 = ( ord_max_int @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.left_idem
% 5.05/5.26 thf(fact_1074_max_Oleft__idem,axiom,
% 5.05/5.26 ! [A: code_integer,B: code_integer] :
% 5.05/5.26 ( ( ord_max_Code_integer @ A @ ( ord_max_Code_integer @ A @ B ) )
% 5.05/5.26 = ( ord_max_Code_integer @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.left_idem
% 5.05/5.26 thf(fact_1075_max_Oidem,axiom,
% 5.05/5.26 ! [A: nat] :
% 5.05/5.26 ( ( ord_max_nat @ A @ A )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % max.idem
% 5.05/5.26 thf(fact_1076_max_Oidem,axiom,
% 5.05/5.26 ! [A: extended_enat] :
% 5.05/5.26 ( ( ord_ma741700101516333627d_enat @ A @ A )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % max.idem
% 5.05/5.26 thf(fact_1077_max_Oidem,axiom,
% 5.05/5.26 ! [A: int] :
% 5.05/5.26 ( ( ord_max_int @ A @ A )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % max.idem
% 5.05/5.26 thf(fact_1078_max_Oidem,axiom,
% 5.05/5.26 ! [A: code_integer] :
% 5.05/5.26 ( ( ord_max_Code_integer @ A @ A )
% 5.05/5.26 = A ) ).
% 5.05/5.26
% 5.05/5.26 % max.idem
% 5.05/5.26 thf(fact_1079_mint__corr__help__empty,axiom,
% 5.05/5.26 ! [T: vEBT_VEBT,N2: nat] :
% 5.05/5.26 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.26 => ( ( ( vEBT_vebt_mint @ T )
% 5.05/5.26 = none_nat )
% 5.05/5.26 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.05/5.26 = bot_bot_set_nat ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % mint_corr_help_empty
% 5.05/5.26 thf(fact_1080_maxt__corr__help__empty,axiom,
% 5.05/5.26 ! [T: vEBT_VEBT,N2: nat] :
% 5.05/5.26 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.26 => ( ( ( vEBT_vebt_maxt @ T )
% 5.05/5.26 = none_nat )
% 5.05/5.26 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.05/5.26 = bot_bot_set_nat ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % maxt_corr_help_empty
% 5.05/5.26 thf(fact_1081_max_Obounded__iff,axiom,
% 5.05/5.26 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.05/5.26 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.05/5.26 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.bounded_iff
% 5.05/5.26 thf(fact_1082_max_Obounded__iff,axiom,
% 5.05/5.26 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.05/5.26 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 5.05/5.26 = ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.05/5.26 & ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.bounded_iff
% 5.05/5.26 thf(fact_1083_max_Obounded__iff,axiom,
% 5.05/5.26 ! [B: rat,C: rat,A: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.05/5.26 = ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.26 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.bounded_iff
% 5.05/5.26 thf(fact_1084_max_Obounded__iff,axiom,
% 5.05/5.26 ! [B: num,C: num,A: num] :
% 5.05/5.26 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.05/5.26 = ( ( ord_less_eq_num @ B @ A )
% 5.05/5.26 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.bounded_iff
% 5.05/5.26 thf(fact_1085_max_Obounded__iff,axiom,
% 5.05/5.26 ! [B: nat,C: nat,A: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.05/5.26 = ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.26 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.bounded_iff
% 5.05/5.26 thf(fact_1086_max_Obounded__iff,axiom,
% 5.05/5.26 ! [B: int,C: int,A: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.05/5.26 = ( ( ord_less_eq_int @ B @ A )
% 5.05/5.26 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.bounded_iff
% 5.05/5.26 thf(fact_1087_max_Oabsorb2,axiom,
% 5.05/5.26 ! [A: extended_enat,B: extended_enat] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.05/5.26 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb2
% 5.05/5.26 thf(fact_1088_max_Oabsorb2,axiom,
% 5.05/5.26 ! [A: code_integer,B: code_integer] :
% 5.05/5.26 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.05/5.26 => ( ( ord_max_Code_integer @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb2
% 5.05/5.26 thf(fact_1089_max_Oabsorb2,axiom,
% 5.05/5.26 ! [A: rat,B: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.26 => ( ( ord_max_rat @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb2
% 5.05/5.26 thf(fact_1090_max_Oabsorb2,axiom,
% 5.05/5.26 ! [A: num,B: num] :
% 5.05/5.26 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.26 => ( ( ord_max_num @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb2
% 5.05/5.26 thf(fact_1091_max_Oabsorb2,axiom,
% 5.05/5.26 ! [A: nat,B: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.26 => ( ( ord_max_nat @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb2
% 5.05/5.26 thf(fact_1092_max_Oabsorb2,axiom,
% 5.05/5.26 ! [A: int,B: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.26 => ( ( ord_max_int @ A @ B )
% 5.05/5.26 = B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb2
% 5.05/5.26 thf(fact_1093_max_Oleft__commute,axiom,
% 5.05/5.26 ! [B: nat,A: nat,C: nat] :
% 5.05/5.26 ( ( ord_max_nat @ B @ ( ord_max_nat @ A @ C ) )
% 5.05/5.26 = ( ord_max_nat @ A @ ( ord_max_nat @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.left_commute
% 5.05/5.26 thf(fact_1094_max_Oleft__commute,axiom,
% 5.05/5.26 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.05/5.26 ( ( ord_ma741700101516333627d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ C ) )
% 5.05/5.26 = ( ord_ma741700101516333627d_enat @ A @ ( ord_ma741700101516333627d_enat @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.left_commute
% 5.05/5.26 thf(fact_1095_max_Oleft__commute,axiom,
% 5.05/5.26 ! [B: int,A: int,C: int] :
% 5.05/5.26 ( ( ord_max_int @ B @ ( ord_max_int @ A @ C ) )
% 5.05/5.26 = ( ord_max_int @ A @ ( ord_max_int @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.left_commute
% 5.05/5.26 thf(fact_1096_max_Oleft__commute,axiom,
% 5.05/5.26 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.05/5.26 ( ( ord_max_Code_integer @ B @ ( ord_max_Code_integer @ A @ C ) )
% 5.05/5.26 = ( ord_max_Code_integer @ A @ ( ord_max_Code_integer @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.left_commute
% 5.05/5.26 thf(fact_1097_max_Ocommute,axiom,
% 5.05/5.26 ( ord_max_nat
% 5.05/5.26 = ( ^ [A4: nat,B4: nat] : ( ord_max_nat @ B4 @ A4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.commute
% 5.05/5.26 thf(fact_1098_max_Ocommute,axiom,
% 5.05/5.26 ( ord_ma741700101516333627d_enat
% 5.05/5.26 = ( ^ [A4: extended_enat,B4: extended_enat] : ( ord_ma741700101516333627d_enat @ B4 @ A4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.commute
% 5.05/5.26 thf(fact_1099_max_Ocommute,axiom,
% 5.05/5.26 ( ord_max_int
% 5.05/5.26 = ( ^ [A4: int,B4: int] : ( ord_max_int @ B4 @ A4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.commute
% 5.05/5.26 thf(fact_1100_max_Ocommute,axiom,
% 5.05/5.26 ( ord_max_Code_integer
% 5.05/5.26 = ( ^ [A4: code_integer,B4: code_integer] : ( ord_max_Code_integer @ B4 @ A4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.commute
% 5.05/5.26 thf(fact_1101_max_Oassoc,axiom,
% 5.05/5.26 ! [A: nat,B: nat,C: nat] :
% 5.05/5.26 ( ( ord_max_nat @ ( ord_max_nat @ A @ B ) @ C )
% 5.05/5.26 = ( ord_max_nat @ A @ ( ord_max_nat @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.assoc
% 5.05/5.26 thf(fact_1102_max_Oassoc,axiom,
% 5.05/5.26 ! [A: extended_enat,B: extended_enat,C: extended_enat] :
% 5.05/5.26 ( ( ord_ma741700101516333627d_enat @ ( ord_ma741700101516333627d_enat @ A @ B ) @ C )
% 5.05/5.26 = ( ord_ma741700101516333627d_enat @ A @ ( ord_ma741700101516333627d_enat @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.assoc
% 5.05/5.26 thf(fact_1103_max_Oassoc,axiom,
% 5.05/5.26 ! [A: int,B: int,C: int] :
% 5.05/5.26 ( ( ord_max_int @ ( ord_max_int @ A @ B ) @ C )
% 5.05/5.26 = ( ord_max_int @ A @ ( ord_max_int @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.assoc
% 5.05/5.26 thf(fact_1104_max_Oassoc,axiom,
% 5.05/5.26 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.05/5.26 ( ( ord_max_Code_integer @ ( ord_max_Code_integer @ A @ B ) @ C )
% 5.05/5.26 = ( ord_max_Code_integer @ A @ ( ord_max_Code_integer @ B @ C ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.assoc
% 5.05/5.26 thf(fact_1105_mult__commute__abs,axiom,
% 5.05/5.26 ! [C: real] :
% 5.05/5.26 ( ( ^ [X2: real] : ( times_times_real @ X2 @ C ) )
% 5.05/5.26 = ( times_times_real @ C ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_commute_abs
% 5.05/5.26 thf(fact_1106_mult__commute__abs,axiom,
% 5.05/5.26 ! [C: rat] :
% 5.05/5.26 ( ( ^ [X2: rat] : ( times_times_rat @ X2 @ C ) )
% 5.05/5.26 = ( times_times_rat @ C ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_commute_abs
% 5.05/5.26 thf(fact_1107_mult__commute__abs,axiom,
% 5.05/5.26 ! [C: nat] :
% 5.05/5.26 ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
% 5.05/5.26 = ( times_times_nat @ C ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_commute_abs
% 5.05/5.26 thf(fact_1108_mult__commute__abs,axiom,
% 5.05/5.26 ! [C: int] :
% 5.05/5.26 ( ( ^ [X2: int] : ( times_times_int @ X2 @ C ) )
% 5.05/5.26 = ( times_times_int @ C ) ) ).
% 5.05/5.26
% 5.05/5.26 % mult_commute_abs
% 5.05/5.26 thf(fact_1109_max_OcoboundedI2,axiom,
% 5.05/5.26 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.05/5.26 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI2
% 5.05/5.26 thf(fact_1110_max_OcoboundedI2,axiom,
% 5.05/5.26 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.05/5.26 ( ( ord_le3102999989581377725nteger @ C @ B )
% 5.05/5.26 => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI2
% 5.05/5.26 thf(fact_1111_max_OcoboundedI2,axiom,
% 5.05/5.26 ! [C: rat,B: rat,A: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ C @ B )
% 5.05/5.26 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI2
% 5.05/5.26 thf(fact_1112_max_OcoboundedI2,axiom,
% 5.05/5.26 ! [C: num,B: num,A: num] :
% 5.05/5.26 ( ( ord_less_eq_num @ C @ B )
% 5.05/5.26 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI2
% 5.05/5.26 thf(fact_1113_max_OcoboundedI2,axiom,
% 5.05/5.26 ! [C: nat,B: nat,A: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ C @ B )
% 5.05/5.26 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI2
% 5.05/5.26 thf(fact_1114_max_OcoboundedI2,axiom,
% 5.05/5.26 ! [C: int,B: int,A: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ C @ B )
% 5.05/5.26 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI2
% 5.05/5.26 thf(fact_1115_max_OcoboundedI1,axiom,
% 5.05/5.26 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.05/5.26 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI1
% 5.05/5.26 thf(fact_1116_max_OcoboundedI1,axiom,
% 5.05/5.26 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.05/5.26 ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.05/5.26 => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI1
% 5.05/5.26 thf(fact_1117_max_OcoboundedI1,axiom,
% 5.05/5.26 ! [C: rat,A: rat,B: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ C @ A )
% 5.05/5.26 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI1
% 5.05/5.26 thf(fact_1118_max_OcoboundedI1,axiom,
% 5.05/5.26 ! [C: num,A: num,B: num] :
% 5.05/5.26 ( ( ord_less_eq_num @ C @ A )
% 5.05/5.26 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI1
% 5.05/5.26 thf(fact_1119_max_OcoboundedI1,axiom,
% 5.05/5.26 ! [C: nat,A: nat,B: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ C @ A )
% 5.05/5.26 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI1
% 5.05/5.26 thf(fact_1120_max_OcoboundedI1,axiom,
% 5.05/5.26 ! [C: int,A: int,B: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ C @ A )
% 5.05/5.26 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.coboundedI1
% 5.05/5.26 thf(fact_1121_max_Oabsorb__iff2,axiom,
% 5.05/5.26 ( ord_le2932123472753598470d_enat
% 5.05/5.26 = ( ^ [A4: extended_enat,B4: extended_enat] :
% 5.05/5.26 ( ( ord_ma741700101516333627d_enat @ A4 @ B4 )
% 5.05/5.26 = B4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff2
% 5.05/5.26 thf(fact_1122_max_Oabsorb__iff2,axiom,
% 5.05/5.26 ( ord_le3102999989581377725nteger
% 5.05/5.26 = ( ^ [A4: code_integer,B4: code_integer] :
% 5.05/5.26 ( ( ord_max_Code_integer @ A4 @ B4 )
% 5.05/5.26 = B4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff2
% 5.05/5.26 thf(fact_1123_max_Oabsorb__iff2,axiom,
% 5.05/5.26 ( ord_less_eq_rat
% 5.05/5.26 = ( ^ [A4: rat,B4: rat] :
% 5.05/5.26 ( ( ord_max_rat @ A4 @ B4 )
% 5.05/5.26 = B4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff2
% 5.05/5.26 thf(fact_1124_max_Oabsorb__iff2,axiom,
% 5.05/5.26 ( ord_less_eq_num
% 5.05/5.26 = ( ^ [A4: num,B4: num] :
% 5.05/5.26 ( ( ord_max_num @ A4 @ B4 )
% 5.05/5.26 = B4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff2
% 5.05/5.26 thf(fact_1125_max_Oabsorb__iff2,axiom,
% 5.05/5.26 ( ord_less_eq_nat
% 5.05/5.26 = ( ^ [A4: nat,B4: nat] :
% 5.05/5.26 ( ( ord_max_nat @ A4 @ B4 )
% 5.05/5.26 = B4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff2
% 5.05/5.26 thf(fact_1126_max_Oabsorb__iff2,axiom,
% 5.05/5.26 ( ord_less_eq_int
% 5.05/5.26 = ( ^ [A4: int,B4: int] :
% 5.05/5.26 ( ( ord_max_int @ A4 @ B4 )
% 5.05/5.26 = B4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff2
% 5.05/5.26 thf(fact_1127_max_Oabsorb__iff1,axiom,
% 5.05/5.26 ( ord_le2932123472753598470d_enat
% 5.05/5.26 = ( ^ [B4: extended_enat,A4: extended_enat] :
% 5.05/5.26 ( ( ord_ma741700101516333627d_enat @ A4 @ B4 )
% 5.05/5.26 = A4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff1
% 5.05/5.26 thf(fact_1128_max_Oabsorb__iff1,axiom,
% 5.05/5.26 ( ord_le3102999989581377725nteger
% 5.05/5.26 = ( ^ [B4: code_integer,A4: code_integer] :
% 5.05/5.26 ( ( ord_max_Code_integer @ A4 @ B4 )
% 5.05/5.26 = A4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff1
% 5.05/5.26 thf(fact_1129_max_Oabsorb__iff1,axiom,
% 5.05/5.26 ( ord_less_eq_rat
% 5.05/5.26 = ( ^ [B4: rat,A4: rat] :
% 5.05/5.26 ( ( ord_max_rat @ A4 @ B4 )
% 5.05/5.26 = A4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff1
% 5.05/5.26 thf(fact_1130_max_Oabsorb__iff1,axiom,
% 5.05/5.26 ( ord_less_eq_num
% 5.05/5.26 = ( ^ [B4: num,A4: num] :
% 5.05/5.26 ( ( ord_max_num @ A4 @ B4 )
% 5.05/5.26 = A4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff1
% 5.05/5.26 thf(fact_1131_max_Oabsorb__iff1,axiom,
% 5.05/5.26 ( ord_less_eq_nat
% 5.05/5.26 = ( ^ [B4: nat,A4: nat] :
% 5.05/5.26 ( ( ord_max_nat @ A4 @ B4 )
% 5.05/5.26 = A4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff1
% 5.05/5.26 thf(fact_1132_max_Oabsorb__iff1,axiom,
% 5.05/5.26 ( ord_less_eq_int
% 5.05/5.26 = ( ^ [B4: int,A4: int] :
% 5.05/5.26 ( ( ord_max_int @ A4 @ B4 )
% 5.05/5.26 = A4 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.absorb_iff1
% 5.05/5.26 thf(fact_1133_le__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 5.05/5.26 = ( ( ord_le2932123472753598470d_enat @ Z @ X )
% 5.05/5.26 | ( ord_le2932123472753598470d_enat @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_max_iff_disj
% 5.05/5.26 thf(fact_1134_le__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 5.05/5.26 ( ( ord_le3102999989581377725nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 5.05/5.26 = ( ( ord_le3102999989581377725nteger @ Z @ X )
% 5.05/5.26 | ( ord_le3102999989581377725nteger @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_max_iff_disj
% 5.05/5.26 thf(fact_1135_le__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: rat,X: rat,Y: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 5.05/5.26 = ( ( ord_less_eq_rat @ Z @ X )
% 5.05/5.26 | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_max_iff_disj
% 5.05/5.26 thf(fact_1136_le__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: num,X: num,Y: num] :
% 5.05/5.26 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y ) )
% 5.05/5.26 = ( ( ord_less_eq_num @ Z @ X )
% 5.05/5.26 | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_max_iff_disj
% 5.05/5.26 thf(fact_1137_le__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: nat,X: nat,Y: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 5.05/5.26 = ( ( ord_less_eq_nat @ Z @ X )
% 5.05/5.26 | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_max_iff_disj
% 5.05/5.26 thf(fact_1138_le__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: int,X: int,Y: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
% 5.05/5.26 = ( ( ord_less_eq_int @ Z @ X )
% 5.05/5.26 | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % le_max_iff_disj
% 5.05/5.26 thf(fact_1139_max_Ocobounded2,axiom,
% 5.05/5.26 ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded2
% 5.05/5.26 thf(fact_1140_max_Ocobounded2,axiom,
% 5.05/5.26 ! [B: code_integer,A: code_integer] : ( ord_le3102999989581377725nteger @ B @ ( ord_max_Code_integer @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded2
% 5.05/5.26 thf(fact_1141_max_Ocobounded2,axiom,
% 5.05/5.26 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded2
% 5.05/5.26 thf(fact_1142_max_Ocobounded2,axiom,
% 5.05/5.26 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded2
% 5.05/5.26 thf(fact_1143_max_Ocobounded2,axiom,
% 5.05/5.26 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded2
% 5.05/5.26 thf(fact_1144_max_Ocobounded2,axiom,
% 5.05/5.26 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded2
% 5.05/5.26 thf(fact_1145_max_Ocobounded1,axiom,
% 5.05/5.26 ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded1
% 5.05/5.26 thf(fact_1146_max_Ocobounded1,axiom,
% 5.05/5.26 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( ord_max_Code_integer @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded1
% 5.05/5.26 thf(fact_1147_max_Ocobounded1,axiom,
% 5.05/5.26 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded1
% 5.05/5.26 thf(fact_1148_max_Ocobounded1,axiom,
% 5.05/5.26 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded1
% 5.05/5.26 thf(fact_1149_max_Ocobounded1,axiom,
% 5.05/5.26 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded1
% 5.05/5.26 thf(fact_1150_max_Ocobounded1,axiom,
% 5.05/5.26 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.cobounded1
% 5.05/5.26 thf(fact_1151_max_Oorder__iff,axiom,
% 5.05/5.26 ( ord_le2932123472753598470d_enat
% 5.05/5.26 = ( ^ [B4: extended_enat,A4: extended_enat] :
% 5.05/5.26 ( A4
% 5.05/5.26 = ( ord_ma741700101516333627d_enat @ A4 @ B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.order_iff
% 5.05/5.26 thf(fact_1152_max_Oorder__iff,axiom,
% 5.05/5.26 ( ord_le3102999989581377725nteger
% 5.05/5.26 = ( ^ [B4: code_integer,A4: code_integer] :
% 5.05/5.26 ( A4
% 5.05/5.26 = ( ord_max_Code_integer @ A4 @ B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.order_iff
% 5.05/5.26 thf(fact_1153_max_Oorder__iff,axiom,
% 5.05/5.26 ( ord_less_eq_rat
% 5.05/5.26 = ( ^ [B4: rat,A4: rat] :
% 5.05/5.26 ( A4
% 5.05/5.26 = ( ord_max_rat @ A4 @ B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.order_iff
% 5.05/5.26 thf(fact_1154_max_Oorder__iff,axiom,
% 5.05/5.26 ( ord_less_eq_num
% 5.05/5.26 = ( ^ [B4: num,A4: num] :
% 5.05/5.26 ( A4
% 5.05/5.26 = ( ord_max_num @ A4 @ B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.order_iff
% 5.05/5.26 thf(fact_1155_max_Oorder__iff,axiom,
% 5.05/5.26 ( ord_less_eq_nat
% 5.05/5.26 = ( ^ [B4: nat,A4: nat] :
% 5.05/5.26 ( A4
% 5.05/5.26 = ( ord_max_nat @ A4 @ B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.order_iff
% 5.05/5.26 thf(fact_1156_max_Oorder__iff,axiom,
% 5.05/5.26 ( ord_less_eq_int
% 5.05/5.26 = ( ^ [B4: int,A4: int] :
% 5.05/5.26 ( A4
% 5.05/5.26 = ( ord_max_int @ A4 @ B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.order_iff
% 5.05/5.26 thf(fact_1157_max_OboundedI,axiom,
% 5.05/5.26 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.05/5.26 => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.05/5.26 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedI
% 5.05/5.26 thf(fact_1158_max_OboundedI,axiom,
% 5.05/5.26 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.05/5.26 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.05/5.26 => ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.05/5.26 => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedI
% 5.05/5.26 thf(fact_1159_max_OboundedI,axiom,
% 5.05/5.26 ! [B: rat,A: rat,C: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.26 => ( ( ord_less_eq_rat @ C @ A )
% 5.05/5.26 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedI
% 5.05/5.26 thf(fact_1160_max_OboundedI,axiom,
% 5.05/5.26 ! [B: num,A: num,C: num] :
% 5.05/5.26 ( ( ord_less_eq_num @ B @ A )
% 5.05/5.26 => ( ( ord_less_eq_num @ C @ A )
% 5.05/5.26 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedI
% 5.05/5.26 thf(fact_1161_max_OboundedI,axiom,
% 5.05/5.26 ! [B: nat,A: nat,C: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.26 => ( ( ord_less_eq_nat @ C @ A )
% 5.05/5.26 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedI
% 5.05/5.26 thf(fact_1162_max_OboundedI,axiom,
% 5.05/5.26 ! [B: int,A: int,C: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ B @ A )
% 5.05/5.26 => ( ( ord_less_eq_int @ C @ A )
% 5.05/5.26 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedI
% 5.05/5.26 thf(fact_1163_max_OboundedE,axiom,
% 5.05/5.26 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.05/5.26 => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedE
% 5.05/5.26 thf(fact_1164_max_OboundedE,axiom,
% 5.05/5.26 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.05/5.26 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.05/5.26 => ~ ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedE
% 5.05/5.26 thf(fact_1165_max_OboundedE,axiom,
% 5.05/5.26 ! [B: rat,C: rat,A: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.26 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedE
% 5.05/5.26 thf(fact_1166_max_OboundedE,axiom,
% 5.05/5.26 ! [B: num,C: num,A: num] :
% 5.05/5.26 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.05/5.26 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedE
% 5.05/5.26 thf(fact_1167_max_OboundedE,axiom,
% 5.05/5.26 ! [B: nat,C: nat,A: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.26 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedE
% 5.05/5.26 thf(fact_1168_max_OboundedE,axiom,
% 5.05/5.26 ! [B: int,C: int,A: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.05/5.26 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.boundedE
% 5.05/5.26 thf(fact_1169_max_OorderI,axiom,
% 5.05/5.26 ! [A: extended_enat,B: extended_enat] :
% 5.05/5.26 ( ( A
% 5.05/5.26 = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.05/5.26 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderI
% 5.05/5.26 thf(fact_1170_max_OorderI,axiom,
% 5.05/5.26 ! [A: code_integer,B: code_integer] :
% 5.05/5.26 ( ( A
% 5.05/5.26 = ( ord_max_Code_integer @ A @ B ) )
% 5.05/5.26 => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderI
% 5.05/5.26 thf(fact_1171_max_OorderI,axiom,
% 5.05/5.26 ! [A: rat,B: rat] :
% 5.05/5.26 ( ( A
% 5.05/5.26 = ( ord_max_rat @ A @ B ) )
% 5.05/5.26 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderI
% 5.05/5.26 thf(fact_1172_max_OorderI,axiom,
% 5.05/5.26 ! [A: num,B: num] :
% 5.05/5.26 ( ( A
% 5.05/5.26 = ( ord_max_num @ A @ B ) )
% 5.05/5.26 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderI
% 5.05/5.26 thf(fact_1173_max_OorderI,axiom,
% 5.05/5.26 ! [A: nat,B: nat] :
% 5.05/5.26 ( ( A
% 5.05/5.26 = ( ord_max_nat @ A @ B ) )
% 5.05/5.26 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderI
% 5.05/5.26 thf(fact_1174_max_OorderI,axiom,
% 5.05/5.26 ! [A: int,B: int] :
% 5.05/5.26 ( ( A
% 5.05/5.26 = ( ord_max_int @ A @ B ) )
% 5.05/5.26 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderI
% 5.05/5.26 thf(fact_1175_max_OorderE,axiom,
% 5.05/5.26 ! [B: extended_enat,A: extended_enat] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.05/5.26 => ( A
% 5.05/5.26 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderE
% 5.05/5.26 thf(fact_1176_max_OorderE,axiom,
% 5.05/5.26 ! [B: code_integer,A: code_integer] :
% 5.05/5.26 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.05/5.26 => ( A
% 5.05/5.26 = ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderE
% 5.05/5.26 thf(fact_1177_max_OorderE,axiom,
% 5.05/5.26 ! [B: rat,A: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.26 => ( A
% 5.05/5.26 = ( ord_max_rat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderE
% 5.05/5.26 thf(fact_1178_max_OorderE,axiom,
% 5.05/5.26 ! [B: num,A: num] :
% 5.05/5.26 ( ( ord_less_eq_num @ B @ A )
% 5.05/5.26 => ( A
% 5.05/5.26 = ( ord_max_num @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderE
% 5.05/5.26 thf(fact_1179_max_OorderE,axiom,
% 5.05/5.26 ! [B: nat,A: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.26 => ( A
% 5.05/5.26 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderE
% 5.05/5.26 thf(fact_1180_max_OorderE,axiom,
% 5.05/5.26 ! [B: int,A: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ B @ A )
% 5.05/5.26 => ( A
% 5.05/5.26 = ( ord_max_int @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.orderE
% 5.05/5.26 thf(fact_1181_max_Omono,axiom,
% 5.05/5.26 ! [C: extended_enat,A: extended_enat,D: extended_enat,B: extended_enat] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.05/5.26 => ( ( ord_le2932123472753598470d_enat @ D @ B )
% 5.05/5.26 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.mono
% 5.05/5.26 thf(fact_1182_max_Omono,axiom,
% 5.05/5.26 ! [C: code_integer,A: code_integer,D: code_integer,B: code_integer] :
% 5.05/5.26 ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.05/5.26 => ( ( ord_le3102999989581377725nteger @ D @ B )
% 5.05/5.26 => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ C @ D ) @ ( ord_max_Code_integer @ A @ B ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.mono
% 5.05/5.26 thf(fact_1183_max_Omono,axiom,
% 5.05/5.26 ! [C: rat,A: rat,D: rat,B: rat] :
% 5.05/5.26 ( ( ord_less_eq_rat @ C @ A )
% 5.05/5.26 => ( ( ord_less_eq_rat @ D @ B )
% 5.05/5.26 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.mono
% 5.05/5.26 thf(fact_1184_max_Omono,axiom,
% 5.05/5.26 ! [C: num,A: num,D: num,B: num] :
% 5.05/5.26 ( ( ord_less_eq_num @ C @ A )
% 5.05/5.26 => ( ( ord_less_eq_num @ D @ B )
% 5.05/5.26 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.mono
% 5.05/5.26 thf(fact_1185_max_Omono,axiom,
% 5.05/5.26 ! [C: nat,A: nat,D: nat,B: nat] :
% 5.05/5.26 ( ( ord_less_eq_nat @ C @ A )
% 5.05/5.26 => ( ( ord_less_eq_nat @ D @ B )
% 5.05/5.26 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.mono
% 5.05/5.26 thf(fact_1186_max_Omono,axiom,
% 5.05/5.26 ! [C: int,A: int,D: int,B: int] :
% 5.05/5.26 ( ( ord_less_eq_int @ C @ A )
% 5.05/5.26 => ( ( ord_less_eq_int @ D @ B )
% 5.05/5.26 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.mono
% 5.05/5.26 thf(fact_1187_max_Ostrict__coboundedI2,axiom,
% 5.05/5.26 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.05/5.26 ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.05/5.26 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI2
% 5.05/5.26 thf(fact_1188_max_Ostrict__coboundedI2,axiom,
% 5.05/5.26 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.05/5.26 ( ( ord_le6747313008572928689nteger @ C @ B )
% 5.05/5.26 => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI2
% 5.05/5.26 thf(fact_1189_max_Ostrict__coboundedI2,axiom,
% 5.05/5.26 ! [C: real,B: real,A: real] :
% 5.05/5.26 ( ( ord_less_real @ C @ B )
% 5.05/5.26 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI2
% 5.05/5.26 thf(fact_1190_max_Ostrict__coboundedI2,axiom,
% 5.05/5.26 ! [C: rat,B: rat,A: rat] :
% 5.05/5.26 ( ( ord_less_rat @ C @ B )
% 5.05/5.26 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI2
% 5.05/5.26 thf(fact_1191_max_Ostrict__coboundedI2,axiom,
% 5.05/5.26 ! [C: num,B: num,A: num] :
% 5.05/5.26 ( ( ord_less_num @ C @ B )
% 5.05/5.26 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI2
% 5.05/5.26 thf(fact_1192_max_Ostrict__coboundedI2,axiom,
% 5.05/5.26 ! [C: nat,B: nat,A: nat] :
% 5.05/5.26 ( ( ord_less_nat @ C @ B )
% 5.05/5.26 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI2
% 5.05/5.26 thf(fact_1193_max_Ostrict__coboundedI2,axiom,
% 5.05/5.26 ! [C: int,B: int,A: int] :
% 5.05/5.26 ( ( ord_less_int @ C @ B )
% 5.05/5.26 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI2
% 5.05/5.26 thf(fact_1194_max_Ostrict__coboundedI1,axiom,
% 5.05/5.26 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.05/5.26 ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.05/5.26 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI1
% 5.05/5.26 thf(fact_1195_max_Ostrict__coboundedI1,axiom,
% 5.05/5.26 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.05/5.26 ( ( ord_le6747313008572928689nteger @ C @ A )
% 5.05/5.26 => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI1
% 5.05/5.26 thf(fact_1196_max_Ostrict__coboundedI1,axiom,
% 5.05/5.26 ! [C: real,A: real,B: real] :
% 5.05/5.26 ( ( ord_less_real @ C @ A )
% 5.05/5.26 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI1
% 5.05/5.26 thf(fact_1197_max_Ostrict__coboundedI1,axiom,
% 5.05/5.26 ! [C: rat,A: rat,B: rat] :
% 5.05/5.26 ( ( ord_less_rat @ C @ A )
% 5.05/5.26 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI1
% 5.05/5.26 thf(fact_1198_max_Ostrict__coboundedI1,axiom,
% 5.05/5.26 ! [C: num,A: num,B: num] :
% 5.05/5.26 ( ( ord_less_num @ C @ A )
% 5.05/5.26 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI1
% 5.05/5.26 thf(fact_1199_max_Ostrict__coboundedI1,axiom,
% 5.05/5.26 ! [C: nat,A: nat,B: nat] :
% 5.05/5.26 ( ( ord_less_nat @ C @ A )
% 5.05/5.26 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI1
% 5.05/5.26 thf(fact_1200_max_Ostrict__coboundedI1,axiom,
% 5.05/5.26 ! [C: int,A: int,B: int] :
% 5.05/5.26 ( ( ord_less_int @ C @ A )
% 5.05/5.26 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_coboundedI1
% 5.05/5.26 thf(fact_1201_max_Ostrict__order__iff,axiom,
% 5.05/5.26 ( ord_le72135733267957522d_enat
% 5.05/5.26 = ( ^ [B4: extended_enat,A4: extended_enat] :
% 5.05/5.26 ( ( A4
% 5.05/5.26 = ( ord_ma741700101516333627d_enat @ A4 @ B4 ) )
% 5.05/5.26 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_order_iff
% 5.05/5.26 thf(fact_1202_max_Ostrict__order__iff,axiom,
% 5.05/5.26 ( ord_le6747313008572928689nteger
% 5.05/5.26 = ( ^ [B4: code_integer,A4: code_integer] :
% 5.05/5.26 ( ( A4
% 5.05/5.26 = ( ord_max_Code_integer @ A4 @ B4 ) )
% 5.05/5.26 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_order_iff
% 5.05/5.26 thf(fact_1203_max_Ostrict__order__iff,axiom,
% 5.05/5.26 ( ord_less_real
% 5.05/5.26 = ( ^ [B4: real,A4: real] :
% 5.05/5.26 ( ( A4
% 5.05/5.26 = ( ord_max_real @ A4 @ B4 ) )
% 5.05/5.26 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_order_iff
% 5.05/5.26 thf(fact_1204_max_Ostrict__order__iff,axiom,
% 5.05/5.26 ( ord_less_rat
% 5.05/5.26 = ( ^ [B4: rat,A4: rat] :
% 5.05/5.26 ( ( A4
% 5.05/5.26 = ( ord_max_rat @ A4 @ B4 ) )
% 5.05/5.26 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_order_iff
% 5.05/5.26 thf(fact_1205_max_Ostrict__order__iff,axiom,
% 5.05/5.26 ( ord_less_num
% 5.05/5.26 = ( ^ [B4: num,A4: num] :
% 5.05/5.26 ( ( A4
% 5.05/5.26 = ( ord_max_num @ A4 @ B4 ) )
% 5.05/5.26 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_order_iff
% 5.05/5.26 thf(fact_1206_max_Ostrict__order__iff,axiom,
% 5.05/5.26 ( ord_less_nat
% 5.05/5.26 = ( ^ [B4: nat,A4: nat] :
% 5.05/5.26 ( ( A4
% 5.05/5.26 = ( ord_max_nat @ A4 @ B4 ) )
% 5.05/5.26 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_order_iff
% 5.05/5.26 thf(fact_1207_max_Ostrict__order__iff,axiom,
% 5.05/5.26 ( ord_less_int
% 5.05/5.26 = ( ^ [B4: int,A4: int] :
% 5.05/5.26 ( ( A4
% 5.05/5.26 = ( ord_max_int @ A4 @ B4 ) )
% 5.05/5.26 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_order_iff
% 5.05/5.26 thf(fact_1208_max_Ostrict__boundedE,axiom,
% 5.05/5.26 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.05/5.26 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.05/5.26 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_boundedE
% 5.05/5.26 thf(fact_1209_max_Ostrict__boundedE,axiom,
% 5.05/5.26 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.05/5.26 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_le6747313008572928689nteger @ B @ A )
% 5.05/5.26 => ~ ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_boundedE
% 5.05/5.26 thf(fact_1210_max_Ostrict__boundedE,axiom,
% 5.05/5.26 ! [B: real,C: real,A: real] :
% 5.05/5.26 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_less_real @ B @ A )
% 5.05/5.26 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_boundedE
% 5.05/5.26 thf(fact_1211_max_Ostrict__boundedE,axiom,
% 5.05/5.26 ! [B: rat,C: rat,A: rat] :
% 5.05/5.26 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_less_rat @ B @ A )
% 5.05/5.26 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_boundedE
% 5.05/5.26 thf(fact_1212_max_Ostrict__boundedE,axiom,
% 5.05/5.26 ! [B: num,C: num,A: num] :
% 5.05/5.26 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_less_num @ B @ A )
% 5.05/5.26 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_boundedE
% 5.05/5.26 thf(fact_1213_max_Ostrict__boundedE,axiom,
% 5.05/5.26 ! [B: nat,C: nat,A: nat] :
% 5.05/5.26 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_less_nat @ B @ A )
% 5.05/5.26 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_boundedE
% 5.05/5.26 thf(fact_1214_max_Ostrict__boundedE,axiom,
% 5.05/5.26 ! [B: int,C: int,A: int] :
% 5.05/5.26 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 5.05/5.26 => ~ ( ( ord_less_int @ B @ A )
% 5.05/5.26 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % max.strict_boundedE
% 5.05/5.26 thf(fact_1215_less__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 5.05/5.26 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 5.05/5.26 = ( ( ord_le72135733267957522d_enat @ Z @ X )
% 5.05/5.26 | ( ord_le72135733267957522d_enat @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_max_iff_disj
% 5.05/5.26 thf(fact_1216_less__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 5.05/5.26 ( ( ord_le6747313008572928689nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 5.05/5.26 = ( ( ord_le6747313008572928689nteger @ Z @ X )
% 5.05/5.26 | ( ord_le6747313008572928689nteger @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_max_iff_disj
% 5.05/5.26 thf(fact_1217_less__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: real,X: real,Y: real] :
% 5.05/5.26 ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
% 5.05/5.26 = ( ( ord_less_real @ Z @ X )
% 5.05/5.26 | ( ord_less_real @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_max_iff_disj
% 5.05/5.26 thf(fact_1218_less__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: rat,X: rat,Y: rat] :
% 5.05/5.26 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 5.05/5.26 = ( ( ord_less_rat @ Z @ X )
% 5.05/5.26 | ( ord_less_rat @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_max_iff_disj
% 5.05/5.26 thf(fact_1219_less__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: num,X: num,Y: num] :
% 5.05/5.26 ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
% 5.05/5.26 = ( ( ord_less_num @ Z @ X )
% 5.05/5.26 | ( ord_less_num @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_max_iff_disj
% 5.05/5.26 thf(fact_1220_less__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: nat,X: nat,Y: nat] :
% 5.05/5.26 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 5.05/5.26 = ( ( ord_less_nat @ Z @ X )
% 5.05/5.26 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_max_iff_disj
% 5.05/5.26 thf(fact_1221_less__max__iff__disj,axiom,
% 5.05/5.26 ! [Z: int,X: int,Y: int] :
% 5.05/5.26 ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 5.05/5.26 = ( ( ord_less_int @ Z @ X )
% 5.05/5.26 | ( ord_less_int @ Z @ Y ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % less_max_iff_disj
% 5.05/5.26 thf(fact_1222_is__succ__in__set__def,axiom,
% 5.05/5.26 ( vEBT_is_succ_in_set
% 5.05/5.26 = ( ^ [Xs: set_nat,X2: nat,Y2: nat] :
% 5.05/5.26 ( ( member_nat @ Y2 @ Xs )
% 5.05/5.26 & ( ord_less_nat @ X2 @ Y2 )
% 5.05/5.26 & ! [Z2: nat] :
% 5.05/5.26 ( ( member_nat @ Z2 @ Xs )
% 5.05/5.26 => ( ( ord_less_nat @ X2 @ Z2 )
% 5.05/5.26 => ( ord_less_eq_nat @ Y2 @ Z2 ) ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % is_succ_in_set_def
% 5.05/5.26 thf(fact_1223_is__pred__in__set__def,axiom,
% 5.05/5.26 ( vEBT_is_pred_in_set
% 5.05/5.26 = ( ^ [Xs: set_nat,X2: nat,Y2: nat] :
% 5.05/5.26 ( ( member_nat @ Y2 @ Xs )
% 5.05/5.26 & ( ord_less_nat @ Y2 @ X2 )
% 5.05/5.26 & ! [Z2: nat] :
% 5.05/5.26 ( ( member_nat @ Z2 @ Xs )
% 5.05/5.26 => ( ( ord_less_nat @ Z2 @ X2 )
% 5.05/5.26 => ( ord_less_eq_nat @ Z2 @ Y2 ) ) ) ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % is_pred_in_set_def
% 5.05/5.26 thf(fact_1224_vebt__pred_Osimps_I4_J,axiom,
% 5.05/5.26 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.05/5.26 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.05/5.26 = none_nat ) ).
% 5.05/5.26
% 5.05/5.26 % vebt_pred.simps(4)
% 5.05/5.26 thf(fact_1225_vebt__succ_Osimps_I3_J,axiom,
% 5.05/5.26 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.05/5.26 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.05/5.26 = none_nat ) ).
% 5.05/5.26
% 5.05/5.26 % vebt_succ.simps(3)
% 5.05/5.26 thf(fact_1226_buildup__gives__empty,axiom,
% 5.05/5.26 ! [N2: nat] :
% 5.05/5.26 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N2 ) )
% 5.05/5.26 = bot_bot_set_nat ) ).
% 5.05/5.26
% 5.05/5.26 % buildup_gives_empty
% 5.05/5.26 thf(fact_1227_max__bot2,axiom,
% 5.05/5.26 ! [X: set_nat] :
% 5.05/5.26 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % max_bot2
% 5.05/5.26 thf(fact_1228_max__bot2,axiom,
% 5.05/5.26 ! [X: set_int] :
% 5.05/5.26 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % max_bot2
% 5.05/5.26 thf(fact_1229_max__bot2,axiom,
% 5.05/5.26 ! [X: set_real] :
% 5.05/5.26 ( ( ord_max_set_real @ X @ bot_bot_set_real )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % max_bot2
% 5.05/5.26 thf(fact_1230_max__bot2,axiom,
% 5.05/5.26 ! [X: nat] :
% 5.05/5.26 ( ( ord_max_nat @ X @ bot_bot_nat )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % max_bot2
% 5.05/5.26 thf(fact_1231_max__bot2,axiom,
% 5.05/5.26 ! [X: extended_enat] :
% 5.05/5.26 ( ( ord_ma741700101516333627d_enat @ X @ bot_bo4199563552545308370d_enat )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % max_bot2
% 5.05/5.26 thf(fact_1232_max__bot,axiom,
% 5.05/5.26 ! [X: set_nat] :
% 5.05/5.26 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % max_bot
% 5.05/5.26 thf(fact_1233_max__bot,axiom,
% 5.05/5.26 ! [X: set_int] :
% 5.05/5.26 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % max_bot
% 5.05/5.26 thf(fact_1234_max__bot,axiom,
% 5.05/5.26 ! [X: set_real] :
% 5.05/5.26 ( ( ord_max_set_real @ bot_bot_set_real @ X )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % max_bot
% 5.05/5.26 thf(fact_1235_max__bot,axiom,
% 5.05/5.26 ! [X: nat] :
% 5.05/5.26 ( ( ord_max_nat @ bot_bot_nat @ X )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % max_bot
% 5.05/5.26 thf(fact_1236_max__bot,axiom,
% 5.05/5.26 ! [X: extended_enat] :
% 5.05/5.26 ( ( ord_ma741700101516333627d_enat @ bot_bo4199563552545308370d_enat @ X )
% 5.05/5.26 = X ) ).
% 5.05/5.26
% 5.05/5.26 % max_bot
% 5.05/5.26 thf(fact_1237_enat__ord__number_I1_J,axiom,
% 5.05/5.26 ! [M: num,N2: num] :
% 5.05/5.26 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.05/5.26 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % enat_ord_number(1)
% 5.05/5.26 thf(fact_1238_empty__subsetI,axiom,
% 5.05/5.26 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 5.05/5.26
% 5.05/5.26 % empty_subsetI
% 5.05/5.26 thf(fact_1239_empty__subsetI,axiom,
% 5.05/5.26 ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 5.05/5.26
% 5.05/5.26 % empty_subsetI
% 5.05/5.26 thf(fact_1240_empty__subsetI,axiom,
% 5.05/5.26 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 5.05/5.26
% 5.05/5.26 % empty_subsetI
% 5.05/5.26 thf(fact_1241_subset__empty,axiom,
% 5.05/5.26 ! [A2: set_nat] :
% 5.05/5.26 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 5.05/5.26 = ( A2 = bot_bot_set_nat ) ) ).
% 5.05/5.26
% 5.05/5.26 % subset_empty
% 5.05/5.26 thf(fact_1242_subset__empty,axiom,
% 5.05/5.26 ! [A2: set_real] :
% 5.05/5.26 ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 5.05/5.26 = ( A2 = bot_bot_set_real ) ) ).
% 5.05/5.26
% 5.05/5.26 % subset_empty
% 5.05/5.26 thf(fact_1243_subset__empty,axiom,
% 5.05/5.26 ! [A2: set_int] :
% 5.05/5.26 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 5.05/5.26 = ( A2 = bot_bot_set_int ) ) ).
% 5.05/5.26
% 5.05/5.26 % subset_empty
% 5.05/5.26 thf(fact_1244_Diff__eq__empty__iff,axiom,
% 5.05/5.26 ! [A2: set_real,B3: set_real] :
% 5.05/5.26 ( ( ( minus_minus_set_real @ A2 @ B3 )
% 5.05/5.26 = bot_bot_set_real )
% 5.05/5.26 = ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 5.05/5.26
% 5.05/5.26 % Diff_eq_empty_iff
% 5.05/5.26 thf(fact_1245_Diff__eq__empty__iff,axiom,
% 5.05/5.26 ! [A2: set_nat,B3: set_nat] :
% 5.05/5.26 ( ( ( minus_minus_set_nat @ A2 @ B3 )
% 5.05/5.26 = bot_bot_set_nat )
% 5.05/5.26 = ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 5.05/5.26
% 5.05/5.26 % Diff_eq_empty_iff
% 5.05/5.26 thf(fact_1246_Diff__eq__empty__iff,axiom,
% 5.05/5.26 ! [A2: set_int,B3: set_int] :
% 5.05/5.26 ( ( ( minus_minus_set_int @ A2 @ B3 )
% 5.05/5.26 = bot_bot_set_int )
% 5.05/5.26 = ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.05/5.26
% 5.05/5.26 % Diff_eq_empty_iff
% 5.05/5.26 thf(fact_1247_enat__ord__number_I2_J,axiom,
% 5.05/5.26 ! [M: num,N2: num] :
% 5.05/5.26 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.05/5.26 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % enat_ord_number(2)
% 5.05/5.26 thf(fact_1248_Suc__double__not__eq__double,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.05/5.26 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.05/5.26
% 5.05/5.26 % Suc_double_not_eq_double
% 5.05/5.26 thf(fact_1249_double__not__eq__Suc__double,axiom,
% 5.05/5.26 ! [M: nat,N2: nat] :
% 5.05/5.26 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.05/5.26 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % double_not_eq_Suc_double
% 5.05/5.26 thf(fact_1250_order__refl,axiom,
% 5.05/5.26 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 5.05/5.26
% 5.05/5.26 % order_refl
% 5.05/5.26 thf(fact_1251_order__refl,axiom,
% 5.05/5.26 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 5.05/5.26
% 5.05/5.26 % order_refl
% 5.05/5.26 thf(fact_1252_order__refl,axiom,
% 5.05/5.26 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 5.05/5.26
% 5.05/5.26 % order_refl
% 5.05/5.26 thf(fact_1253_order__refl,axiom,
% 5.05/5.26 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 5.05/5.26
% 5.05/5.26 % order_refl
% 5.05/5.26 thf(fact_1254_order__refl,axiom,
% 5.05/5.26 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 5.05/5.26
% 5.05/5.26 % order_refl
% 5.05/5.26 thf(fact_1255_dual__order_Orefl,axiom,
% 5.05/5.26 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.05/5.26
% 5.05/5.26 % dual_order.refl
% 5.05/5.26 thf(fact_1256_dual__order_Orefl,axiom,
% 5.05/5.26 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.05/5.26
% 5.05/5.26 % dual_order.refl
% 5.05/5.26 thf(fact_1257_dual__order_Orefl,axiom,
% 5.05/5.26 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.05/5.26
% 5.05/5.26 % dual_order.refl
% 5.05/5.26 thf(fact_1258_dual__order_Orefl,axiom,
% 5.05/5.26 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.05/5.26
% 5.05/5.26 % dual_order.refl
% 5.05/5.26 thf(fact_1259_dual__order_Orefl,axiom,
% 5.05/5.26 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.05/5.26
% 5.05/5.26 % dual_order.refl
% 5.05/5.26 thf(fact_1260_subsetI,axiom,
% 5.05/5.26 ! [A2: set_complex,B3: set_complex] :
% 5.05/5.26 ( ! [X3: complex] :
% 5.05/5.26 ( ( member_complex @ X3 @ A2 )
% 5.05/5.26 => ( member_complex @ X3 @ B3 ) )
% 5.05/5.26 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ).
% 5.05/5.26
% 5.05/5.26 % subsetI
% 5.05/5.26 thf(fact_1261_subsetI,axiom,
% 5.05/5.26 ! [A2: set_real,B3: set_real] :
% 5.05/5.26 ( ! [X3: real] :
% 5.05/5.26 ( ( member_real @ X3 @ A2 )
% 5.05/5.26 => ( member_real @ X3 @ B3 ) )
% 5.05/5.26 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 5.05/5.26
% 5.05/5.26 % subsetI
% 5.05/5.26 thf(fact_1262_subsetI,axiom,
% 5.05/5.26 ! [A2: set_set_nat,B3: set_set_nat] :
% 5.05/5.26 ( ! [X3: set_nat] :
% 5.05/5.26 ( ( member_set_nat @ X3 @ A2 )
% 5.05/5.26 => ( member_set_nat @ X3 @ B3 ) )
% 5.05/5.26 => ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ).
% 5.05/5.26
% 5.05/5.26 % subsetI
% 5.05/5.26 thf(fact_1263_subsetI,axiom,
% 5.05/5.26 ! [A2: set_nat,B3: set_nat] :
% 5.05/5.26 ( ! [X3: nat] :
% 5.05/5.26 ( ( member_nat @ X3 @ A2 )
% 5.05/5.26 => ( member_nat @ X3 @ B3 ) )
% 5.05/5.26 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 5.05/5.26
% 5.05/5.26 % subsetI
% 5.05/5.26 thf(fact_1264_subsetI,axiom,
% 5.05/5.26 ! [A2: set_int,B3: set_int] :
% 5.05/5.26 ( ! [X3: int] :
% 5.05/5.26 ( ( member_int @ X3 @ A2 )
% 5.05/5.26 => ( member_int @ X3 @ B3 ) )
% 5.05/5.26 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.05/5.26
% 5.05/5.26 % subsetI
% 5.05/5.26 thf(fact_1265_psubsetI,axiom,
% 5.05/5.26 ! [A2: set_int,B3: set_int] :
% 5.05/5.26 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.05/5.26 => ( ( A2 != B3 )
% 5.05/5.26 => ( ord_less_set_int @ A2 @ B3 ) ) ) ).
% 5.05/5.26
% 5.05/5.26 % psubsetI
% 5.05/5.26 thf(fact_1266_subset__antisym,axiom,
% 5.05/5.26 ! [A2: set_int,B3: set_int] :
% 5.05/5.26 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.05/5.27 => ( A2 = B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_antisym
% 5.05/5.27 thf(fact_1267_Diff__idemp,axiom,
% 5.05/5.27 ! [A2: set_nat,B3: set_nat] :
% 5.05/5.27 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ B3 )
% 5.05/5.27 = ( minus_minus_set_nat @ A2 @ B3 ) ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_idemp
% 5.05/5.27 thf(fact_1268_Diff__iff,axiom,
% 5.05/5.27 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.05/5.27 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.05/5.27 = ( ( member_complex @ C @ A2 )
% 5.05/5.27 & ~ ( member_complex @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_iff
% 5.05/5.27 thf(fact_1269_Diff__iff,axiom,
% 5.05/5.27 ! [C: real,A2: set_real,B3: set_real] :
% 5.05/5.27 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.05/5.27 = ( ( member_real @ C @ A2 )
% 5.05/5.27 & ~ ( member_real @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_iff
% 5.05/5.27 thf(fact_1270_Diff__iff,axiom,
% 5.05/5.27 ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.05/5.27 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 5.05/5.27 = ( ( member_set_nat @ C @ A2 )
% 5.05/5.27 & ~ ( member_set_nat @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_iff
% 5.05/5.27 thf(fact_1271_Diff__iff,axiom,
% 5.05/5.27 ! [C: int,A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.05/5.27 = ( ( member_int @ C @ A2 )
% 5.05/5.27 & ~ ( member_int @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_iff
% 5.05/5.27 thf(fact_1272_Diff__iff,axiom,
% 5.05/5.27 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.05/5.27 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.05/5.27 = ( ( member_nat @ C @ A2 )
% 5.05/5.27 & ~ ( member_nat @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_iff
% 5.05/5.27 thf(fact_1273_DiffI,axiom,
% 5.05/5.27 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.05/5.27 ( ( member_complex @ C @ A2 )
% 5.05/5.27 => ( ~ ( member_complex @ C @ B3 )
% 5.05/5.27 => ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffI
% 5.05/5.27 thf(fact_1274_DiffI,axiom,
% 5.05/5.27 ! [C: real,A2: set_real,B3: set_real] :
% 5.05/5.27 ( ( member_real @ C @ A2 )
% 5.05/5.27 => ( ~ ( member_real @ C @ B3 )
% 5.05/5.27 => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffI
% 5.05/5.27 thf(fact_1275_DiffI,axiom,
% 5.05/5.27 ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.05/5.27 ( ( member_set_nat @ C @ A2 )
% 5.05/5.27 => ( ~ ( member_set_nat @ C @ B3 )
% 5.05/5.27 => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffI
% 5.05/5.27 thf(fact_1276_DiffI,axiom,
% 5.05/5.27 ! [C: int,A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( member_int @ C @ A2 )
% 5.05/5.27 => ( ~ ( member_int @ C @ B3 )
% 5.05/5.27 => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffI
% 5.05/5.27 thf(fact_1277_DiffI,axiom,
% 5.05/5.27 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.05/5.27 ( ( member_nat @ C @ A2 )
% 5.05/5.27 => ( ~ ( member_nat @ C @ B3 )
% 5.05/5.27 => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffI
% 5.05/5.27 thf(fact_1278_Diff__empty,axiom,
% 5.05/5.27 ! [A2: set_int] :
% 5.05/5.27 ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 5.05/5.27 = A2 ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_empty
% 5.05/5.27 thf(fact_1279_Diff__empty,axiom,
% 5.05/5.27 ! [A2: set_real] :
% 5.05/5.27 ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 5.05/5.27 = A2 ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_empty
% 5.05/5.27 thf(fact_1280_Diff__empty,axiom,
% 5.05/5.27 ! [A2: set_nat] :
% 5.05/5.27 ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 5.05/5.27 = A2 ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_empty
% 5.05/5.27 thf(fact_1281_empty__Diff,axiom,
% 5.05/5.27 ! [A2: set_int] :
% 5.05/5.27 ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 5.05/5.27 = bot_bot_set_int ) ).
% 5.05/5.27
% 5.05/5.27 % empty_Diff
% 5.05/5.27 thf(fact_1282_empty__Diff,axiom,
% 5.05/5.27 ! [A2: set_real] :
% 5.05/5.27 ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 5.05/5.27 = bot_bot_set_real ) ).
% 5.05/5.27
% 5.05/5.27 % empty_Diff
% 5.05/5.27 thf(fact_1283_empty__Diff,axiom,
% 5.05/5.27 ! [A2: set_nat] :
% 5.05/5.27 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 5.05/5.27 = bot_bot_set_nat ) ).
% 5.05/5.27
% 5.05/5.27 % empty_Diff
% 5.05/5.27 thf(fact_1284_Diff__cancel,axiom,
% 5.05/5.27 ! [A2: set_int] :
% 5.05/5.27 ( ( minus_minus_set_int @ A2 @ A2 )
% 5.05/5.27 = bot_bot_set_int ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_cancel
% 5.05/5.27 thf(fact_1285_Diff__cancel,axiom,
% 5.05/5.27 ! [A2: set_real] :
% 5.05/5.27 ( ( minus_minus_set_real @ A2 @ A2 )
% 5.05/5.27 = bot_bot_set_real ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_cancel
% 5.05/5.27 thf(fact_1286_Diff__cancel,axiom,
% 5.05/5.27 ! [A2: set_nat] :
% 5.05/5.27 ( ( minus_minus_set_nat @ A2 @ A2 )
% 5.05/5.27 = bot_bot_set_nat ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_cancel
% 5.05/5.27 thf(fact_1287_minus__set__def,axiom,
% 5.05/5.27 ( minus_minus_set_real
% 5.05/5.27 = ( ^ [A5: set_real,B5: set_real] :
% 5.05/5.27 ( collect_real
% 5.05/5.27 @ ( minus_minus_real_o
% 5.05/5.27 @ ^ [X2: real] : ( member_real @ X2 @ A5 )
% 5.05/5.27 @ ^ [X2: real] : ( member_real @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % minus_set_def
% 5.05/5.27 thf(fact_1288_minus__set__def,axiom,
% 5.05/5.27 ( minus_1052850069191792384nt_int
% 5.05/5.27 = ( ^ [A5: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
% 5.05/5.27 ( collec213857154873943460nt_int
% 5.05/5.27 @ ( minus_711738161318947805_int_o
% 5.05/5.27 @ ^ [X2: product_prod_int_int] : ( member5262025264175285858nt_int @ X2 @ A5 )
% 5.05/5.27 @ ^ [X2: product_prod_int_int] : ( member5262025264175285858nt_int @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % minus_set_def
% 5.05/5.27 thf(fact_1289_minus__set__def,axiom,
% 5.05/5.27 ( minus_811609699411566653omplex
% 5.05/5.27 = ( ^ [A5: set_complex,B5: set_complex] :
% 5.05/5.27 ( collect_complex
% 5.05/5.27 @ ( minus_8727706125548526216plex_o
% 5.05/5.27 @ ^ [X2: complex] : ( member_complex @ X2 @ A5 )
% 5.05/5.27 @ ^ [X2: complex] : ( member_complex @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % minus_set_def
% 5.05/5.27 thf(fact_1290_minus__set__def,axiom,
% 5.05/5.27 ( minus_2163939370556025621et_nat
% 5.05/5.27 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 5.05/5.27 ( collect_set_nat
% 5.05/5.27 @ ( minus_6910147592129066416_nat_o
% 5.05/5.27 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 )
% 5.05/5.27 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % minus_set_def
% 5.05/5.27 thf(fact_1291_minus__set__def,axiom,
% 5.05/5.27 ( minus_minus_set_int
% 5.05/5.27 = ( ^ [A5: set_int,B5: set_int] :
% 5.05/5.27 ( collect_int
% 5.05/5.27 @ ( minus_minus_int_o
% 5.05/5.27 @ ^ [X2: int] : ( member_int @ X2 @ A5 )
% 5.05/5.27 @ ^ [X2: int] : ( member_int @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % minus_set_def
% 5.05/5.27 thf(fact_1292_minus__set__def,axiom,
% 5.05/5.27 ( minus_minus_set_nat
% 5.05/5.27 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.05/5.27 ( collect_nat
% 5.05/5.27 @ ( minus_minus_nat_o
% 5.05/5.27 @ ^ [X2: nat] : ( member_nat @ X2 @ A5 )
% 5.05/5.27 @ ^ [X2: nat] : ( member_nat @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % minus_set_def
% 5.05/5.27 thf(fact_1293_set__diff__eq,axiom,
% 5.05/5.27 ( minus_minus_set_real
% 5.05/5.27 = ( ^ [A5: set_real,B5: set_real] :
% 5.05/5.27 ( collect_real
% 5.05/5.27 @ ^ [X2: real] :
% 5.05/5.27 ( ( member_real @ X2 @ A5 )
% 5.05/5.27 & ~ ( member_real @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % set_diff_eq
% 5.05/5.27 thf(fact_1294_set__diff__eq,axiom,
% 5.05/5.27 ( minus_1052850069191792384nt_int
% 5.05/5.27 = ( ^ [A5: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
% 5.05/5.27 ( collec213857154873943460nt_int
% 5.05/5.27 @ ^ [X2: product_prod_int_int] :
% 5.05/5.27 ( ( member5262025264175285858nt_int @ X2 @ A5 )
% 5.05/5.27 & ~ ( member5262025264175285858nt_int @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % set_diff_eq
% 5.05/5.27 thf(fact_1295_set__diff__eq,axiom,
% 5.05/5.27 ( minus_811609699411566653omplex
% 5.05/5.27 = ( ^ [A5: set_complex,B5: set_complex] :
% 5.05/5.27 ( collect_complex
% 5.05/5.27 @ ^ [X2: complex] :
% 5.05/5.27 ( ( member_complex @ X2 @ A5 )
% 5.05/5.27 & ~ ( member_complex @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % set_diff_eq
% 5.05/5.27 thf(fact_1296_set__diff__eq,axiom,
% 5.05/5.27 ( minus_2163939370556025621et_nat
% 5.05/5.27 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 5.05/5.27 ( collect_set_nat
% 5.05/5.27 @ ^ [X2: set_nat] :
% 5.05/5.27 ( ( member_set_nat @ X2 @ A5 )
% 5.05/5.27 & ~ ( member_set_nat @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % set_diff_eq
% 5.05/5.27 thf(fact_1297_set__diff__eq,axiom,
% 5.05/5.27 ( minus_minus_set_int
% 5.05/5.27 = ( ^ [A5: set_int,B5: set_int] :
% 5.05/5.27 ( collect_int
% 5.05/5.27 @ ^ [X2: int] :
% 5.05/5.27 ( ( member_int @ X2 @ A5 )
% 5.05/5.27 & ~ ( member_int @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % set_diff_eq
% 5.05/5.27 thf(fact_1298_set__diff__eq,axiom,
% 5.05/5.27 ( minus_minus_set_nat
% 5.05/5.27 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.05/5.27 ( collect_nat
% 5.05/5.27 @ ^ [X2: nat] :
% 5.05/5.27 ( ( member_nat @ X2 @ A5 )
% 5.05/5.27 & ~ ( member_nat @ X2 @ B5 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % set_diff_eq
% 5.05/5.27 thf(fact_1299_DiffD2,axiom,
% 5.05/5.27 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.05/5.27 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.05/5.27 => ~ ( member_complex @ C @ B3 ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffD2
% 5.05/5.27 thf(fact_1300_DiffD2,axiom,
% 5.05/5.27 ! [C: real,A2: set_real,B3: set_real] :
% 5.05/5.27 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.05/5.27 => ~ ( member_real @ C @ B3 ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffD2
% 5.05/5.27 thf(fact_1301_DiffD2,axiom,
% 5.05/5.27 ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.05/5.27 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 5.05/5.27 => ~ ( member_set_nat @ C @ B3 ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffD2
% 5.05/5.27 thf(fact_1302_DiffD2,axiom,
% 5.05/5.27 ! [C: int,A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.05/5.27 => ~ ( member_int @ C @ B3 ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffD2
% 5.05/5.27 thf(fact_1303_DiffD2,axiom,
% 5.05/5.27 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.05/5.27 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.05/5.27 => ~ ( member_nat @ C @ B3 ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffD2
% 5.05/5.27 thf(fact_1304_DiffD1,axiom,
% 5.05/5.27 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.05/5.27 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.05/5.27 => ( member_complex @ C @ A2 ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffD1
% 5.05/5.27 thf(fact_1305_DiffD1,axiom,
% 5.05/5.27 ! [C: real,A2: set_real,B3: set_real] :
% 5.05/5.27 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.05/5.27 => ( member_real @ C @ A2 ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffD1
% 5.05/5.27 thf(fact_1306_DiffD1,axiom,
% 5.05/5.27 ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.05/5.27 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 5.05/5.27 => ( member_set_nat @ C @ A2 ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffD1
% 5.05/5.27 thf(fact_1307_DiffD1,axiom,
% 5.05/5.27 ! [C: int,A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.05/5.27 => ( member_int @ C @ A2 ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffD1
% 5.05/5.27 thf(fact_1308_DiffD1,axiom,
% 5.05/5.27 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.05/5.27 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.05/5.27 => ( member_nat @ C @ A2 ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffD1
% 5.05/5.27 thf(fact_1309_DiffE,axiom,
% 5.05/5.27 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.05/5.27 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.05/5.27 => ~ ( ( member_complex @ C @ A2 )
% 5.05/5.27 => ( member_complex @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffE
% 5.05/5.27 thf(fact_1310_DiffE,axiom,
% 5.05/5.27 ! [C: real,A2: set_real,B3: set_real] :
% 5.05/5.27 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.05/5.27 => ~ ( ( member_real @ C @ A2 )
% 5.05/5.27 => ( member_real @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffE
% 5.05/5.27 thf(fact_1311_DiffE,axiom,
% 5.05/5.27 ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.05/5.27 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 5.05/5.27 => ~ ( ( member_set_nat @ C @ A2 )
% 5.05/5.27 => ( member_set_nat @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffE
% 5.05/5.27 thf(fact_1312_DiffE,axiom,
% 5.05/5.27 ! [C: int,A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.05/5.27 => ~ ( ( member_int @ C @ A2 )
% 5.05/5.27 => ( member_int @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffE
% 5.05/5.27 thf(fact_1313_DiffE,axiom,
% 5.05/5.27 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.05/5.27 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.05/5.27 => ~ ( ( member_nat @ C @ A2 )
% 5.05/5.27 => ( member_nat @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % DiffE
% 5.05/5.27 thf(fact_1314_add__diff__assoc__enat,axiom,
% 5.05/5.27 ! [Z: extended_enat,Y: extended_enat,X: extended_enat] :
% 5.05/5.27 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 5.05/5.27 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 5.05/5.27 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % add_diff_assoc_enat
% 5.05/5.27 thf(fact_1315_psubset__imp__ex__mem,axiom,
% 5.05/5.27 ! [A2: set_complex,B3: set_complex] :
% 5.05/5.27 ( ( ord_less_set_complex @ A2 @ B3 )
% 5.05/5.27 => ? [B2: complex] : ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B3 @ A2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % psubset_imp_ex_mem
% 5.05/5.27 thf(fact_1316_psubset__imp__ex__mem,axiom,
% 5.05/5.27 ! [A2: set_real,B3: set_real] :
% 5.05/5.27 ( ( ord_less_set_real @ A2 @ B3 )
% 5.05/5.27 => ? [B2: real] : ( member_real @ B2 @ ( minus_minus_set_real @ B3 @ A2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % psubset_imp_ex_mem
% 5.05/5.27 thf(fact_1317_psubset__imp__ex__mem,axiom,
% 5.05/5.27 ! [A2: set_set_nat,B3: set_set_nat] :
% 5.05/5.27 ( ( ord_less_set_set_nat @ A2 @ B3 )
% 5.05/5.27 => ? [B2: set_nat] : ( member_set_nat @ B2 @ ( minus_2163939370556025621et_nat @ B3 @ A2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % psubset_imp_ex_mem
% 5.05/5.27 thf(fact_1318_psubset__imp__ex__mem,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( ord_less_set_int @ A2 @ B3 )
% 5.05/5.27 => ? [B2: int] : ( member_int @ B2 @ ( minus_minus_set_int @ B3 @ A2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % psubset_imp_ex_mem
% 5.05/5.27 thf(fact_1319_psubset__imp__ex__mem,axiom,
% 5.05/5.27 ! [A2: set_nat,B3: set_nat] :
% 5.05/5.27 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.05/5.27 => ? [B2: nat] : ( member_nat @ B2 @ ( minus_minus_set_nat @ B3 @ A2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % psubset_imp_ex_mem
% 5.05/5.27 thf(fact_1320_nle__le,axiom,
% 5.05/5.27 ! [A: rat,B: rat] :
% 5.05/5.27 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.05/5.27 = ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.27 & ( B != A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % nle_le
% 5.05/5.27 thf(fact_1321_nle__le,axiom,
% 5.05/5.27 ! [A: num,B: num] :
% 5.05/5.27 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.05/5.27 = ( ( ord_less_eq_num @ B @ A )
% 5.05/5.27 & ( B != A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % nle_le
% 5.05/5.27 thf(fact_1322_nle__le,axiom,
% 5.05/5.27 ! [A: nat,B: nat] :
% 5.05/5.27 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.05/5.27 = ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.27 & ( B != A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % nle_le
% 5.05/5.27 thf(fact_1323_nle__le,axiom,
% 5.05/5.27 ! [A: int,B: int] :
% 5.05/5.27 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.05/5.27 = ( ( ord_less_eq_int @ B @ A )
% 5.05/5.27 & ( B != A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % nle_le
% 5.05/5.27 thf(fact_1324_le__cases3,axiom,
% 5.05/5.27 ! [X: rat,Y: rat,Z: rat] :
% 5.05/5.27 ( ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 5.05/5.27 => ( ( ( ord_less_eq_rat @ Y @ X )
% 5.05/5.27 => ~ ( ord_less_eq_rat @ X @ Z ) )
% 5.05/5.27 => ( ( ( ord_less_eq_rat @ X @ Z )
% 5.05/5.27 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 5.05/5.27 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 5.05/5.27 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 5.05/5.27 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 5.05/5.27 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 5.05/5.27 => ~ ( ( ord_less_eq_rat @ Z @ X )
% 5.05/5.27 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % le_cases3
% 5.05/5.27 thf(fact_1325_le__cases3,axiom,
% 5.05/5.27 ! [X: num,Y: num,Z: num] :
% 5.05/5.27 ( ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 5.05/5.27 => ( ( ( ord_less_eq_num @ Y @ X )
% 5.05/5.27 => ~ ( ord_less_eq_num @ X @ Z ) )
% 5.05/5.27 => ( ( ( ord_less_eq_num @ X @ Z )
% 5.05/5.27 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 5.05/5.27 => ( ( ( ord_less_eq_num @ Z @ Y )
% 5.05/5.27 => ~ ( ord_less_eq_num @ Y @ X ) )
% 5.05/5.27 => ( ( ( ord_less_eq_num @ Y @ Z )
% 5.05/5.27 => ~ ( ord_less_eq_num @ Z @ X ) )
% 5.05/5.27 => ~ ( ( ord_less_eq_num @ Z @ X )
% 5.05/5.27 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % le_cases3
% 5.05/5.27 thf(fact_1326_le__cases3,axiom,
% 5.05/5.27 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.27 ( ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 5.05/5.27 => ( ( ( ord_less_eq_nat @ Y @ X )
% 5.05/5.27 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 5.05/5.27 => ( ( ( ord_less_eq_nat @ X @ Z )
% 5.05/5.27 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 5.05/5.27 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 5.05/5.27 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 5.05/5.27 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 5.05/5.27 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 5.05/5.27 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 5.05/5.27 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % le_cases3
% 5.05/5.27 thf(fact_1327_le__cases3,axiom,
% 5.05/5.27 ! [X: int,Y: int,Z: int] :
% 5.05/5.27 ( ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 5.05/5.27 => ( ( ( ord_less_eq_int @ Y @ X )
% 5.05/5.27 => ~ ( ord_less_eq_int @ X @ Z ) )
% 5.05/5.27 => ( ( ( ord_less_eq_int @ X @ Z )
% 5.05/5.27 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 5.05/5.27 => ( ( ( ord_less_eq_int @ Z @ Y )
% 5.05/5.27 => ~ ( ord_less_eq_int @ Y @ X ) )
% 5.05/5.27 => ( ( ( ord_less_eq_int @ Y @ Z )
% 5.05/5.27 => ~ ( ord_less_eq_int @ Z @ X ) )
% 5.05/5.27 => ~ ( ( ord_less_eq_int @ Z @ X )
% 5.05/5.27 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % le_cases3
% 5.05/5.27 thf(fact_1328_order__class_Oorder__eq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: set_int,Z3: set_int] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [X2: set_int,Y2: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ X2 @ Y2 )
% 5.05/5.27 & ( ord_less_eq_set_int @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_class.order_eq_iff
% 5.05/5.27 thf(fact_1329_order__class_Oorder__eq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: rat,Z3: rat] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [X2: rat,Y2: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.05/5.27 & ( ord_less_eq_rat @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_class.order_eq_iff
% 5.05/5.27 thf(fact_1330_order__class_Oorder__eq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: num,Z3: num] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [X2: num,Y2: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X2 @ Y2 )
% 5.05/5.27 & ( ord_less_eq_num @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_class.order_eq_iff
% 5.05/5.27 thf(fact_1331_order__class_Oorder__eq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [X2: nat,Y2: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 5.05/5.27 & ( ord_less_eq_nat @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_class.order_eq_iff
% 5.05/5.27 thf(fact_1332_order__class_Oorder__eq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: int,Z3: int] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [X2: int,Y2: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ X2 @ Y2 )
% 5.05/5.27 & ( ord_less_eq_int @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_class.order_eq_iff
% 5.05/5.27 thf(fact_1333_ord__eq__le__trans,axiom,
% 5.05/5.27 ! [A: set_int,B: set_int,C: set_int] :
% 5.05/5.27 ( ( A = B )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ B @ C )
% 5.05/5.27 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_trans
% 5.05/5.27 thf(fact_1334_ord__eq__le__trans,axiom,
% 5.05/5.27 ! [A: rat,B: rat,C: rat] :
% 5.05/5.27 ( ( A = B )
% 5.05/5.27 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.27 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_trans
% 5.05/5.27 thf(fact_1335_ord__eq__le__trans,axiom,
% 5.05/5.27 ! [A: num,B: num,C: num] :
% 5.05/5.27 ( ( A = B )
% 5.05/5.27 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.27 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_trans
% 5.05/5.27 thf(fact_1336_ord__eq__le__trans,axiom,
% 5.05/5.27 ! [A: nat,B: nat,C: nat] :
% 5.05/5.27 ( ( A = B )
% 5.05/5.27 => ( ( ord_less_eq_nat @ B @ C )
% 5.05/5.27 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_trans
% 5.05/5.27 thf(fact_1337_ord__eq__le__trans,axiom,
% 5.05/5.27 ! [A: int,B: int,C: int] :
% 5.05/5.27 ( ( A = B )
% 5.05/5.27 => ( ( ord_less_eq_int @ B @ C )
% 5.05/5.27 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_trans
% 5.05/5.27 thf(fact_1338_ord__le__eq__trans,axiom,
% 5.05/5.27 ! [A: set_int,B: set_int,C: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A @ B )
% 5.05/5.27 => ( ( B = C )
% 5.05/5.27 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_trans
% 5.05/5.27 thf(fact_1339_ord__le__eq__trans,axiom,
% 5.05/5.27 ! [A: rat,B: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( B = C )
% 5.05/5.27 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_trans
% 5.05/5.27 thf(fact_1340_ord__le__eq__trans,axiom,
% 5.05/5.27 ! [A: num,B: num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( B = C )
% 5.05/5.27 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_trans
% 5.05/5.27 thf(fact_1341_ord__le__eq__trans,axiom,
% 5.05/5.27 ! [A: nat,B: nat,C: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.27 => ( ( B = C )
% 5.05/5.27 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_trans
% 5.05/5.27 thf(fact_1342_ord__le__eq__trans,axiom,
% 5.05/5.27 ! [A: int,B: int,C: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.27 => ( ( B = C )
% 5.05/5.27 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_trans
% 5.05/5.27 thf(fact_1343_order__antisym,axiom,
% 5.05/5.27 ! [X: set_int,Y: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ X @ Y )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ Y @ X )
% 5.05/5.27 => ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_antisym
% 5.05/5.27 thf(fact_1344_order__antisym,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.27 => ( ( ord_less_eq_rat @ Y @ X )
% 5.05/5.27 => ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_antisym
% 5.05/5.27 thf(fact_1345_order__antisym,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.27 => ( ( ord_less_eq_num @ Y @ X )
% 5.05/5.27 => ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_antisym
% 5.05/5.27 thf(fact_1346_order__antisym,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.27 => ( ( ord_less_eq_nat @ Y @ X )
% 5.05/5.27 => ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_antisym
% 5.05/5.27 thf(fact_1347_order__antisym,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.27 => ( ( ord_less_eq_int @ Y @ X )
% 5.05/5.27 => ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_antisym
% 5.05/5.27 thf(fact_1348_order_Otrans,axiom,
% 5.05/5.27 ! [A: set_int,B: set_int,C: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ B @ C )
% 5.05/5.27 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.trans
% 5.05/5.27 thf(fact_1349_order_Otrans,axiom,
% 5.05/5.27 ! [A: rat,B: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.27 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.trans
% 5.05/5.27 thf(fact_1350_order_Otrans,axiom,
% 5.05/5.27 ! [A: num,B: num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.27 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.trans
% 5.05/5.27 thf(fact_1351_order_Otrans,axiom,
% 5.05/5.27 ! [A: nat,B: nat,C: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_nat @ B @ C )
% 5.05/5.27 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.trans
% 5.05/5.27 thf(fact_1352_order_Otrans,axiom,
% 5.05/5.27 ! [A: int,B: int,C: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_int @ B @ C )
% 5.05/5.27 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.trans
% 5.05/5.27 thf(fact_1353_order__trans,axiom,
% 5.05/5.27 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ X @ Y )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.05/5.27 => ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_trans
% 5.05/5.27 thf(fact_1354_order__trans,axiom,
% 5.05/5.27 ! [X: rat,Y: rat,Z: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.27 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.05/5.27 => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_trans
% 5.05/5.27 thf(fact_1355_order__trans,axiom,
% 5.05/5.27 ! [X: num,Y: num,Z: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.27 => ( ( ord_less_eq_num @ Y @ Z )
% 5.05/5.27 => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_trans
% 5.05/5.27 thf(fact_1356_order__trans,axiom,
% 5.05/5.27 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.27 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.05/5.27 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_trans
% 5.05/5.27 thf(fact_1357_order__trans,axiom,
% 5.05/5.27 ! [X: int,Y: int,Z: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.27 => ( ( ord_less_eq_int @ Y @ Z )
% 5.05/5.27 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_trans
% 5.05/5.27 thf(fact_1358_linorder__wlog,axiom,
% 5.05/5.27 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.05/5.27 ( ! [A3: rat,B2: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( ! [A3: rat,B2: rat] :
% 5.05/5.27 ( ( P @ B2 @ A3 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( P @ A @ B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_wlog
% 5.05/5.27 thf(fact_1359_linorder__wlog,axiom,
% 5.05/5.27 ! [P: num > num > $o,A: num,B: num] :
% 5.05/5.27 ( ! [A3: num,B2: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( ! [A3: num,B2: num] :
% 5.05/5.27 ( ( P @ B2 @ A3 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( P @ A @ B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_wlog
% 5.05/5.27 thf(fact_1360_linorder__wlog,axiom,
% 5.05/5.27 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.05/5.27 ( ! [A3: nat,B2: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( ! [A3: nat,B2: nat] :
% 5.05/5.27 ( ( P @ B2 @ A3 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( P @ A @ B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_wlog
% 5.05/5.27 thf(fact_1361_linorder__wlog,axiom,
% 5.05/5.27 ! [P: int > int > $o,A: int,B: int] :
% 5.05/5.27 ( ! [A3: int,B2: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( ! [A3: int,B2: int] :
% 5.05/5.27 ( ( P @ B2 @ A3 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( P @ A @ B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_wlog
% 5.05/5.27 thf(fact_1362_dual__order_Oeq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: set_int,Z3: set_int] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A4: set_int,B4: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.05/5.27 & ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.eq_iff
% 5.05/5.27 thf(fact_1363_dual__order_Oeq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: rat,Z3: rat] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A4: rat,B4: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ B4 @ A4 )
% 5.05/5.27 & ( ord_less_eq_rat @ A4 @ B4 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.eq_iff
% 5.05/5.27 thf(fact_1364_dual__order_Oeq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: num,Z3: num] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A4: num,B4: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ B4 @ A4 )
% 5.05/5.27 & ( ord_less_eq_num @ A4 @ B4 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.eq_iff
% 5.05/5.27 thf(fact_1365_dual__order_Oeq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A4: nat,B4: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ B4 @ A4 )
% 5.05/5.27 & ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.eq_iff
% 5.05/5.27 thf(fact_1366_dual__order_Oeq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: int,Z3: int] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A4: int,B4: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ B4 @ A4 )
% 5.05/5.27 & ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.eq_iff
% 5.05/5.27 thf(fact_1367_dual__order_Oantisym,axiom,
% 5.05/5.27 ! [B: set_int,A: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ B @ A )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ A @ B )
% 5.05/5.27 => ( A = B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.antisym
% 5.05/5.27 thf(fact_1368_dual__order_Oantisym,axiom,
% 5.05/5.27 ! [B: rat,A: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.27 => ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( A = B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.antisym
% 5.05/5.27 thf(fact_1369_dual__order_Oantisym,axiom,
% 5.05/5.27 ! [B: num,A: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ B @ A )
% 5.05/5.27 => ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( A = B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.antisym
% 5.05/5.27 thf(fact_1370_dual__order_Oantisym,axiom,
% 5.05/5.27 ! [B: nat,A: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.27 => ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.27 => ( A = B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.antisym
% 5.05/5.27 thf(fact_1371_dual__order_Oantisym,axiom,
% 5.05/5.27 ! [B: int,A: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ B @ A )
% 5.05/5.27 => ( ( ord_less_eq_int @ A @ B )
% 5.05/5.27 => ( A = B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.antisym
% 5.05/5.27 thf(fact_1372_dual__order_Otrans,axiom,
% 5.05/5.27 ! [B: set_int,A: set_int,C: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ B @ A )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ C @ B )
% 5.05/5.27 => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.trans
% 5.05/5.27 thf(fact_1373_dual__order_Otrans,axiom,
% 5.05/5.27 ! [B: rat,A: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.27 => ( ( ord_less_eq_rat @ C @ B )
% 5.05/5.27 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.trans
% 5.05/5.27 thf(fact_1374_dual__order_Otrans,axiom,
% 5.05/5.27 ! [B: num,A: num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ B @ A )
% 5.05/5.27 => ( ( ord_less_eq_num @ C @ B )
% 5.05/5.27 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.trans
% 5.05/5.27 thf(fact_1375_dual__order_Otrans,axiom,
% 5.05/5.27 ! [B: nat,A: nat,C: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.27 => ( ( ord_less_eq_nat @ C @ B )
% 5.05/5.27 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.trans
% 5.05/5.27 thf(fact_1376_dual__order_Otrans,axiom,
% 5.05/5.27 ! [B: int,A: int,C: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ B @ A )
% 5.05/5.27 => ( ( ord_less_eq_int @ C @ B )
% 5.05/5.27 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.trans
% 5.05/5.27 thf(fact_1377_antisym,axiom,
% 5.05/5.27 ! [A: set_int,B: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ B @ A )
% 5.05/5.27 => ( A = B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % antisym
% 5.05/5.27 thf(fact_1378_antisym,axiom,
% 5.05/5.27 ! [A: rat,B: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.27 => ( A = B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % antisym
% 5.05/5.27 thf(fact_1379_antisym,axiom,
% 5.05/5.27 ! [A: num,B: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_num @ B @ A )
% 5.05/5.27 => ( A = B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % antisym
% 5.05/5.27 thf(fact_1380_antisym,axiom,
% 5.05/5.27 ! [A: nat,B: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.27 => ( A = B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % antisym
% 5.05/5.27 thf(fact_1381_antisym,axiom,
% 5.05/5.27 ! [A: int,B: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_int @ B @ A )
% 5.05/5.27 => ( A = B ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % antisym
% 5.05/5.27 thf(fact_1382_Orderings_Oorder__eq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: set_int,Z3: set_int] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A4: set_int,B4: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.05/5.27 & ( ord_less_eq_set_int @ B4 @ A4 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Orderings.order_eq_iff
% 5.05/5.27 thf(fact_1383_Orderings_Oorder__eq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: rat,Z3: rat] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A4: rat,B4: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A4 @ B4 )
% 5.05/5.27 & ( ord_less_eq_rat @ B4 @ A4 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Orderings.order_eq_iff
% 5.05/5.27 thf(fact_1384_Orderings_Oorder__eq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: num,Z3: num] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A4: num,B4: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ A4 @ B4 )
% 5.05/5.27 & ( ord_less_eq_num @ B4 @ A4 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Orderings.order_eq_iff
% 5.05/5.27 thf(fact_1385_Orderings_Oorder__eq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A4: nat,B4: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A4 @ B4 )
% 5.05/5.27 & ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Orderings.order_eq_iff
% 5.05/5.27 thf(fact_1386_Orderings_Oorder__eq__iff,axiom,
% 5.05/5.27 ( ( ^ [Y4: int,Z3: int] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A4: int,B4: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.05/5.27 & ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Orderings.order_eq_iff
% 5.05/5.27 thf(fact_1387_order__subst1,axiom,
% 5.05/5.27 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst1
% 5.05/5.27 thf(fact_1388_order__subst1,axiom,
% 5.05/5.27 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst1
% 5.05/5.27 thf(fact_1389_order__subst1,axiom,
% 5.05/5.27 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_nat @ B @ C )
% 5.05/5.27 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst1
% 5.05/5.27 thf(fact_1390_order__subst1,axiom,
% 5.05/5.27 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_int @ B @ C )
% 5.05/5.27 => ( ! [X3: int,Y5: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst1
% 5.05/5.27 thf(fact_1391_order__subst1,axiom,
% 5.05/5.27 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst1
% 5.05/5.27 thf(fact_1392_order__subst1,axiom,
% 5.05/5.27 ! [A: num,F: num > num,B: num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst1
% 5.05/5.27 thf(fact_1393_order__subst1,axiom,
% 5.05/5.27 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_nat @ B @ C )
% 5.05/5.27 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst1
% 5.05/5.27 thf(fact_1394_order__subst1,axiom,
% 5.05/5.27 ! [A: num,F: int > num,B: int,C: int] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_int @ B @ C )
% 5.05/5.27 => ( ! [X3: int,Y5: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst1
% 5.05/5.27 thf(fact_1395_order__subst1,axiom,
% 5.05/5.27 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst1
% 5.05/5.27 thf(fact_1396_order__subst1,axiom,
% 5.05/5.27 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst1
% 5.05/5.27 thf(fact_1397_order__subst2,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst2
% 5.05/5.27 thf(fact_1398_order__subst2,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst2
% 5.05/5.27 thf(fact_1399_order__subst2,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst2
% 5.05/5.27 thf(fact_1400_order__subst2,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst2
% 5.05/5.27 thf(fact_1401_order__subst2,axiom,
% 5.05/5.27 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst2
% 5.05/5.27 thf(fact_1402_order__subst2,axiom,
% 5.05/5.27 ! [A: num,B: num,F: num > num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst2
% 5.05/5.27 thf(fact_1403_order__subst2,axiom,
% 5.05/5.27 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst2
% 5.05/5.27 thf(fact_1404_order__subst2,axiom,
% 5.05/5.27 ! [A: num,B: num,F: num > int,C: int] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst2
% 5.05/5.27 thf(fact_1405_order__subst2,axiom,
% 5.05/5.27 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst2
% 5.05/5.27 thf(fact_1406_order__subst2,axiom,
% 5.05/5.27 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.27 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_subst2
% 5.05/5.27 thf(fact_1407_order__eq__refl,axiom,
% 5.05/5.27 ! [X: set_int,Y: set_int] :
% 5.05/5.27 ( ( X = Y )
% 5.05/5.27 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_eq_refl
% 5.05/5.27 thf(fact_1408_order__eq__refl,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( X = Y )
% 5.05/5.27 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_eq_refl
% 5.05/5.27 thf(fact_1409_order__eq__refl,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( X = Y )
% 5.05/5.27 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_eq_refl
% 5.05/5.27 thf(fact_1410_order__eq__refl,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( X = Y )
% 5.05/5.27 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_eq_refl
% 5.05/5.27 thf(fact_1411_order__eq__refl,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( X = Y )
% 5.05/5.27 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_eq_refl
% 5.05/5.27 thf(fact_1412_linorder__linear,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.27 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_linear
% 5.05/5.27 thf(fact_1413_linorder__linear,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.27 | ( ord_less_eq_num @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_linear
% 5.05/5.27 thf(fact_1414_linorder__linear,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.27 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_linear
% 5.05/5.27 thf(fact_1415_linorder__linear,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.27 | ( ord_less_eq_int @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_linear
% 5.05/5.27 thf(fact_1416_ord__eq__le__subst,axiom,
% 5.05/5.27 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_subst
% 5.05/5.27 thf(fact_1417_ord__eq__le__subst,axiom,
% 5.05/5.27 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_subst
% 5.05/5.27 thf(fact_1418_ord__eq__le__subst,axiom,
% 5.05/5.27 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_subst
% 5.05/5.27 thf(fact_1419_ord__eq__le__subst,axiom,
% 5.05/5.27 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_subst
% 5.05/5.27 thf(fact_1420_ord__eq__le__subst,axiom,
% 5.05/5.27 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_subst
% 5.05/5.27 thf(fact_1421_ord__eq__le__subst,axiom,
% 5.05/5.27 ! [A: num,F: num > num,B: num,C: num] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_subst
% 5.05/5.27 thf(fact_1422_ord__eq__le__subst,axiom,
% 5.05/5.27 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_subst
% 5.05/5.27 thf(fact_1423_ord__eq__le__subst,axiom,
% 5.05/5.27 ! [A: int,F: num > int,B: num,C: num] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_subst
% 5.05/5.27 thf(fact_1424_ord__eq__le__subst,axiom,
% 5.05/5.27 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_nat @ B @ C )
% 5.05/5.27 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_subst
% 5.05/5.27 thf(fact_1425_ord__eq__le__subst,axiom,
% 5.05/5.27 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_eq_nat @ B @ C )
% 5.05/5.27 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_le_subst
% 5.05/5.27 thf(fact_1426_ord__le__eq__subst,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_subst
% 5.05/5.27 thf(fact_1427_ord__le__eq__subst,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_subst
% 5.05/5.27 thf(fact_1428_ord__le__eq__subst,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_subst
% 5.05/5.27 thf(fact_1429_ord__le__eq__subst,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.05/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_subst
% 5.05/5.27 thf(fact_1430_ord__le__eq__subst,axiom,
% 5.05/5.27 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_subst
% 5.05/5.27 thf(fact_1431_ord__le__eq__subst,axiom,
% 5.05/5.27 ! [A: num,B: num,F: num > num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_subst
% 5.05/5.27 thf(fact_1432_ord__le__eq__subst,axiom,
% 5.05/5.27 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_subst
% 5.05/5.27 thf(fact_1433_ord__le__eq__subst,axiom,
% 5.05/5.27 ! [A: num,B: num,F: num > int,C: int] :
% 5.05/5.27 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_subst
% 5.05/5.27 thf(fact_1434_ord__le__eq__subst,axiom,
% 5.05/5.27 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_subst
% 5.05/5.27 thf(fact_1435_ord__le__eq__subst,axiom,
% 5.05/5.27 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.05/5.27 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_le_eq_subst
% 5.05/5.27 thf(fact_1436_linorder__le__cases,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ~ ( ord_less_eq_rat @ X @ Y )
% 5.05/5.27 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_le_cases
% 5.05/5.27 thf(fact_1437_linorder__le__cases,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ~ ( ord_less_eq_num @ X @ Y )
% 5.05/5.27 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_le_cases
% 5.05/5.27 thf(fact_1438_linorder__le__cases,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ~ ( ord_less_eq_nat @ X @ Y )
% 5.05/5.27 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_le_cases
% 5.05/5.27 thf(fact_1439_linorder__le__cases,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ~ ( ord_less_eq_int @ X @ Y )
% 5.05/5.27 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_le_cases
% 5.05/5.27 thf(fact_1440_order__antisym__conv,axiom,
% 5.05/5.27 ! [Y: set_int,X: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ Y @ X )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ X @ Y )
% 5.05/5.27 = ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_antisym_conv
% 5.05/5.27 thf(fact_1441_order__antisym__conv,axiom,
% 5.05/5.27 ! [Y: rat,X: rat] :
% 5.05/5.27 ( ( ord_less_eq_rat @ Y @ X )
% 5.05/5.27 => ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.27 = ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_antisym_conv
% 5.05/5.27 thf(fact_1442_order__antisym__conv,axiom,
% 5.05/5.27 ! [Y: num,X: num] :
% 5.05/5.27 ( ( ord_less_eq_num @ Y @ X )
% 5.05/5.27 => ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.27 = ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_antisym_conv
% 5.05/5.27 thf(fact_1443_order__antisym__conv,axiom,
% 5.05/5.27 ! [Y: nat,X: nat] :
% 5.05/5.27 ( ( ord_less_eq_nat @ Y @ X )
% 5.05/5.27 => ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.27 = ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_antisym_conv
% 5.05/5.27 thf(fact_1444_order__antisym__conv,axiom,
% 5.05/5.27 ! [Y: int,X: int] :
% 5.05/5.27 ( ( ord_less_eq_int @ Y @ X )
% 5.05/5.27 => ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.27 = ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_antisym_conv
% 5.05/5.27 thf(fact_1445_lt__ex,axiom,
% 5.05/5.27 ! [X: real] :
% 5.05/5.27 ? [Y5: real] : ( ord_less_real @ Y5 @ X ) ).
% 5.05/5.27
% 5.05/5.27 % lt_ex
% 5.05/5.27 thf(fact_1446_lt__ex,axiom,
% 5.05/5.27 ! [X: rat] :
% 5.05/5.27 ? [Y5: rat] : ( ord_less_rat @ Y5 @ X ) ).
% 5.05/5.27
% 5.05/5.27 % lt_ex
% 5.05/5.27 thf(fact_1447_lt__ex,axiom,
% 5.05/5.27 ! [X: int] :
% 5.05/5.27 ? [Y5: int] : ( ord_less_int @ Y5 @ X ) ).
% 5.05/5.27
% 5.05/5.27 % lt_ex
% 5.05/5.27 thf(fact_1448_gt__ex,axiom,
% 5.05/5.27 ! [X: real] :
% 5.05/5.27 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 5.05/5.27
% 5.05/5.27 % gt_ex
% 5.05/5.27 thf(fact_1449_gt__ex,axiom,
% 5.05/5.27 ! [X: rat] :
% 5.05/5.27 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 5.05/5.27
% 5.05/5.27 % gt_ex
% 5.05/5.27 thf(fact_1450_gt__ex,axiom,
% 5.05/5.27 ! [X: nat] :
% 5.05/5.27 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 5.05/5.27
% 5.05/5.27 % gt_ex
% 5.05/5.27 thf(fact_1451_gt__ex,axiom,
% 5.05/5.27 ! [X: int] :
% 5.05/5.27 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 5.05/5.27
% 5.05/5.27 % gt_ex
% 5.05/5.27 thf(fact_1452_dense,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( ord_less_real @ X @ Y )
% 5.05/5.27 => ? [Z4: real] :
% 5.05/5.27 ( ( ord_less_real @ X @ Z4 )
% 5.05/5.27 & ( ord_less_real @ Z4 @ Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dense
% 5.05/5.27 thf(fact_1453_dense,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ? [Z4: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Z4 )
% 5.05/5.27 & ( ord_less_rat @ Z4 @ Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dense
% 5.05/5.27 thf(fact_1454_less__imp__neq,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( ord_less_real @ X @ Y )
% 5.05/5.27 => ( X != Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % less_imp_neq
% 5.05/5.27 thf(fact_1455_less__imp__neq,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ( X != Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % less_imp_neq
% 5.05/5.27 thf(fact_1456_less__imp__neq,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( ord_less_num @ X @ Y )
% 5.05/5.27 => ( X != Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % less_imp_neq
% 5.05/5.27 thf(fact_1457_less__imp__neq,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( ord_less_nat @ X @ Y )
% 5.05/5.27 => ( X != Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % less_imp_neq
% 5.05/5.27 thf(fact_1458_less__imp__neq,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( ord_less_int @ X @ Y )
% 5.05/5.27 => ( X != Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % less_imp_neq
% 5.05/5.27 thf(fact_1459_order_Oasym,axiom,
% 5.05/5.27 ! [A: real,B: real] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.asym
% 5.05/5.27 thf(fact_1460_order_Oasym,axiom,
% 5.05/5.27 ! [A: rat,B: rat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.asym
% 5.05/5.27 thf(fact_1461_order_Oasym,axiom,
% 5.05/5.27 ! [A: num,B: num] :
% 5.05/5.27 ( ( ord_less_num @ A @ B )
% 5.05/5.27 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.asym
% 5.05/5.27 thf(fact_1462_order_Oasym,axiom,
% 5.05/5.27 ! [A: nat,B: nat] :
% 5.05/5.27 ( ( ord_less_nat @ A @ B )
% 5.05/5.27 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.asym
% 5.05/5.27 thf(fact_1463_order_Oasym,axiom,
% 5.05/5.27 ! [A: int,B: int] :
% 5.05/5.27 ( ( ord_less_int @ A @ B )
% 5.05/5.27 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.asym
% 5.05/5.27 thf(fact_1464_ord__eq__less__trans,axiom,
% 5.05/5.27 ! [A: real,B: real,C: real] :
% 5.05/5.27 ( ( A = B )
% 5.05/5.27 => ( ( ord_less_real @ B @ C )
% 5.05/5.27 => ( ord_less_real @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_trans
% 5.05/5.27 thf(fact_1465_ord__eq__less__trans,axiom,
% 5.05/5.27 ! [A: rat,B: rat,C: rat] :
% 5.05/5.27 ( ( A = B )
% 5.05/5.27 => ( ( ord_less_rat @ B @ C )
% 5.05/5.27 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_trans
% 5.05/5.27 thf(fact_1466_ord__eq__less__trans,axiom,
% 5.05/5.27 ! [A: num,B: num,C: num] :
% 5.05/5.27 ( ( A = B )
% 5.05/5.27 => ( ( ord_less_num @ B @ C )
% 5.05/5.27 => ( ord_less_num @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_trans
% 5.05/5.27 thf(fact_1467_ord__eq__less__trans,axiom,
% 5.05/5.27 ! [A: nat,B: nat,C: nat] :
% 5.05/5.27 ( ( A = B )
% 5.05/5.27 => ( ( ord_less_nat @ B @ C )
% 5.05/5.27 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_trans
% 5.05/5.27 thf(fact_1468_ord__eq__less__trans,axiom,
% 5.05/5.27 ! [A: int,B: int,C: int] :
% 5.05/5.27 ( ( A = B )
% 5.05/5.27 => ( ( ord_less_int @ B @ C )
% 5.05/5.27 => ( ord_less_int @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_trans
% 5.05/5.27 thf(fact_1469_ord__less__eq__trans,axiom,
% 5.05/5.27 ! [A: real,B: real,C: real] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( B = C )
% 5.05/5.27 => ( ord_less_real @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_trans
% 5.05/5.27 thf(fact_1470_ord__less__eq__trans,axiom,
% 5.05/5.27 ! [A: rat,B: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( B = C )
% 5.05/5.27 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_trans
% 5.05/5.27 thf(fact_1471_ord__less__eq__trans,axiom,
% 5.05/5.27 ! [A: num,B: num,C: num] :
% 5.05/5.27 ( ( ord_less_num @ A @ B )
% 5.05/5.27 => ( ( B = C )
% 5.05/5.27 => ( ord_less_num @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_trans
% 5.05/5.27 thf(fact_1472_ord__less__eq__trans,axiom,
% 5.05/5.27 ! [A: nat,B: nat,C: nat] :
% 5.05/5.27 ( ( ord_less_nat @ A @ B )
% 5.05/5.27 => ( ( B = C )
% 5.05/5.27 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_trans
% 5.05/5.27 thf(fact_1473_ord__less__eq__trans,axiom,
% 5.05/5.27 ! [A: int,B: int,C: int] :
% 5.05/5.27 ( ( ord_less_int @ A @ B )
% 5.05/5.27 => ( ( B = C )
% 5.05/5.27 => ( ord_less_int @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_trans
% 5.05/5.27 thf(fact_1474_less__induct,axiom,
% 5.05/5.27 ! [P: nat > $o,A: nat] :
% 5.05/5.27 ( ! [X3: nat] :
% 5.05/5.27 ( ! [Y3: nat] :
% 5.05/5.27 ( ( ord_less_nat @ Y3 @ X3 )
% 5.05/5.27 => ( P @ Y3 ) )
% 5.05/5.27 => ( P @ X3 ) )
% 5.05/5.27 => ( P @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % less_induct
% 5.05/5.27 thf(fact_1475_antisym__conv3,axiom,
% 5.05/5.27 ! [Y: real,X: real] :
% 5.05/5.27 ( ~ ( ord_less_real @ Y @ X )
% 5.05/5.27 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.05/5.27 = ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % antisym_conv3
% 5.05/5.27 thf(fact_1476_antisym__conv3,axiom,
% 5.05/5.27 ! [Y: rat,X: rat] :
% 5.05/5.27 ( ~ ( ord_less_rat @ Y @ X )
% 5.05/5.27 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.05/5.27 = ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % antisym_conv3
% 5.05/5.27 thf(fact_1477_antisym__conv3,axiom,
% 5.05/5.27 ! [Y: num,X: num] :
% 5.05/5.27 ( ~ ( ord_less_num @ Y @ X )
% 5.05/5.27 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.05/5.27 = ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % antisym_conv3
% 5.05/5.27 thf(fact_1478_antisym__conv3,axiom,
% 5.05/5.27 ! [Y: nat,X: nat] :
% 5.05/5.27 ( ~ ( ord_less_nat @ Y @ X )
% 5.05/5.27 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.05/5.27 = ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % antisym_conv3
% 5.05/5.27 thf(fact_1479_antisym__conv3,axiom,
% 5.05/5.27 ! [Y: int,X: int] :
% 5.05/5.27 ( ~ ( ord_less_int @ Y @ X )
% 5.05/5.27 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.05/5.27 = ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % antisym_conv3
% 5.05/5.27 thf(fact_1480_linorder__cases,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ~ ( ord_less_real @ X @ Y )
% 5.05/5.27 => ( ( X != Y )
% 5.05/5.27 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_cases
% 5.05/5.27 thf(fact_1481_linorder__cases,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ~ ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ( ( X != Y )
% 5.05/5.27 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_cases
% 5.05/5.27 thf(fact_1482_linorder__cases,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ~ ( ord_less_num @ X @ Y )
% 5.05/5.27 => ( ( X != Y )
% 5.05/5.27 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_cases
% 5.05/5.27 thf(fact_1483_linorder__cases,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ~ ( ord_less_nat @ X @ Y )
% 5.05/5.27 => ( ( X != Y )
% 5.05/5.27 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_cases
% 5.05/5.27 thf(fact_1484_linorder__cases,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ~ ( ord_less_int @ X @ Y )
% 5.05/5.27 => ( ( X != Y )
% 5.05/5.27 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_cases
% 5.05/5.27 thf(fact_1485_dual__order_Oasym,axiom,
% 5.05/5.27 ! [B: real,A: real] :
% 5.05/5.27 ( ( ord_less_real @ B @ A )
% 5.05/5.27 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.asym
% 5.05/5.27 thf(fact_1486_dual__order_Oasym,axiom,
% 5.05/5.27 ! [B: rat,A: rat] :
% 5.05/5.27 ( ( ord_less_rat @ B @ A )
% 5.05/5.27 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.asym
% 5.05/5.27 thf(fact_1487_dual__order_Oasym,axiom,
% 5.05/5.27 ! [B: num,A: num] :
% 5.05/5.27 ( ( ord_less_num @ B @ A )
% 5.05/5.27 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.asym
% 5.05/5.27 thf(fact_1488_dual__order_Oasym,axiom,
% 5.05/5.27 ! [B: nat,A: nat] :
% 5.05/5.27 ( ( ord_less_nat @ B @ A )
% 5.05/5.27 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.asym
% 5.05/5.27 thf(fact_1489_dual__order_Oasym,axiom,
% 5.05/5.27 ! [B: int,A: int] :
% 5.05/5.27 ( ( ord_less_int @ B @ A )
% 5.05/5.27 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.asym
% 5.05/5.27 thf(fact_1490_dual__order_Oirrefl,axiom,
% 5.05/5.27 ! [A: real] :
% 5.05/5.27 ~ ( ord_less_real @ A @ A ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.irrefl
% 5.05/5.27 thf(fact_1491_dual__order_Oirrefl,axiom,
% 5.05/5.27 ! [A: rat] :
% 5.05/5.27 ~ ( ord_less_rat @ A @ A ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.irrefl
% 5.05/5.27 thf(fact_1492_dual__order_Oirrefl,axiom,
% 5.05/5.27 ! [A: num] :
% 5.05/5.27 ~ ( ord_less_num @ A @ A ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.irrefl
% 5.05/5.27 thf(fact_1493_dual__order_Oirrefl,axiom,
% 5.05/5.27 ! [A: nat] :
% 5.05/5.27 ~ ( ord_less_nat @ A @ A ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.irrefl
% 5.05/5.27 thf(fact_1494_dual__order_Oirrefl,axiom,
% 5.05/5.27 ! [A: int] :
% 5.05/5.27 ~ ( ord_less_int @ A @ A ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.irrefl
% 5.05/5.27 thf(fact_1495_exists__least__iff,axiom,
% 5.05/5.27 ( ( ^ [P2: nat > $o] :
% 5.05/5.27 ? [X6: nat] : ( P2 @ X6 ) )
% 5.05/5.27 = ( ^ [P3: nat > $o] :
% 5.05/5.27 ? [N: nat] :
% 5.05/5.27 ( ( P3 @ N )
% 5.05/5.27 & ! [M6: nat] :
% 5.05/5.27 ( ( ord_less_nat @ M6 @ N )
% 5.05/5.27 => ~ ( P3 @ M6 ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % exists_least_iff
% 5.05/5.27 thf(fact_1496_linorder__less__wlog,axiom,
% 5.05/5.27 ! [P: real > real > $o,A: real,B: real] :
% 5.05/5.27 ( ! [A3: real,B2: real] :
% 5.05/5.27 ( ( ord_less_real @ A3 @ B2 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( ! [A3: real] : ( P @ A3 @ A3 )
% 5.05/5.27 => ( ! [A3: real,B2: real] :
% 5.05/5.27 ( ( P @ B2 @ A3 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( P @ A @ B ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_less_wlog
% 5.05/5.27 thf(fact_1497_linorder__less__wlog,axiom,
% 5.05/5.27 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.05/5.27 ( ! [A3: rat,B2: rat] :
% 5.05/5.27 ( ( ord_less_rat @ A3 @ B2 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( ! [A3: rat] : ( P @ A3 @ A3 )
% 5.05/5.27 => ( ! [A3: rat,B2: rat] :
% 5.05/5.27 ( ( P @ B2 @ A3 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( P @ A @ B ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_less_wlog
% 5.05/5.27 thf(fact_1498_linorder__less__wlog,axiom,
% 5.05/5.27 ! [P: num > num > $o,A: num,B: num] :
% 5.05/5.27 ( ! [A3: num,B2: num] :
% 5.05/5.27 ( ( ord_less_num @ A3 @ B2 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( ! [A3: num] : ( P @ A3 @ A3 )
% 5.05/5.27 => ( ! [A3: num,B2: num] :
% 5.05/5.27 ( ( P @ B2 @ A3 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( P @ A @ B ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_less_wlog
% 5.05/5.27 thf(fact_1499_linorder__less__wlog,axiom,
% 5.05/5.27 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.05/5.27 ( ! [A3: nat,B2: nat] :
% 5.05/5.27 ( ( ord_less_nat @ A3 @ B2 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 5.05/5.27 => ( ! [A3: nat,B2: nat] :
% 5.05/5.27 ( ( P @ B2 @ A3 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( P @ A @ B ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_less_wlog
% 5.05/5.27 thf(fact_1500_linorder__less__wlog,axiom,
% 5.05/5.27 ! [P: int > int > $o,A: int,B: int] :
% 5.05/5.27 ( ! [A3: int,B2: int] :
% 5.05/5.27 ( ( ord_less_int @ A3 @ B2 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( ! [A3: int] : ( P @ A3 @ A3 )
% 5.05/5.27 => ( ! [A3: int,B2: int] :
% 5.05/5.27 ( ( P @ B2 @ A3 )
% 5.05/5.27 => ( P @ A3 @ B2 ) )
% 5.05/5.27 => ( P @ A @ B ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_less_wlog
% 5.05/5.27 thf(fact_1501_order_Ostrict__trans,axiom,
% 5.05/5.27 ! [A: real,B: real,C: real] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ord_less_real @ B @ C )
% 5.05/5.27 => ( ord_less_real @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.strict_trans
% 5.05/5.27 thf(fact_1502_order_Ostrict__trans,axiom,
% 5.05/5.27 ! [A: rat,B: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_rat @ B @ C )
% 5.05/5.27 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.strict_trans
% 5.05/5.27 thf(fact_1503_order_Ostrict__trans,axiom,
% 5.05/5.27 ! [A: num,B: num,C: num] :
% 5.05/5.27 ( ( ord_less_num @ A @ B )
% 5.05/5.27 => ( ( ord_less_num @ B @ C )
% 5.05/5.27 => ( ord_less_num @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.strict_trans
% 5.05/5.27 thf(fact_1504_order_Ostrict__trans,axiom,
% 5.05/5.27 ! [A: nat,B: nat,C: nat] :
% 5.05/5.27 ( ( ord_less_nat @ A @ B )
% 5.05/5.27 => ( ( ord_less_nat @ B @ C )
% 5.05/5.27 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.strict_trans
% 5.05/5.27 thf(fact_1505_order_Ostrict__trans,axiom,
% 5.05/5.27 ! [A: int,B: int,C: int] :
% 5.05/5.27 ( ( ord_less_int @ A @ B )
% 5.05/5.27 => ( ( ord_less_int @ B @ C )
% 5.05/5.27 => ( ord_less_int @ A @ C ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.strict_trans
% 5.05/5.27 thf(fact_1506_not__less__iff__gr__or__eq,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.05/5.27 = ( ( ord_less_real @ Y @ X )
% 5.05/5.27 | ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % not_less_iff_gr_or_eq
% 5.05/5.27 thf(fact_1507_not__less__iff__gr__or__eq,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.05/5.27 = ( ( ord_less_rat @ Y @ X )
% 5.05/5.27 | ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % not_less_iff_gr_or_eq
% 5.05/5.27 thf(fact_1508_not__less__iff__gr__or__eq,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.05/5.27 = ( ( ord_less_num @ Y @ X )
% 5.05/5.27 | ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % not_less_iff_gr_or_eq
% 5.05/5.27 thf(fact_1509_not__less__iff__gr__or__eq,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.05/5.27 = ( ( ord_less_nat @ Y @ X )
% 5.05/5.27 | ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % not_less_iff_gr_or_eq
% 5.05/5.27 thf(fact_1510_not__less__iff__gr__or__eq,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.05/5.27 = ( ( ord_less_int @ Y @ X )
% 5.05/5.27 | ( X = Y ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % not_less_iff_gr_or_eq
% 5.05/5.27 thf(fact_1511_dual__order_Ostrict__trans,axiom,
% 5.05/5.27 ! [B: real,A: real,C: real] :
% 5.05/5.27 ( ( ord_less_real @ B @ A )
% 5.05/5.27 => ( ( ord_less_real @ C @ B )
% 5.05/5.27 => ( ord_less_real @ C @ A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.strict_trans
% 5.05/5.27 thf(fact_1512_dual__order_Ostrict__trans,axiom,
% 5.05/5.27 ! [B: rat,A: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_rat @ B @ A )
% 5.05/5.27 => ( ( ord_less_rat @ C @ B )
% 5.05/5.27 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.strict_trans
% 5.05/5.27 thf(fact_1513_dual__order_Ostrict__trans,axiom,
% 5.05/5.27 ! [B: num,A: num,C: num] :
% 5.05/5.27 ( ( ord_less_num @ B @ A )
% 5.05/5.27 => ( ( ord_less_num @ C @ B )
% 5.05/5.27 => ( ord_less_num @ C @ A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.strict_trans
% 5.05/5.27 thf(fact_1514_dual__order_Ostrict__trans,axiom,
% 5.05/5.27 ! [B: nat,A: nat,C: nat] :
% 5.05/5.27 ( ( ord_less_nat @ B @ A )
% 5.05/5.27 => ( ( ord_less_nat @ C @ B )
% 5.05/5.27 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.strict_trans
% 5.05/5.27 thf(fact_1515_dual__order_Ostrict__trans,axiom,
% 5.05/5.27 ! [B: int,A: int,C: int] :
% 5.05/5.27 ( ( ord_less_int @ B @ A )
% 5.05/5.27 => ( ( ord_less_int @ C @ B )
% 5.05/5.27 => ( ord_less_int @ C @ A ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.strict_trans
% 5.05/5.27 thf(fact_1516_order_Ostrict__implies__not__eq,axiom,
% 5.05/5.27 ! [A: real,B: real] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( A != B ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.strict_implies_not_eq
% 5.05/5.27 thf(fact_1517_order_Ostrict__implies__not__eq,axiom,
% 5.05/5.27 ! [A: rat,B: rat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( A != B ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.strict_implies_not_eq
% 5.05/5.27 thf(fact_1518_order_Ostrict__implies__not__eq,axiom,
% 5.05/5.27 ! [A: num,B: num] :
% 5.05/5.27 ( ( ord_less_num @ A @ B )
% 5.05/5.27 => ( A != B ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.strict_implies_not_eq
% 5.05/5.27 thf(fact_1519_order_Ostrict__implies__not__eq,axiom,
% 5.05/5.27 ! [A: nat,B: nat] :
% 5.05/5.27 ( ( ord_less_nat @ A @ B )
% 5.05/5.27 => ( A != B ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.strict_implies_not_eq
% 5.05/5.27 thf(fact_1520_order_Ostrict__implies__not__eq,axiom,
% 5.05/5.27 ! [A: int,B: int] :
% 5.05/5.27 ( ( ord_less_int @ A @ B )
% 5.05/5.27 => ( A != B ) ) ).
% 5.05/5.27
% 5.05/5.27 % order.strict_implies_not_eq
% 5.05/5.27 thf(fact_1521_dual__order_Ostrict__implies__not__eq,axiom,
% 5.05/5.27 ! [B: real,A: real] :
% 5.05/5.27 ( ( ord_less_real @ B @ A )
% 5.05/5.27 => ( A != B ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.strict_implies_not_eq
% 5.05/5.27 thf(fact_1522_dual__order_Ostrict__implies__not__eq,axiom,
% 5.05/5.27 ! [B: rat,A: rat] :
% 5.05/5.27 ( ( ord_less_rat @ B @ A )
% 5.05/5.27 => ( A != B ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.strict_implies_not_eq
% 5.05/5.27 thf(fact_1523_dual__order_Ostrict__implies__not__eq,axiom,
% 5.05/5.27 ! [B: num,A: num] :
% 5.05/5.27 ( ( ord_less_num @ B @ A )
% 5.05/5.27 => ( A != B ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.strict_implies_not_eq
% 5.05/5.27 thf(fact_1524_dual__order_Ostrict__implies__not__eq,axiom,
% 5.05/5.27 ! [B: nat,A: nat] :
% 5.05/5.27 ( ( ord_less_nat @ B @ A )
% 5.05/5.27 => ( A != B ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.strict_implies_not_eq
% 5.05/5.27 thf(fact_1525_dual__order_Ostrict__implies__not__eq,axiom,
% 5.05/5.27 ! [B: int,A: int] :
% 5.05/5.27 ( ( ord_less_int @ B @ A )
% 5.05/5.27 => ( A != B ) ) ).
% 5.05/5.27
% 5.05/5.27 % dual_order.strict_implies_not_eq
% 5.05/5.27 thf(fact_1526_linorder__neqE,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( X != Y )
% 5.05/5.27 => ( ~ ( ord_less_real @ X @ Y )
% 5.05/5.27 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_neqE
% 5.05/5.27 thf(fact_1527_linorder__neqE,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( X != Y )
% 5.05/5.27 => ( ~ ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_neqE
% 5.05/5.27 thf(fact_1528_linorder__neqE,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( X != Y )
% 5.05/5.27 => ( ~ ( ord_less_num @ X @ Y )
% 5.05/5.27 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_neqE
% 5.05/5.27 thf(fact_1529_linorder__neqE,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( X != Y )
% 5.05/5.27 => ( ~ ( ord_less_nat @ X @ Y )
% 5.05/5.27 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_neqE
% 5.05/5.27 thf(fact_1530_linorder__neqE,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( X != Y )
% 5.05/5.27 => ( ~ ( ord_less_int @ X @ Y )
% 5.05/5.27 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_neqE
% 5.05/5.27 thf(fact_1531_order__less__asym,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( ord_less_real @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_asym
% 5.05/5.27 thf(fact_1532_order__less__asym,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_asym
% 5.05/5.27 thf(fact_1533_order__less__asym,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( ord_less_num @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_asym
% 5.05/5.27 thf(fact_1534_order__less__asym,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( ord_less_nat @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_asym
% 5.05/5.27 thf(fact_1535_order__less__asym,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( ord_less_int @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_asym
% 5.05/5.27 thf(fact_1536_linorder__neq__iff,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( X != Y )
% 5.05/5.27 = ( ( ord_less_real @ X @ Y )
% 5.05/5.27 | ( ord_less_real @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_neq_iff
% 5.05/5.27 thf(fact_1537_linorder__neq__iff,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( X != Y )
% 5.05/5.27 = ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 | ( ord_less_rat @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_neq_iff
% 5.05/5.27 thf(fact_1538_linorder__neq__iff,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( X != Y )
% 5.05/5.27 = ( ( ord_less_num @ X @ Y )
% 5.05/5.27 | ( ord_less_num @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_neq_iff
% 5.05/5.27 thf(fact_1539_linorder__neq__iff,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( X != Y )
% 5.05/5.27 = ( ( ord_less_nat @ X @ Y )
% 5.05/5.27 | ( ord_less_nat @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_neq_iff
% 5.05/5.27 thf(fact_1540_linorder__neq__iff,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( X != Y )
% 5.05/5.27 = ( ( ord_less_int @ X @ Y )
% 5.05/5.27 | ( ord_less_int @ Y @ X ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_neq_iff
% 5.05/5.27 thf(fact_1541_order__less__asym_H,axiom,
% 5.05/5.27 ! [A: real,B: real] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_asym'
% 5.05/5.27 thf(fact_1542_order__less__asym_H,axiom,
% 5.05/5.27 ! [A: rat,B: rat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_asym'
% 5.05/5.27 thf(fact_1543_order__less__asym_H,axiom,
% 5.05/5.27 ! [A: num,B: num] :
% 5.05/5.27 ( ( ord_less_num @ A @ B )
% 5.05/5.27 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_asym'
% 5.05/5.27 thf(fact_1544_order__less__asym_H,axiom,
% 5.05/5.27 ! [A: nat,B: nat] :
% 5.05/5.27 ( ( ord_less_nat @ A @ B )
% 5.05/5.27 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_asym'
% 5.05/5.27 thf(fact_1545_order__less__asym_H,axiom,
% 5.05/5.27 ! [A: int,B: int] :
% 5.05/5.27 ( ( ord_less_int @ A @ B )
% 5.05/5.27 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_asym'
% 5.05/5.27 thf(fact_1546_order__less__trans,axiom,
% 5.05/5.27 ! [X: real,Y: real,Z: real] :
% 5.05/5.27 ( ( ord_less_real @ X @ Y )
% 5.05/5.27 => ( ( ord_less_real @ Y @ Z )
% 5.05/5.27 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_trans
% 5.05/5.27 thf(fact_1547_order__less__trans,axiom,
% 5.05/5.27 ! [X: rat,Y: rat,Z: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ( ( ord_less_rat @ Y @ Z )
% 5.05/5.27 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_trans
% 5.05/5.27 thf(fact_1548_order__less__trans,axiom,
% 5.05/5.27 ! [X: num,Y: num,Z: num] :
% 5.05/5.27 ( ( ord_less_num @ X @ Y )
% 5.05/5.27 => ( ( ord_less_num @ Y @ Z )
% 5.05/5.27 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_trans
% 5.05/5.27 thf(fact_1549_order__less__trans,axiom,
% 5.05/5.27 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.27 ( ( ord_less_nat @ X @ Y )
% 5.05/5.27 => ( ( ord_less_nat @ Y @ Z )
% 5.05/5.27 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_trans
% 5.05/5.27 thf(fact_1550_order__less__trans,axiom,
% 5.05/5.27 ! [X: int,Y: int,Z: int] :
% 5.05/5.27 ( ( ord_less_int @ X @ Y )
% 5.05/5.27 => ( ( ord_less_int @ Y @ Z )
% 5.05/5.27 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_trans
% 5.05/5.27 thf(fact_1551_ord__eq__less__subst,axiom,
% 5.05/5.27 ! [A: real,F: real > real,B: real,C: real] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_real @ B @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_subst
% 5.05/5.27 thf(fact_1552_ord__eq__less__subst,axiom,
% 5.05/5.27 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_real @ B @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_subst
% 5.05/5.27 thf(fact_1553_ord__eq__less__subst,axiom,
% 5.05/5.27 ! [A: num,F: real > num,B: real,C: real] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_real @ B @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_subst
% 5.05/5.27 thf(fact_1554_ord__eq__less__subst,axiom,
% 5.05/5.27 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_real @ B @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_subst
% 5.05/5.27 thf(fact_1555_ord__eq__less__subst,axiom,
% 5.05/5.27 ! [A: int,F: real > int,B: real,C: real] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_real @ B @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_subst
% 5.05/5.27 thf(fact_1556_ord__eq__less__subst,axiom,
% 5.05/5.27 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_subst
% 5.05/5.27 thf(fact_1557_ord__eq__less__subst,axiom,
% 5.05/5.27 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_subst
% 5.05/5.27 thf(fact_1558_ord__eq__less__subst,axiom,
% 5.05/5.27 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_subst
% 5.05/5.27 thf(fact_1559_ord__eq__less__subst,axiom,
% 5.05/5.27 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_subst
% 5.05/5.27 thf(fact_1560_ord__eq__less__subst,axiom,
% 5.05/5.27 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.05/5.27 ( ( A
% 5.05/5.27 = ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_eq_less_subst
% 5.05/5.27 thf(fact_1561_ord__less__eq__subst,axiom,
% 5.05/5.27 ! [A: real,B: real,F: real > real,C: real] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_subst
% 5.05/5.27 thf(fact_1562_ord__less__eq__subst,axiom,
% 5.05/5.27 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_subst
% 5.05/5.27 thf(fact_1563_ord__less__eq__subst,axiom,
% 5.05/5.27 ! [A: real,B: real,F: real > num,C: num] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_subst
% 5.05/5.27 thf(fact_1564_ord__less__eq__subst,axiom,
% 5.05/5.27 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_subst
% 5.05/5.27 thf(fact_1565_ord__less__eq__subst,axiom,
% 5.05/5.27 ! [A: real,B: real,F: real > int,C: int] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_subst
% 5.05/5.27 thf(fact_1566_ord__less__eq__subst,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_subst
% 5.05/5.27 thf(fact_1567_ord__less__eq__subst,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_subst
% 5.05/5.27 thf(fact_1568_ord__less__eq__subst,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_subst
% 5.05/5.27 thf(fact_1569_ord__less__eq__subst,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_subst
% 5.05/5.27 thf(fact_1570_ord__less__eq__subst,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ( F @ B )
% 5.05/5.27 = C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % ord_less_eq_subst
% 5.05/5.27 thf(fact_1571_order__less__irrefl,axiom,
% 5.05/5.27 ! [X: real] :
% 5.05/5.27 ~ ( ord_less_real @ X @ X ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_irrefl
% 5.05/5.27 thf(fact_1572_order__less__irrefl,axiom,
% 5.05/5.27 ! [X: rat] :
% 5.05/5.27 ~ ( ord_less_rat @ X @ X ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_irrefl
% 5.05/5.27 thf(fact_1573_order__less__irrefl,axiom,
% 5.05/5.27 ! [X: num] :
% 5.05/5.27 ~ ( ord_less_num @ X @ X ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_irrefl
% 5.05/5.27 thf(fact_1574_order__less__irrefl,axiom,
% 5.05/5.27 ! [X: nat] :
% 5.05/5.27 ~ ( ord_less_nat @ X @ X ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_irrefl
% 5.05/5.27 thf(fact_1575_order__less__irrefl,axiom,
% 5.05/5.27 ! [X: int] :
% 5.05/5.27 ~ ( ord_less_int @ X @ X ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_irrefl
% 5.05/5.27 thf(fact_1576_order__less__subst1,axiom,
% 5.05/5.27 ! [A: real,F: real > real,B: real,C: real] :
% 5.05/5.27 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_real @ B @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst1
% 5.05/5.27 thf(fact_1577_order__less__subst1,axiom,
% 5.05/5.27 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst1
% 5.05/5.27 thf(fact_1578_order__less__subst1,axiom,
% 5.05/5.27 ! [A: real,F: num > real,B: num,C: num] :
% 5.05/5.27 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_num @ B @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst1
% 5.05/5.27 thf(fact_1579_order__less__subst1,axiom,
% 5.05/5.27 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.05/5.27 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_nat @ B @ C )
% 5.05/5.27 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.27 ( ( ord_less_nat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst1
% 5.05/5.27 thf(fact_1580_order__less__subst1,axiom,
% 5.05/5.27 ! [A: real,F: int > real,B: int,C: int] :
% 5.05/5.27 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_int @ B @ C )
% 5.05/5.27 => ( ! [X3: int,Y5: int] :
% 5.05/5.27 ( ( ord_less_int @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst1
% 5.05/5.27 thf(fact_1581_order__less__subst1,axiom,
% 5.05/5.27 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.05/5.27 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_real @ B @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst1
% 5.05/5.27 thf(fact_1582_order__less__subst1,axiom,
% 5.05/5.27 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_rat @ B @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst1
% 5.05/5.27 thf(fact_1583_order__less__subst1,axiom,
% 5.05/5.27 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.05/5.27 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_num @ B @ C )
% 5.05/5.27 => ( ! [X3: num,Y5: num] :
% 5.05/5.27 ( ( ord_less_num @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst1
% 5.05/5.27 thf(fact_1584_order__less__subst1,axiom,
% 5.05/5.27 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_nat @ B @ C )
% 5.05/5.27 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.27 ( ( ord_less_nat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst1
% 5.05/5.27 thf(fact_1585_order__less__subst1,axiom,
% 5.05/5.27 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.05/5.27 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.05/5.27 => ( ( ord_less_int @ B @ C )
% 5.05/5.27 => ( ! [X3: int,Y5: int] :
% 5.05/5.27 ( ( ord_less_int @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst1
% 5.05/5.27 thf(fact_1586_order__less__subst2,axiom,
% 5.05/5.27 ! [A: real,B: real,F: real > real,C: real] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst2
% 5.05/5.27 thf(fact_1587_order__less__subst2,axiom,
% 5.05/5.27 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst2
% 5.05/5.27 thf(fact_1588_order__less__subst2,axiom,
% 5.05/5.27 ! [A: real,B: real,F: real > num,C: num] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst2
% 5.05/5.27 thf(fact_1589_order__less__subst2,axiom,
% 5.05/5.27 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst2
% 5.05/5.27 thf(fact_1590_order__less__subst2,axiom,
% 5.05/5.27 ! [A: real,B: real,F: real > int,C: int] :
% 5.05/5.27 ( ( ord_less_real @ A @ B )
% 5.05/5.27 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: real,Y5: real] :
% 5.05/5.27 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst2
% 5.05/5.27 thf(fact_1591_order__less__subst2,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst2
% 5.05/5.27 thf(fact_1592_order__less__subst2,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst2
% 5.05/5.27 thf(fact_1593_order__less__subst2,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst2
% 5.05/5.27 thf(fact_1594_order__less__subst2,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst2
% 5.05/5.27 thf(fact_1595_order__less__subst2,axiom,
% 5.05/5.27 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.05/5.27 ( ( ord_less_rat @ A @ B )
% 5.05/5.27 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.05/5.27 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.27 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.27 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_subst2
% 5.05/5.27 thf(fact_1596_order__less__not__sym,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( ord_less_real @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_not_sym
% 5.05/5.27 thf(fact_1597_order__less__not__sym,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_not_sym
% 5.05/5.27 thf(fact_1598_order__less__not__sym,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( ord_less_num @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_not_sym
% 5.05/5.27 thf(fact_1599_order__less__not__sym,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( ord_less_nat @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_not_sym
% 5.05/5.27 thf(fact_1600_order__less__not__sym,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( ord_less_int @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_not_sym
% 5.05/5.27 thf(fact_1601_order__less__imp__triv,axiom,
% 5.05/5.27 ! [X: real,Y: real,P: $o] :
% 5.05/5.27 ( ( ord_less_real @ X @ Y )
% 5.05/5.27 => ( ( ord_less_real @ Y @ X )
% 5.05/5.27 => P ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_triv
% 5.05/5.27 thf(fact_1602_order__less__imp__triv,axiom,
% 5.05/5.27 ! [X: rat,Y: rat,P: $o] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ( ( ord_less_rat @ Y @ X )
% 5.05/5.27 => P ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_triv
% 5.05/5.27 thf(fact_1603_order__less__imp__triv,axiom,
% 5.05/5.27 ! [X: num,Y: num,P: $o] :
% 5.05/5.27 ( ( ord_less_num @ X @ Y )
% 5.05/5.27 => ( ( ord_less_num @ Y @ X )
% 5.05/5.27 => P ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_triv
% 5.05/5.27 thf(fact_1604_order__less__imp__triv,axiom,
% 5.05/5.27 ! [X: nat,Y: nat,P: $o] :
% 5.05/5.27 ( ( ord_less_nat @ X @ Y )
% 5.05/5.27 => ( ( ord_less_nat @ Y @ X )
% 5.05/5.27 => P ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_triv
% 5.05/5.27 thf(fact_1605_order__less__imp__triv,axiom,
% 5.05/5.27 ! [X: int,Y: int,P: $o] :
% 5.05/5.27 ( ( ord_less_int @ X @ Y )
% 5.05/5.27 => ( ( ord_less_int @ Y @ X )
% 5.05/5.27 => P ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_triv
% 5.05/5.27 thf(fact_1606_linorder__less__linear,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( ord_less_real @ X @ Y )
% 5.05/5.27 | ( X = Y )
% 5.05/5.27 | ( ord_less_real @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_less_linear
% 5.05/5.27 thf(fact_1607_linorder__less__linear,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 | ( X = Y )
% 5.05/5.27 | ( ord_less_rat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_less_linear
% 5.05/5.27 thf(fact_1608_linorder__less__linear,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( ord_less_num @ X @ Y )
% 5.05/5.27 | ( X = Y )
% 5.05/5.27 | ( ord_less_num @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_less_linear
% 5.05/5.27 thf(fact_1609_linorder__less__linear,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( ord_less_nat @ X @ Y )
% 5.05/5.27 | ( X = Y )
% 5.05/5.27 | ( ord_less_nat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_less_linear
% 5.05/5.27 thf(fact_1610_linorder__less__linear,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( ord_less_int @ X @ Y )
% 5.05/5.27 | ( X = Y )
% 5.05/5.27 | ( ord_less_int @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % linorder_less_linear
% 5.05/5.27 thf(fact_1611_order__less__imp__not__eq,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( ord_less_real @ X @ Y )
% 5.05/5.27 => ( X != Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_eq
% 5.05/5.27 thf(fact_1612_order__less__imp__not__eq,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ( X != Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_eq
% 5.05/5.27 thf(fact_1613_order__less__imp__not__eq,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( ord_less_num @ X @ Y )
% 5.05/5.27 => ( X != Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_eq
% 5.05/5.27 thf(fact_1614_order__less__imp__not__eq,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( ord_less_nat @ X @ Y )
% 5.05/5.27 => ( X != Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_eq
% 5.05/5.27 thf(fact_1615_order__less__imp__not__eq,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( ord_less_int @ X @ Y )
% 5.05/5.27 => ( X != Y ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_eq
% 5.05/5.27 thf(fact_1616_order__less__imp__not__eq2,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( ord_less_real @ X @ Y )
% 5.05/5.27 => ( Y != X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_eq2
% 5.05/5.27 thf(fact_1617_order__less__imp__not__eq2,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ( Y != X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_eq2
% 5.05/5.27 thf(fact_1618_order__less__imp__not__eq2,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( ord_less_num @ X @ Y )
% 5.05/5.27 => ( Y != X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_eq2
% 5.05/5.27 thf(fact_1619_order__less__imp__not__eq2,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( ord_less_nat @ X @ Y )
% 5.05/5.27 => ( Y != X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_eq2
% 5.05/5.27 thf(fact_1620_order__less__imp__not__eq2,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( ord_less_int @ X @ Y )
% 5.05/5.27 => ( Y != X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_eq2
% 5.05/5.27 thf(fact_1621_order__less__imp__not__less,axiom,
% 5.05/5.27 ! [X: real,Y: real] :
% 5.05/5.27 ( ( ord_less_real @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_less
% 5.05/5.27 thf(fact_1622_order__less__imp__not__less,axiom,
% 5.05/5.27 ! [X: rat,Y: rat] :
% 5.05/5.27 ( ( ord_less_rat @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_less
% 5.05/5.27 thf(fact_1623_order__less__imp__not__less,axiom,
% 5.05/5.27 ! [X: num,Y: num] :
% 5.05/5.27 ( ( ord_less_num @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_less
% 5.05/5.27 thf(fact_1624_order__less__imp__not__less,axiom,
% 5.05/5.27 ! [X: nat,Y: nat] :
% 5.05/5.27 ( ( ord_less_nat @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_less
% 5.05/5.27 thf(fact_1625_order__less__imp__not__less,axiom,
% 5.05/5.27 ! [X: int,Y: int] :
% 5.05/5.27 ( ( ord_less_int @ X @ Y )
% 5.05/5.27 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.05/5.27
% 5.05/5.27 % order_less_imp_not_less
% 5.05/5.27 thf(fact_1626_Diff__mono,axiom,
% 5.05/5.27 ! [A2: set_nat,C2: set_nat,D3: set_nat,B3: set_nat] :
% 5.05/5.27 ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 5.05/5.27 => ( ( ord_less_eq_set_nat @ D3 @ B3 )
% 5.05/5.27 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( minus_minus_set_nat @ C2 @ D3 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_mono
% 5.05/5.27 thf(fact_1627_Diff__mono,axiom,
% 5.05/5.27 ! [A2: set_int,C2: set_int,D3: set_int,B3: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A2 @ C2 )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ D3 @ B3 )
% 5.05/5.27 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( minus_minus_set_int @ C2 @ D3 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_mono
% 5.05/5.27 thf(fact_1628_Diff__subset,axiom,
% 5.05/5.27 ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ A2 ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_subset
% 5.05/5.27 thf(fact_1629_Diff__subset,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ A2 ) ).
% 5.05/5.27
% 5.05/5.27 % Diff_subset
% 5.05/5.27 thf(fact_1630_double__diff,axiom,
% 5.05/5.27 ! [A2: set_nat,B3: set_nat,C2: set_nat] :
% 5.05/5.27 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.05/5.27 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 5.05/5.27 => ( ( minus_minus_set_nat @ B3 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 5.05/5.27 = A2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % double_diff
% 5.05/5.27 thf(fact_1631_double__diff,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int,C2: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ B3 @ C2 )
% 5.05/5.27 => ( ( minus_minus_set_int @ B3 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 5.05/5.27 = A2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % double_diff
% 5.05/5.27 thf(fact_1632_in__mono,axiom,
% 5.05/5.27 ! [A2: set_complex,B3: set_complex,X: complex] :
% 5.05/5.27 ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.05/5.27 => ( ( member_complex @ X @ A2 )
% 5.05/5.27 => ( member_complex @ X @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % in_mono
% 5.05/5.27 thf(fact_1633_in__mono,axiom,
% 5.05/5.27 ! [A2: set_real,B3: set_real,X: real] :
% 5.05/5.27 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.05/5.27 => ( ( member_real @ X @ A2 )
% 5.05/5.27 => ( member_real @ X @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % in_mono
% 5.05/5.27 thf(fact_1634_in__mono,axiom,
% 5.05/5.27 ! [A2: set_set_nat,B3: set_set_nat,X: set_nat] :
% 5.05/5.27 ( ( ord_le6893508408891458716et_nat @ A2 @ B3 )
% 5.05/5.27 => ( ( member_set_nat @ X @ A2 )
% 5.05/5.27 => ( member_set_nat @ X @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % in_mono
% 5.05/5.27 thf(fact_1635_in__mono,axiom,
% 5.05/5.27 ! [A2: set_nat,B3: set_nat,X: nat] :
% 5.05/5.27 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.05/5.27 => ( ( member_nat @ X @ A2 )
% 5.05/5.27 => ( member_nat @ X @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % in_mono
% 5.05/5.27 thf(fact_1636_in__mono,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int,X: int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.05/5.27 => ( ( member_int @ X @ A2 )
% 5.05/5.27 => ( member_int @ X @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % in_mono
% 5.05/5.27 thf(fact_1637_subsetD,axiom,
% 5.05/5.27 ! [A2: set_complex,B3: set_complex,C: complex] :
% 5.05/5.27 ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.05/5.27 => ( ( member_complex @ C @ A2 )
% 5.05/5.27 => ( member_complex @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subsetD
% 5.05/5.27 thf(fact_1638_subsetD,axiom,
% 5.05/5.27 ! [A2: set_real,B3: set_real,C: real] :
% 5.05/5.27 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.05/5.27 => ( ( member_real @ C @ A2 )
% 5.05/5.27 => ( member_real @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subsetD
% 5.05/5.27 thf(fact_1639_subsetD,axiom,
% 5.05/5.27 ! [A2: set_set_nat,B3: set_set_nat,C: set_nat] :
% 5.05/5.27 ( ( ord_le6893508408891458716et_nat @ A2 @ B3 )
% 5.05/5.27 => ( ( member_set_nat @ C @ A2 )
% 5.05/5.27 => ( member_set_nat @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subsetD
% 5.05/5.27 thf(fact_1640_subsetD,axiom,
% 5.05/5.27 ! [A2: set_nat,B3: set_nat,C: nat] :
% 5.05/5.27 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.05/5.27 => ( ( member_nat @ C @ A2 )
% 5.05/5.27 => ( member_nat @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subsetD
% 5.05/5.27 thf(fact_1641_subsetD,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int,C: int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.05/5.27 => ( ( member_int @ C @ A2 )
% 5.05/5.27 => ( member_int @ C @ B3 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subsetD
% 5.05/5.27 thf(fact_1642_psubsetE,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( ord_less_set_int @ A2 @ B3 )
% 5.05/5.27 => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.05/5.27 => ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % psubsetE
% 5.05/5.27 thf(fact_1643_equalityE,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( A2 = B3 )
% 5.05/5.27 => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.05/5.27 => ~ ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % equalityE
% 5.05/5.27 thf(fact_1644_subset__eq,axiom,
% 5.05/5.27 ( ord_le211207098394363844omplex
% 5.05/5.27 = ( ^ [A5: set_complex,B5: set_complex] :
% 5.05/5.27 ! [X2: complex] :
% 5.05/5.27 ( ( member_complex @ X2 @ A5 )
% 5.05/5.27 => ( member_complex @ X2 @ B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_eq
% 5.05/5.27 thf(fact_1645_subset__eq,axiom,
% 5.05/5.27 ( ord_less_eq_set_real
% 5.05/5.27 = ( ^ [A5: set_real,B5: set_real] :
% 5.05/5.27 ! [X2: real] :
% 5.05/5.27 ( ( member_real @ X2 @ A5 )
% 5.05/5.27 => ( member_real @ X2 @ B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_eq
% 5.05/5.27 thf(fact_1646_subset__eq,axiom,
% 5.05/5.27 ( ord_le6893508408891458716et_nat
% 5.05/5.27 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 5.05/5.27 ! [X2: set_nat] :
% 5.05/5.27 ( ( member_set_nat @ X2 @ A5 )
% 5.05/5.27 => ( member_set_nat @ X2 @ B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_eq
% 5.05/5.27 thf(fact_1647_subset__eq,axiom,
% 5.05/5.27 ( ord_less_eq_set_nat
% 5.05/5.27 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.05/5.27 ! [X2: nat] :
% 5.05/5.27 ( ( member_nat @ X2 @ A5 )
% 5.05/5.27 => ( member_nat @ X2 @ B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_eq
% 5.05/5.27 thf(fact_1648_subset__eq,axiom,
% 5.05/5.27 ( ord_less_eq_set_int
% 5.05/5.27 = ( ^ [A5: set_int,B5: set_int] :
% 5.05/5.27 ! [X2: int] :
% 5.05/5.27 ( ( member_int @ X2 @ A5 )
% 5.05/5.27 => ( member_int @ X2 @ B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_eq
% 5.05/5.27 thf(fact_1649_equalityD1,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( A2 = B3 )
% 5.05/5.27 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.05/5.27
% 5.05/5.27 % equalityD1
% 5.05/5.27 thf(fact_1650_equalityD2,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( A2 = B3 )
% 5.05/5.27 => ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 5.05/5.27
% 5.05/5.27 % equalityD2
% 5.05/5.27 thf(fact_1651_psubset__eq,axiom,
% 5.05/5.27 ( ord_less_set_int
% 5.05/5.27 = ( ^ [A5: set_int,B5: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 5.05/5.27 & ( A5 != B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % psubset_eq
% 5.05/5.27 thf(fact_1652_subset__iff,axiom,
% 5.05/5.27 ( ord_le211207098394363844omplex
% 5.05/5.27 = ( ^ [A5: set_complex,B5: set_complex] :
% 5.05/5.27 ! [T2: complex] :
% 5.05/5.27 ( ( member_complex @ T2 @ A5 )
% 5.05/5.27 => ( member_complex @ T2 @ B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_iff
% 5.05/5.27 thf(fact_1653_subset__iff,axiom,
% 5.05/5.27 ( ord_less_eq_set_real
% 5.05/5.27 = ( ^ [A5: set_real,B5: set_real] :
% 5.05/5.27 ! [T2: real] :
% 5.05/5.27 ( ( member_real @ T2 @ A5 )
% 5.05/5.27 => ( member_real @ T2 @ B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_iff
% 5.05/5.27 thf(fact_1654_subset__iff,axiom,
% 5.05/5.27 ( ord_le6893508408891458716et_nat
% 5.05/5.27 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 5.05/5.27 ! [T2: set_nat] :
% 5.05/5.27 ( ( member_set_nat @ T2 @ A5 )
% 5.05/5.27 => ( member_set_nat @ T2 @ B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_iff
% 5.05/5.27 thf(fact_1655_subset__iff,axiom,
% 5.05/5.27 ( ord_less_eq_set_nat
% 5.05/5.27 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.05/5.27 ! [T2: nat] :
% 5.05/5.27 ( ( member_nat @ T2 @ A5 )
% 5.05/5.27 => ( member_nat @ T2 @ B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_iff
% 5.05/5.27 thf(fact_1656_subset__iff,axiom,
% 5.05/5.27 ( ord_less_eq_set_int
% 5.05/5.27 = ( ^ [A5: set_int,B5: set_int] :
% 5.05/5.27 ! [T2: int] :
% 5.05/5.27 ( ( member_int @ T2 @ A5 )
% 5.05/5.27 => ( member_int @ T2 @ B5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_iff
% 5.05/5.27 thf(fact_1657_subset__refl,axiom,
% 5.05/5.27 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.05/5.27
% 5.05/5.27 % subset_refl
% 5.05/5.27 thf(fact_1658_Collect__mono,axiom,
% 5.05/5.27 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.05/5.27 ( ! [X3: product_prod_int_int] :
% 5.05/5.27 ( ( P @ X3 )
% 5.05/5.27 => ( Q @ X3 ) )
% 5.05/5.27 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Collect_mono
% 5.05/5.27 thf(fact_1659_Collect__mono,axiom,
% 5.05/5.27 ! [P: complex > $o,Q: complex > $o] :
% 5.05/5.27 ( ! [X3: complex] :
% 5.05/5.27 ( ( P @ X3 )
% 5.05/5.27 => ( Q @ X3 ) )
% 5.05/5.27 => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Collect_mono
% 5.05/5.27 thf(fact_1660_Collect__mono,axiom,
% 5.05/5.27 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.05/5.27 ( ! [X3: set_nat] :
% 5.05/5.27 ( ( P @ X3 )
% 5.05/5.27 => ( Q @ X3 ) )
% 5.05/5.27 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Collect_mono
% 5.05/5.27 thf(fact_1661_Collect__mono,axiom,
% 5.05/5.27 ! [P: nat > $o,Q: nat > $o] :
% 5.05/5.27 ( ! [X3: nat] :
% 5.05/5.27 ( ( P @ X3 )
% 5.05/5.27 => ( Q @ X3 ) )
% 5.05/5.27 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Collect_mono
% 5.05/5.27 thf(fact_1662_Collect__mono,axiom,
% 5.05/5.27 ! [P: int > $o,Q: int > $o] :
% 5.05/5.27 ( ! [X3: int] :
% 5.05/5.27 ( ( P @ X3 )
% 5.05/5.27 => ( Q @ X3 ) )
% 5.05/5.27 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Collect_mono
% 5.05/5.27 thf(fact_1663_subset__trans,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int,C2: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ B3 @ C2 )
% 5.05/5.27 => ( ord_less_eq_set_int @ A2 @ C2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_trans
% 5.05/5.27 thf(fact_1664_set__eq__subset,axiom,
% 5.05/5.27 ( ( ^ [Y4: set_int,Z3: set_int] : ( Y4 = Z3 ) )
% 5.05/5.27 = ( ^ [A5: set_int,B5: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 5.05/5.27 & ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % set_eq_subset
% 5.05/5.27 thf(fact_1665_Collect__mono__iff,axiom,
% 5.05/5.27 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.05/5.27 ( ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) )
% 5.05/5.27 = ( ! [X2: product_prod_int_int] :
% 5.05/5.27 ( ( P @ X2 )
% 5.05/5.27 => ( Q @ X2 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Collect_mono_iff
% 5.05/5.27 thf(fact_1666_Collect__mono__iff,axiom,
% 5.05/5.27 ! [P: complex > $o,Q: complex > $o] :
% 5.05/5.27 ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 5.05/5.27 = ( ! [X2: complex] :
% 5.05/5.27 ( ( P @ X2 )
% 5.05/5.27 => ( Q @ X2 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Collect_mono_iff
% 5.05/5.27 thf(fact_1667_Collect__mono__iff,axiom,
% 5.05/5.27 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.05/5.27 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 5.05/5.27 = ( ! [X2: set_nat] :
% 5.05/5.27 ( ( P @ X2 )
% 5.05/5.27 => ( Q @ X2 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Collect_mono_iff
% 5.05/5.27 thf(fact_1668_Collect__mono__iff,axiom,
% 5.05/5.27 ! [P: nat > $o,Q: nat > $o] :
% 5.05/5.27 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.05/5.27 = ( ! [X2: nat] :
% 5.05/5.27 ( ( P @ X2 )
% 5.05/5.27 => ( Q @ X2 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Collect_mono_iff
% 5.05/5.27 thf(fact_1669_Collect__mono__iff,axiom,
% 5.05/5.27 ! [P: int > $o,Q: int > $o] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.05/5.27 = ( ! [X2: int] :
% 5.05/5.27 ( ( P @ X2 )
% 5.05/5.27 => ( Q @ X2 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % Collect_mono_iff
% 5.05/5.27 thf(fact_1670_psubset__imp__subset,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int] :
% 5.05/5.27 ( ( ord_less_set_int @ A2 @ B3 )
% 5.05/5.27 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.05/5.27
% 5.05/5.27 % psubset_imp_subset
% 5.05/5.27 thf(fact_1671_psubset__subset__trans,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int,C2: set_int] :
% 5.05/5.27 ( ( ord_less_set_int @ A2 @ B3 )
% 5.05/5.27 => ( ( ord_less_eq_set_int @ B3 @ C2 )
% 5.05/5.27 => ( ord_less_set_int @ A2 @ C2 ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % psubset_subset_trans
% 5.05/5.27 thf(fact_1672_subset__not__subset__eq,axiom,
% 5.05/5.27 ( ord_less_set_int
% 5.05/5.27 = ( ^ [A5: set_int,B5: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 5.05/5.27 & ~ ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 5.05/5.27
% 5.05/5.27 % subset_not_subset_eq
% 5.05/5.27 thf(fact_1673_subset__psubset__trans,axiom,
% 5.05/5.27 ! [A2: set_int,B3: set_int,C2: set_int] :
% 5.05/5.27 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.05/5.27 => ( ( ord_less_set_int @ B3 @ C2 )
% 5.05/5.27 => ( ord_less_set_int @ A2 @ C2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % subset_psubset_trans
% 5.05/5.28 thf(fact_1674_subset__iff__psubset__eq,axiom,
% 5.05/5.28 ( ord_less_eq_set_int
% 5.05/5.28 = ( ^ [A5: set_int,B5: set_int] :
% 5.05/5.28 ( ( ord_less_set_int @ A5 @ B5 )
% 5.05/5.28 | ( A5 = B5 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % subset_iff_psubset_eq
% 5.05/5.28 thf(fact_1675_empty__def,axiom,
% 5.05/5.28 ( bot_bo1796632182523588997nt_int
% 5.05/5.28 = ( collec213857154873943460nt_int
% 5.05/5.28 @ ^ [X2: product_prod_int_int] : $false ) ) ).
% 5.05/5.28
% 5.05/5.28 % empty_def
% 5.05/5.28 thf(fact_1676_empty__def,axiom,
% 5.05/5.28 ( bot_bot_set_complex
% 5.05/5.28 = ( collect_complex
% 5.05/5.28 @ ^ [X2: complex] : $false ) ) ).
% 5.05/5.28
% 5.05/5.28 % empty_def
% 5.05/5.28 thf(fact_1677_empty__def,axiom,
% 5.05/5.28 ( bot_bot_set_set_nat
% 5.05/5.28 = ( collect_set_nat
% 5.05/5.28 @ ^ [X2: set_nat] : $false ) ) ).
% 5.05/5.28
% 5.05/5.28 % empty_def
% 5.05/5.28 thf(fact_1678_empty__def,axiom,
% 5.05/5.28 ( bot_bot_set_nat
% 5.05/5.28 = ( collect_nat
% 5.05/5.28 @ ^ [X2: nat] : $false ) ) ).
% 5.05/5.28
% 5.05/5.28 % empty_def
% 5.05/5.28 thf(fact_1679_empty__def,axiom,
% 5.05/5.28 ( bot_bot_set_int
% 5.05/5.28 = ( collect_int
% 5.05/5.28 @ ^ [X2: int] : $false ) ) ).
% 5.05/5.28
% 5.05/5.28 % empty_def
% 5.05/5.28 thf(fact_1680_empty__def,axiom,
% 5.05/5.28 ( bot_bot_set_real
% 5.05/5.28 = ( collect_real
% 5.05/5.28 @ ^ [X2: real] : $false ) ) ).
% 5.05/5.28
% 5.05/5.28 % empty_def
% 5.05/5.28 thf(fact_1681_Collect__subset,axiom,
% 5.05/5.28 ! [A2: set_real,P: real > $o] :
% 5.05/5.28 ( ord_less_eq_set_real
% 5.05/5.28 @ ( collect_real
% 5.05/5.28 @ ^ [X2: real] :
% 5.05/5.28 ( ( member_real @ X2 @ A2 )
% 5.05/5.28 & ( P @ X2 ) ) )
% 5.05/5.28 @ A2 ) ).
% 5.05/5.28
% 5.05/5.28 % Collect_subset
% 5.05/5.28 thf(fact_1682_Collect__subset,axiom,
% 5.05/5.28 ! [A2: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 5.05/5.28 ( ord_le2843351958646193337nt_int
% 5.05/5.28 @ ( collec213857154873943460nt_int
% 5.05/5.28 @ ^ [X2: product_prod_int_int] :
% 5.05/5.28 ( ( member5262025264175285858nt_int @ X2 @ A2 )
% 5.05/5.28 & ( P @ X2 ) ) )
% 5.05/5.28 @ A2 ) ).
% 5.05/5.28
% 5.05/5.28 % Collect_subset
% 5.05/5.28 thf(fact_1683_Collect__subset,axiom,
% 5.05/5.28 ! [A2: set_complex,P: complex > $o] :
% 5.05/5.28 ( ord_le211207098394363844omplex
% 5.05/5.28 @ ( collect_complex
% 5.05/5.28 @ ^ [X2: complex] :
% 5.05/5.28 ( ( member_complex @ X2 @ A2 )
% 5.05/5.28 & ( P @ X2 ) ) )
% 5.05/5.28 @ A2 ) ).
% 5.05/5.28
% 5.05/5.28 % Collect_subset
% 5.05/5.28 thf(fact_1684_Collect__subset,axiom,
% 5.05/5.28 ! [A2: set_set_nat,P: set_nat > $o] :
% 5.05/5.28 ( ord_le6893508408891458716et_nat
% 5.05/5.28 @ ( collect_set_nat
% 5.05/5.28 @ ^ [X2: set_nat] :
% 5.05/5.28 ( ( member_set_nat @ X2 @ A2 )
% 5.05/5.28 & ( P @ X2 ) ) )
% 5.05/5.28 @ A2 ) ).
% 5.05/5.28
% 5.05/5.28 % Collect_subset
% 5.05/5.28 thf(fact_1685_Collect__subset,axiom,
% 5.05/5.28 ! [A2: set_nat,P: nat > $o] :
% 5.05/5.28 ( ord_less_eq_set_nat
% 5.05/5.28 @ ( collect_nat
% 5.05/5.28 @ ^ [X2: nat] :
% 5.05/5.28 ( ( member_nat @ X2 @ A2 )
% 5.05/5.28 & ( P @ X2 ) ) )
% 5.05/5.28 @ A2 ) ).
% 5.05/5.28
% 5.05/5.28 % Collect_subset
% 5.05/5.28 thf(fact_1686_Collect__subset,axiom,
% 5.05/5.28 ! [A2: set_int,P: int > $o] :
% 5.05/5.28 ( ord_less_eq_set_int
% 5.05/5.28 @ ( collect_int
% 5.05/5.28 @ ^ [X2: int] :
% 5.05/5.28 ( ( member_int @ X2 @ A2 )
% 5.05/5.28 & ( P @ X2 ) ) )
% 5.05/5.28 @ A2 ) ).
% 5.05/5.28
% 5.05/5.28 % Collect_subset
% 5.05/5.28 thf(fact_1687_less__eq__set__def,axiom,
% 5.05/5.28 ( ord_le211207098394363844omplex
% 5.05/5.28 = ( ^ [A5: set_complex,B5: set_complex] :
% 5.05/5.28 ( ord_le4573692005234683329plex_o
% 5.05/5.28 @ ^ [X2: complex] : ( member_complex @ X2 @ A5 )
% 5.05/5.28 @ ^ [X2: complex] : ( member_complex @ X2 @ B5 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_eq_set_def
% 5.05/5.28 thf(fact_1688_less__eq__set__def,axiom,
% 5.05/5.28 ( ord_less_eq_set_real
% 5.05/5.28 = ( ^ [A5: set_real,B5: set_real] :
% 5.05/5.28 ( ord_less_eq_real_o
% 5.05/5.28 @ ^ [X2: real] : ( member_real @ X2 @ A5 )
% 5.05/5.28 @ ^ [X2: real] : ( member_real @ X2 @ B5 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_eq_set_def
% 5.05/5.28 thf(fact_1689_less__eq__set__def,axiom,
% 5.05/5.28 ( ord_le6893508408891458716et_nat
% 5.05/5.28 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 5.05/5.28 ( ord_le3964352015994296041_nat_o
% 5.05/5.28 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 )
% 5.05/5.28 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ B5 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_eq_set_def
% 5.05/5.28 thf(fact_1690_less__eq__set__def,axiom,
% 5.05/5.28 ( ord_less_eq_set_nat
% 5.05/5.28 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.05/5.28 ( ord_less_eq_nat_o
% 5.05/5.28 @ ^ [X2: nat] : ( member_nat @ X2 @ A5 )
% 5.05/5.28 @ ^ [X2: nat] : ( member_nat @ X2 @ B5 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_eq_set_def
% 5.05/5.28 thf(fact_1691_less__eq__set__def,axiom,
% 5.05/5.28 ( ord_less_eq_set_int
% 5.05/5.28 = ( ^ [A5: set_int,B5: set_int] :
% 5.05/5.28 ( ord_less_eq_int_o
% 5.05/5.28 @ ^ [X2: int] : ( member_int @ X2 @ A5 )
% 5.05/5.28 @ ^ [X2: int] : ( member_int @ X2 @ B5 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_eq_set_def
% 5.05/5.28 thf(fact_1692_leD,axiom,
% 5.05/5.28 ! [Y: real,X: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ Y @ X )
% 5.05/5.28 => ~ ( ord_less_real @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % leD
% 5.05/5.28 thf(fact_1693_leD,axiom,
% 5.05/5.28 ! [Y: set_int,X: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ Y @ X )
% 5.05/5.28 => ~ ( ord_less_set_int @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % leD
% 5.05/5.28 thf(fact_1694_leD,axiom,
% 5.05/5.28 ! [Y: rat,X: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ Y @ X )
% 5.05/5.28 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % leD
% 5.05/5.28 thf(fact_1695_leD,axiom,
% 5.05/5.28 ! [Y: num,X: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ Y @ X )
% 5.05/5.28 => ~ ( ord_less_num @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % leD
% 5.05/5.28 thf(fact_1696_leD,axiom,
% 5.05/5.28 ! [Y: nat,X: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ Y @ X )
% 5.05/5.28 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % leD
% 5.05/5.28 thf(fact_1697_leD,axiom,
% 5.05/5.28 ! [Y: int,X: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ Y @ X )
% 5.05/5.28 => ~ ( ord_less_int @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % leD
% 5.05/5.28 thf(fact_1698_leI,axiom,
% 5.05/5.28 ! [X: real,Y: real] :
% 5.05/5.28 ( ~ ( ord_less_real @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_real @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % leI
% 5.05/5.28 thf(fact_1699_leI,axiom,
% 5.05/5.28 ! [X: rat,Y: rat] :
% 5.05/5.28 ( ~ ( ord_less_rat @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % leI
% 5.05/5.28 thf(fact_1700_leI,axiom,
% 5.05/5.28 ! [X: num,Y: num] :
% 5.05/5.28 ( ~ ( ord_less_num @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % leI
% 5.05/5.28 thf(fact_1701_leI,axiom,
% 5.05/5.28 ! [X: nat,Y: nat] :
% 5.05/5.28 ( ~ ( ord_less_nat @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % leI
% 5.05/5.28 thf(fact_1702_leI,axiom,
% 5.05/5.28 ! [X: int,Y: int] :
% 5.05/5.28 ( ~ ( ord_less_int @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % leI
% 5.05/5.28 thf(fact_1703_nless__le,axiom,
% 5.05/5.28 ! [A: real,B: real] :
% 5.05/5.28 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.05/5.28 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.05/5.28 | ( A = B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % nless_le
% 5.05/5.28 thf(fact_1704_nless__le,axiom,
% 5.05/5.28 ! [A: set_int,B: set_int] :
% 5.05/5.28 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 5.05/5.28 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.05/5.28 | ( A = B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % nless_le
% 5.05/5.28 thf(fact_1705_nless__le,axiom,
% 5.05/5.28 ! [A: rat,B: rat] :
% 5.05/5.28 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.05/5.28 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 | ( A = B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % nless_le
% 5.05/5.28 thf(fact_1706_nless__le,axiom,
% 5.05/5.28 ! [A: num,B: num] :
% 5.05/5.28 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.05/5.28 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.05/5.28 | ( A = B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % nless_le
% 5.05/5.28 thf(fact_1707_nless__le,axiom,
% 5.05/5.28 ! [A: nat,B: nat] :
% 5.05/5.28 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.05/5.28 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.05/5.28 | ( A = B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % nless_le
% 5.05/5.28 thf(fact_1708_nless__le,axiom,
% 5.05/5.28 ! [A: int,B: int] :
% 5.05/5.28 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.05/5.28 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.05/5.28 | ( A = B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % nless_le
% 5.05/5.28 thf(fact_1709_antisym__conv1,axiom,
% 5.05/5.28 ! [X: real,Y: real] :
% 5.05/5.28 ( ~ ( ord_less_real @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_real @ X @ Y )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv1
% 5.05/5.28 thf(fact_1710_antisym__conv1,axiom,
% 5.05/5.28 ! [X: set_int,Y: set_int] :
% 5.05/5.28 ( ~ ( ord_less_set_int @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_set_int @ X @ Y )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv1
% 5.05/5.28 thf(fact_1711_antisym__conv1,axiom,
% 5.05/5.28 ! [X: rat,Y: rat] :
% 5.05/5.28 ( ~ ( ord_less_rat @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv1
% 5.05/5.28 thf(fact_1712_antisym__conv1,axiom,
% 5.05/5.28 ! [X: num,Y: num] :
% 5.05/5.28 ( ~ ( ord_less_num @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv1
% 5.05/5.28 thf(fact_1713_antisym__conv1,axiom,
% 5.05/5.28 ! [X: nat,Y: nat] :
% 5.05/5.28 ( ~ ( ord_less_nat @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv1
% 5.05/5.28 thf(fact_1714_antisym__conv1,axiom,
% 5.05/5.28 ! [X: int,Y: int] :
% 5.05/5.28 ( ~ ( ord_less_int @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv1
% 5.05/5.28 thf(fact_1715_antisym__conv2,axiom,
% 5.05/5.28 ! [X: real,Y: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ X @ Y )
% 5.05/5.28 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv2
% 5.05/5.28 thf(fact_1716_antisym__conv2,axiom,
% 5.05/5.28 ! [X: set_int,Y: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ X @ Y )
% 5.05/5.28 => ( ( ~ ( ord_less_set_int @ X @ Y ) )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv2
% 5.05/5.28 thf(fact_1717_antisym__conv2,axiom,
% 5.05/5.28 ! [X: rat,Y: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.28 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv2
% 5.05/5.28 thf(fact_1718_antisym__conv2,axiom,
% 5.05/5.28 ! [X: num,Y: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.28 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv2
% 5.05/5.28 thf(fact_1719_antisym__conv2,axiom,
% 5.05/5.28 ! [X: nat,Y: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.28 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv2
% 5.05/5.28 thf(fact_1720_antisym__conv2,axiom,
% 5.05/5.28 ! [X: int,Y: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.28 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.05/5.28 = ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % antisym_conv2
% 5.05/5.28 thf(fact_1721_dense__ge,axiom,
% 5.05/5.28 ! [Z: real,Y: real] :
% 5.05/5.28 ( ! [X3: real] :
% 5.05/5.28 ( ( ord_less_real @ Z @ X3 )
% 5.05/5.28 => ( ord_less_eq_real @ Y @ X3 ) )
% 5.05/5.28 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.05/5.28
% 5.05/5.28 % dense_ge
% 5.05/5.28 thf(fact_1722_dense__ge,axiom,
% 5.05/5.28 ! [Z: rat,Y: rat] :
% 5.05/5.28 ( ! [X3: rat] :
% 5.05/5.28 ( ( ord_less_rat @ Z @ X3 )
% 5.05/5.28 => ( ord_less_eq_rat @ Y @ X3 ) )
% 5.05/5.28 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.05/5.28
% 5.05/5.28 % dense_ge
% 5.05/5.28 thf(fact_1723_dense__le,axiom,
% 5.05/5.28 ! [Y: real,Z: real] :
% 5.05/5.28 ( ! [X3: real] :
% 5.05/5.28 ( ( ord_less_real @ X3 @ Y )
% 5.05/5.28 => ( ord_less_eq_real @ X3 @ Z ) )
% 5.05/5.28 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.05/5.28
% 5.05/5.28 % dense_le
% 5.05/5.28 thf(fact_1724_dense__le,axiom,
% 5.05/5.28 ! [Y: rat,Z: rat] :
% 5.05/5.28 ( ! [X3: rat] :
% 5.05/5.28 ( ( ord_less_rat @ X3 @ Y )
% 5.05/5.28 => ( ord_less_eq_rat @ X3 @ Z ) )
% 5.05/5.28 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.05/5.28
% 5.05/5.28 % dense_le
% 5.05/5.28 thf(fact_1725_less__le__not__le,axiom,
% 5.05/5.28 ( ord_less_real
% 5.05/5.28 = ( ^ [X2: real,Y2: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.05/5.28 & ~ ( ord_less_eq_real @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_le_not_le
% 5.05/5.28 thf(fact_1726_less__le__not__le,axiom,
% 5.05/5.28 ( ord_less_set_int
% 5.05/5.28 = ( ^ [X2: set_int,Y2: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ X2 @ Y2 )
% 5.05/5.28 & ~ ( ord_less_eq_set_int @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_le_not_le
% 5.05/5.28 thf(fact_1727_less__le__not__le,axiom,
% 5.05/5.28 ( ord_less_rat
% 5.05/5.28 = ( ^ [X2: rat,Y2: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.05/5.28 & ~ ( ord_less_eq_rat @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_le_not_le
% 5.05/5.28 thf(fact_1728_less__le__not__le,axiom,
% 5.05/5.28 ( ord_less_num
% 5.05/5.28 = ( ^ [X2: num,Y2: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X2 @ Y2 )
% 5.05/5.28 & ~ ( ord_less_eq_num @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_le_not_le
% 5.05/5.28 thf(fact_1729_less__le__not__le,axiom,
% 5.05/5.28 ( ord_less_nat
% 5.05/5.28 = ( ^ [X2: nat,Y2: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 5.05/5.28 & ~ ( ord_less_eq_nat @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_le_not_le
% 5.05/5.28 thf(fact_1730_less__le__not__le,axiom,
% 5.05/5.28 ( ord_less_int
% 5.05/5.28 = ( ^ [X2: int,Y2: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ X2 @ Y2 )
% 5.05/5.28 & ~ ( ord_less_eq_int @ Y2 @ X2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_le_not_le
% 5.05/5.28 thf(fact_1731_not__le__imp__less,axiom,
% 5.05/5.28 ! [Y: real,X: real] :
% 5.05/5.28 ( ~ ( ord_less_eq_real @ Y @ X )
% 5.05/5.28 => ( ord_less_real @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % not_le_imp_less
% 5.05/5.28 thf(fact_1732_not__le__imp__less,axiom,
% 5.05/5.28 ! [Y: rat,X: rat] :
% 5.05/5.28 ( ~ ( ord_less_eq_rat @ Y @ X )
% 5.05/5.28 => ( ord_less_rat @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % not_le_imp_less
% 5.05/5.28 thf(fact_1733_not__le__imp__less,axiom,
% 5.05/5.28 ! [Y: num,X: num] :
% 5.05/5.28 ( ~ ( ord_less_eq_num @ Y @ X )
% 5.05/5.28 => ( ord_less_num @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % not_le_imp_less
% 5.05/5.28 thf(fact_1734_not__le__imp__less,axiom,
% 5.05/5.28 ! [Y: nat,X: nat] :
% 5.05/5.28 ( ~ ( ord_less_eq_nat @ Y @ X )
% 5.05/5.28 => ( ord_less_nat @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % not_le_imp_less
% 5.05/5.28 thf(fact_1735_not__le__imp__less,axiom,
% 5.05/5.28 ! [Y: int,X: int] :
% 5.05/5.28 ( ~ ( ord_less_eq_int @ Y @ X )
% 5.05/5.28 => ( ord_less_int @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % not_le_imp_less
% 5.05/5.28 thf(fact_1736_order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_real
% 5.05/5.28 = ( ^ [A4: real,B4: real] :
% 5.05/5.28 ( ( ord_less_real @ A4 @ B4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.order_iff_strict
% 5.05/5.28 thf(fact_1737_order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_set_int
% 5.05/5.28 = ( ^ [A4: set_int,B4: set_int] :
% 5.05/5.28 ( ( ord_less_set_int @ A4 @ B4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.order_iff_strict
% 5.05/5.28 thf(fact_1738_order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_rat
% 5.05/5.28 = ( ^ [A4: rat,B4: rat] :
% 5.05/5.28 ( ( ord_less_rat @ A4 @ B4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.order_iff_strict
% 5.05/5.28 thf(fact_1739_order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_num
% 5.05/5.28 = ( ^ [A4: num,B4: num] :
% 5.05/5.28 ( ( ord_less_num @ A4 @ B4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.order_iff_strict
% 5.05/5.28 thf(fact_1740_order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_nat
% 5.05/5.28 = ( ^ [A4: nat,B4: nat] :
% 5.05/5.28 ( ( ord_less_nat @ A4 @ B4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.order_iff_strict
% 5.05/5.28 thf(fact_1741_order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_int
% 5.05/5.28 = ( ^ [A4: int,B4: int] :
% 5.05/5.28 ( ( ord_less_int @ A4 @ B4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.order_iff_strict
% 5.05/5.28 thf(fact_1742_order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_real
% 5.05/5.28 = ( ^ [A4: real,B4: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ A4 @ B4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_order
% 5.05/5.28 thf(fact_1743_order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_set_int
% 5.05/5.28 = ( ^ [A4: set_int,B4: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_order
% 5.05/5.28 thf(fact_1744_order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_rat
% 5.05/5.28 = ( ^ [A4: rat,B4: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A4 @ B4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_order
% 5.05/5.28 thf(fact_1745_order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_num
% 5.05/5.28 = ( ^ [A4: num,B4: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ A4 @ B4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_order
% 5.05/5.28 thf(fact_1746_order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_nat
% 5.05/5.28 = ( ^ [A4: nat,B4: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ A4 @ B4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_order
% 5.05/5.28 thf(fact_1747_order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_int
% 5.05/5.28 = ( ^ [A4: int,B4: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_order
% 5.05/5.28 thf(fact_1748_order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ A @ B )
% 5.05/5.28 => ( ( ord_less_real @ B @ C )
% 5.05/5.28 => ( ord_less_real @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans1
% 5.05/5.28 thf(fact_1749_order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [A: set_int,B: set_int,C: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ A @ B )
% 5.05/5.28 => ( ( ord_less_set_int @ B @ C )
% 5.05/5.28 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans1
% 5.05/5.28 thf(fact_1750_order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ( ord_less_rat @ B @ C )
% 5.05/5.28 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans1
% 5.05/5.28 thf(fact_1751_order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [A: num,B: num,C: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.28 => ( ( ord_less_num @ B @ C )
% 5.05/5.28 => ( ord_less_num @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans1
% 5.05/5.28 thf(fact_1752_order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [A: nat,B: nat,C: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.28 => ( ( ord_less_nat @ B @ C )
% 5.05/5.28 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans1
% 5.05/5.28 thf(fact_1753_order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.28 => ( ( ord_less_int @ B @ C )
% 5.05/5.28 => ( ord_less_int @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans1
% 5.05/5.28 thf(fact_1754_order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( ord_less_real @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_real @ B @ C )
% 5.05/5.28 => ( ord_less_real @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans2
% 5.05/5.28 thf(fact_1755_order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [A: set_int,B: set_int,C: set_int] :
% 5.05/5.28 ( ( ord_less_set_int @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_set_int @ B @ C )
% 5.05/5.28 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans2
% 5.05/5.28 thf(fact_1756_order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_rat @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.28 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans2
% 5.05/5.28 thf(fact_1757_order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [A: num,B: num,C: num] :
% 5.05/5.28 ( ( ord_less_num @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.28 => ( ord_less_num @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans2
% 5.05/5.28 thf(fact_1758_order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [A: nat,B: nat,C: nat] :
% 5.05/5.28 ( ( ord_less_nat @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_nat @ B @ C )
% 5.05/5.28 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans2
% 5.05/5.28 thf(fact_1759_order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int] :
% 5.05/5.28 ( ( ord_less_int @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_int @ B @ C )
% 5.05/5.28 => ( ord_less_int @ A @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_trans2
% 5.05/5.28 thf(fact_1760_order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_real
% 5.05/5.28 = ( ^ [A4: real,B4: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ A4 @ B4 )
% 5.05/5.28 & ~ ( ord_less_eq_real @ B4 @ A4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_not
% 5.05/5.28 thf(fact_1761_order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_set_int
% 5.05/5.28 = ( ^ [A4: set_int,B4: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.05/5.28 & ~ ( ord_less_eq_set_int @ B4 @ A4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_not
% 5.05/5.28 thf(fact_1762_order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_rat
% 5.05/5.28 = ( ^ [A4: rat,B4: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A4 @ B4 )
% 5.05/5.28 & ~ ( ord_less_eq_rat @ B4 @ A4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_not
% 5.05/5.28 thf(fact_1763_order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_num
% 5.05/5.28 = ( ^ [A4: num,B4: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ A4 @ B4 )
% 5.05/5.28 & ~ ( ord_less_eq_num @ B4 @ A4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_not
% 5.05/5.28 thf(fact_1764_order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_nat
% 5.05/5.28 = ( ^ [A4: nat,B4: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ A4 @ B4 )
% 5.05/5.28 & ~ ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_not
% 5.05/5.28 thf(fact_1765_order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_int
% 5.05/5.28 = ( ^ [A4: int,B4: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.05/5.28 & ~ ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_iff_not
% 5.05/5.28 thf(fact_1766_dense__ge__bounded,axiom,
% 5.05/5.28 ! [Z: real,X: real,Y: real] :
% 5.05/5.28 ( ( ord_less_real @ Z @ X )
% 5.05/5.28 => ( ! [W2: real] :
% 5.05/5.28 ( ( ord_less_real @ Z @ W2 )
% 5.05/5.28 => ( ( ord_less_real @ W2 @ X )
% 5.05/5.28 => ( ord_less_eq_real @ Y @ W2 ) ) )
% 5.05/5.28 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dense_ge_bounded
% 5.05/5.28 thf(fact_1767_dense__ge__bounded,axiom,
% 5.05/5.28 ! [Z: rat,X: rat,Y: rat] :
% 5.05/5.28 ( ( ord_less_rat @ Z @ X )
% 5.05/5.28 => ( ! [W2: rat] :
% 5.05/5.28 ( ( ord_less_rat @ Z @ W2 )
% 5.05/5.28 => ( ( ord_less_rat @ W2 @ X )
% 5.05/5.28 => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 5.05/5.28 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dense_ge_bounded
% 5.05/5.28 thf(fact_1768_dense__le__bounded,axiom,
% 5.05/5.28 ! [X: real,Y: real,Z: real] :
% 5.05/5.28 ( ( ord_less_real @ X @ Y )
% 5.05/5.28 => ( ! [W2: real] :
% 5.05/5.28 ( ( ord_less_real @ X @ W2 )
% 5.05/5.28 => ( ( ord_less_real @ W2 @ Y )
% 5.05/5.28 => ( ord_less_eq_real @ W2 @ Z ) ) )
% 5.05/5.28 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dense_le_bounded
% 5.05/5.28 thf(fact_1769_dense__le__bounded,axiom,
% 5.05/5.28 ! [X: rat,Y: rat,Z: rat] :
% 5.05/5.28 ( ( ord_less_rat @ X @ Y )
% 5.05/5.28 => ( ! [W2: rat] :
% 5.05/5.28 ( ( ord_less_rat @ X @ W2 )
% 5.05/5.28 => ( ( ord_less_rat @ W2 @ Y )
% 5.05/5.28 => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 5.05/5.28 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dense_le_bounded
% 5.05/5.28 thf(fact_1770_dual__order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_real
% 5.05/5.28 = ( ^ [B4: real,A4: real] :
% 5.05/5.28 ( ( ord_less_real @ B4 @ A4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.order_iff_strict
% 5.05/5.28 thf(fact_1771_dual__order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_set_int
% 5.05/5.28 = ( ^ [B4: set_int,A4: set_int] :
% 5.05/5.28 ( ( ord_less_set_int @ B4 @ A4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.order_iff_strict
% 5.05/5.28 thf(fact_1772_dual__order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_rat
% 5.05/5.28 = ( ^ [B4: rat,A4: rat] :
% 5.05/5.28 ( ( ord_less_rat @ B4 @ A4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.order_iff_strict
% 5.05/5.28 thf(fact_1773_dual__order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_num
% 5.05/5.28 = ( ^ [B4: num,A4: num] :
% 5.05/5.28 ( ( ord_less_num @ B4 @ A4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.order_iff_strict
% 5.05/5.28 thf(fact_1774_dual__order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_nat
% 5.05/5.28 = ( ^ [B4: nat,A4: nat] :
% 5.05/5.28 ( ( ord_less_nat @ B4 @ A4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.order_iff_strict
% 5.05/5.28 thf(fact_1775_dual__order_Oorder__iff__strict,axiom,
% 5.05/5.28 ( ord_less_eq_int
% 5.05/5.28 = ( ^ [B4: int,A4: int] :
% 5.05/5.28 ( ( ord_less_int @ B4 @ A4 )
% 5.05/5.28 | ( A4 = B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.order_iff_strict
% 5.05/5.28 thf(fact_1776_dual__order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_real
% 5.05/5.28 = ( ^ [B4: real,A4: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ B4 @ A4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_order
% 5.05/5.28 thf(fact_1777_dual__order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_set_int
% 5.05/5.28 = ( ^ [B4: set_int,A4: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_order
% 5.05/5.28 thf(fact_1778_dual__order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_rat
% 5.05/5.28 = ( ^ [B4: rat,A4: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ B4 @ A4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_order
% 5.05/5.28 thf(fact_1779_dual__order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_num
% 5.05/5.28 = ( ^ [B4: num,A4: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ B4 @ A4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_order
% 5.05/5.28 thf(fact_1780_dual__order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_nat
% 5.05/5.28 = ( ^ [B4: nat,A4: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ B4 @ A4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_order
% 5.05/5.28 thf(fact_1781_dual__order_Ostrict__iff__order,axiom,
% 5.05/5.28 ( ord_less_int
% 5.05/5.28 = ( ^ [B4: int,A4: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ B4 @ A4 )
% 5.05/5.28 & ( A4 != B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_order
% 5.05/5.28 thf(fact_1782_dual__order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [B: real,A: real,C: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ B @ A )
% 5.05/5.28 => ( ( ord_less_real @ C @ B )
% 5.05/5.28 => ( ord_less_real @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans1
% 5.05/5.28 thf(fact_1783_dual__order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [B: set_int,A: set_int,C: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ B @ A )
% 5.05/5.28 => ( ( ord_less_set_int @ C @ B )
% 5.05/5.28 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans1
% 5.05/5.28 thf(fact_1784_dual__order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [B: rat,A: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.28 => ( ( ord_less_rat @ C @ B )
% 5.05/5.28 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans1
% 5.05/5.28 thf(fact_1785_dual__order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [B: num,A: num,C: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ B @ A )
% 5.05/5.28 => ( ( ord_less_num @ C @ B )
% 5.05/5.28 => ( ord_less_num @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans1
% 5.05/5.28 thf(fact_1786_dual__order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [B: nat,A: nat,C: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ B @ A )
% 5.05/5.28 => ( ( ord_less_nat @ C @ B )
% 5.05/5.28 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans1
% 5.05/5.28 thf(fact_1787_dual__order_Ostrict__trans1,axiom,
% 5.05/5.28 ! [B: int,A: int,C: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ B @ A )
% 5.05/5.28 => ( ( ord_less_int @ C @ B )
% 5.05/5.28 => ( ord_less_int @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans1
% 5.05/5.28 thf(fact_1788_dual__order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [B: real,A: real,C: real] :
% 5.05/5.28 ( ( ord_less_real @ B @ A )
% 5.05/5.28 => ( ( ord_less_eq_real @ C @ B )
% 5.05/5.28 => ( ord_less_real @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans2
% 5.05/5.28 thf(fact_1789_dual__order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [B: set_int,A: set_int,C: set_int] :
% 5.05/5.28 ( ( ord_less_set_int @ B @ A )
% 5.05/5.28 => ( ( ord_less_eq_set_int @ C @ B )
% 5.05/5.28 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans2
% 5.05/5.28 thf(fact_1790_dual__order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [B: rat,A: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_rat @ B @ A )
% 5.05/5.28 => ( ( ord_less_eq_rat @ C @ B )
% 5.05/5.28 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans2
% 5.05/5.28 thf(fact_1791_dual__order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [B: num,A: num,C: num] :
% 5.05/5.28 ( ( ord_less_num @ B @ A )
% 5.05/5.28 => ( ( ord_less_eq_num @ C @ B )
% 5.05/5.28 => ( ord_less_num @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans2
% 5.05/5.28 thf(fact_1792_dual__order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [B: nat,A: nat,C: nat] :
% 5.05/5.28 ( ( ord_less_nat @ B @ A )
% 5.05/5.28 => ( ( ord_less_eq_nat @ C @ B )
% 5.05/5.28 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans2
% 5.05/5.28 thf(fact_1793_dual__order_Ostrict__trans2,axiom,
% 5.05/5.28 ! [B: int,A: int,C: int] :
% 5.05/5.28 ( ( ord_less_int @ B @ A )
% 5.05/5.28 => ( ( ord_less_eq_int @ C @ B )
% 5.05/5.28 => ( ord_less_int @ C @ A ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_trans2
% 5.05/5.28 thf(fact_1794_dual__order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_real
% 5.05/5.28 = ( ^ [B4: real,A4: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ B4 @ A4 )
% 5.05/5.28 & ~ ( ord_less_eq_real @ A4 @ B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_not
% 5.05/5.28 thf(fact_1795_dual__order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_set_int
% 5.05/5.28 = ( ^ [B4: set_int,A4: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.05/5.28 & ~ ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_not
% 5.05/5.28 thf(fact_1796_dual__order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_rat
% 5.05/5.28 = ( ^ [B4: rat,A4: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ B4 @ A4 )
% 5.05/5.28 & ~ ( ord_less_eq_rat @ A4 @ B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_not
% 5.05/5.28 thf(fact_1797_dual__order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_num
% 5.05/5.28 = ( ^ [B4: num,A4: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ B4 @ A4 )
% 5.05/5.28 & ~ ( ord_less_eq_num @ A4 @ B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_not
% 5.05/5.28 thf(fact_1798_dual__order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_nat
% 5.05/5.28 = ( ^ [B4: nat,A4: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ B4 @ A4 )
% 5.05/5.28 & ~ ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_not
% 5.05/5.28 thf(fact_1799_dual__order_Ostrict__iff__not,axiom,
% 5.05/5.28 ( ord_less_int
% 5.05/5.28 = ( ^ [B4: int,A4: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ B4 @ A4 )
% 5.05/5.28 & ~ ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_iff_not
% 5.05/5.28 thf(fact_1800_order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [A: real,B: real] :
% 5.05/5.28 ( ( ord_less_real @ A @ B )
% 5.05/5.28 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_implies_order
% 5.05/5.28 thf(fact_1801_order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [A: set_int,B: set_int] :
% 5.05/5.28 ( ( ord_less_set_int @ A @ B )
% 5.05/5.28 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_implies_order
% 5.05/5.28 thf(fact_1802_order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [A: rat,B: rat] :
% 5.05/5.28 ( ( ord_less_rat @ A @ B )
% 5.05/5.28 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_implies_order
% 5.05/5.28 thf(fact_1803_order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [A: num,B: num] :
% 5.05/5.28 ( ( ord_less_num @ A @ B )
% 5.05/5.28 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_implies_order
% 5.05/5.28 thf(fact_1804_order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [A: nat,B: nat] :
% 5.05/5.28 ( ( ord_less_nat @ A @ B )
% 5.05/5.28 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_implies_order
% 5.05/5.28 thf(fact_1805_order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [A: int,B: int] :
% 5.05/5.28 ( ( ord_less_int @ A @ B )
% 5.05/5.28 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % order.strict_implies_order
% 5.05/5.28 thf(fact_1806_dual__order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [B: real,A: real] :
% 5.05/5.28 ( ( ord_less_real @ B @ A )
% 5.05/5.28 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_implies_order
% 5.05/5.28 thf(fact_1807_dual__order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [B: set_int,A: set_int] :
% 5.05/5.28 ( ( ord_less_set_int @ B @ A )
% 5.05/5.28 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_implies_order
% 5.05/5.28 thf(fact_1808_dual__order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [B: rat,A: rat] :
% 5.05/5.28 ( ( ord_less_rat @ B @ A )
% 5.05/5.28 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_implies_order
% 5.05/5.28 thf(fact_1809_dual__order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [B: num,A: num] :
% 5.05/5.28 ( ( ord_less_num @ B @ A )
% 5.05/5.28 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_implies_order
% 5.05/5.28 thf(fact_1810_dual__order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [B: nat,A: nat] :
% 5.05/5.28 ( ( ord_less_nat @ B @ A )
% 5.05/5.28 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_implies_order
% 5.05/5.28 thf(fact_1811_dual__order_Ostrict__implies__order,axiom,
% 5.05/5.28 ! [B: int,A: int] :
% 5.05/5.28 ( ( ord_less_int @ B @ A )
% 5.05/5.28 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.05/5.28
% 5.05/5.28 % dual_order.strict_implies_order
% 5.05/5.28 thf(fact_1812_order__le__less,axiom,
% 5.05/5.28 ( ord_less_eq_real
% 5.05/5.28 = ( ^ [X2: real,Y2: real] :
% 5.05/5.28 ( ( ord_less_real @ X2 @ Y2 )
% 5.05/5.28 | ( X2 = Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less
% 5.05/5.28 thf(fact_1813_order__le__less,axiom,
% 5.05/5.28 ( ord_less_eq_set_int
% 5.05/5.28 = ( ^ [X2: set_int,Y2: set_int] :
% 5.05/5.28 ( ( ord_less_set_int @ X2 @ Y2 )
% 5.05/5.28 | ( X2 = Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less
% 5.05/5.28 thf(fact_1814_order__le__less,axiom,
% 5.05/5.28 ( ord_less_eq_rat
% 5.05/5.28 = ( ^ [X2: rat,Y2: rat] :
% 5.05/5.28 ( ( ord_less_rat @ X2 @ Y2 )
% 5.05/5.28 | ( X2 = Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less
% 5.05/5.28 thf(fact_1815_order__le__less,axiom,
% 5.05/5.28 ( ord_less_eq_num
% 5.05/5.28 = ( ^ [X2: num,Y2: num] :
% 5.05/5.28 ( ( ord_less_num @ X2 @ Y2 )
% 5.05/5.28 | ( X2 = Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less
% 5.05/5.28 thf(fact_1816_order__le__less,axiom,
% 5.05/5.28 ( ord_less_eq_nat
% 5.05/5.28 = ( ^ [X2: nat,Y2: nat] :
% 5.05/5.28 ( ( ord_less_nat @ X2 @ Y2 )
% 5.05/5.28 | ( X2 = Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less
% 5.05/5.28 thf(fact_1817_order__le__less,axiom,
% 5.05/5.28 ( ord_less_eq_int
% 5.05/5.28 = ( ^ [X2: int,Y2: int] :
% 5.05/5.28 ( ( ord_less_int @ X2 @ Y2 )
% 5.05/5.28 | ( X2 = Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less
% 5.05/5.28 thf(fact_1818_order__less__le,axiom,
% 5.05/5.28 ( ord_less_real
% 5.05/5.28 = ( ^ [X2: real,Y2: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ X2 @ Y2 )
% 5.05/5.28 & ( X2 != Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le
% 5.05/5.28 thf(fact_1819_order__less__le,axiom,
% 5.05/5.28 ( ord_less_set_int
% 5.05/5.28 = ( ^ [X2: set_int,Y2: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ X2 @ Y2 )
% 5.05/5.28 & ( X2 != Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le
% 5.05/5.28 thf(fact_1820_order__less__le,axiom,
% 5.05/5.28 ( ord_less_rat
% 5.05/5.28 = ( ^ [X2: rat,Y2: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X2 @ Y2 )
% 5.05/5.28 & ( X2 != Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le
% 5.05/5.28 thf(fact_1821_order__less__le,axiom,
% 5.05/5.28 ( ord_less_num
% 5.05/5.28 = ( ^ [X2: num,Y2: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X2 @ Y2 )
% 5.05/5.28 & ( X2 != Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le
% 5.05/5.28 thf(fact_1822_order__less__le,axiom,
% 5.05/5.28 ( ord_less_nat
% 5.05/5.28 = ( ^ [X2: nat,Y2: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 5.05/5.28 & ( X2 != Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le
% 5.05/5.28 thf(fact_1823_order__less__le,axiom,
% 5.05/5.28 ( ord_less_int
% 5.05/5.28 = ( ^ [X2: int,Y2: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ X2 @ Y2 )
% 5.05/5.28 & ( X2 != Y2 ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le
% 5.05/5.28 thf(fact_1824_linorder__not__le,axiom,
% 5.05/5.28 ! [X: real,Y: real] :
% 5.05/5.28 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 5.05/5.28 = ( ord_less_real @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_not_le
% 5.05/5.28 thf(fact_1825_linorder__not__le,axiom,
% 5.05/5.28 ! [X: rat,Y: rat] :
% 5.05/5.28 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 5.05/5.28 = ( ord_less_rat @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_not_le
% 5.05/5.28 thf(fact_1826_linorder__not__le,axiom,
% 5.05/5.28 ! [X: num,Y: num] :
% 5.05/5.28 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 5.05/5.28 = ( ord_less_num @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_not_le
% 5.05/5.28 thf(fact_1827_linorder__not__le,axiom,
% 5.05/5.28 ! [X: nat,Y: nat] :
% 5.05/5.28 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 5.05/5.28 = ( ord_less_nat @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_not_le
% 5.05/5.28 thf(fact_1828_linorder__not__le,axiom,
% 5.05/5.28 ! [X: int,Y: int] :
% 5.05/5.28 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 5.05/5.28 = ( ord_less_int @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_not_le
% 5.05/5.28 thf(fact_1829_linorder__not__less,axiom,
% 5.05/5.28 ! [X: real,Y: real] :
% 5.05/5.28 ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.05/5.28 = ( ord_less_eq_real @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_not_less
% 5.05/5.28 thf(fact_1830_linorder__not__less,axiom,
% 5.05/5.28 ! [X: rat,Y: rat] :
% 5.05/5.28 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.05/5.28 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_not_less
% 5.05/5.28 thf(fact_1831_linorder__not__less,axiom,
% 5.05/5.28 ! [X: num,Y: num] :
% 5.05/5.28 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.05/5.28 = ( ord_less_eq_num @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_not_less
% 5.05/5.28 thf(fact_1832_linorder__not__less,axiom,
% 5.05/5.28 ! [X: nat,Y: nat] :
% 5.05/5.28 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.05/5.28 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_not_less
% 5.05/5.28 thf(fact_1833_linorder__not__less,axiom,
% 5.05/5.28 ! [X: int,Y: int] :
% 5.05/5.28 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.05/5.28 = ( ord_less_eq_int @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_not_less
% 5.05/5.28 thf(fact_1834_order__less__imp__le,axiom,
% 5.05/5.28 ! [X: real,Y: real] :
% 5.05/5.28 ( ( ord_less_real @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_imp_le
% 5.05/5.28 thf(fact_1835_order__less__imp__le,axiom,
% 5.05/5.28 ! [X: set_int,Y: set_int] :
% 5.05/5.28 ( ( ord_less_set_int @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_imp_le
% 5.05/5.28 thf(fact_1836_order__less__imp__le,axiom,
% 5.05/5.28 ! [X: rat,Y: rat] :
% 5.05/5.28 ( ( ord_less_rat @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_imp_le
% 5.05/5.28 thf(fact_1837_order__less__imp__le,axiom,
% 5.05/5.28 ! [X: num,Y: num] :
% 5.05/5.28 ( ( ord_less_num @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_imp_le
% 5.05/5.28 thf(fact_1838_order__less__imp__le,axiom,
% 5.05/5.28 ! [X: nat,Y: nat] :
% 5.05/5.28 ( ( ord_less_nat @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_imp_le
% 5.05/5.28 thf(fact_1839_order__less__imp__le,axiom,
% 5.05/5.28 ! [X: int,Y: int] :
% 5.05/5.28 ( ( ord_less_int @ X @ Y )
% 5.05/5.28 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_imp_le
% 5.05/5.28 thf(fact_1840_order__le__neq__trans,axiom,
% 5.05/5.28 ! [A: real,B: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ A @ B )
% 5.05/5.28 => ( ( A != B )
% 5.05/5.28 => ( ord_less_real @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_neq_trans
% 5.05/5.28 thf(fact_1841_order__le__neq__trans,axiom,
% 5.05/5.28 ! [A: set_int,B: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ A @ B )
% 5.05/5.28 => ( ( A != B )
% 5.05/5.28 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_neq_trans
% 5.05/5.28 thf(fact_1842_order__le__neq__trans,axiom,
% 5.05/5.28 ! [A: rat,B: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ( A != B )
% 5.05/5.28 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_neq_trans
% 5.05/5.28 thf(fact_1843_order__le__neq__trans,axiom,
% 5.05/5.28 ! [A: num,B: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.28 => ( ( A != B )
% 5.05/5.28 => ( ord_less_num @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_neq_trans
% 5.05/5.28 thf(fact_1844_order__le__neq__trans,axiom,
% 5.05/5.28 ! [A: nat,B: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.28 => ( ( A != B )
% 5.05/5.28 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_neq_trans
% 5.05/5.28 thf(fact_1845_order__le__neq__trans,axiom,
% 5.05/5.28 ! [A: int,B: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.28 => ( ( A != B )
% 5.05/5.28 => ( ord_less_int @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_neq_trans
% 5.05/5.28 thf(fact_1846_order__neq__le__trans,axiom,
% 5.05/5.28 ! [A: real,B: real] :
% 5.05/5.28 ( ( A != B )
% 5.05/5.28 => ( ( ord_less_eq_real @ A @ B )
% 5.05/5.28 => ( ord_less_real @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_neq_le_trans
% 5.05/5.28 thf(fact_1847_order__neq__le__trans,axiom,
% 5.05/5.28 ! [A: set_int,B: set_int] :
% 5.05/5.28 ( ( A != B )
% 5.05/5.28 => ( ( ord_less_eq_set_int @ A @ B )
% 5.05/5.28 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_neq_le_trans
% 5.05/5.28 thf(fact_1848_order__neq__le__trans,axiom,
% 5.05/5.28 ! [A: rat,B: rat] :
% 5.05/5.28 ( ( A != B )
% 5.05/5.28 => ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_neq_le_trans
% 5.05/5.28 thf(fact_1849_order__neq__le__trans,axiom,
% 5.05/5.28 ! [A: num,B: num] :
% 5.05/5.28 ( ( A != B )
% 5.05/5.28 => ( ( ord_less_eq_num @ A @ B )
% 5.05/5.28 => ( ord_less_num @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_neq_le_trans
% 5.05/5.28 thf(fact_1850_order__neq__le__trans,axiom,
% 5.05/5.28 ! [A: nat,B: nat] :
% 5.05/5.28 ( ( A != B )
% 5.05/5.28 => ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.28 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_neq_le_trans
% 5.05/5.28 thf(fact_1851_order__neq__le__trans,axiom,
% 5.05/5.28 ! [A: int,B: int] :
% 5.05/5.28 ( ( A != B )
% 5.05/5.28 => ( ( ord_less_eq_int @ A @ B )
% 5.05/5.28 => ( ord_less_int @ A @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_neq_le_trans
% 5.05/5.28 thf(fact_1852_order__le__less__trans,axiom,
% 5.05/5.28 ! [X: real,Y: real,Z: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ X @ Y )
% 5.05/5.28 => ( ( ord_less_real @ Y @ Z )
% 5.05/5.28 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_trans
% 5.05/5.28 thf(fact_1853_order__le__less__trans,axiom,
% 5.05/5.28 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ X @ Y )
% 5.05/5.28 => ( ( ord_less_set_int @ Y @ Z )
% 5.05/5.28 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_trans
% 5.05/5.28 thf(fact_1854_order__le__less__trans,axiom,
% 5.05/5.28 ! [X: rat,Y: rat,Z: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.28 => ( ( ord_less_rat @ Y @ Z )
% 5.05/5.28 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_trans
% 5.05/5.28 thf(fact_1855_order__le__less__trans,axiom,
% 5.05/5.28 ! [X: num,Y: num,Z: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.28 => ( ( ord_less_num @ Y @ Z )
% 5.05/5.28 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_trans
% 5.05/5.28 thf(fact_1856_order__le__less__trans,axiom,
% 5.05/5.28 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.28 => ( ( ord_less_nat @ Y @ Z )
% 5.05/5.28 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_trans
% 5.05/5.28 thf(fact_1857_order__le__less__trans,axiom,
% 5.05/5.28 ! [X: int,Y: int,Z: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.28 => ( ( ord_less_int @ Y @ Z )
% 5.05/5.28 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_trans
% 5.05/5.28 thf(fact_1858_order__less__le__trans,axiom,
% 5.05/5.28 ! [X: real,Y: real,Z: real] :
% 5.05/5.28 ( ( ord_less_real @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_real @ Y @ Z )
% 5.05/5.28 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_trans
% 5.05/5.28 thf(fact_1859_order__less__le__trans,axiom,
% 5.05/5.28 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.05/5.28 ( ( ord_less_set_int @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.05/5.28 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_trans
% 5.05/5.28 thf(fact_1860_order__less__le__trans,axiom,
% 5.05/5.28 ! [X: rat,Y: rat,Z: rat] :
% 5.05/5.28 ( ( ord_less_rat @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.05/5.28 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_trans
% 5.05/5.28 thf(fact_1861_order__less__le__trans,axiom,
% 5.05/5.28 ! [X: num,Y: num,Z: num] :
% 5.05/5.28 ( ( ord_less_num @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_num @ Y @ Z )
% 5.05/5.28 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_trans
% 5.05/5.28 thf(fact_1862_order__less__le__trans,axiom,
% 5.05/5.28 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.28 ( ( ord_less_nat @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.05/5.28 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_trans
% 5.05/5.28 thf(fact_1863_order__less__le__trans,axiom,
% 5.05/5.28 ! [X: int,Y: int,Z: int] :
% 5.05/5.28 ( ( ord_less_int @ X @ Y )
% 5.05/5.28 => ( ( ord_less_eq_int @ Y @ Z )
% 5.05/5.28 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_trans
% 5.05/5.28 thf(fact_1864_order__le__less__subst1,axiom,
% 5.05/5.28 ! [A: real,F: real > real,B: real,C: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_real @ B @ C )
% 5.05/5.28 => ( ! [X3: real,Y5: real] :
% 5.05/5.28 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst1
% 5.05/5.28 thf(fact_1865_order__le__less__subst1,axiom,
% 5.05/5.28 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_rat @ B @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst1
% 5.05/5.28 thf(fact_1866_order__le__less__subst1,axiom,
% 5.05/5.28 ! [A: real,F: num > real,B: num,C: num] :
% 5.05/5.28 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_num @ B @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst1
% 5.05/5.28 thf(fact_1867_order__le__less__subst1,axiom,
% 5.05/5.28 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.05/5.28 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_nat @ B @ C )
% 5.05/5.28 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.28 ( ( ord_less_nat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst1
% 5.05/5.28 thf(fact_1868_order__le__less__subst1,axiom,
% 5.05/5.28 ! [A: real,F: int > real,B: int,C: int] :
% 5.05/5.28 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_int @ B @ C )
% 5.05/5.28 => ( ! [X3: int,Y5: int] :
% 5.05/5.28 ( ( ord_less_int @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst1
% 5.05/5.28 thf(fact_1869_order__le__less__subst1,axiom,
% 5.05/5.28 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_real @ B @ C )
% 5.05/5.28 => ( ! [X3: real,Y5: real] :
% 5.05/5.28 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst1
% 5.05/5.28 thf(fact_1870_order__le__less__subst1,axiom,
% 5.05/5.28 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_rat @ B @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst1
% 5.05/5.28 thf(fact_1871_order__le__less__subst1,axiom,
% 5.05/5.28 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_num @ B @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst1
% 5.05/5.28 thf(fact_1872_order__le__less__subst1,axiom,
% 5.05/5.28 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_nat @ B @ C )
% 5.05/5.28 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.28 ( ( ord_less_nat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst1
% 5.05/5.28 thf(fact_1873_order__le__less__subst1,axiom,
% 5.05/5.28 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_int @ B @ C )
% 5.05/5.28 => ( ! [X3: int,Y5: int] :
% 5.05/5.28 ( ( ord_less_int @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst1
% 5.05/5.28 thf(fact_1874_order__le__less__subst2,axiom,
% 5.05/5.28 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst2
% 5.05/5.28 thf(fact_1875_order__le__less__subst2,axiom,
% 5.05/5.28 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst2
% 5.05/5.28 thf(fact_1876_order__le__less__subst2,axiom,
% 5.05/5.28 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst2
% 5.05/5.28 thf(fact_1877_order__le__less__subst2,axiom,
% 5.05/5.28 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst2
% 5.05/5.28 thf(fact_1878_order__le__less__subst2,axiom,
% 5.05/5.28 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst2
% 5.05/5.28 thf(fact_1879_order__le__less__subst2,axiom,
% 5.05/5.28 ! [A: num,B: num,F: num > real,C: real] :
% 5.05/5.28 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.28 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst2
% 5.05/5.28 thf(fact_1880_order__le__less__subst2,axiom,
% 5.05/5.28 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.05/5.28 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.28 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst2
% 5.05/5.28 thf(fact_1881_order__le__less__subst2,axiom,
% 5.05/5.28 ! [A: num,B: num,F: num > num,C: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.28 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst2
% 5.05/5.28 thf(fact_1882_order__le__less__subst2,axiom,
% 5.05/5.28 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.05/5.28 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.28 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst2
% 5.05/5.28 thf(fact_1883_order__le__less__subst2,axiom,
% 5.05/5.28 ! [A: num,B: num,F: num > int,C: int] :
% 5.05/5.28 ( ( ord_less_eq_num @ A @ B )
% 5.05/5.28 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_less_subst2
% 5.05/5.28 thf(fact_1884_order__less__le__subst1,axiom,
% 5.05/5.28 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst1
% 5.05/5.28 thf(fact_1885_order__less__le__subst1,axiom,
% 5.05/5.28 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst1
% 5.05/5.28 thf(fact_1886_order__less__le__subst1,axiom,
% 5.05/5.28 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst1
% 5.05/5.28 thf(fact_1887_order__less__le__subst1,axiom,
% 5.05/5.28 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst1
% 5.05/5.28 thf(fact_1888_order__less__le__subst1,axiom,
% 5.05/5.28 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_eq_rat @ B @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst1
% 5.05/5.28 thf(fact_1889_order__less__le__subst1,axiom,
% 5.05/5.28 ! [A: real,F: num > real,B: num,C: num] :
% 5.05/5.28 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst1
% 5.05/5.28 thf(fact_1890_order__less__le__subst1,axiom,
% 5.05/5.28 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.05/5.28 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst1
% 5.05/5.28 thf(fact_1891_order__less__le__subst1,axiom,
% 5.05/5.28 ! [A: num,F: num > num,B: num,C: num] :
% 5.05/5.28 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst1
% 5.05/5.28 thf(fact_1892_order__less__le__subst1,axiom,
% 5.05/5.28 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.05/5.28 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst1
% 5.05/5.28 thf(fact_1893_order__less__le__subst1,axiom,
% 5.05/5.28 ! [A: int,F: num > int,B: num,C: num] :
% 5.05/5.28 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.05/5.28 => ( ( ord_less_eq_num @ B @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst1
% 5.05/5.28 thf(fact_1894_order__less__le__subst2,axiom,
% 5.05/5.28 ! [A: real,B: real,F: real > real,C: real] :
% 5.05/5.28 ( ( ord_less_real @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: real,Y5: real] :
% 5.05/5.28 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst2
% 5.05/5.28 thf(fact_1895_order__less__le__subst2,axiom,
% 5.05/5.28 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.05/5.28 ( ( ord_less_rat @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst2
% 5.05/5.28 thf(fact_1896_order__less__le__subst2,axiom,
% 5.05/5.28 ! [A: num,B: num,F: num > real,C: real] :
% 5.05/5.28 ( ( ord_less_num @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst2
% 5.05/5.28 thf(fact_1897_order__less__le__subst2,axiom,
% 5.05/5.28 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.05/5.28 ( ( ord_less_nat @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.28 ( ( ord_less_nat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst2
% 5.05/5.28 thf(fact_1898_order__less__le__subst2,axiom,
% 5.05/5.28 ! [A: int,B: int,F: int > real,C: real] :
% 5.05/5.28 ( ( ord_less_int @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: int,Y5: int] :
% 5.05/5.28 ( ( ord_less_int @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst2
% 5.05/5.28 thf(fact_1899_order__less__le__subst2,axiom,
% 5.05/5.28 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.05/5.28 ( ( ord_less_real @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: real,Y5: real] :
% 5.05/5.28 ( ( ord_less_real @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst2
% 5.05/5.28 thf(fact_1900_order__less__le__subst2,axiom,
% 5.05/5.28 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.05/5.28 ( ( ord_less_rat @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: rat,Y5: rat] :
% 5.05/5.28 ( ( ord_less_rat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst2
% 5.05/5.28 thf(fact_1901_order__less__le__subst2,axiom,
% 5.05/5.28 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.05/5.28 ( ( ord_less_num @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: num,Y5: num] :
% 5.05/5.28 ( ( ord_less_num @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst2
% 5.05/5.28 thf(fact_1902_order__less__le__subst2,axiom,
% 5.05/5.28 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.05/5.28 ( ( ord_less_nat @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: nat,Y5: nat] :
% 5.05/5.28 ( ( ord_less_nat @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst2
% 5.05/5.28 thf(fact_1903_order__less__le__subst2,axiom,
% 5.05/5.28 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.05/5.28 ( ( ord_less_int @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.05/5.28 => ( ! [X3: int,Y5: int] :
% 5.05/5.28 ( ( ord_less_int @ X3 @ Y5 )
% 5.05/5.28 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y5 ) ) )
% 5.05/5.28 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_less_le_subst2
% 5.05/5.28 thf(fact_1904_linorder__le__less__linear,axiom,
% 5.05/5.28 ! [X: real,Y: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ X @ Y )
% 5.05/5.28 | ( ord_less_real @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_le_less_linear
% 5.05/5.28 thf(fact_1905_linorder__le__less__linear,axiom,
% 5.05/5.28 ! [X: rat,Y: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.28 | ( ord_less_rat @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_le_less_linear
% 5.05/5.28 thf(fact_1906_linorder__le__less__linear,axiom,
% 5.05/5.28 ! [X: num,Y: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.28 | ( ord_less_num @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_le_less_linear
% 5.05/5.28 thf(fact_1907_linorder__le__less__linear,axiom,
% 5.05/5.28 ! [X: nat,Y: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.28 | ( ord_less_nat @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_le_less_linear
% 5.05/5.28 thf(fact_1908_linorder__le__less__linear,axiom,
% 5.05/5.28 ! [X: int,Y: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.28 | ( ord_less_int @ Y @ X ) ) ).
% 5.05/5.28
% 5.05/5.28 % linorder_le_less_linear
% 5.05/5.28 thf(fact_1909_order__le__imp__less__or__eq,axiom,
% 5.05/5.28 ! [X: real,Y: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ X @ Y )
% 5.05/5.28 => ( ( ord_less_real @ X @ Y )
% 5.05/5.28 | ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_imp_less_or_eq
% 5.05/5.28 thf(fact_1910_order__le__imp__less__or__eq,axiom,
% 5.05/5.28 ! [X: set_int,Y: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ X @ Y )
% 5.05/5.28 => ( ( ord_less_set_int @ X @ Y )
% 5.05/5.28 | ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_imp_less_or_eq
% 5.05/5.28 thf(fact_1911_order__le__imp__less__or__eq,axiom,
% 5.05/5.28 ! [X: rat,Y: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.28 => ( ( ord_less_rat @ X @ Y )
% 5.05/5.28 | ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_imp_less_or_eq
% 5.05/5.28 thf(fact_1912_order__le__imp__less__or__eq,axiom,
% 5.05/5.28 ! [X: num,Y: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.28 => ( ( ord_less_num @ X @ Y )
% 5.05/5.28 | ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_imp_less_or_eq
% 5.05/5.28 thf(fact_1913_order__le__imp__less__or__eq,axiom,
% 5.05/5.28 ! [X: nat,Y: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.28 => ( ( ord_less_nat @ X @ Y )
% 5.05/5.28 | ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_imp_less_or_eq
% 5.05/5.28 thf(fact_1914_order__le__imp__less__or__eq,axiom,
% 5.05/5.28 ! [X: int,Y: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.28 => ( ( ord_less_int @ X @ Y )
% 5.05/5.28 | ( X = Y ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % order_le_imp_less_or_eq
% 5.05/5.28 thf(fact_1915_bot_Oextremum,axiom,
% 5.05/5.28 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum
% 5.05/5.28 thf(fact_1916_bot_Oextremum,axiom,
% 5.05/5.28 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum
% 5.05/5.28 thf(fact_1917_bot_Oextremum,axiom,
% 5.05/5.28 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum
% 5.05/5.28 thf(fact_1918_bot_Oextremum,axiom,
% 5.05/5.28 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum
% 5.05/5.28 thf(fact_1919_bot_Oextremum__unique,axiom,
% 5.05/5.28 ! [A: set_nat] :
% 5.05/5.28 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.05/5.28 = ( A = bot_bot_set_nat ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_unique
% 5.05/5.28 thf(fact_1920_bot_Oextremum__unique,axiom,
% 5.05/5.28 ! [A: set_real] :
% 5.05/5.28 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.05/5.28 = ( A = bot_bot_set_real ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_unique
% 5.05/5.28 thf(fact_1921_bot_Oextremum__unique,axiom,
% 5.05/5.28 ! [A: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.05/5.28 = ( A = bot_bot_set_int ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_unique
% 5.05/5.28 thf(fact_1922_bot_Oextremum__unique,axiom,
% 5.05/5.28 ! [A: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.05/5.28 = ( A = bot_bot_nat ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_unique
% 5.05/5.28 thf(fact_1923_bot_Oextremum__uniqueI,axiom,
% 5.05/5.28 ! [A: set_nat] :
% 5.05/5.28 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.05/5.28 => ( A = bot_bot_set_nat ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_uniqueI
% 5.05/5.28 thf(fact_1924_bot_Oextremum__uniqueI,axiom,
% 5.05/5.28 ! [A: set_real] :
% 5.05/5.28 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.05/5.28 => ( A = bot_bot_set_real ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_uniqueI
% 5.05/5.28 thf(fact_1925_bot_Oextremum__uniqueI,axiom,
% 5.05/5.28 ! [A: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.05/5.28 => ( A = bot_bot_set_int ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_uniqueI
% 5.05/5.28 thf(fact_1926_bot_Oextremum__uniqueI,axiom,
% 5.05/5.28 ! [A: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.05/5.28 => ( A = bot_bot_nat ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_uniqueI
% 5.05/5.28 thf(fact_1927_bot_Oextremum__strict,axiom,
% 5.05/5.28 ! [A: set_nat] :
% 5.05/5.28 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_strict
% 5.05/5.28 thf(fact_1928_bot_Oextremum__strict,axiom,
% 5.05/5.28 ! [A: set_int] :
% 5.05/5.28 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_strict
% 5.05/5.28 thf(fact_1929_bot_Oextremum__strict,axiom,
% 5.05/5.28 ! [A: set_real] :
% 5.05/5.28 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_strict
% 5.05/5.28 thf(fact_1930_bot_Oextremum__strict,axiom,
% 5.05/5.28 ! [A: nat] :
% 5.05/5.28 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.05/5.28
% 5.05/5.28 % bot.extremum_strict
% 5.05/5.28 thf(fact_1931_bot_Onot__eq__extremum,axiom,
% 5.05/5.28 ! [A: set_nat] :
% 5.05/5.28 ( ( A != bot_bot_set_nat )
% 5.05/5.28 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.not_eq_extremum
% 5.05/5.28 thf(fact_1932_bot_Onot__eq__extremum,axiom,
% 5.05/5.28 ! [A: set_int] :
% 5.05/5.28 ( ( A != bot_bot_set_int )
% 5.05/5.28 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.not_eq_extremum
% 5.05/5.28 thf(fact_1933_bot_Onot__eq__extremum,axiom,
% 5.05/5.28 ! [A: set_real] :
% 5.05/5.28 ( ( A != bot_bot_set_real )
% 5.05/5.28 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.not_eq_extremum
% 5.05/5.28 thf(fact_1934_bot_Onot__eq__extremum,axiom,
% 5.05/5.28 ! [A: nat] :
% 5.05/5.28 ( ( A != bot_bot_nat )
% 5.05/5.28 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.05/5.28
% 5.05/5.28 % bot.not_eq_extremum
% 5.05/5.28 thf(fact_1935_max__def,axiom,
% 5.05/5.28 ( ord_ma741700101516333627d_enat
% 5.05/5.28 = ( ^ [A4: extended_enat,B4: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_def
% 5.05/5.28 thf(fact_1936_max__def,axiom,
% 5.05/5.28 ( ord_max_Code_integer
% 5.05/5.28 = ( ^ [A4: code_integer,B4: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_def
% 5.05/5.28 thf(fact_1937_max__def,axiom,
% 5.05/5.28 ( ord_max_set_int
% 5.05/5.28 = ( ^ [A4: set_int,B4: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_def
% 5.05/5.28 thf(fact_1938_max__def,axiom,
% 5.05/5.28 ( ord_max_rat
% 5.05/5.28 = ( ^ [A4: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_def
% 5.05/5.28 thf(fact_1939_max__def,axiom,
% 5.05/5.28 ( ord_max_num
% 5.05/5.28 = ( ^ [A4: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_def
% 5.05/5.28 thf(fact_1940_max__def,axiom,
% 5.05/5.28 ( ord_max_nat
% 5.05/5.28 = ( ^ [A4: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_def
% 5.05/5.28 thf(fact_1941_max__def,axiom,
% 5.05/5.28 ( ord_max_int
% 5.05/5.28 = ( ^ [A4: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_def
% 5.05/5.28 thf(fact_1942_max__absorb1,axiom,
% 5.05/5.28 ! [Y: extended_enat,X: extended_enat] :
% 5.05/5.28 ( ( ord_le2932123472753598470d_enat @ Y @ X )
% 5.05/5.28 => ( ( ord_ma741700101516333627d_enat @ X @ Y )
% 5.05/5.28 = X ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb1
% 5.05/5.28 thf(fact_1943_max__absorb1,axiom,
% 5.05/5.28 ! [Y: code_integer,X: code_integer] :
% 5.05/5.28 ( ( ord_le3102999989581377725nteger @ Y @ X )
% 5.05/5.28 => ( ( ord_max_Code_integer @ X @ Y )
% 5.05/5.28 = X ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb1
% 5.05/5.28 thf(fact_1944_max__absorb1,axiom,
% 5.05/5.28 ! [Y: set_int,X: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ Y @ X )
% 5.05/5.28 => ( ( ord_max_set_int @ X @ Y )
% 5.05/5.28 = X ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb1
% 5.05/5.28 thf(fact_1945_max__absorb1,axiom,
% 5.05/5.28 ! [Y: rat,X: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ Y @ X )
% 5.05/5.28 => ( ( ord_max_rat @ X @ Y )
% 5.05/5.28 = X ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb1
% 5.05/5.28 thf(fact_1946_max__absorb1,axiom,
% 5.05/5.28 ! [Y: num,X: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ Y @ X )
% 5.05/5.28 => ( ( ord_max_num @ X @ Y )
% 5.05/5.28 = X ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb1
% 5.05/5.28 thf(fact_1947_max__absorb1,axiom,
% 5.05/5.28 ! [Y: nat,X: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ Y @ X )
% 5.05/5.28 => ( ( ord_max_nat @ X @ Y )
% 5.05/5.28 = X ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb1
% 5.05/5.28 thf(fact_1948_max__absorb1,axiom,
% 5.05/5.28 ! [Y: int,X: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ Y @ X )
% 5.05/5.28 => ( ( ord_max_int @ X @ Y )
% 5.05/5.28 = X ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb1
% 5.05/5.28 thf(fact_1949_max__absorb2,axiom,
% 5.05/5.28 ! [X: extended_enat,Y: extended_enat] :
% 5.05/5.28 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 5.05/5.28 => ( ( ord_ma741700101516333627d_enat @ X @ Y )
% 5.05/5.28 = Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb2
% 5.05/5.28 thf(fact_1950_max__absorb2,axiom,
% 5.05/5.28 ! [X: code_integer,Y: code_integer] :
% 5.05/5.28 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 5.05/5.28 => ( ( ord_max_Code_integer @ X @ Y )
% 5.05/5.28 = Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb2
% 5.05/5.28 thf(fact_1951_max__absorb2,axiom,
% 5.05/5.28 ! [X: set_int,Y: set_int] :
% 5.05/5.28 ( ( ord_less_eq_set_int @ X @ Y )
% 5.05/5.28 => ( ( ord_max_set_int @ X @ Y )
% 5.05/5.28 = Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb2
% 5.05/5.28 thf(fact_1952_max__absorb2,axiom,
% 5.05/5.28 ! [X: rat,Y: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ X @ Y )
% 5.05/5.28 => ( ( ord_max_rat @ X @ Y )
% 5.05/5.28 = Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb2
% 5.05/5.28 thf(fact_1953_max__absorb2,axiom,
% 5.05/5.28 ! [X: num,Y: num] :
% 5.05/5.28 ( ( ord_less_eq_num @ X @ Y )
% 5.05/5.28 => ( ( ord_max_num @ X @ Y )
% 5.05/5.28 = Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb2
% 5.05/5.28 thf(fact_1954_max__absorb2,axiom,
% 5.05/5.28 ! [X: nat,Y: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ X @ Y )
% 5.05/5.28 => ( ( ord_max_nat @ X @ Y )
% 5.05/5.28 = Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb2
% 5.05/5.28 thf(fact_1955_max__absorb2,axiom,
% 5.05/5.28 ! [X: int,Y: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ X @ Y )
% 5.05/5.28 => ( ( ord_max_int @ X @ Y )
% 5.05/5.28 = Y ) ) ).
% 5.05/5.28
% 5.05/5.28 % max_absorb2
% 5.05/5.28 thf(fact_1956_add__diff__cancel__right_H,axiom,
% 5.05/5.28 ! [A: real,B: real] :
% 5.05/5.28 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_right'
% 5.05/5.28 thf(fact_1957_add__diff__cancel__right_H,axiom,
% 5.05/5.28 ! [A: rat,B: rat] :
% 5.05/5.28 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_right'
% 5.05/5.28 thf(fact_1958_add__diff__cancel__right_H,axiom,
% 5.05/5.28 ! [A: nat,B: nat] :
% 5.05/5.28 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_right'
% 5.05/5.28 thf(fact_1959_add__diff__cancel__right_H,axiom,
% 5.05/5.28 ! [A: int,B: int] :
% 5.05/5.28 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_right'
% 5.05/5.28 thf(fact_1960_add__diff__cancel__right,axiom,
% 5.05/5.28 ! [A: real,C: real,B: real] :
% 5.05/5.28 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.05/5.28 = ( minus_minus_real @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_right
% 5.05/5.28 thf(fact_1961_add__diff__cancel__right,axiom,
% 5.05/5.28 ! [A: rat,C: rat,B: rat] :
% 5.05/5.28 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.05/5.28 = ( minus_minus_rat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_right
% 5.05/5.28 thf(fact_1962_add__diff__cancel__right,axiom,
% 5.05/5.28 ! [A: nat,C: nat,B: nat] :
% 5.05/5.28 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.05/5.28 = ( minus_minus_nat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_right
% 5.05/5.28 thf(fact_1963_add__diff__cancel__right,axiom,
% 5.05/5.28 ! [A: int,C: int,B: int] :
% 5.05/5.28 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.05/5.28 = ( minus_minus_int @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_right
% 5.05/5.28 thf(fact_1964_add__diff__cancel__left_H,axiom,
% 5.05/5.28 ! [A: real,B: real] :
% 5.05/5.28 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.05/5.28 = B ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_left'
% 5.05/5.28 thf(fact_1965_add__diff__cancel__left_H,axiom,
% 5.05/5.28 ! [A: rat,B: rat] :
% 5.05/5.28 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.05/5.28 = B ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_left'
% 5.05/5.28 thf(fact_1966_add__diff__cancel__left_H,axiom,
% 5.05/5.28 ! [A: nat,B: nat] :
% 5.05/5.28 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.05/5.28 = B ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_left'
% 5.05/5.28 thf(fact_1967_add__diff__cancel__left_H,axiom,
% 5.05/5.28 ! [A: int,B: int] :
% 5.05/5.28 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.05/5.28 = B ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_left'
% 5.05/5.28 thf(fact_1968_add__diff__cancel__left,axiom,
% 5.05/5.28 ! [C: real,A: real,B: real] :
% 5.05/5.28 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.05/5.28 = ( minus_minus_real @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_left
% 5.05/5.28 thf(fact_1969_add__diff__cancel__left,axiom,
% 5.05/5.28 ! [C: rat,A: rat,B: rat] :
% 5.05/5.28 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.05/5.28 = ( minus_minus_rat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_left
% 5.05/5.28 thf(fact_1970_add__diff__cancel__left,axiom,
% 5.05/5.28 ! [C: nat,A: nat,B: nat] :
% 5.05/5.28 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.05/5.28 = ( minus_minus_nat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_left
% 5.05/5.28 thf(fact_1971_add__diff__cancel__left,axiom,
% 5.05/5.28 ! [C: int,A: int,B: int] :
% 5.05/5.28 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.05/5.28 = ( minus_minus_int @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel_left
% 5.05/5.28 thf(fact_1972_diff__add__cancel,axiom,
% 5.05/5.28 ! [A: real,B: real] :
% 5.05/5.28 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % diff_add_cancel
% 5.05/5.28 thf(fact_1973_diff__add__cancel,axiom,
% 5.05/5.28 ! [A: rat,B: rat] :
% 5.05/5.28 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % diff_add_cancel
% 5.05/5.28 thf(fact_1974_diff__add__cancel,axiom,
% 5.05/5.28 ! [A: int,B: int] :
% 5.05/5.28 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % diff_add_cancel
% 5.05/5.28 thf(fact_1975_add__diff__cancel,axiom,
% 5.05/5.28 ! [A: real,B: real] :
% 5.05/5.28 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel
% 5.05/5.28 thf(fact_1976_add__diff__cancel,axiom,
% 5.05/5.28 ! [A: rat,B: rat] :
% 5.05/5.28 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel
% 5.05/5.28 thf(fact_1977_add__diff__cancel,axiom,
% 5.05/5.28 ! [A: int,B: int] :
% 5.05/5.28 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % add_diff_cancel
% 5.05/5.28 thf(fact_1978_times__divide__eq__right,axiom,
% 5.05/5.28 ! [A: complex,B: complex,C: complex] :
% 5.05/5.28 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.05/5.28 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.05/5.28
% 5.05/5.28 % times_divide_eq_right
% 5.05/5.28 thf(fact_1979_times__divide__eq__right,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.05/5.28 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.05/5.28
% 5.05/5.28 % times_divide_eq_right
% 5.05/5.28 thf(fact_1980_times__divide__eq__right,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.05/5.28 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.05/5.28
% 5.05/5.28 % times_divide_eq_right
% 5.05/5.28 thf(fact_1981_divide__divide__eq__right,axiom,
% 5.05/5.28 ! [A: complex,B: complex,C: complex] :
% 5.05/5.28 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.05/5.28 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % divide_divide_eq_right
% 5.05/5.28 thf(fact_1982_divide__divide__eq__right,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.05/5.28 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % divide_divide_eq_right
% 5.05/5.28 thf(fact_1983_divide__divide__eq__right,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.05/5.28 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % divide_divide_eq_right
% 5.05/5.28 thf(fact_1984_divide__divide__eq__left,axiom,
% 5.05/5.28 ! [A: complex,B: complex,C: complex] :
% 5.05/5.28 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.05/5.28 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % divide_divide_eq_left
% 5.05/5.28 thf(fact_1985_divide__divide__eq__left,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.05/5.28 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % divide_divide_eq_left
% 5.05/5.28 thf(fact_1986_divide__divide__eq__left,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.05/5.28 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % divide_divide_eq_left
% 5.05/5.28 thf(fact_1987_times__divide__eq__left,axiom,
% 5.05/5.28 ! [B: complex,C: complex,A: complex] :
% 5.05/5.28 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.05/5.28 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.05/5.28
% 5.05/5.28 % times_divide_eq_left
% 5.05/5.28 thf(fact_1988_times__divide__eq__left,axiom,
% 5.05/5.28 ! [B: real,C: real,A: real] :
% 5.05/5.28 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.05/5.28 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.05/5.28
% 5.05/5.28 % times_divide_eq_left
% 5.05/5.28 thf(fact_1989_times__divide__eq__left,axiom,
% 5.05/5.28 ! [B: rat,C: rat,A: rat] :
% 5.05/5.28 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.05/5.28 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.05/5.28
% 5.05/5.28 % times_divide_eq_left
% 5.05/5.28 thf(fact_1990_add__left__cancel,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( ( plus_plus_real @ A @ B )
% 5.05/5.28 = ( plus_plus_real @ A @ C ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_cancel
% 5.05/5.28 thf(fact_1991_add__left__cancel,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( ( plus_plus_rat @ A @ B )
% 5.05/5.28 = ( plus_plus_rat @ A @ C ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_cancel
% 5.05/5.28 thf(fact_1992_add__left__cancel,axiom,
% 5.05/5.28 ! [A: nat,B: nat,C: nat] :
% 5.05/5.28 ( ( ( plus_plus_nat @ A @ B )
% 5.05/5.28 = ( plus_plus_nat @ A @ C ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_cancel
% 5.05/5.28 thf(fact_1993_add__left__cancel,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int] :
% 5.05/5.28 ( ( ( plus_plus_int @ A @ B )
% 5.05/5.28 = ( plus_plus_int @ A @ C ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_cancel
% 5.05/5.28 thf(fact_1994_add__right__cancel,axiom,
% 5.05/5.28 ! [B: real,A: real,C: real] :
% 5.05/5.28 ( ( ( plus_plus_real @ B @ A )
% 5.05/5.28 = ( plus_plus_real @ C @ A ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_right_cancel
% 5.05/5.28 thf(fact_1995_add__right__cancel,axiom,
% 5.05/5.28 ! [B: rat,A: rat,C: rat] :
% 5.05/5.28 ( ( ( plus_plus_rat @ B @ A )
% 5.05/5.28 = ( plus_plus_rat @ C @ A ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_right_cancel
% 5.05/5.28 thf(fact_1996_add__right__cancel,axiom,
% 5.05/5.28 ! [B: nat,A: nat,C: nat] :
% 5.05/5.28 ( ( ( plus_plus_nat @ B @ A )
% 5.05/5.28 = ( plus_plus_nat @ C @ A ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_right_cancel
% 5.05/5.28 thf(fact_1997_add__right__cancel,axiom,
% 5.05/5.28 ! [B: int,A: int,C: int] :
% 5.05/5.28 ( ( ( plus_plus_int @ B @ A )
% 5.05/5.28 = ( plus_plus_int @ C @ A ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_right_cancel
% 5.05/5.28 thf(fact_1998_add__le__cancel__left,axiom,
% 5.05/5.28 ! [C: real,A: real,B: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.05/5.28 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_le_cancel_left
% 5.05/5.28 thf(fact_1999_add__le__cancel__left,axiom,
% 5.05/5.28 ! [C: rat,A: rat,B: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.05/5.28 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_le_cancel_left
% 5.05/5.28 thf(fact_2000_add__le__cancel__left,axiom,
% 5.05/5.28 ! [C: nat,A: nat,B: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.05/5.28 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_le_cancel_left
% 5.05/5.28 thf(fact_2001_add__le__cancel__left,axiom,
% 5.05/5.28 ! [C: int,A: int,B: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.05/5.28 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_le_cancel_left
% 5.05/5.28 thf(fact_2002_add__le__cancel__right,axiom,
% 5.05/5.28 ! [A: real,C: real,B: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.05/5.28 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_le_cancel_right
% 5.05/5.28 thf(fact_2003_add__le__cancel__right,axiom,
% 5.05/5.28 ! [A: rat,C: rat,B: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.05/5.28 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_le_cancel_right
% 5.05/5.28 thf(fact_2004_add__le__cancel__right,axiom,
% 5.05/5.28 ! [A: nat,C: nat,B: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.05/5.28 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_le_cancel_right
% 5.05/5.28 thf(fact_2005_add__le__cancel__right,axiom,
% 5.05/5.28 ! [A: int,C: int,B: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.05/5.28 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_le_cancel_right
% 5.05/5.28 thf(fact_2006_add__less__cancel__left,axiom,
% 5.05/5.28 ! [C: real,A: real,B: real] :
% 5.05/5.28 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.05/5.28 = ( ord_less_real @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_less_cancel_left
% 5.05/5.28 thf(fact_2007_add__less__cancel__left,axiom,
% 5.05/5.28 ! [C: rat,A: rat,B: rat] :
% 5.05/5.28 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.05/5.28 = ( ord_less_rat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_less_cancel_left
% 5.05/5.28 thf(fact_2008_add__less__cancel__left,axiom,
% 5.05/5.28 ! [C: nat,A: nat,B: nat] :
% 5.05/5.28 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.05/5.28 = ( ord_less_nat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_less_cancel_left
% 5.05/5.28 thf(fact_2009_add__less__cancel__left,axiom,
% 5.05/5.28 ! [C: int,A: int,B: int] :
% 5.05/5.28 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.05/5.28 = ( ord_less_int @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_less_cancel_left
% 5.05/5.28 thf(fact_2010_add__less__cancel__right,axiom,
% 5.05/5.28 ! [A: real,C: real,B: real] :
% 5.05/5.28 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.05/5.28 = ( ord_less_real @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_less_cancel_right
% 5.05/5.28 thf(fact_2011_add__less__cancel__right,axiom,
% 5.05/5.28 ! [A: rat,C: rat,B: rat] :
% 5.05/5.28 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.05/5.28 = ( ord_less_rat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_less_cancel_right
% 5.05/5.28 thf(fact_2012_add__less__cancel__right,axiom,
% 5.05/5.28 ! [A: nat,C: nat,B: nat] :
% 5.05/5.28 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.05/5.28 = ( ord_less_nat @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_less_cancel_right
% 5.05/5.28 thf(fact_2013_add__less__cancel__right,axiom,
% 5.05/5.28 ! [A: int,C: int,B: int] :
% 5.05/5.28 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.05/5.28 = ( ord_less_int @ A @ B ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_less_cancel_right
% 5.05/5.28 thf(fact_2014_mult_Oright__neutral,axiom,
% 5.05/5.28 ! [A: complex] :
% 5.05/5.28 ( ( times_times_complex @ A @ one_one_complex )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % mult.right_neutral
% 5.05/5.28 thf(fact_2015_mult_Oright__neutral,axiom,
% 5.05/5.28 ! [A: real] :
% 5.05/5.28 ( ( times_times_real @ A @ one_one_real )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % mult.right_neutral
% 5.05/5.28 thf(fact_2016_mult_Oright__neutral,axiom,
% 5.05/5.28 ! [A: rat] :
% 5.05/5.28 ( ( times_times_rat @ A @ one_one_rat )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % mult.right_neutral
% 5.05/5.28 thf(fact_2017_mult_Oright__neutral,axiom,
% 5.05/5.28 ! [A: nat] :
% 5.05/5.28 ( ( times_times_nat @ A @ one_one_nat )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % mult.right_neutral
% 5.05/5.28 thf(fact_2018_mult_Oright__neutral,axiom,
% 5.05/5.28 ! [A: int] :
% 5.05/5.28 ( ( times_times_int @ A @ one_one_int )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % mult.right_neutral
% 5.05/5.28 thf(fact_2019_mult__1,axiom,
% 5.05/5.28 ! [A: complex] :
% 5.05/5.28 ( ( times_times_complex @ one_one_complex @ A )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % mult_1
% 5.05/5.28 thf(fact_2020_mult__1,axiom,
% 5.05/5.28 ! [A: real] :
% 5.05/5.28 ( ( times_times_real @ one_one_real @ A )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % mult_1
% 5.05/5.28 thf(fact_2021_mult__1,axiom,
% 5.05/5.28 ! [A: rat] :
% 5.05/5.28 ( ( times_times_rat @ one_one_rat @ A )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % mult_1
% 5.05/5.28 thf(fact_2022_mult__1,axiom,
% 5.05/5.28 ! [A: nat] :
% 5.05/5.28 ( ( times_times_nat @ one_one_nat @ A )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % mult_1
% 5.05/5.28 thf(fact_2023_mult__1,axiom,
% 5.05/5.28 ! [A: int] :
% 5.05/5.28 ( ( times_times_int @ one_one_int @ A )
% 5.05/5.28 = A ) ).
% 5.05/5.28
% 5.05/5.28 % mult_1
% 5.05/5.28 thf(fact_2024_linordered__field__no__ub,axiom,
% 5.05/5.28 ! [X5: real] :
% 5.05/5.28 ? [X_1: real] : ( ord_less_real @ X5 @ X_1 ) ).
% 5.05/5.28
% 5.05/5.28 % linordered_field_no_ub
% 5.05/5.28 thf(fact_2025_linordered__field__no__ub,axiom,
% 5.05/5.28 ! [X5: rat] :
% 5.05/5.28 ? [X_1: rat] : ( ord_less_rat @ X5 @ X_1 ) ).
% 5.05/5.28
% 5.05/5.28 % linordered_field_no_ub
% 5.05/5.28 thf(fact_2026_linordered__field__no__lb,axiom,
% 5.05/5.28 ! [X5: real] :
% 5.05/5.28 ? [Y5: real] : ( ord_less_real @ Y5 @ X5 ) ).
% 5.05/5.28
% 5.05/5.28 % linordered_field_no_lb
% 5.05/5.28 thf(fact_2027_linordered__field__no__lb,axiom,
% 5.05/5.28 ! [X5: rat] :
% 5.05/5.28 ? [Y5: rat] : ( ord_less_rat @ Y5 @ X5 ) ).
% 5.05/5.28
% 5.05/5.28 % linordered_field_no_lb
% 5.05/5.28 thf(fact_2028_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.05/5.28 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % ab_semigroup_mult_class.mult_ac(1)
% 5.05/5.28 thf(fact_2029_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.05/5.28 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % ab_semigroup_mult_class.mult_ac(1)
% 5.05/5.28 thf(fact_2030_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.05/5.28 ! [A: nat,B: nat,C: nat] :
% 5.05/5.28 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.05/5.28 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % ab_semigroup_mult_class.mult_ac(1)
% 5.05/5.28 thf(fact_2031_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int] :
% 5.05/5.28 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.05/5.28 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % ab_semigroup_mult_class.mult_ac(1)
% 5.05/5.28 thf(fact_2032_mult_Oassoc,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.05/5.28 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.assoc
% 5.05/5.28 thf(fact_2033_mult_Oassoc,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.05/5.28 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.assoc
% 5.05/5.28 thf(fact_2034_mult_Oassoc,axiom,
% 5.05/5.28 ! [A: nat,B: nat,C: nat] :
% 5.05/5.28 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.05/5.28 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.assoc
% 5.05/5.28 thf(fact_2035_mult_Oassoc,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int] :
% 5.05/5.28 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.05/5.28 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.assoc
% 5.05/5.28 thf(fact_2036_mult_Ocommute,axiom,
% 5.05/5.28 ( times_times_real
% 5.05/5.28 = ( ^ [A4: real,B4: real] : ( times_times_real @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.commute
% 5.05/5.28 thf(fact_2037_mult_Ocommute,axiom,
% 5.05/5.28 ( times_times_rat
% 5.05/5.28 = ( ^ [A4: rat,B4: rat] : ( times_times_rat @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.commute
% 5.05/5.28 thf(fact_2038_mult_Ocommute,axiom,
% 5.05/5.28 ( times_times_nat
% 5.05/5.28 = ( ^ [A4: nat,B4: nat] : ( times_times_nat @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.commute
% 5.05/5.28 thf(fact_2039_mult_Ocommute,axiom,
% 5.05/5.28 ( times_times_int
% 5.05/5.28 = ( ^ [A4: int,B4: int] : ( times_times_int @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.commute
% 5.05/5.28 thf(fact_2040_mult_Oleft__commute,axiom,
% 5.05/5.28 ! [B: real,A: real,C: real] :
% 5.05/5.28 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.05/5.28 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.left_commute
% 5.05/5.28 thf(fact_2041_mult_Oleft__commute,axiom,
% 5.05/5.28 ! [B: rat,A: rat,C: rat] :
% 5.05/5.28 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.05/5.28 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.left_commute
% 5.05/5.28 thf(fact_2042_mult_Oleft__commute,axiom,
% 5.05/5.28 ! [B: nat,A: nat,C: nat] :
% 5.05/5.28 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.05/5.28 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.left_commute
% 5.05/5.28 thf(fact_2043_mult_Oleft__commute,axiom,
% 5.05/5.28 ! [B: int,A: int,C: int] :
% 5.05/5.28 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.05/5.28 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % mult.left_commute
% 5.05/5.28 thf(fact_2044_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.05/5.28 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % ab_semigroup_add_class.add_ac(1)
% 5.05/5.28 thf(fact_2045_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.05/5.28 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % ab_semigroup_add_class.add_ac(1)
% 5.05/5.28 thf(fact_2046_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.05/5.28 ! [A: nat,B: nat,C: nat] :
% 5.05/5.28 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.05/5.28 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % ab_semigroup_add_class.add_ac(1)
% 5.05/5.28 thf(fact_2047_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int] :
% 5.05/5.28 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.05/5.28 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % ab_semigroup_add_class.add_ac(1)
% 5.05/5.28 thf(fact_2048_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.05/5.28 ! [I2: real,J: real,K: real,L2: real] :
% 5.05/5.28 ( ( ( I2 = J )
% 5.05/5.28 & ( K = L2 ) )
% 5.05/5.28 => ( ( plus_plus_real @ I2 @ K )
% 5.05/5.28 = ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(4)
% 5.05/5.28 thf(fact_2049_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.05/5.28 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.05/5.28 ( ( ( I2 = J )
% 5.05/5.28 & ( K = L2 ) )
% 5.05/5.28 => ( ( plus_plus_rat @ I2 @ K )
% 5.05/5.28 = ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(4)
% 5.05/5.28 thf(fact_2050_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.05/5.28 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.28 ( ( ( I2 = J )
% 5.05/5.28 & ( K = L2 ) )
% 5.05/5.28 => ( ( plus_plus_nat @ I2 @ K )
% 5.05/5.28 = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(4)
% 5.05/5.28 thf(fact_2051_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.05/5.28 ! [I2: int,J: int,K: int,L2: int] :
% 5.05/5.28 ( ( ( I2 = J )
% 5.05/5.28 & ( K = L2 ) )
% 5.05/5.28 => ( ( plus_plus_int @ I2 @ K )
% 5.05/5.28 = ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(4)
% 5.05/5.28 thf(fact_2052_group__cancel_Oadd1,axiom,
% 5.05/5.28 ! [A2: real,K: real,A: real,B: real] :
% 5.05/5.28 ( ( A2
% 5.05/5.28 = ( plus_plus_real @ K @ A ) )
% 5.05/5.28 => ( ( plus_plus_real @ A2 @ B )
% 5.05/5.28 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % group_cancel.add1
% 5.05/5.28 thf(fact_2053_group__cancel_Oadd1,axiom,
% 5.05/5.28 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.05/5.28 ( ( A2
% 5.05/5.28 = ( plus_plus_rat @ K @ A ) )
% 5.05/5.28 => ( ( plus_plus_rat @ A2 @ B )
% 5.05/5.28 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % group_cancel.add1
% 5.05/5.28 thf(fact_2054_group__cancel_Oadd1,axiom,
% 5.05/5.28 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.05/5.28 ( ( A2
% 5.05/5.28 = ( plus_plus_nat @ K @ A ) )
% 5.05/5.28 => ( ( plus_plus_nat @ A2 @ B )
% 5.05/5.28 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % group_cancel.add1
% 5.05/5.28 thf(fact_2055_group__cancel_Oadd1,axiom,
% 5.05/5.28 ! [A2: int,K: int,A: int,B: int] :
% 5.05/5.28 ( ( A2
% 5.05/5.28 = ( plus_plus_int @ K @ A ) )
% 5.05/5.28 => ( ( plus_plus_int @ A2 @ B )
% 5.05/5.28 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % group_cancel.add1
% 5.05/5.28 thf(fact_2056_group__cancel_Oadd2,axiom,
% 5.05/5.28 ! [B3: real,K: real,B: real,A: real] :
% 5.05/5.28 ( ( B3
% 5.05/5.28 = ( plus_plus_real @ K @ B ) )
% 5.05/5.28 => ( ( plus_plus_real @ A @ B3 )
% 5.05/5.28 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % group_cancel.add2
% 5.05/5.28 thf(fact_2057_group__cancel_Oadd2,axiom,
% 5.05/5.28 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.05/5.28 ( ( B3
% 5.05/5.28 = ( plus_plus_rat @ K @ B ) )
% 5.05/5.28 => ( ( plus_plus_rat @ A @ B3 )
% 5.05/5.28 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % group_cancel.add2
% 5.05/5.28 thf(fact_2058_group__cancel_Oadd2,axiom,
% 5.05/5.28 ! [B3: nat,K: nat,B: nat,A: nat] :
% 5.05/5.28 ( ( B3
% 5.05/5.28 = ( plus_plus_nat @ K @ B ) )
% 5.05/5.28 => ( ( plus_plus_nat @ A @ B3 )
% 5.05/5.28 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % group_cancel.add2
% 5.05/5.28 thf(fact_2059_group__cancel_Oadd2,axiom,
% 5.05/5.28 ! [B3: int,K: int,B: int,A: int] :
% 5.05/5.28 ( ( B3
% 5.05/5.28 = ( plus_plus_int @ K @ B ) )
% 5.05/5.28 => ( ( plus_plus_int @ A @ B3 )
% 5.05/5.28 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % group_cancel.add2
% 5.05/5.28 thf(fact_2060_add_Oassoc,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.05/5.28 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.assoc
% 5.05/5.28 thf(fact_2061_add_Oassoc,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.05/5.28 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.assoc
% 5.05/5.28 thf(fact_2062_add_Oassoc,axiom,
% 5.05/5.28 ! [A: nat,B: nat,C: nat] :
% 5.05/5.28 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.05/5.28 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.assoc
% 5.05/5.28 thf(fact_2063_add_Oassoc,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int] :
% 5.05/5.28 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.05/5.28 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.assoc
% 5.05/5.28 thf(fact_2064_add_Oleft__cancel,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( ( plus_plus_real @ A @ B )
% 5.05/5.28 = ( plus_plus_real @ A @ C ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.left_cancel
% 5.05/5.28 thf(fact_2065_add_Oleft__cancel,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( ( plus_plus_rat @ A @ B )
% 5.05/5.28 = ( plus_plus_rat @ A @ C ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.left_cancel
% 5.05/5.28 thf(fact_2066_add_Oleft__cancel,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int] :
% 5.05/5.28 ( ( ( plus_plus_int @ A @ B )
% 5.05/5.28 = ( plus_plus_int @ A @ C ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.left_cancel
% 5.05/5.28 thf(fact_2067_add_Oright__cancel,axiom,
% 5.05/5.28 ! [B: real,A: real,C: real] :
% 5.05/5.28 ( ( ( plus_plus_real @ B @ A )
% 5.05/5.28 = ( plus_plus_real @ C @ A ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.right_cancel
% 5.05/5.28 thf(fact_2068_add_Oright__cancel,axiom,
% 5.05/5.28 ! [B: rat,A: rat,C: rat] :
% 5.05/5.28 ( ( ( plus_plus_rat @ B @ A )
% 5.05/5.28 = ( plus_plus_rat @ C @ A ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.right_cancel
% 5.05/5.28 thf(fact_2069_add_Oright__cancel,axiom,
% 5.05/5.28 ! [B: int,A: int,C: int] :
% 5.05/5.28 ( ( ( plus_plus_int @ B @ A )
% 5.05/5.28 = ( plus_plus_int @ C @ A ) )
% 5.05/5.28 = ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.right_cancel
% 5.05/5.28 thf(fact_2070_add_Ocommute,axiom,
% 5.05/5.28 ( plus_plus_real
% 5.05/5.28 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.commute
% 5.05/5.28 thf(fact_2071_add_Ocommute,axiom,
% 5.05/5.28 ( plus_plus_rat
% 5.05/5.28 = ( ^ [A4: rat,B4: rat] : ( plus_plus_rat @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.commute
% 5.05/5.28 thf(fact_2072_add_Ocommute,axiom,
% 5.05/5.28 ( plus_plus_nat
% 5.05/5.28 = ( ^ [A4: nat,B4: nat] : ( plus_plus_nat @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.commute
% 5.05/5.28 thf(fact_2073_add_Ocommute,axiom,
% 5.05/5.28 ( plus_plus_int
% 5.05/5.28 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ B4 @ A4 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.commute
% 5.05/5.28 thf(fact_2074_add_Oleft__commute,axiom,
% 5.05/5.28 ! [B: real,A: real,C: real] :
% 5.05/5.28 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.05/5.28 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.left_commute
% 5.05/5.28 thf(fact_2075_add_Oleft__commute,axiom,
% 5.05/5.28 ! [B: rat,A: rat,C: rat] :
% 5.05/5.28 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.05/5.28 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.left_commute
% 5.05/5.28 thf(fact_2076_add_Oleft__commute,axiom,
% 5.05/5.28 ! [B: nat,A: nat,C: nat] :
% 5.05/5.28 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.05/5.28 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.left_commute
% 5.05/5.28 thf(fact_2077_add_Oleft__commute,axiom,
% 5.05/5.28 ! [B: int,A: int,C: int] :
% 5.05/5.28 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.05/5.28 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add.left_commute
% 5.05/5.28 thf(fact_2078_add__left__imp__eq,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( ( plus_plus_real @ A @ B )
% 5.05/5.28 = ( plus_plus_real @ A @ C ) )
% 5.05/5.28 => ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_imp_eq
% 5.05/5.28 thf(fact_2079_add__left__imp__eq,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( ( plus_plus_rat @ A @ B )
% 5.05/5.28 = ( plus_plus_rat @ A @ C ) )
% 5.05/5.28 => ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_imp_eq
% 5.05/5.28 thf(fact_2080_add__left__imp__eq,axiom,
% 5.05/5.28 ! [A: nat,B: nat,C: nat] :
% 5.05/5.28 ( ( ( plus_plus_nat @ A @ B )
% 5.05/5.28 = ( plus_plus_nat @ A @ C ) )
% 5.05/5.28 => ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_imp_eq
% 5.05/5.28 thf(fact_2081_add__left__imp__eq,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int] :
% 5.05/5.28 ( ( ( plus_plus_int @ A @ B )
% 5.05/5.28 = ( plus_plus_int @ A @ C ) )
% 5.05/5.28 => ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_imp_eq
% 5.05/5.28 thf(fact_2082_add__right__imp__eq,axiom,
% 5.05/5.28 ! [B: real,A: real,C: real] :
% 5.05/5.28 ( ( ( plus_plus_real @ B @ A )
% 5.05/5.28 = ( plus_plus_real @ C @ A ) )
% 5.05/5.28 => ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_right_imp_eq
% 5.05/5.28 thf(fact_2083_add__right__imp__eq,axiom,
% 5.05/5.28 ! [B: rat,A: rat,C: rat] :
% 5.05/5.28 ( ( ( plus_plus_rat @ B @ A )
% 5.05/5.28 = ( plus_plus_rat @ C @ A ) )
% 5.05/5.28 => ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_right_imp_eq
% 5.05/5.28 thf(fact_2084_add__right__imp__eq,axiom,
% 5.05/5.28 ! [B: nat,A: nat,C: nat] :
% 5.05/5.28 ( ( ( plus_plus_nat @ B @ A )
% 5.05/5.28 = ( plus_plus_nat @ C @ A ) )
% 5.05/5.28 => ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_right_imp_eq
% 5.05/5.28 thf(fact_2085_add__right__imp__eq,axiom,
% 5.05/5.28 ! [B: int,A: int,C: int] :
% 5.05/5.28 ( ( ( plus_plus_int @ B @ A )
% 5.05/5.28 = ( plus_plus_int @ C @ A ) )
% 5.05/5.28 => ( B = C ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_right_imp_eq
% 5.05/5.28 thf(fact_2086_one__reorient,axiom,
% 5.05/5.28 ! [X: complex] :
% 5.05/5.28 ( ( one_one_complex = X )
% 5.05/5.28 = ( X = one_one_complex ) ) ).
% 5.05/5.28
% 5.05/5.28 % one_reorient
% 5.05/5.28 thf(fact_2087_one__reorient,axiom,
% 5.05/5.28 ! [X: real] :
% 5.05/5.28 ( ( one_one_real = X )
% 5.05/5.28 = ( X = one_one_real ) ) ).
% 5.05/5.28
% 5.05/5.28 % one_reorient
% 5.05/5.28 thf(fact_2088_one__reorient,axiom,
% 5.05/5.28 ! [X: rat] :
% 5.05/5.28 ( ( one_one_rat = X )
% 5.05/5.28 = ( X = one_one_rat ) ) ).
% 5.05/5.28
% 5.05/5.28 % one_reorient
% 5.05/5.28 thf(fact_2089_one__reorient,axiom,
% 5.05/5.28 ! [X: nat] :
% 5.05/5.28 ( ( one_one_nat = X )
% 5.05/5.28 = ( X = one_one_nat ) ) ).
% 5.05/5.28
% 5.05/5.28 % one_reorient
% 5.05/5.28 thf(fact_2090_one__reorient,axiom,
% 5.05/5.28 ! [X: int] :
% 5.05/5.28 ( ( one_one_int = X )
% 5.05/5.28 = ( X = one_one_int ) ) ).
% 5.05/5.28
% 5.05/5.28 % one_reorient
% 5.05/5.28 thf(fact_2091_diff__right__commute,axiom,
% 5.05/5.28 ! [A: real,C: real,B: real] :
% 5.05/5.28 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 5.05/5.28 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 5.05/5.28
% 5.05/5.28 % diff_right_commute
% 5.05/5.28 thf(fact_2092_diff__right__commute,axiom,
% 5.05/5.28 ! [A: rat,C: rat,B: rat] :
% 5.05/5.28 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.05/5.28 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.05/5.28
% 5.05/5.28 % diff_right_commute
% 5.05/5.28 thf(fact_2093_diff__right__commute,axiom,
% 5.05/5.28 ! [A: nat,C: nat,B: nat] :
% 5.05/5.28 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.05/5.28 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.05/5.28
% 5.05/5.28 % diff_right_commute
% 5.05/5.28 thf(fact_2094_diff__right__commute,axiom,
% 5.05/5.28 ! [A: int,C: int,B: int] :
% 5.05/5.28 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.05/5.28 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.05/5.28
% 5.05/5.28 % diff_right_commute
% 5.05/5.28 thf(fact_2095_diff__eq__diff__eq,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real,D: real] :
% 5.05/5.28 ( ( ( minus_minus_real @ A @ B )
% 5.05/5.28 = ( minus_minus_real @ C @ D ) )
% 5.05/5.28 => ( ( A = B )
% 5.05/5.28 = ( C = D ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % diff_eq_diff_eq
% 5.05/5.28 thf(fact_2096_diff__eq__diff__eq,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.05/5.28 ( ( ( minus_minus_rat @ A @ B )
% 5.05/5.28 = ( minus_minus_rat @ C @ D ) )
% 5.05/5.28 => ( ( A = B )
% 5.05/5.28 = ( C = D ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % diff_eq_diff_eq
% 5.05/5.28 thf(fact_2097_diff__eq__diff__eq,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int,D: int] :
% 5.05/5.28 ( ( ( minus_minus_int @ A @ B )
% 5.05/5.28 = ( minus_minus_int @ C @ D ) )
% 5.05/5.28 => ( ( A = B )
% 5.05/5.28 = ( C = D ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % diff_eq_diff_eq
% 5.05/5.28 thf(fact_2098_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.05/5.28 ! [I2: real,J: real,K: real,L2: real] :
% 5.05/5.28 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.05/5.28 & ( K = L2 ) )
% 5.05/5.28 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(3)
% 5.05/5.28 thf(fact_2099_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.05/5.28 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.05/5.28 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.05/5.28 & ( K = L2 ) )
% 5.05/5.28 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(3)
% 5.05/5.28 thf(fact_2100_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.05/5.28 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.28 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.28 & ( K = L2 ) )
% 5.05/5.28 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(3)
% 5.05/5.28 thf(fact_2101_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.05/5.28 ! [I2: int,J: int,K: int,L2: int] :
% 5.05/5.28 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.05/5.28 & ( K = L2 ) )
% 5.05/5.28 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(3)
% 5.05/5.28 thf(fact_2102_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.05/5.28 ! [I2: real,J: real,K: real,L2: real] :
% 5.05/5.28 ( ( ( I2 = J )
% 5.05/5.28 & ( ord_less_eq_real @ K @ L2 ) )
% 5.05/5.28 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(2)
% 5.05/5.28 thf(fact_2103_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.05/5.28 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.05/5.28 ( ( ( I2 = J )
% 5.05/5.28 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.05/5.28 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(2)
% 5.05/5.28 thf(fact_2104_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.05/5.28 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.28 ( ( ( I2 = J )
% 5.05/5.28 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.05/5.28 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(2)
% 5.05/5.28 thf(fact_2105_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.05/5.28 ! [I2: int,J: int,K: int,L2: int] :
% 5.05/5.28 ( ( ( I2 = J )
% 5.05/5.28 & ( ord_less_eq_int @ K @ L2 ) )
% 5.05/5.28 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(2)
% 5.05/5.28 thf(fact_2106_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.05/5.28 ! [I2: real,J: real,K: real,L2: real] :
% 5.05/5.28 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.05/5.28 & ( ord_less_eq_real @ K @ L2 ) )
% 5.05/5.28 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(1)
% 5.05/5.28 thf(fact_2107_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.05/5.28 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.05/5.28 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.05/5.28 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.05/5.28 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(1)
% 5.05/5.28 thf(fact_2108_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.05/5.28 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.28 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.28 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.05/5.28 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(1)
% 5.05/5.28 thf(fact_2109_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.05/5.28 ! [I2: int,J: int,K: int,L2: int] :
% 5.05/5.28 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.05/5.28 & ( ord_less_eq_int @ K @ L2 ) )
% 5.05/5.28 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono_thms_linordered_semiring(1)
% 5.05/5.28 thf(fact_2110_add__mono,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real,D: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_real @ C @ D )
% 5.05/5.28 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono
% 5.05/5.28 thf(fact_2111_add__mono,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_rat @ C @ D )
% 5.05/5.28 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono
% 5.05/5.28 thf(fact_2112_add__mono,axiom,
% 5.05/5.28 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_nat @ C @ D )
% 5.05/5.28 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono
% 5.05/5.28 thf(fact_2113_add__mono,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int,D: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.28 => ( ( ord_less_eq_int @ C @ D )
% 5.05/5.28 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_mono
% 5.05/5.28 thf(fact_2114_add__left__mono,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ A @ B )
% 5.05/5.28 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_mono
% 5.05/5.28 thf(fact_2115_add__left__mono,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_mono
% 5.05/5.28 thf(fact_2116_add__left__mono,axiom,
% 5.05/5.28 ! [A: nat,B: nat,C: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.28 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_mono
% 5.05/5.28 thf(fact_2117_add__left__mono,axiom,
% 5.05/5.28 ! [A: int,B: int,C: int] :
% 5.05/5.28 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.28 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_left_mono
% 5.05/5.28 thf(fact_2118_less__eqE,axiom,
% 5.05/5.28 ! [A: nat,B: nat] :
% 5.05/5.28 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.28 => ~ ! [C3: nat] :
% 5.05/5.28 ( B
% 5.05/5.28 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % less_eqE
% 5.05/5.28 thf(fact_2119_add__right__mono,axiom,
% 5.05/5.28 ! [A: real,B: real,C: real] :
% 5.05/5.28 ( ( ord_less_eq_real @ A @ B )
% 5.05/5.28 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.05/5.28
% 5.05/5.28 % add_right_mono
% 5.05/5.28 thf(fact_2120_add__right__mono,axiom,
% 5.05/5.28 ! [A: rat,B: rat,C: rat] :
% 5.05/5.28 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.28 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_right_mono
% 5.05/5.29 thf(fact_2121_add__right__mono,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_right_mono
% 5.05/5.29 thf(fact_2122_add__right__mono,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.29 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_right_mono
% 5.05/5.29 thf(fact_2123_le__iff__add,axiom,
% 5.05/5.29 ( ord_less_eq_nat
% 5.05/5.29 = ( ^ [A4: nat,B4: nat] :
% 5.05/5.29 ? [C4: nat] :
% 5.05/5.29 ( B4
% 5.05/5.29 = ( plus_plus_nat @ A4 @ C4 ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_iff_add
% 5.05/5.29 thf(fact_2124_add__le__imp__le__left,axiom,
% 5.05/5.29 ! [C: real,A: real,B: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.05/5.29 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_imp_le_left
% 5.05/5.29 thf(fact_2125_add__le__imp__le__left,axiom,
% 5.05/5.29 ! [C: rat,A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.05/5.29 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_imp_le_left
% 5.05/5.29 thf(fact_2126_add__le__imp__le__left,axiom,
% 5.05/5.29 ! [C: nat,A: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.05/5.29 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_imp_le_left
% 5.05/5.29 thf(fact_2127_add__le__imp__le__left,axiom,
% 5.05/5.29 ! [C: int,A: int,B: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.05/5.29 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_imp_le_left
% 5.05/5.29 thf(fact_2128_add__le__imp__le__right,axiom,
% 5.05/5.29 ! [A: real,C: real,B: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.05/5.29 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_imp_le_right
% 5.05/5.29 thf(fact_2129_add__le__imp__le__right,axiom,
% 5.05/5.29 ! [A: rat,C: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.05/5.29 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_imp_le_right
% 5.05/5.29 thf(fact_2130_add__le__imp__le__right,axiom,
% 5.05/5.29 ! [A: nat,C: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.05/5.29 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_imp_le_right
% 5.05/5.29 thf(fact_2131_add__le__imp__le__right,axiom,
% 5.05/5.29 ! [A: int,C: int,B: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.05/5.29 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_imp_le_right
% 5.05/5.29 thf(fact_2132_add__mono__thms__linordered__field_I5_J,axiom,
% 5.05/5.29 ! [I2: real,J: real,K: real,L2: real] :
% 5.05/5.29 ( ( ( ord_less_real @ I2 @ J )
% 5.05/5.29 & ( ord_less_real @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(5)
% 5.05/5.29 thf(fact_2133_add__mono__thms__linordered__field_I5_J,axiom,
% 5.05/5.29 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.05/5.29 ( ( ( ord_less_rat @ I2 @ J )
% 5.05/5.29 & ( ord_less_rat @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(5)
% 5.05/5.29 thf(fact_2134_add__mono__thms__linordered__field_I5_J,axiom,
% 5.05/5.29 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.29 ( ( ( ord_less_nat @ I2 @ J )
% 5.05/5.29 & ( ord_less_nat @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(5)
% 5.05/5.29 thf(fact_2135_add__mono__thms__linordered__field_I5_J,axiom,
% 5.05/5.29 ! [I2: int,J: int,K: int,L2: int] :
% 5.05/5.29 ( ( ( ord_less_int @ I2 @ J )
% 5.05/5.29 & ( ord_less_int @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(5)
% 5.05/5.29 thf(fact_2136_add__mono__thms__linordered__field_I2_J,axiom,
% 5.05/5.29 ! [I2: real,J: real,K: real,L2: real] :
% 5.05/5.29 ( ( ( I2 = J )
% 5.05/5.29 & ( ord_less_real @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(2)
% 5.05/5.29 thf(fact_2137_add__mono__thms__linordered__field_I2_J,axiom,
% 5.05/5.29 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.05/5.29 ( ( ( I2 = J )
% 5.05/5.29 & ( ord_less_rat @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(2)
% 5.05/5.29 thf(fact_2138_add__mono__thms__linordered__field_I2_J,axiom,
% 5.05/5.29 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.29 ( ( ( I2 = J )
% 5.05/5.29 & ( ord_less_nat @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(2)
% 5.05/5.29 thf(fact_2139_add__mono__thms__linordered__field_I2_J,axiom,
% 5.05/5.29 ! [I2: int,J: int,K: int,L2: int] :
% 5.05/5.29 ( ( ( I2 = J )
% 5.05/5.29 & ( ord_less_int @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(2)
% 5.05/5.29 thf(fact_2140_add__mono__thms__linordered__field_I1_J,axiom,
% 5.05/5.29 ! [I2: real,J: real,K: real,L2: real] :
% 5.05/5.29 ( ( ( ord_less_real @ I2 @ J )
% 5.05/5.29 & ( K = L2 ) )
% 5.05/5.29 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(1)
% 5.05/5.29 thf(fact_2141_add__mono__thms__linordered__field_I1_J,axiom,
% 5.05/5.29 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.05/5.29 ( ( ( ord_less_rat @ I2 @ J )
% 5.05/5.29 & ( K = L2 ) )
% 5.05/5.29 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(1)
% 5.05/5.29 thf(fact_2142_add__mono__thms__linordered__field_I1_J,axiom,
% 5.05/5.29 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.29 ( ( ( ord_less_nat @ I2 @ J )
% 5.05/5.29 & ( K = L2 ) )
% 5.05/5.29 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(1)
% 5.05/5.29 thf(fact_2143_add__mono__thms__linordered__field_I1_J,axiom,
% 5.05/5.29 ! [I2: int,J: int,K: int,L2: int] :
% 5.05/5.29 ( ( ( ord_less_int @ I2 @ J )
% 5.05/5.29 & ( K = L2 ) )
% 5.05/5.29 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(1)
% 5.05/5.29 thf(fact_2144_add__strict__mono,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real,D: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ B )
% 5.05/5.29 => ( ( ord_less_real @ C @ D )
% 5.05/5.29 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_mono
% 5.05/5.29 thf(fact_2145_add__strict__mono,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ B )
% 5.05/5.29 => ( ( ord_less_rat @ C @ D )
% 5.05/5.29 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_mono
% 5.05/5.29 thf(fact_2146_add__strict__mono,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.05/5.29 ( ( ord_less_nat @ A @ B )
% 5.05/5.29 => ( ( ord_less_nat @ C @ D )
% 5.05/5.29 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_mono
% 5.05/5.29 thf(fact_2147_add__strict__mono,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int,D: int] :
% 5.05/5.29 ( ( ord_less_int @ A @ B )
% 5.05/5.29 => ( ( ord_less_int @ C @ D )
% 5.05/5.29 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_mono
% 5.05/5.29 thf(fact_2148_add__strict__left__mono,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ B )
% 5.05/5.29 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_left_mono
% 5.05/5.29 thf(fact_2149_add__strict__left__mono,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ B )
% 5.05/5.29 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_left_mono
% 5.05/5.29 thf(fact_2150_add__strict__left__mono,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_nat @ A @ B )
% 5.05/5.29 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_left_mono
% 5.05/5.29 thf(fact_2151_add__strict__left__mono,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( ord_less_int @ A @ B )
% 5.05/5.29 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_left_mono
% 5.05/5.29 thf(fact_2152_add__strict__right__mono,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ B )
% 5.05/5.29 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_right_mono
% 5.05/5.29 thf(fact_2153_add__strict__right__mono,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ B )
% 5.05/5.29 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_right_mono
% 5.05/5.29 thf(fact_2154_add__strict__right__mono,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_nat @ A @ B )
% 5.05/5.29 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_right_mono
% 5.05/5.29 thf(fact_2155_add__strict__right__mono,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( ord_less_int @ A @ B )
% 5.05/5.29 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_strict_right_mono
% 5.05/5.29 thf(fact_2156_add__less__imp__less__left,axiom,
% 5.05/5.29 ! [C: real,A: real,B: real] :
% 5.05/5.29 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.05/5.29 => ( ord_less_real @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_imp_less_left
% 5.05/5.29 thf(fact_2157_add__less__imp__less__left,axiom,
% 5.05/5.29 ! [C: rat,A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.05/5.29 => ( ord_less_rat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_imp_less_left
% 5.05/5.29 thf(fact_2158_add__less__imp__less__left,axiom,
% 5.05/5.29 ! [C: nat,A: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.05/5.29 => ( ord_less_nat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_imp_less_left
% 5.05/5.29 thf(fact_2159_add__less__imp__less__left,axiom,
% 5.05/5.29 ! [C: int,A: int,B: int] :
% 5.05/5.29 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.05/5.29 => ( ord_less_int @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_imp_less_left
% 5.05/5.29 thf(fact_2160_add__less__imp__less__right,axiom,
% 5.05/5.29 ! [A: real,C: real,B: real] :
% 5.05/5.29 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.05/5.29 => ( ord_less_real @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_imp_less_right
% 5.05/5.29 thf(fact_2161_add__less__imp__less__right,axiom,
% 5.05/5.29 ! [A: rat,C: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.05/5.29 => ( ord_less_rat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_imp_less_right
% 5.05/5.29 thf(fact_2162_add__less__imp__less__right,axiom,
% 5.05/5.29 ! [A: nat,C: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.05/5.29 => ( ord_less_nat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_imp_less_right
% 5.05/5.29 thf(fact_2163_add__less__imp__less__right,axiom,
% 5.05/5.29 ! [A: int,C: int,B: int] :
% 5.05/5.29 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.05/5.29 => ( ord_less_int @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_imp_less_right
% 5.05/5.29 thf(fact_2164_diff__eq__diff__less__eq,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real,D: real] :
% 5.05/5.29 ( ( ( minus_minus_real @ A @ B )
% 5.05/5.29 = ( minus_minus_real @ C @ D ) )
% 5.05/5.29 => ( ( ord_less_eq_real @ A @ B )
% 5.05/5.29 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_eq_diff_less_eq
% 5.05/5.29 thf(fact_2165_diff__eq__diff__less__eq,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.05/5.29 ( ( ( minus_minus_rat @ A @ B )
% 5.05/5.29 = ( minus_minus_rat @ C @ D ) )
% 5.05/5.29 => ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.29 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_eq_diff_less_eq
% 5.05/5.29 thf(fact_2166_diff__eq__diff__less__eq,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int,D: int] :
% 5.05/5.29 ( ( ( minus_minus_int @ A @ B )
% 5.05/5.29 = ( minus_minus_int @ C @ D ) )
% 5.05/5.29 => ( ( ord_less_eq_int @ A @ B )
% 5.05/5.29 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_eq_diff_less_eq
% 5.05/5.29 thf(fact_2167_diff__right__mono,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ A @ B )
% 5.05/5.29 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_right_mono
% 5.05/5.29 thf(fact_2168_diff__right__mono,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.29 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_right_mono
% 5.05/5.29 thf(fact_2169_diff__right__mono,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.29 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_right_mono
% 5.05/5.29 thf(fact_2170_diff__left__mono,axiom,
% 5.05/5.29 ! [B: real,A: real,C: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ B @ A )
% 5.05/5.29 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_left_mono
% 5.05/5.29 thf(fact_2171_diff__left__mono,axiom,
% 5.05/5.29 ! [B: rat,A: rat,C: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ B @ A )
% 5.05/5.29 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_left_mono
% 5.05/5.29 thf(fact_2172_diff__left__mono,axiom,
% 5.05/5.29 ! [B: int,A: int,C: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ B @ A )
% 5.05/5.29 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_left_mono
% 5.05/5.29 thf(fact_2173_diff__mono,axiom,
% 5.05/5.29 ! [A: real,B: real,D: real,C: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ A @ B )
% 5.05/5.29 => ( ( ord_less_eq_real @ D @ C )
% 5.05/5.29 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_mono
% 5.05/5.29 thf(fact_2174_diff__mono,axiom,
% 5.05/5.29 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.29 => ( ( ord_less_eq_rat @ D @ C )
% 5.05/5.29 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_mono
% 5.05/5.29 thf(fact_2175_diff__mono,axiom,
% 5.05/5.29 ! [A: int,B: int,D: int,C: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.29 => ( ( ord_less_eq_int @ D @ C )
% 5.05/5.29 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_mono
% 5.05/5.29 thf(fact_2176_diff__strict__right__mono,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ B )
% 5.05/5.29 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_strict_right_mono
% 5.05/5.29 thf(fact_2177_diff__strict__right__mono,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ B )
% 5.05/5.29 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_strict_right_mono
% 5.05/5.29 thf(fact_2178_diff__strict__right__mono,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( ord_less_int @ A @ B )
% 5.05/5.29 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_strict_right_mono
% 5.05/5.29 thf(fact_2179_diff__strict__left__mono,axiom,
% 5.05/5.29 ! [B: real,A: real,C: real] :
% 5.05/5.29 ( ( ord_less_real @ B @ A )
% 5.05/5.29 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_strict_left_mono
% 5.05/5.29 thf(fact_2180_diff__strict__left__mono,axiom,
% 5.05/5.29 ! [B: rat,A: rat,C: rat] :
% 5.05/5.29 ( ( ord_less_rat @ B @ A )
% 5.05/5.29 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_strict_left_mono
% 5.05/5.29 thf(fact_2181_diff__strict__left__mono,axiom,
% 5.05/5.29 ! [B: int,A: int,C: int] :
% 5.05/5.29 ( ( ord_less_int @ B @ A )
% 5.05/5.29 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_strict_left_mono
% 5.05/5.29 thf(fact_2182_diff__eq__diff__less,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real,D: real] :
% 5.05/5.29 ( ( ( minus_minus_real @ A @ B )
% 5.05/5.29 = ( minus_minus_real @ C @ D ) )
% 5.05/5.29 => ( ( ord_less_real @ A @ B )
% 5.05/5.29 = ( ord_less_real @ C @ D ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_eq_diff_less
% 5.05/5.29 thf(fact_2183_diff__eq__diff__less,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.05/5.29 ( ( ( minus_minus_rat @ A @ B )
% 5.05/5.29 = ( minus_minus_rat @ C @ D ) )
% 5.05/5.29 => ( ( ord_less_rat @ A @ B )
% 5.05/5.29 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_eq_diff_less
% 5.05/5.29 thf(fact_2184_diff__eq__diff__less,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int,D: int] :
% 5.05/5.29 ( ( ( minus_minus_int @ A @ B )
% 5.05/5.29 = ( minus_minus_int @ C @ D ) )
% 5.05/5.29 => ( ( ord_less_int @ A @ B )
% 5.05/5.29 = ( ord_less_int @ C @ D ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_eq_diff_less
% 5.05/5.29 thf(fact_2185_diff__strict__mono,axiom,
% 5.05/5.29 ! [A: real,B: real,D: real,C: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ B )
% 5.05/5.29 => ( ( ord_less_real @ D @ C )
% 5.05/5.29 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_strict_mono
% 5.05/5.29 thf(fact_2186_diff__strict__mono,axiom,
% 5.05/5.29 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ B )
% 5.05/5.29 => ( ( ord_less_rat @ D @ C )
% 5.05/5.29 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_strict_mono
% 5.05/5.29 thf(fact_2187_diff__strict__mono,axiom,
% 5.05/5.29 ! [A: int,B: int,D: int,C: int] :
% 5.05/5.29 ( ( ord_less_int @ A @ B )
% 5.05/5.29 => ( ( ord_less_int @ D @ C )
% 5.05/5.29 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_strict_mono
% 5.05/5.29 thf(fact_2188_comm__monoid__mult__class_Omult__1,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( times_times_complex @ one_one_complex @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % comm_monoid_mult_class.mult_1
% 5.05/5.29 thf(fact_2189_comm__monoid__mult__class_Omult__1,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( times_times_real @ one_one_real @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % comm_monoid_mult_class.mult_1
% 5.05/5.29 thf(fact_2190_comm__monoid__mult__class_Omult__1,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( times_times_rat @ one_one_rat @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % comm_monoid_mult_class.mult_1
% 5.05/5.29 thf(fact_2191_comm__monoid__mult__class_Omult__1,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( times_times_nat @ one_one_nat @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % comm_monoid_mult_class.mult_1
% 5.05/5.29 thf(fact_2192_comm__monoid__mult__class_Omult__1,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( times_times_int @ one_one_int @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % comm_monoid_mult_class.mult_1
% 5.05/5.29 thf(fact_2193_mult_Ocomm__neutral,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( times_times_complex @ A @ one_one_complex )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % mult.comm_neutral
% 5.05/5.29 thf(fact_2194_mult_Ocomm__neutral,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( times_times_real @ A @ one_one_real )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % mult.comm_neutral
% 5.05/5.29 thf(fact_2195_mult_Ocomm__neutral,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( times_times_rat @ A @ one_one_rat )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % mult.comm_neutral
% 5.05/5.29 thf(fact_2196_mult_Ocomm__neutral,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( times_times_nat @ A @ one_one_nat )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % mult.comm_neutral
% 5.05/5.29 thf(fact_2197_mult_Ocomm__neutral,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( times_times_int @ A @ one_one_int )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % mult.comm_neutral
% 5.05/5.29 thf(fact_2198_times__divide__times__eq,axiom,
% 5.05/5.29 ! [X: complex,Y: complex,Z: complex,W: complex] :
% 5.05/5.29 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.05/5.29 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % times_divide_times_eq
% 5.05/5.29 thf(fact_2199_times__divide__times__eq,axiom,
% 5.05/5.29 ! [X: real,Y: real,Z: real,W: real] :
% 5.05/5.29 ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.05/5.29 = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % times_divide_times_eq
% 5.05/5.29 thf(fact_2200_times__divide__times__eq,axiom,
% 5.05/5.29 ! [X: rat,Y: rat,Z: rat,W: rat] :
% 5.05/5.29 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 5.05/5.29 = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % times_divide_times_eq
% 5.05/5.29 thf(fact_2201_divide__divide__times__eq,axiom,
% 5.05/5.29 ! [X: complex,Y: complex,Z: complex,W: complex] :
% 5.05/5.29 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.05/5.29 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_divide_times_eq
% 5.05/5.29 thf(fact_2202_divide__divide__times__eq,axiom,
% 5.05/5.29 ! [X: real,Y: real,Z: real,W: real] :
% 5.05/5.29 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.05/5.29 = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_divide_times_eq
% 5.05/5.29 thf(fact_2203_divide__divide__times__eq,axiom,
% 5.05/5.29 ! [X: rat,Y: rat,Z: rat,W: rat] :
% 5.05/5.29 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 5.05/5.29 = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_divide_times_eq
% 5.05/5.29 thf(fact_2204_divide__divide__eq__left_H,axiom,
% 5.05/5.29 ! [A: complex,B: complex,C: complex] :
% 5.05/5.29 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.05/5.29 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_divide_eq_left'
% 5.05/5.29 thf(fact_2205_divide__divide__eq__left_H,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.05/5.29 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_divide_eq_left'
% 5.05/5.29 thf(fact_2206_divide__divide__eq__left_H,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.05/5.29 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_divide_eq_left'
% 5.05/5.29 thf(fact_2207_group__cancel_Osub1,axiom,
% 5.05/5.29 ! [A2: real,K: real,A: real,B: real] :
% 5.05/5.29 ( ( A2
% 5.05/5.29 = ( plus_plus_real @ K @ A ) )
% 5.05/5.29 => ( ( minus_minus_real @ A2 @ B )
% 5.05/5.29 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % group_cancel.sub1
% 5.05/5.29 thf(fact_2208_group__cancel_Osub1,axiom,
% 5.05/5.29 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.05/5.29 ( ( A2
% 5.05/5.29 = ( plus_plus_rat @ K @ A ) )
% 5.05/5.29 => ( ( minus_minus_rat @ A2 @ B )
% 5.05/5.29 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % group_cancel.sub1
% 5.05/5.29 thf(fact_2209_group__cancel_Osub1,axiom,
% 5.05/5.29 ! [A2: int,K: int,A: int,B: int] :
% 5.05/5.29 ( ( A2
% 5.05/5.29 = ( plus_plus_int @ K @ A ) )
% 5.05/5.29 => ( ( minus_minus_int @ A2 @ B )
% 5.05/5.29 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % group_cancel.sub1
% 5.05/5.29 thf(fact_2210_diff__eq__eq,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( ( minus_minus_real @ A @ B )
% 5.05/5.29 = C )
% 5.05/5.29 = ( A
% 5.05/5.29 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_eq_eq
% 5.05/5.29 thf(fact_2211_diff__eq__eq,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( ( minus_minus_rat @ A @ B )
% 5.05/5.29 = C )
% 5.05/5.29 = ( A
% 5.05/5.29 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_eq_eq
% 5.05/5.29 thf(fact_2212_diff__eq__eq,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( ( minus_minus_int @ A @ B )
% 5.05/5.29 = C )
% 5.05/5.29 = ( A
% 5.05/5.29 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_eq_eq
% 5.05/5.29 thf(fact_2213_eq__diff__eq,axiom,
% 5.05/5.29 ! [A: real,C: real,B: real] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( minus_minus_real @ C @ B ) )
% 5.05/5.29 = ( ( plus_plus_real @ A @ B )
% 5.05/5.29 = C ) ) ).
% 5.05/5.29
% 5.05/5.29 % eq_diff_eq
% 5.05/5.29 thf(fact_2214_eq__diff__eq,axiom,
% 5.05/5.29 ! [A: rat,C: rat,B: rat] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( minus_minus_rat @ C @ B ) )
% 5.05/5.29 = ( ( plus_plus_rat @ A @ B )
% 5.05/5.29 = C ) ) ).
% 5.05/5.29
% 5.05/5.29 % eq_diff_eq
% 5.05/5.29 thf(fact_2215_eq__diff__eq,axiom,
% 5.05/5.29 ! [A: int,C: int,B: int] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( minus_minus_int @ C @ B ) )
% 5.05/5.29 = ( ( plus_plus_int @ A @ B )
% 5.05/5.29 = C ) ) ).
% 5.05/5.29
% 5.05/5.29 % eq_diff_eq
% 5.05/5.29 thf(fact_2216_add__diff__eq,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.05/5.29 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_diff_eq
% 5.05/5.29 thf(fact_2217_add__diff__eq,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.05/5.29 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_diff_eq
% 5.05/5.29 thf(fact_2218_add__diff__eq,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.05/5.29 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_diff_eq
% 5.05/5.29 thf(fact_2219_diff__diff__eq2,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.05/5.29 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_diff_eq2
% 5.05/5.29 thf(fact_2220_diff__diff__eq2,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.05/5.29 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_diff_eq2
% 5.05/5.29 thf(fact_2221_diff__diff__eq2,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.05/5.29 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_diff_eq2
% 5.05/5.29 thf(fact_2222_diff__add__eq,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.05/5.29 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_add_eq
% 5.05/5.29 thf(fact_2223_diff__add__eq,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.05/5.29 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_add_eq
% 5.05/5.29 thf(fact_2224_diff__add__eq,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.05/5.29 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_add_eq
% 5.05/5.29 thf(fact_2225_diff__add__eq__diff__diff__swap,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.05/5.29 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_add_eq_diff_diff_swap
% 5.05/5.29 thf(fact_2226_diff__add__eq__diff__diff__swap,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.05/5.29 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_add_eq_diff_diff_swap
% 5.05/5.29 thf(fact_2227_diff__add__eq__diff__diff__swap,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.05/5.29 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_add_eq_diff_diff_swap
% 5.05/5.29 thf(fact_2228_add__implies__diff,axiom,
% 5.05/5.29 ! [C: real,B: real,A: real] :
% 5.05/5.29 ( ( ( plus_plus_real @ C @ B )
% 5.05/5.29 = A )
% 5.05/5.29 => ( C
% 5.05/5.29 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_implies_diff
% 5.05/5.29 thf(fact_2229_add__implies__diff,axiom,
% 5.05/5.29 ! [C: rat,B: rat,A: rat] :
% 5.05/5.29 ( ( ( plus_plus_rat @ C @ B )
% 5.05/5.29 = A )
% 5.05/5.29 => ( C
% 5.05/5.29 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_implies_diff
% 5.05/5.29 thf(fact_2230_add__implies__diff,axiom,
% 5.05/5.29 ! [C: nat,B: nat,A: nat] :
% 5.05/5.29 ( ( ( plus_plus_nat @ C @ B )
% 5.05/5.29 = A )
% 5.05/5.29 => ( C
% 5.05/5.29 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_implies_diff
% 5.05/5.29 thf(fact_2231_add__implies__diff,axiom,
% 5.05/5.29 ! [C: int,B: int,A: int] :
% 5.05/5.29 ( ( ( plus_plus_int @ C @ B )
% 5.05/5.29 = A )
% 5.05/5.29 => ( C
% 5.05/5.29 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_implies_diff
% 5.05/5.29 thf(fact_2232_diff__diff__eq,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.05/5.29 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_diff_eq
% 5.05/5.29 thf(fact_2233_diff__diff__eq,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.05/5.29 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_diff_eq
% 5.05/5.29 thf(fact_2234_diff__diff__eq,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.05/5.29 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_diff_eq
% 5.05/5.29 thf(fact_2235_diff__diff__eq,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.05/5.29 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_diff_eq
% 5.05/5.29 thf(fact_2236_add__divide__distrib,axiom,
% 5.05/5.29 ! [A: complex,B: complex,C: complex] :
% 5.05/5.29 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.05/5.29 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_divide_distrib
% 5.05/5.29 thf(fact_2237_add__divide__distrib,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.05/5.29 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_divide_distrib
% 5.05/5.29 thf(fact_2238_add__divide__distrib,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.05/5.29 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_divide_distrib
% 5.05/5.29 thf(fact_2239_diff__divide__distrib,axiom,
% 5.05/5.29 ! [A: complex,B: complex,C: complex] :
% 5.05/5.29 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.05/5.29 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_divide_distrib
% 5.05/5.29 thf(fact_2240_diff__divide__distrib,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.05/5.29 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_divide_distrib
% 5.05/5.29 thf(fact_2241_diff__divide__distrib,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.05/5.29 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_divide_distrib
% 5.05/5.29 thf(fact_2242_max__add__distrib__left,axiom,
% 5.05/5.29 ! [X: real,Y: real,Z: real] :
% 5.05/5.29 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.05/5.29 = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_add_distrib_left
% 5.05/5.29 thf(fact_2243_max__add__distrib__left,axiom,
% 5.05/5.29 ! [X: rat,Y: rat,Z: rat] :
% 5.05/5.29 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 5.05/5.29 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_add_distrib_left
% 5.05/5.29 thf(fact_2244_max__add__distrib__left,axiom,
% 5.05/5.29 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.29 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 5.05/5.29 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_add_distrib_left
% 5.05/5.29 thf(fact_2245_max__add__distrib__left,axiom,
% 5.05/5.29 ! [X: int,Y: int,Z: int] :
% 5.05/5.29 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.05/5.29 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_add_distrib_left
% 5.05/5.29 thf(fact_2246_max__add__distrib__left,axiom,
% 5.05/5.29 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.05/5.29 ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 5.05/5.29 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_add_distrib_left
% 5.05/5.29 thf(fact_2247_max__add__distrib__right,axiom,
% 5.05/5.29 ! [X: real,Y: real,Z: real] :
% 5.05/5.29 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
% 5.05/5.29 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_add_distrib_right
% 5.05/5.29 thf(fact_2248_max__add__distrib__right,axiom,
% 5.05/5.29 ! [X: rat,Y: rat,Z: rat] :
% 5.05/5.29 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 5.05/5.29 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_add_distrib_right
% 5.05/5.29 thf(fact_2249_max__add__distrib__right,axiom,
% 5.05/5.29 ! [X: nat,Y: nat,Z: nat] :
% 5.05/5.29 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 5.05/5.29 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_add_distrib_right
% 5.05/5.29 thf(fact_2250_max__add__distrib__right,axiom,
% 5.05/5.29 ! [X: int,Y: int,Z: int] :
% 5.05/5.29 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 5.05/5.29 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_add_distrib_right
% 5.05/5.29 thf(fact_2251_max__add__distrib__right,axiom,
% 5.05/5.29 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.05/5.29 ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 5.05/5.29 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_add_distrib_right
% 5.05/5.29 thf(fact_2252_max__diff__distrib__left,axiom,
% 5.05/5.29 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.05/5.29 ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 5.05/5.29 = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_diff_distrib_left
% 5.05/5.29 thf(fact_2253_max__diff__distrib__left,axiom,
% 5.05/5.29 ! [X: real,Y: real,Z: real] :
% 5.05/5.29 ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.05/5.29 = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_diff_distrib_left
% 5.05/5.29 thf(fact_2254_max__diff__distrib__left,axiom,
% 5.05/5.29 ! [X: rat,Y: rat,Z: rat] :
% 5.05/5.29 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 5.05/5.29 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_diff_distrib_left
% 5.05/5.29 thf(fact_2255_max__diff__distrib__left,axiom,
% 5.05/5.29 ! [X: int,Y: int,Z: int] :
% 5.05/5.29 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.05/5.29 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_diff_distrib_left
% 5.05/5.29 thf(fact_2256_add__less__le__mono,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real,D: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ B )
% 5.05/5.29 => ( ( ord_less_eq_real @ C @ D )
% 5.05/5.29 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_le_mono
% 5.05/5.29 thf(fact_2257_add__less__le__mono,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ B )
% 5.05/5.29 => ( ( ord_less_eq_rat @ C @ D )
% 5.05/5.29 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_le_mono
% 5.05/5.29 thf(fact_2258_add__less__le__mono,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.05/5.29 ( ( ord_less_nat @ A @ B )
% 5.05/5.29 => ( ( ord_less_eq_nat @ C @ D )
% 5.05/5.29 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_le_mono
% 5.05/5.29 thf(fact_2259_add__less__le__mono,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int,D: int] :
% 5.05/5.29 ( ( ord_less_int @ A @ B )
% 5.05/5.29 => ( ( ord_less_eq_int @ C @ D )
% 5.05/5.29 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_le_mono
% 5.05/5.29 thf(fact_2260_add__le__less__mono,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real,D: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ A @ B )
% 5.05/5.29 => ( ( ord_less_real @ C @ D )
% 5.05/5.29 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_less_mono
% 5.05/5.29 thf(fact_2261_add__le__less__mono,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ A @ B )
% 5.05/5.29 => ( ( ord_less_rat @ C @ D )
% 5.05/5.29 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_less_mono
% 5.05/5.29 thf(fact_2262_add__le__less__mono,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( ord_less_nat @ C @ D )
% 5.05/5.29 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_less_mono
% 5.05/5.29 thf(fact_2263_add__le__less__mono,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int,D: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ A @ B )
% 5.05/5.29 => ( ( ord_less_int @ C @ D )
% 5.05/5.29 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_less_mono
% 5.05/5.29 thf(fact_2264_add__mono__thms__linordered__field_I3_J,axiom,
% 5.05/5.29 ! [I2: real,J: real,K: real,L2: real] :
% 5.05/5.29 ( ( ( ord_less_real @ I2 @ J )
% 5.05/5.29 & ( ord_less_eq_real @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(3)
% 5.05/5.29 thf(fact_2265_add__mono__thms__linordered__field_I3_J,axiom,
% 5.05/5.29 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.05/5.29 ( ( ( ord_less_rat @ I2 @ J )
% 5.05/5.29 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(3)
% 5.05/5.29 thf(fact_2266_add__mono__thms__linordered__field_I3_J,axiom,
% 5.05/5.29 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.29 ( ( ( ord_less_nat @ I2 @ J )
% 5.05/5.29 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(3)
% 5.05/5.29 thf(fact_2267_add__mono__thms__linordered__field_I3_J,axiom,
% 5.05/5.29 ! [I2: int,J: int,K: int,L2: int] :
% 5.05/5.29 ( ( ( ord_less_int @ I2 @ J )
% 5.05/5.29 & ( ord_less_eq_int @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(3)
% 5.05/5.29 thf(fact_2268_add__mono__thms__linordered__field_I4_J,axiom,
% 5.05/5.29 ! [I2: real,J: real,K: real,L2: real] :
% 5.05/5.29 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.05/5.29 & ( ord_less_real @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(4)
% 5.05/5.29 thf(fact_2269_add__mono__thms__linordered__field_I4_J,axiom,
% 5.05/5.29 ! [I2: rat,J: rat,K: rat,L2: rat] :
% 5.05/5.29 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.05/5.29 & ( ord_less_rat @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(4)
% 5.05/5.29 thf(fact_2270_add__mono__thms__linordered__field_I4_J,axiom,
% 5.05/5.29 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 5.05/5.29 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.05/5.29 & ( ord_less_nat @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(4)
% 5.05/5.29 thf(fact_2271_add__mono__thms__linordered__field_I4_J,axiom,
% 5.05/5.29 ! [I2: int,J: int,K: int,L2: int] :
% 5.05/5.29 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.05/5.29 & ( ord_less_int @ K @ L2 ) )
% 5.05/5.29 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_mono_thms_linordered_field(4)
% 5.05/5.29 thf(fact_2272_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( ( minus_minus_nat @ B @ A )
% 5.05/5.29 = C )
% 5.05/5.29 = ( B
% 5.05/5.29 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.05/5.29 thf(fact_2273_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.05/5.29 = B ) ) ).
% 5.05/5.29
% 5.05/5.29 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.05/5.29 thf(fact_2274_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.05/5.29 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.05/5.29 thf(fact_2275_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.05/5.29 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.05/5.29 thf(fact_2276_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.05/5.29 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.05/5.29 thf(fact_2277_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.05/5.29 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.05/5.29 thf(fact_2278_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.05/5.29 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.05/5.29 thf(fact_2279_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.05/5.29 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.05/5.29 thf(fact_2280_le__add__diff,axiom,
% 5.05/5.29 ! [A: nat,B: nat,C: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_add_diff
% 5.05/5.29 thf(fact_2281_diff__add,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ B )
% 5.05/5.29 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.05/5.29 = B ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_add
% 5.05/5.29 thf(fact_2282_le__diff__eq,axiom,
% 5.05/5.29 ! [A: real,C: real,B: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.05/5.29 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_diff_eq
% 5.05/5.29 thf(fact_2283_le__diff__eq,axiom,
% 5.05/5.29 ! [A: rat,C: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.05/5.29 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_diff_eq
% 5.05/5.29 thf(fact_2284_le__diff__eq,axiom,
% 5.05/5.29 ! [A: int,C: int,B: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.05/5.29 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_diff_eq
% 5.05/5.29 thf(fact_2285_diff__le__eq,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.05/5.29 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_le_eq
% 5.05/5.29 thf(fact_2286_diff__le__eq,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.05/5.29 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_le_eq
% 5.05/5.29 thf(fact_2287_diff__le__eq,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.05/5.29 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_le_eq
% 5.05/5.29 thf(fact_2288_less__diff__eq,axiom,
% 5.05/5.29 ! [A: real,C: real,B: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.05/5.29 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_diff_eq
% 5.05/5.29 thf(fact_2289_less__diff__eq,axiom,
% 5.05/5.29 ! [A: rat,C: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.05/5.29 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_diff_eq
% 5.05/5.29 thf(fact_2290_less__diff__eq,axiom,
% 5.05/5.29 ! [A: int,C: int,B: int] :
% 5.05/5.29 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.05/5.29 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_diff_eq
% 5.05/5.29 thf(fact_2291_diff__less__eq,axiom,
% 5.05/5.29 ! [A: real,B: real,C: real] :
% 5.05/5.29 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.05/5.29 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_less_eq
% 5.05/5.29 thf(fact_2292_diff__less__eq,axiom,
% 5.05/5.29 ! [A: rat,B: rat,C: rat] :
% 5.05/5.29 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.05/5.29 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_less_eq
% 5.05/5.29 thf(fact_2293_diff__less__eq,axiom,
% 5.05/5.29 ! [A: int,B: int,C: int] :
% 5.05/5.29 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.05/5.29 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_less_eq
% 5.05/5.29 thf(fact_2294_gt__half__sum,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ B )
% 5.05/5.29 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % gt_half_sum
% 5.05/5.29 thf(fact_2295_gt__half__sum,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ B )
% 5.05/5.29 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % gt_half_sum
% 5.05/5.29 thf(fact_2296_less__half__sum,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ B )
% 5.05/5.29 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_half_sum
% 5.05/5.29 thf(fact_2297_less__half__sum,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ B )
% 5.05/5.29 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_half_sum
% 5.05/5.29 thf(fact_2298_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.05/5.29 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.05/5.29 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X )
% 5.05/5.29 = ( ( X = Mi )
% 5.05/5.29 | ( X = Ma )
% 5.05/5.29 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.29 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % VEBT_internal.membermima.simps(4)
% 5.05/5.29 thf(fact_2299_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.05/5.29 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.05/5.29 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S2 ) @ X )
% 5.05/5.29 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.29 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % VEBT_internal.naive_member.simps(3)
% 5.05/5.29 thf(fact_2300_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.05/5.29 ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 5.05/5.29 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X )
% 5.05/5.29 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.05/5.29 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % VEBT_internal.membermima.simps(5)
% 5.05/5.29 thf(fact_2301_divmod__step__eq,axiom,
% 5.05/5.29 ! [L2: num,R2: nat,Q2: nat] :
% 5.05/5.29 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 )
% 5.05/5.29 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.05/5.29 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L2 ) ) ) ) )
% 5.05/5.29 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R2 )
% 5.05/5.29 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.05/5.29 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divmod_step_eq
% 5.05/5.29 thf(fact_2302_divmod__step__eq,axiom,
% 5.05/5.29 ! [L2: num,R2: int,Q2: int] :
% 5.05/5.29 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 )
% 5.05/5.29 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.05/5.29 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L2 ) ) ) ) )
% 5.05/5.29 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R2 )
% 5.05/5.29 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.05/5.29 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divmod_step_eq
% 5.05/5.29 thf(fact_2303_divmod__step__eq,axiom,
% 5.05/5.29 ! [L2: num,R2: code_integer,Q2: code_integer] :
% 5.05/5.29 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 )
% 5.05/5.29 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.05/5.29 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 5.05/5.29 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R2 )
% 5.05/5.29 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.05/5.29 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divmod_step_eq
% 5.05/5.29 thf(fact_2304_buildup__nothing__in__leaf,axiom,
% 5.05/5.29 ! [N2: nat,X: nat] :
% 5.05/5.29 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N2 ) @ X ) ).
% 5.05/5.29
% 5.05/5.29 % buildup_nothing_in_leaf
% 5.05/5.29 thf(fact_2305_vebt__pred_Oelims,axiom,
% 5.05/5.29 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.05/5.29 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.05/5.29 = Y )
% 5.05/5.29 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.05/5.29 ( X
% 5.05/5.29 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.05/5.29 => ( ( Xa2 = zero_zero_nat )
% 5.05/5.29 => ( Y != none_nat ) ) )
% 5.05/5.29 => ( ! [A3: $o] :
% 5.05/5.29 ( ? [Uw2: $o] :
% 5.05/5.29 ( X
% 5.05/5.29 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.05/5.29 => ( ( Xa2
% 5.05/5.29 = ( suc @ zero_zero_nat ) )
% 5.05/5.29 => ~ ( ( A3
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( some_nat @ zero_zero_nat ) ) )
% 5.05/5.29 & ( ~ A3
% 5.05/5.29 => ( Y = none_nat ) ) ) ) )
% 5.05/5.29 => ( ! [A3: $o,B2: $o] :
% 5.05/5.29 ( ( X
% 5.05/5.29 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.05/5.29 => ( ? [Va2: nat] :
% 5.05/5.29 ( Xa2
% 5.05/5.29 = ( suc @ ( suc @ Va2 ) ) )
% 5.05/5.29 => ~ ( ( B2
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( some_nat @ one_one_nat ) ) )
% 5.05/5.29 & ( ~ B2
% 5.05/5.29 => ( ( A3
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( some_nat @ zero_zero_nat ) ) )
% 5.05/5.29 & ( ~ A3
% 5.05/5.29 => ( Y = none_nat ) ) ) ) ) ) )
% 5.05/5.29 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 5.05/5.29 ( X
% 5.05/5.29 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 5.05/5.29 => ( Y != none_nat ) )
% 5.05/5.29 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.05/5.29 ( X
% 5.05/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.05/5.29 => ( Y != none_nat ) )
% 5.05/5.29 => ( ( ? [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.05/5.29 ( X
% 5.05/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.05/5.29 => ( Y != none_nat ) )
% 5.05/5.29 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.05/5.29 ( ( X
% 5.05/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.05/5.29 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( some_nat @ Ma2 ) ) )
% 5.05/5.29 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.05/5.29 @ ( if_option_nat
% 5.05/5.29 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 != none_nat )
% 5.05/5.29 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.29 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 @ ( if_option_nat
% 5.05/5.29 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.29 = none_nat )
% 5.05/5.29 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.05/5.29 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.05/5.29 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % vebt_pred.elims
% 5.05/5.29 thf(fact_2306_vebt__succ_Oelims,axiom,
% 5.05/5.29 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.05/5.29 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 5.05/5.29 = Y )
% 5.05/5.29 => ( ! [Uu2: $o,B2: $o] :
% 5.05/5.29 ( ( X
% 5.05/5.29 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 5.05/5.29 => ( ( Xa2 = zero_zero_nat )
% 5.05/5.29 => ~ ( ( B2
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( some_nat @ one_one_nat ) ) )
% 5.05/5.29 & ( ~ B2
% 5.05/5.29 => ( Y = none_nat ) ) ) ) )
% 5.05/5.29 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.05/5.29 ( X
% 5.05/5.29 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.05/5.29 => ( ? [N3: nat] :
% 5.05/5.29 ( Xa2
% 5.05/5.29 = ( suc @ N3 ) )
% 5.05/5.29 => ( Y != none_nat ) ) )
% 5.05/5.29 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.05/5.29 ( X
% 5.05/5.29 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.05/5.29 => ( Y != none_nat ) )
% 5.05/5.29 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.05/5.29 ( X
% 5.05/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.05/5.29 => ( Y != none_nat ) )
% 5.05/5.29 => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.05/5.29 ( X
% 5.05/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.05/5.29 => ( Y != none_nat ) )
% 5.05/5.29 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.05/5.29 ( ( X
% 5.05/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.05/5.29 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( some_nat @ Mi2 ) ) )
% 5.05/5.29 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.05/5.29 @ ( if_option_nat
% 5.05/5.29 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 != none_nat )
% 5.05/5.29 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.29 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 @ ( if_option_nat
% 5.05/5.29 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.05/5.29 = none_nat )
% 5.05/5.29 @ none_nat
% 5.05/5.29 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.05/5.29 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % vebt_succ.elims
% 5.05/5.29 thf(fact_2307_discrete,axiom,
% 5.05/5.29 ( ord_less_nat
% 5.05/5.29 = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % discrete
% 5.05/5.29 thf(fact_2308_discrete,axiom,
% 5.05/5.29 ( ord_less_int
% 5.05/5.29 = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % discrete
% 5.05/5.29 thf(fact_2309_vebt__delete_Oelims,axiom,
% 5.05/5.29 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.05/5.29 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 5.05/5.29 = Y )
% 5.05/5.29 => ( ! [A3: $o,B2: $o] :
% 5.05/5.29 ( ( X
% 5.05/5.29 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.05/5.29 => ( ( Xa2 = zero_zero_nat )
% 5.05/5.29 => ( Y
% 5.05/5.29 != ( vEBT_Leaf @ $false @ B2 ) ) ) )
% 5.05/5.29 => ( ! [A3: $o] :
% 5.05/5.29 ( ? [B2: $o] :
% 5.05/5.29 ( X
% 5.05/5.29 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.05/5.29 => ( ( Xa2
% 5.05/5.29 = ( suc @ zero_zero_nat ) )
% 5.05/5.29 => ( Y
% 5.05/5.29 != ( vEBT_Leaf @ A3 @ $false ) ) ) )
% 5.05/5.29 => ( ! [A3: $o,B2: $o] :
% 5.05/5.29 ( ( X
% 5.05/5.29 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.05/5.29 => ( ? [N3: nat] :
% 5.05/5.29 ( Xa2
% 5.05/5.29 = ( suc @ ( suc @ N3 ) ) )
% 5.05/5.29 => ( Y
% 5.05/5.29 != ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.05/5.29 => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.05/5.29 ( ( X
% 5.05/5.29 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.05/5.29 => ( Y
% 5.05/5.29 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) ) )
% 5.05/5.29 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT] :
% 5.05/5.29 ( ( X
% 5.05/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 5.05/5.29 => ( Y
% 5.05/5.29 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) ) )
% 5.05/5.29 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT] :
% 5.05/5.29 ( ( X
% 5.05/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 5.05/5.29 => ( Y
% 5.05/5.29 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) )
% 5.05/5.29 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.05/5.29 ( ( X
% 5.05/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.05/5.29 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.05/5.29 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.05/5.29 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.05/5.29 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.05/5.29 => ( ( ( ( Xa2 = Mi2 )
% 5.05/5.29 & ( Xa2 = Ma2 ) )
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.05/5.29 & ( ~ ( ( Xa2 = Mi2 )
% 5.05/5.29 & ( Xa2 = Ma2 ) )
% 5.05/5.29 => ( Y
% 5.05/5.29 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.05/5.29 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 @ ( vEBT_Node
% 5.05/5.29 @ ( some_P7363390416028606310at_nat
% 5.05/5.29 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.05/5.29 @ ( if_nat
% 5.05/5.29 @ ( ( ( Xa2 = Mi2 )
% 5.05/5.29 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.05/5.29 = Ma2 ) )
% 5.05/5.29 & ( ( Xa2 != Mi2 )
% 5.05/5.29 => ( Xa2 = Ma2 ) ) )
% 5.05/5.29 @ ( if_nat
% 5.05/5.29 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 = none_nat )
% 5.05/5.29 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.05/5.29 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.05/5.29 @ Ma2 ) ) )
% 5.05/5.29 @ ( suc @ ( suc @ Va2 ) )
% 5.05/5.29 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 @ ( vEBT_Node
% 5.05/5.29 @ ( some_P7363390416028606310at_nat
% 5.05/5.29 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.05/5.29 @ ( if_nat
% 5.05/5.29 @ ( ( ( Xa2 = Mi2 )
% 5.05/5.29 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.05/5.29 = Ma2 ) )
% 5.05/5.29 & ( ( Xa2 != Mi2 )
% 5.05/5.29 => ( Xa2 = Ma2 ) ) )
% 5.05/5.29 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.05/5.29 @ Ma2 ) ) )
% 5.05/5.29 @ ( suc @ ( suc @ Va2 ) )
% 5.05/5.29 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.05/5.29 @ Summary2 ) )
% 5.05/5.29 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % vebt_delete.elims
% 5.05/5.29 thf(fact_2310_low__def,axiom,
% 5.05/5.29 ( vEBT_VEBT_low
% 5.05/5.29 = ( ^ [X2: nat,N: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % low_def
% 5.05/5.29 thf(fact_2311_valid__0__not,axiom,
% 5.05/5.29 ! [T: vEBT_VEBT] :
% 5.05/5.29 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % valid_0_not
% 5.05/5.29 thf(fact_2312_valid__tree__deg__neq__0,axiom,
% 5.05/5.29 ! [T: vEBT_VEBT] :
% 5.05/5.29 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % valid_tree_deg_neq_0
% 5.05/5.29 thf(fact_2313_buildup__nothing__in__min__max,axiom,
% 5.05/5.29 ! [N2: nat,X: nat] :
% 5.05/5.29 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N2 ) @ X ) ).
% 5.05/5.29
% 5.05/5.29 % buildup_nothing_in_min_max
% 5.05/5.29 thf(fact_2314_deg__not__0,axiom,
% 5.05/5.29 ! [T: vEBT_VEBT,N2: nat] :
% 5.05/5.29 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.29 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.05/5.29
% 5.05/5.29 % deg_not_0
% 5.05/5.29 thf(fact_2315_Leaf__0__not,axiom,
% 5.05/5.29 ! [A: $o,B: $o] :
% 5.05/5.29 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % Leaf_0_not
% 5.05/5.29 thf(fact_2316_deg1Leaf,axiom,
% 5.05/5.29 ! [T: vEBT_VEBT] :
% 5.05/5.29 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.05/5.29 = ( ? [A4: $o,B4: $o] :
% 5.05/5.29 ( T
% 5.05/5.29 = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % deg1Leaf
% 5.05/5.29 thf(fact_2317_deg__1__Leaf,axiom,
% 5.05/5.29 ! [T: vEBT_VEBT] :
% 5.05/5.29 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.05/5.29 => ? [A3: $o,B2: $o] :
% 5.05/5.29 ( T
% 5.05/5.29 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % deg_1_Leaf
% 5.05/5.29 thf(fact_2318_deg__1__Leafy,axiom,
% 5.05/5.29 ! [T: vEBT_VEBT,N2: nat] :
% 5.05/5.29 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.05/5.29 => ( ( N2 = one_one_nat )
% 5.05/5.29 => ? [A3: $o,B2: $o] :
% 5.05/5.29 ( T
% 5.05/5.29 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % deg_1_Leafy
% 5.05/5.29 thf(fact_2319_both__member__options__def,axiom,
% 5.05/5.29 ( vEBT_V8194947554948674370ptions
% 5.05/5.29 = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 5.05/5.29 ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 5.05/5.29 | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % both_member_options_def
% 5.05/5.29 thf(fact_2320_buildup__gives__valid,axiom,
% 5.05/5.29 ! [N2: nat] :
% 5.05/5.29 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.05/5.29 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N2 ) @ N2 ) ) ).
% 5.05/5.29
% 5.05/5.29 % buildup_gives_valid
% 5.05/5.29 thf(fact_2321_zdiv__numeral__Bit0,axiom,
% 5.05/5.29 ! [V: num,W: num] :
% 5.05/5.29 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.05/5.29 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % zdiv_numeral_Bit0
% 5.05/5.29 thf(fact_2322_mod__mod__trivial,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.05/5.29 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % mod_mod_trivial
% 5.05/5.29 thf(fact_2323_mod__mod__trivial,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.05/5.29 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % mod_mod_trivial
% 5.05/5.29 thf(fact_2324_mod__mod__trivial,axiom,
% 5.05/5.29 ! [A: code_integer,B: code_integer] :
% 5.05/5.29 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.05/5.29 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % mod_mod_trivial
% 5.05/5.29 thf(fact_2325_member__valid__both__member__options,axiom,
% 5.05/5.29 ! [Tree: vEBT_VEBT,N2: nat,X: nat] :
% 5.05/5.29 ( ( vEBT_invar_vebt @ Tree @ N2 )
% 5.05/5.29 => ( ( vEBT_vebt_member @ Tree @ X )
% 5.05/5.29 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 5.05/5.29 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % member_valid_both_member_options
% 5.05/5.29 thf(fact_2326_VEBT_Oinject_I2_J,axiom,
% 5.05/5.29 ! [X21: $o,X222: $o,Y21: $o,Y222: $o] :
% 5.05/5.29 ( ( ( vEBT_Leaf @ X21 @ X222 )
% 5.05/5.29 = ( vEBT_Leaf @ Y21 @ Y222 ) )
% 5.05/5.29 = ( ( X21 = Y21 )
% 5.05/5.29 & ( X222 = Y222 ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % VEBT.inject(2)
% 5.05/5.29 thf(fact_2327_le__zero__eq,axiom,
% 5.05/5.29 ! [N2: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 5.05/5.29 = ( N2 = zero_zero_nat ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_zero_eq
% 5.05/5.29 thf(fact_2328_not__gr__zero,axiom,
% 5.05/5.29 ! [N2: nat] :
% 5.05/5.29 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.05/5.29 = ( N2 = zero_zero_nat ) ) ).
% 5.05/5.29
% 5.05/5.29 % not_gr_zero
% 5.05/5.29 thf(fact_2329_mult__cancel__right,axiom,
% 5.05/5.29 ! [A: complex,C: complex,B: complex] :
% 5.05/5.29 ( ( ( times_times_complex @ A @ C )
% 5.05/5.29 = ( times_times_complex @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_complex )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right
% 5.05/5.29 thf(fact_2330_mult__cancel__right,axiom,
% 5.05/5.29 ! [A: real,C: real,B: real] :
% 5.05/5.29 ( ( ( times_times_real @ A @ C )
% 5.05/5.29 = ( times_times_real @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_real )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right
% 5.05/5.29 thf(fact_2331_mult__cancel__right,axiom,
% 5.05/5.29 ! [A: rat,C: rat,B: rat] :
% 5.05/5.29 ( ( ( times_times_rat @ A @ C )
% 5.05/5.29 = ( times_times_rat @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_rat )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right
% 5.05/5.29 thf(fact_2332_mult__cancel__right,axiom,
% 5.05/5.29 ! [A: nat,C: nat,B: nat] :
% 5.05/5.29 ( ( ( times_times_nat @ A @ C )
% 5.05/5.29 = ( times_times_nat @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_nat )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right
% 5.05/5.29 thf(fact_2333_mult__cancel__right,axiom,
% 5.05/5.29 ! [A: int,C: int,B: int] :
% 5.05/5.29 ( ( ( times_times_int @ A @ C )
% 5.05/5.29 = ( times_times_int @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_int )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right
% 5.05/5.29 thf(fact_2334_mult__cancel__left,axiom,
% 5.05/5.29 ! [C: complex,A: complex,B: complex] :
% 5.05/5.29 ( ( ( times_times_complex @ C @ A )
% 5.05/5.29 = ( times_times_complex @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_complex )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left
% 5.05/5.29 thf(fact_2335_mult__cancel__left,axiom,
% 5.05/5.29 ! [C: real,A: real,B: real] :
% 5.05/5.29 ( ( ( times_times_real @ C @ A )
% 5.05/5.29 = ( times_times_real @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_real )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left
% 5.05/5.29 thf(fact_2336_mult__cancel__left,axiom,
% 5.05/5.29 ! [C: rat,A: rat,B: rat] :
% 5.05/5.29 ( ( ( times_times_rat @ C @ A )
% 5.05/5.29 = ( times_times_rat @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_rat )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left
% 5.05/5.29 thf(fact_2337_mult__cancel__left,axiom,
% 5.05/5.29 ! [C: nat,A: nat,B: nat] :
% 5.05/5.29 ( ( ( times_times_nat @ C @ A )
% 5.05/5.29 = ( times_times_nat @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_nat )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left
% 5.05/5.29 thf(fact_2338_mult__cancel__left,axiom,
% 5.05/5.29 ! [C: int,A: int,B: int] :
% 5.05/5.29 ( ( ( times_times_int @ C @ A )
% 5.05/5.29 = ( times_times_int @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_int )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left
% 5.05/5.29 thf(fact_2339_mult__eq__0__iff,axiom,
% 5.05/5.29 ! [A: complex,B: complex] :
% 5.05/5.29 ( ( ( times_times_complex @ A @ B )
% 5.05/5.29 = zero_zero_complex )
% 5.05/5.29 = ( ( A = zero_zero_complex )
% 5.05/5.29 | ( B = zero_zero_complex ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_eq_0_iff
% 5.05/5.29 thf(fact_2340_mult__eq__0__iff,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ( times_times_real @ A @ B )
% 5.05/5.29 = zero_zero_real )
% 5.05/5.29 = ( ( A = zero_zero_real )
% 5.05/5.29 | ( B = zero_zero_real ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_eq_0_iff
% 5.05/5.29 thf(fact_2341_mult__eq__0__iff,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ( times_times_rat @ A @ B )
% 5.05/5.29 = zero_zero_rat )
% 5.05/5.29 = ( ( A = zero_zero_rat )
% 5.05/5.29 | ( B = zero_zero_rat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_eq_0_iff
% 5.05/5.29 thf(fact_2342_mult__eq__0__iff,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ( times_times_nat @ A @ B )
% 5.05/5.29 = zero_zero_nat )
% 5.05/5.29 = ( ( A = zero_zero_nat )
% 5.05/5.29 | ( B = zero_zero_nat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_eq_0_iff
% 5.05/5.29 thf(fact_2343_mult__eq__0__iff,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( ( times_times_int @ A @ B )
% 5.05/5.29 = zero_zero_int )
% 5.05/5.29 = ( ( A = zero_zero_int )
% 5.05/5.29 | ( B = zero_zero_int ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_eq_0_iff
% 5.05/5.29 thf(fact_2344_mult__zero__right,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.05/5.29 = zero_zero_complex ) ).
% 5.05/5.29
% 5.05/5.29 % mult_zero_right
% 5.05/5.29 thf(fact_2345_mult__zero__right,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( times_times_real @ A @ zero_zero_real )
% 5.05/5.29 = zero_zero_real ) ).
% 5.05/5.29
% 5.05/5.29 % mult_zero_right
% 5.05/5.29 thf(fact_2346_mult__zero__right,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.05/5.29 = zero_zero_rat ) ).
% 5.05/5.29
% 5.05/5.29 % mult_zero_right
% 5.05/5.29 thf(fact_2347_mult__zero__right,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % mult_zero_right
% 5.05/5.29 thf(fact_2348_mult__zero__right,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( times_times_int @ A @ zero_zero_int )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % mult_zero_right
% 5.05/5.29 thf(fact_2349_mult__zero__left,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.05/5.29 = zero_zero_complex ) ).
% 5.05/5.29
% 5.05/5.29 % mult_zero_left
% 5.05/5.29 thf(fact_2350_mult__zero__left,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( times_times_real @ zero_zero_real @ A )
% 5.05/5.29 = zero_zero_real ) ).
% 5.05/5.29
% 5.05/5.29 % mult_zero_left
% 5.05/5.29 thf(fact_2351_mult__zero__left,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.05/5.29 = zero_zero_rat ) ).
% 5.05/5.29
% 5.05/5.29 % mult_zero_left
% 5.05/5.29 thf(fact_2352_mult__zero__left,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % mult_zero_left
% 5.05/5.29 thf(fact_2353_mult__zero__left,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( times_times_int @ zero_zero_int @ A )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % mult_zero_left
% 5.05/5.29 thf(fact_2354_add__0,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % add_0
% 5.05/5.29 thf(fact_2355_add__0,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % add_0
% 5.05/5.29 thf(fact_2356_add__0,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % add_0
% 5.05/5.29 thf(fact_2357_add__0,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % add_0
% 5.05/5.29 thf(fact_2358_add__0,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % add_0
% 5.05/5.29 thf(fact_2359_zero__eq__add__iff__both__eq__0,axiom,
% 5.05/5.29 ! [X: nat,Y: nat] :
% 5.05/5.29 ( ( zero_zero_nat
% 5.05/5.29 = ( plus_plus_nat @ X @ Y ) )
% 5.05/5.29 = ( ( X = zero_zero_nat )
% 5.05/5.29 & ( Y = zero_zero_nat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % zero_eq_add_iff_both_eq_0
% 5.05/5.29 thf(fact_2360_add__eq__0__iff__both__eq__0,axiom,
% 5.05/5.29 ! [X: nat,Y: nat] :
% 5.05/5.29 ( ( ( plus_plus_nat @ X @ Y )
% 5.05/5.29 = zero_zero_nat )
% 5.05/5.29 = ( ( X = zero_zero_nat )
% 5.05/5.29 & ( Y = zero_zero_nat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_eq_0_iff_both_eq_0
% 5.05/5.29 thf(fact_2361_add__cancel__right__right,axiom,
% 5.05/5.29 ! [A: complex,B: complex] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( plus_plus_complex @ A @ B ) )
% 5.05/5.29 = ( B = zero_zero_complex ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_right_right
% 5.05/5.29 thf(fact_2362_add__cancel__right__right,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( plus_plus_real @ A @ B ) )
% 5.05/5.29 = ( B = zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_right_right
% 5.05/5.29 thf(fact_2363_add__cancel__right__right,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( plus_plus_rat @ A @ B ) )
% 5.05/5.29 = ( B = zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_right_right
% 5.05/5.29 thf(fact_2364_add__cancel__right__right,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( plus_plus_nat @ A @ B ) )
% 5.05/5.29 = ( B = zero_zero_nat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_right_right
% 5.05/5.29 thf(fact_2365_add__cancel__right__right,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( plus_plus_int @ A @ B ) )
% 5.05/5.29 = ( B = zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_right_right
% 5.05/5.29 thf(fact_2366_add__cancel__right__left,axiom,
% 5.05/5.29 ! [A: complex,B: complex] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( plus_plus_complex @ B @ A ) )
% 5.05/5.29 = ( B = zero_zero_complex ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_right_left
% 5.05/5.29 thf(fact_2367_add__cancel__right__left,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( plus_plus_real @ B @ A ) )
% 5.05/5.29 = ( B = zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_right_left
% 5.05/5.29 thf(fact_2368_add__cancel__right__left,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( plus_plus_rat @ B @ A ) )
% 5.05/5.29 = ( B = zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_right_left
% 5.05/5.29 thf(fact_2369_add__cancel__right__left,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( plus_plus_nat @ B @ A ) )
% 5.05/5.29 = ( B = zero_zero_nat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_right_left
% 5.05/5.29 thf(fact_2370_add__cancel__right__left,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( A
% 5.05/5.29 = ( plus_plus_int @ B @ A ) )
% 5.05/5.29 = ( B = zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_right_left
% 5.05/5.29 thf(fact_2371_add__cancel__left__right,axiom,
% 5.05/5.29 ! [A: complex,B: complex] :
% 5.05/5.29 ( ( ( plus_plus_complex @ A @ B )
% 5.05/5.29 = A )
% 5.05/5.29 = ( B = zero_zero_complex ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_left_right
% 5.05/5.29 thf(fact_2372_add__cancel__left__right,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ( plus_plus_real @ A @ B )
% 5.05/5.29 = A )
% 5.05/5.29 = ( B = zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_left_right
% 5.05/5.29 thf(fact_2373_add__cancel__left__right,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ( plus_plus_rat @ A @ B )
% 5.05/5.29 = A )
% 5.05/5.29 = ( B = zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_left_right
% 5.05/5.29 thf(fact_2374_add__cancel__left__right,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ( plus_plus_nat @ A @ B )
% 5.05/5.29 = A )
% 5.05/5.29 = ( B = zero_zero_nat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_left_right
% 5.05/5.29 thf(fact_2375_add__cancel__left__right,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( ( plus_plus_int @ A @ B )
% 5.05/5.29 = A )
% 5.05/5.29 = ( B = zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_left_right
% 5.05/5.29 thf(fact_2376_add__cancel__left__left,axiom,
% 5.05/5.29 ! [B: complex,A: complex] :
% 5.05/5.29 ( ( ( plus_plus_complex @ B @ A )
% 5.05/5.29 = A )
% 5.05/5.29 = ( B = zero_zero_complex ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_left_left
% 5.05/5.29 thf(fact_2377_add__cancel__left__left,axiom,
% 5.05/5.29 ! [B: real,A: real] :
% 5.05/5.29 ( ( ( plus_plus_real @ B @ A )
% 5.05/5.29 = A )
% 5.05/5.29 = ( B = zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_left_left
% 5.05/5.29 thf(fact_2378_add__cancel__left__left,axiom,
% 5.05/5.29 ! [B: rat,A: rat] :
% 5.05/5.29 ( ( ( plus_plus_rat @ B @ A )
% 5.05/5.29 = A )
% 5.05/5.29 = ( B = zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_left_left
% 5.05/5.29 thf(fact_2379_add__cancel__left__left,axiom,
% 5.05/5.29 ! [B: nat,A: nat] :
% 5.05/5.29 ( ( ( plus_plus_nat @ B @ A )
% 5.05/5.29 = A )
% 5.05/5.29 = ( B = zero_zero_nat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_left_left
% 5.05/5.29 thf(fact_2380_add__cancel__left__left,axiom,
% 5.05/5.29 ! [B: int,A: int] :
% 5.05/5.29 ( ( ( plus_plus_int @ B @ A )
% 5.05/5.29 = A )
% 5.05/5.29 = ( B = zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_cancel_left_left
% 5.05/5.29 thf(fact_2381_double__zero__sym,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( zero_zero_real
% 5.05/5.29 = ( plus_plus_real @ A @ A ) )
% 5.05/5.29 = ( A = zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % double_zero_sym
% 5.05/5.29 thf(fact_2382_double__zero__sym,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( zero_zero_rat
% 5.05/5.29 = ( plus_plus_rat @ A @ A ) )
% 5.05/5.29 = ( A = zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % double_zero_sym
% 5.05/5.29 thf(fact_2383_double__zero__sym,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( zero_zero_int
% 5.05/5.29 = ( plus_plus_int @ A @ A ) )
% 5.05/5.29 = ( A = zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % double_zero_sym
% 5.05/5.29 thf(fact_2384_add_Oright__neutral,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % add.right_neutral
% 5.05/5.29 thf(fact_2385_add_Oright__neutral,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % add.right_neutral
% 5.05/5.29 thf(fact_2386_add_Oright__neutral,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % add.right_neutral
% 5.05/5.29 thf(fact_2387_add_Oright__neutral,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % add.right_neutral
% 5.05/5.29 thf(fact_2388_add_Oright__neutral,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % add.right_neutral
% 5.05/5.29 thf(fact_2389_diff__self,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( minus_minus_complex @ A @ A )
% 5.05/5.29 = zero_zero_complex ) ).
% 5.05/5.29
% 5.05/5.29 % diff_self
% 5.05/5.29 thf(fact_2390_diff__self,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( minus_minus_real @ A @ A )
% 5.05/5.29 = zero_zero_real ) ).
% 5.05/5.29
% 5.05/5.29 % diff_self
% 5.05/5.29 thf(fact_2391_diff__self,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( minus_minus_rat @ A @ A )
% 5.05/5.29 = zero_zero_rat ) ).
% 5.05/5.29
% 5.05/5.29 % diff_self
% 5.05/5.29 thf(fact_2392_diff__self,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( minus_minus_int @ A @ A )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % diff_self
% 5.05/5.29 thf(fact_2393_diff__0__right,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % diff_0_right
% 5.05/5.29 thf(fact_2394_diff__0__right,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % diff_0_right
% 5.05/5.29 thf(fact_2395_diff__0__right,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % diff_0_right
% 5.05/5.29 thf(fact_2396_diff__0__right,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % diff_0_right
% 5.05/5.29 thf(fact_2397_zero__diff,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % zero_diff
% 5.05/5.29 thf(fact_2398_diff__zero,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % diff_zero
% 5.05/5.29 thf(fact_2399_diff__zero,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % diff_zero
% 5.05/5.29 thf(fact_2400_diff__zero,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % diff_zero
% 5.05/5.29 thf(fact_2401_diff__zero,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % diff_zero
% 5.05/5.29 thf(fact_2402_diff__zero,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % diff_zero
% 5.05/5.29 thf(fact_2403_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( minus_minus_complex @ A @ A )
% 5.05/5.29 = zero_zero_complex ) ).
% 5.05/5.29
% 5.05/5.29 % cancel_comm_monoid_add_class.diff_cancel
% 5.05/5.29 thf(fact_2404_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( minus_minus_real @ A @ A )
% 5.05/5.29 = zero_zero_real ) ).
% 5.05/5.29
% 5.05/5.29 % cancel_comm_monoid_add_class.diff_cancel
% 5.05/5.29 thf(fact_2405_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( minus_minus_rat @ A @ A )
% 5.05/5.29 = zero_zero_rat ) ).
% 5.05/5.29
% 5.05/5.29 % cancel_comm_monoid_add_class.diff_cancel
% 5.05/5.29 thf(fact_2406_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( minus_minus_nat @ A @ A )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % cancel_comm_monoid_add_class.diff_cancel
% 5.05/5.29 thf(fact_2407_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( minus_minus_int @ A @ A )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % cancel_comm_monoid_add_class.diff_cancel
% 5.05/5.29 thf(fact_2408_bits__div__by__0,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % bits_div_by_0
% 5.05/5.29 thf(fact_2409_bits__div__by__0,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % bits_div_by_0
% 5.05/5.29 thf(fact_2410_bits__div__0,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % bits_div_0
% 5.05/5.29 thf(fact_2411_bits__div__0,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % bits_div_0
% 5.05/5.29 thf(fact_2412_div__by__0,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.05/5.29 = zero_zero_complex ) ).
% 5.05/5.29
% 5.05/5.29 % div_by_0
% 5.05/5.29 thf(fact_2413_div__by__0,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.05/5.29 = zero_zero_real ) ).
% 5.05/5.29
% 5.05/5.29 % div_by_0
% 5.05/5.29 thf(fact_2414_div__by__0,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.05/5.29 = zero_zero_rat ) ).
% 5.05/5.29
% 5.05/5.29 % div_by_0
% 5.05/5.29 thf(fact_2415_div__by__0,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % div_by_0
% 5.05/5.29 thf(fact_2416_div__by__0,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % div_by_0
% 5.05/5.29 thf(fact_2417_div__0,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.05/5.29 = zero_zero_complex ) ).
% 5.05/5.29
% 5.05/5.29 % div_0
% 5.05/5.29 thf(fact_2418_div__0,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.05/5.29 = zero_zero_real ) ).
% 5.05/5.29
% 5.05/5.29 % div_0
% 5.05/5.29 thf(fact_2419_div__0,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.05/5.29 = zero_zero_rat ) ).
% 5.05/5.29
% 5.05/5.29 % div_0
% 5.05/5.29 thf(fact_2420_div__0,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % div_0
% 5.05/5.29 thf(fact_2421_div__0,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % div_0
% 5.05/5.29 thf(fact_2422_division__ring__divide__zero,axiom,
% 5.05/5.29 ! [A: complex] :
% 5.05/5.29 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.05/5.29 = zero_zero_complex ) ).
% 5.05/5.29
% 5.05/5.29 % division_ring_divide_zero
% 5.05/5.29 thf(fact_2423_division__ring__divide__zero,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.05/5.29 = zero_zero_real ) ).
% 5.05/5.29
% 5.05/5.29 % division_ring_divide_zero
% 5.05/5.29 thf(fact_2424_division__ring__divide__zero,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.05/5.29 = zero_zero_rat ) ).
% 5.05/5.29
% 5.05/5.29 % division_ring_divide_zero
% 5.05/5.29 thf(fact_2425_divide__cancel__right,axiom,
% 5.05/5.29 ! [A: complex,C: complex,B: complex] :
% 5.05/5.29 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.05/5.29 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_complex )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_cancel_right
% 5.05/5.29 thf(fact_2426_divide__cancel__right,axiom,
% 5.05/5.29 ! [A: real,C: real,B: real] :
% 5.05/5.29 ( ( ( divide_divide_real @ A @ C )
% 5.05/5.29 = ( divide_divide_real @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_real )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_cancel_right
% 5.05/5.29 thf(fact_2427_divide__cancel__right,axiom,
% 5.05/5.29 ! [A: rat,C: rat,B: rat] :
% 5.05/5.29 ( ( ( divide_divide_rat @ A @ C )
% 5.05/5.29 = ( divide_divide_rat @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_rat )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_cancel_right
% 5.05/5.29 thf(fact_2428_divide__cancel__left,axiom,
% 5.05/5.29 ! [C: complex,A: complex,B: complex] :
% 5.05/5.29 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.05/5.29 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_complex )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_cancel_left
% 5.05/5.29 thf(fact_2429_divide__cancel__left,axiom,
% 5.05/5.29 ! [C: real,A: real,B: real] :
% 5.05/5.29 ( ( ( divide_divide_real @ C @ A )
% 5.05/5.29 = ( divide_divide_real @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_real )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_cancel_left
% 5.05/5.29 thf(fact_2430_divide__cancel__left,axiom,
% 5.05/5.29 ! [C: rat,A: rat,B: rat] :
% 5.05/5.29 ( ( ( divide_divide_rat @ C @ A )
% 5.05/5.29 = ( divide_divide_rat @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_rat )
% 5.05/5.29 | ( A = B ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_cancel_left
% 5.05/5.29 thf(fact_2431_divide__eq__0__iff,axiom,
% 5.05/5.29 ! [A: complex,B: complex] :
% 5.05/5.29 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.05/5.29 = zero_zero_complex )
% 5.05/5.29 = ( ( A = zero_zero_complex )
% 5.05/5.29 | ( B = zero_zero_complex ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_eq_0_iff
% 5.05/5.29 thf(fact_2432_divide__eq__0__iff,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ( divide_divide_real @ A @ B )
% 5.05/5.29 = zero_zero_real )
% 5.05/5.29 = ( ( A = zero_zero_real )
% 5.05/5.29 | ( B = zero_zero_real ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_eq_0_iff
% 5.05/5.29 thf(fact_2433_divide__eq__0__iff,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ( divide_divide_rat @ A @ B )
% 5.05/5.29 = zero_zero_rat )
% 5.05/5.29 = ( ( A = zero_zero_rat )
% 5.05/5.29 | ( B = zero_zero_rat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % divide_eq_0_iff
% 5.05/5.29 thf(fact_2434_bits__mod__0,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % bits_mod_0
% 5.05/5.29 thf(fact_2435_bits__mod__0,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % bits_mod_0
% 5.05/5.29 thf(fact_2436_bits__mod__0,axiom,
% 5.05/5.29 ! [A: code_integer] :
% 5.05/5.29 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.05/5.29 = zero_z3403309356797280102nteger ) ).
% 5.05/5.29
% 5.05/5.29 % bits_mod_0
% 5.05/5.29 thf(fact_2437_mod__self,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( modulo_modulo_nat @ A @ A )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % mod_self
% 5.05/5.29 thf(fact_2438_mod__self,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( modulo_modulo_int @ A @ A )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % mod_self
% 5.05/5.29 thf(fact_2439_mod__self,axiom,
% 5.05/5.29 ! [A: code_integer] :
% 5.05/5.29 ( ( modulo364778990260209775nteger @ A @ A )
% 5.05/5.29 = zero_z3403309356797280102nteger ) ).
% 5.05/5.29
% 5.05/5.29 % mod_self
% 5.05/5.29 thf(fact_2440_mod__by__0,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % mod_by_0
% 5.05/5.29 thf(fact_2441_mod__by__0,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % mod_by_0
% 5.05/5.29 thf(fact_2442_mod__by__0,axiom,
% 5.05/5.29 ! [A: code_integer] :
% 5.05/5.29 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % mod_by_0
% 5.05/5.29 thf(fact_2443_mod__0,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % mod_0
% 5.05/5.29 thf(fact_2444_mod__0,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.05/5.29 = zero_zero_int ) ).
% 5.05/5.29
% 5.05/5.29 % mod_0
% 5.05/5.29 thf(fact_2445_mod__0,axiom,
% 5.05/5.29 ! [A: code_integer] :
% 5.05/5.29 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.05/5.29 = zero_z3403309356797280102nteger ) ).
% 5.05/5.29
% 5.05/5.29 % mod_0
% 5.05/5.29 thf(fact_2446_bot__nat__0_Onot__eq__extremum,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( A != zero_zero_nat )
% 5.05/5.29 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % bot_nat_0.not_eq_extremum
% 5.05/5.29 thf(fact_2447_neq0__conv,axiom,
% 5.05/5.29 ! [N2: nat] :
% 5.05/5.29 ( ( N2 != zero_zero_nat )
% 5.05/5.29 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.05/5.29
% 5.05/5.29 % neq0_conv
% 5.05/5.29 thf(fact_2448_less__nat__zero__code,axiom,
% 5.05/5.29 ! [N2: nat] :
% 5.05/5.29 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % less_nat_zero_code
% 5.05/5.29 thf(fact_2449_bot__nat__0_Oextremum,axiom,
% 5.05/5.29 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.05/5.29
% 5.05/5.29 % bot_nat_0.extremum
% 5.05/5.29 thf(fact_2450_le0,axiom,
% 5.05/5.29 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 5.05/5.29
% 5.05/5.29 % le0
% 5.05/5.29 thf(fact_2451_mod__add__self2,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.05/5.29 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % mod_add_self2
% 5.05/5.29 thf(fact_2452_mod__add__self2,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.05/5.29 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % mod_add_self2
% 5.05/5.29 thf(fact_2453_mod__add__self2,axiom,
% 5.05/5.29 ! [A: code_integer,B: code_integer] :
% 5.05/5.29 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.05/5.29 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % mod_add_self2
% 5.05/5.29 thf(fact_2454_mod__add__self1,axiom,
% 5.05/5.29 ! [B: nat,A: nat] :
% 5.05/5.29 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.05/5.29 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % mod_add_self1
% 5.05/5.29 thf(fact_2455_mod__add__self1,axiom,
% 5.05/5.29 ! [B: int,A: int] :
% 5.05/5.29 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.05/5.29 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % mod_add_self1
% 5.05/5.29 thf(fact_2456_mod__add__self1,axiom,
% 5.05/5.29 ! [B: code_integer,A: code_integer] :
% 5.05/5.29 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.05/5.29 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % mod_add_self1
% 5.05/5.29 thf(fact_2457_Nat_Oadd__0__right,axiom,
% 5.05/5.29 ! [M: nat] :
% 5.05/5.29 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.05/5.29 = M ) ).
% 5.05/5.29
% 5.05/5.29 % Nat.add_0_right
% 5.05/5.29 thf(fact_2458_add__is__0,axiom,
% 5.05/5.29 ! [M: nat,N2: nat] :
% 5.05/5.29 ( ( ( plus_plus_nat @ M @ N2 )
% 5.05/5.29 = zero_zero_nat )
% 5.05/5.29 = ( ( M = zero_zero_nat )
% 5.05/5.29 & ( N2 = zero_zero_nat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_is_0
% 5.05/5.29 thf(fact_2459_minus__mod__self2,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.05/5.29 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % minus_mod_self2
% 5.05/5.29 thf(fact_2460_minus__mod__self2,axiom,
% 5.05/5.29 ! [A: code_integer,B: code_integer] :
% 5.05/5.29 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 5.05/5.29 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % minus_mod_self2
% 5.05/5.29 thf(fact_2461_mult__cancel2,axiom,
% 5.05/5.29 ! [M: nat,K: nat,N2: nat] :
% 5.05/5.29 ( ( ( times_times_nat @ M @ K )
% 5.05/5.29 = ( times_times_nat @ N2 @ K ) )
% 5.05/5.29 = ( ( M = N2 )
% 5.05/5.29 | ( K = zero_zero_nat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel2
% 5.05/5.29 thf(fact_2462_mult__cancel1,axiom,
% 5.05/5.29 ! [K: nat,M: nat,N2: nat] :
% 5.05/5.29 ( ( ( times_times_nat @ K @ M )
% 5.05/5.29 = ( times_times_nat @ K @ N2 ) )
% 5.05/5.29 = ( ( M = N2 )
% 5.05/5.29 | ( K = zero_zero_nat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel1
% 5.05/5.29 thf(fact_2463_mult__0__right,axiom,
% 5.05/5.29 ! [M: nat] :
% 5.05/5.29 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % mult_0_right
% 5.05/5.29 thf(fact_2464_mult__is__0,axiom,
% 5.05/5.29 ! [M: nat,N2: nat] :
% 5.05/5.29 ( ( ( times_times_nat @ M @ N2 )
% 5.05/5.29 = zero_zero_nat )
% 5.05/5.29 = ( ( M = zero_zero_nat )
% 5.05/5.29 | ( N2 = zero_zero_nat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_is_0
% 5.05/5.29 thf(fact_2465_diff__0__eq__0,axiom,
% 5.05/5.29 ! [N2: nat] :
% 5.05/5.29 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % diff_0_eq_0
% 5.05/5.29 thf(fact_2466_diff__self__eq__0,axiom,
% 5.05/5.29 ! [M: nat] :
% 5.05/5.29 ( ( minus_minus_nat @ M @ M )
% 5.05/5.29 = zero_zero_nat ) ).
% 5.05/5.29
% 5.05/5.29 % diff_self_eq_0
% 5.05/5.29 thf(fact_2467_mod__less,axiom,
% 5.05/5.29 ! [M: nat,N2: nat] :
% 5.05/5.29 ( ( ord_less_nat @ M @ N2 )
% 5.05/5.29 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.05/5.29 = M ) ) ).
% 5.05/5.29
% 5.05/5.29 % mod_less
% 5.05/5.29 thf(fact_2468_max__nat_Oeq__neutr__iff,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ( ord_max_nat @ A @ B )
% 5.05/5.29 = zero_zero_nat )
% 5.05/5.29 = ( ( A = zero_zero_nat )
% 5.05/5.29 & ( B = zero_zero_nat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_nat.eq_neutr_iff
% 5.05/5.29 thf(fact_2469_max__nat_Oleft__neutral,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % max_nat.left_neutral
% 5.05/5.29 thf(fact_2470_max__nat_Oneutr__eq__iff,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( zero_zero_nat
% 5.05/5.29 = ( ord_max_nat @ A @ B ) )
% 5.05/5.29 = ( ( A = zero_zero_nat )
% 5.05/5.29 & ( B = zero_zero_nat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % max_nat.neutr_eq_iff
% 5.05/5.29 thf(fact_2471_max__nat_Oright__neutral,axiom,
% 5.05/5.29 ! [A: nat] :
% 5.05/5.29 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.05/5.29 = A ) ).
% 5.05/5.29
% 5.05/5.29 % max_nat.right_neutral
% 5.05/5.29 thf(fact_2472_max__0L,axiom,
% 5.05/5.29 ! [N2: nat] :
% 5.05/5.29 ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 5.05/5.29 = N2 ) ).
% 5.05/5.29
% 5.05/5.29 % max_0L
% 5.05/5.29 thf(fact_2473_max__0R,axiom,
% 5.05/5.29 ! [N2: nat] :
% 5.05/5.29 ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 5.05/5.29 = N2 ) ).
% 5.05/5.29
% 5.05/5.29 % max_0R
% 5.05/5.29 thf(fact_2474_add__le__same__cancel1,axiom,
% 5.05/5.29 ! [B: real,A: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.05/5.29 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_same_cancel1
% 5.05/5.29 thf(fact_2475_add__le__same__cancel1,axiom,
% 5.05/5.29 ! [B: rat,A: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.05/5.29 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_same_cancel1
% 5.05/5.29 thf(fact_2476_add__le__same__cancel1,axiom,
% 5.05/5.29 ! [B: nat,A: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.05/5.29 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_same_cancel1
% 5.05/5.29 thf(fact_2477_add__le__same__cancel1,axiom,
% 5.05/5.29 ! [B: int,A: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.05/5.29 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_same_cancel1
% 5.05/5.29 thf(fact_2478_add__le__same__cancel2,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.05/5.29 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_same_cancel2
% 5.05/5.29 thf(fact_2479_add__le__same__cancel2,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.05/5.29 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_same_cancel2
% 5.05/5.29 thf(fact_2480_add__le__same__cancel2,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.05/5.29 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_same_cancel2
% 5.05/5.29 thf(fact_2481_add__le__same__cancel2,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.05/5.29 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_le_same_cancel2
% 5.05/5.29 thf(fact_2482_le__add__same__cancel1,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.05/5.29 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_add_same_cancel1
% 5.05/5.29 thf(fact_2483_le__add__same__cancel1,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.05/5.29 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_add_same_cancel1
% 5.05/5.29 thf(fact_2484_le__add__same__cancel1,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.05/5.29 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_add_same_cancel1
% 5.05/5.29 thf(fact_2485_le__add__same__cancel1,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.05/5.29 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_add_same_cancel1
% 5.05/5.29 thf(fact_2486_le__add__same__cancel2,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.05/5.29 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_add_same_cancel2
% 5.05/5.29 thf(fact_2487_le__add__same__cancel2,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.05/5.29 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_add_same_cancel2
% 5.05/5.29 thf(fact_2488_le__add__same__cancel2,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.05/5.29 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_add_same_cancel2
% 5.05/5.29 thf(fact_2489_le__add__same__cancel2,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.05/5.29 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % le_add_same_cancel2
% 5.05/5.29 thf(fact_2490_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.05/5.29 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % double_add_le_zero_iff_single_add_le_zero
% 5.05/5.29 thf(fact_2491_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.05/5.29 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % double_add_le_zero_iff_single_add_le_zero
% 5.05/5.29 thf(fact_2492_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.05/5.29 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % double_add_le_zero_iff_single_add_le_zero
% 5.05/5.29 thf(fact_2493_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.05/5.29 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % zero_le_double_add_iff_zero_le_single_add
% 5.05/5.29 thf(fact_2494_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.05/5.29 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % zero_le_double_add_iff_zero_le_single_add
% 5.05/5.29 thf(fact_2495_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.05/5.29 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % zero_le_double_add_iff_zero_le_single_add
% 5.05/5.29 thf(fact_2496_add__less__same__cancel1,axiom,
% 5.05/5.29 ! [B: real,A: real] :
% 5.05/5.29 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.05/5.29 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_same_cancel1
% 5.05/5.29 thf(fact_2497_add__less__same__cancel1,axiom,
% 5.05/5.29 ! [B: rat,A: rat] :
% 5.05/5.29 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.05/5.29 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_same_cancel1
% 5.05/5.29 thf(fact_2498_add__less__same__cancel1,axiom,
% 5.05/5.29 ! [B: nat,A: nat] :
% 5.05/5.29 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.05/5.29 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_same_cancel1
% 5.05/5.29 thf(fact_2499_add__less__same__cancel1,axiom,
% 5.05/5.29 ! [B: int,A: int] :
% 5.05/5.29 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.05/5.29 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_same_cancel1
% 5.05/5.29 thf(fact_2500_add__less__same__cancel2,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.05/5.29 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_same_cancel2
% 5.05/5.29 thf(fact_2501_add__less__same__cancel2,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.05/5.29 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_same_cancel2
% 5.05/5.29 thf(fact_2502_add__less__same__cancel2,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.05/5.29 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_same_cancel2
% 5.05/5.29 thf(fact_2503_add__less__same__cancel2,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.05/5.29 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % add_less_same_cancel2
% 5.05/5.29 thf(fact_2504_less__add__same__cancel1,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.05/5.29 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_add_same_cancel1
% 5.05/5.29 thf(fact_2505_less__add__same__cancel1,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.05/5.29 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_add_same_cancel1
% 5.05/5.29 thf(fact_2506_less__add__same__cancel1,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.05/5.29 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_add_same_cancel1
% 5.05/5.29 thf(fact_2507_less__add__same__cancel1,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.05/5.29 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_add_same_cancel1
% 5.05/5.29 thf(fact_2508_less__add__same__cancel2,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.05/5.29 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_add_same_cancel2
% 5.05/5.29 thf(fact_2509_less__add__same__cancel2,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.05/5.29 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_add_same_cancel2
% 5.05/5.29 thf(fact_2510_less__add__same__cancel2,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.05/5.29 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_add_same_cancel2
% 5.05/5.29 thf(fact_2511_less__add__same__cancel2,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.05/5.29 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.05/5.29
% 5.05/5.29 % less_add_same_cancel2
% 5.05/5.29 thf(fact_2512_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.05/5.29 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.05/5.29
% 5.05/5.29 % double_add_less_zero_iff_single_add_less_zero
% 5.05/5.29 thf(fact_2513_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.05/5.29 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.05/5.29
% 5.05/5.29 % double_add_less_zero_iff_single_add_less_zero
% 5.05/5.29 thf(fact_2514_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.05/5.29 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.05/5.29
% 5.05/5.29 % double_add_less_zero_iff_single_add_less_zero
% 5.05/5.29 thf(fact_2515_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.05/5.29 ! [A: real] :
% 5.05/5.29 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.05/5.29 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % zero_less_double_add_iff_zero_less_single_add
% 5.05/5.29 thf(fact_2516_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.05/5.29 ! [A: rat] :
% 5.05/5.29 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.05/5.29 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % zero_less_double_add_iff_zero_less_single_add
% 5.05/5.29 thf(fact_2517_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.05/5.29 ! [A: int] :
% 5.05/5.29 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.05/5.29 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % zero_less_double_add_iff_zero_less_single_add
% 5.05/5.29 thf(fact_2518_diff__ge__0__iff__ge,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.05/5.29 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_ge_0_iff_ge
% 5.05/5.29 thf(fact_2519_diff__ge__0__iff__ge,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.05/5.29 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_ge_0_iff_ge
% 5.05/5.29 thf(fact_2520_diff__ge__0__iff__ge,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.05/5.29 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_ge_0_iff_ge
% 5.05/5.29 thf(fact_2521_diff__gt__0__iff__gt,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.05/5.29 = ( ord_less_real @ B @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_gt_0_iff_gt
% 5.05/5.29 thf(fact_2522_diff__gt__0__iff__gt,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.05/5.29 = ( ord_less_rat @ B @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_gt_0_iff_gt
% 5.05/5.29 thf(fact_2523_diff__gt__0__iff__gt,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.05/5.29 = ( ord_less_int @ B @ A ) ) ).
% 5.05/5.29
% 5.05/5.29 % diff_gt_0_iff_gt
% 5.05/5.29 thf(fact_2524_sum__squares__eq__zero__iff,axiom,
% 5.05/5.29 ! [X: real,Y: real] :
% 5.05/5.29 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.05/5.29 = zero_zero_real )
% 5.05/5.29 = ( ( X = zero_zero_real )
% 5.05/5.29 & ( Y = zero_zero_real ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % sum_squares_eq_zero_iff
% 5.05/5.29 thf(fact_2525_sum__squares__eq__zero__iff,axiom,
% 5.05/5.29 ! [X: rat,Y: rat] :
% 5.05/5.29 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.05/5.29 = zero_zero_rat )
% 5.05/5.29 = ( ( X = zero_zero_rat )
% 5.05/5.29 & ( Y = zero_zero_rat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % sum_squares_eq_zero_iff
% 5.05/5.29 thf(fact_2526_sum__squares__eq__zero__iff,axiom,
% 5.05/5.29 ! [X: int,Y: int] :
% 5.05/5.29 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.05/5.29 = zero_zero_int )
% 5.05/5.29 = ( ( X = zero_zero_int )
% 5.05/5.29 & ( Y = zero_zero_int ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % sum_squares_eq_zero_iff
% 5.05/5.29 thf(fact_2527_mult__cancel__right2,axiom,
% 5.05/5.29 ! [A: complex,C: complex] :
% 5.05/5.29 ( ( ( times_times_complex @ A @ C )
% 5.05/5.29 = C )
% 5.05/5.29 = ( ( C = zero_zero_complex )
% 5.05/5.29 | ( A = one_one_complex ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right2
% 5.05/5.29 thf(fact_2528_mult__cancel__right2,axiom,
% 5.05/5.29 ! [A: real,C: real] :
% 5.05/5.29 ( ( ( times_times_real @ A @ C )
% 5.05/5.29 = C )
% 5.05/5.29 = ( ( C = zero_zero_real )
% 5.05/5.29 | ( A = one_one_real ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right2
% 5.05/5.29 thf(fact_2529_mult__cancel__right2,axiom,
% 5.05/5.29 ! [A: rat,C: rat] :
% 5.05/5.29 ( ( ( times_times_rat @ A @ C )
% 5.05/5.29 = C )
% 5.05/5.29 = ( ( C = zero_zero_rat )
% 5.05/5.29 | ( A = one_one_rat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right2
% 5.05/5.29 thf(fact_2530_mult__cancel__right2,axiom,
% 5.05/5.29 ! [A: int,C: int] :
% 5.05/5.29 ( ( ( times_times_int @ A @ C )
% 5.05/5.29 = C )
% 5.05/5.29 = ( ( C = zero_zero_int )
% 5.05/5.29 | ( A = one_one_int ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right2
% 5.05/5.29 thf(fact_2531_mult__cancel__right1,axiom,
% 5.05/5.29 ! [C: complex,B: complex] :
% 5.05/5.29 ( ( C
% 5.05/5.29 = ( times_times_complex @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_complex )
% 5.05/5.29 | ( B = one_one_complex ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right1
% 5.05/5.29 thf(fact_2532_mult__cancel__right1,axiom,
% 5.05/5.29 ! [C: real,B: real] :
% 5.05/5.29 ( ( C
% 5.05/5.29 = ( times_times_real @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_real )
% 5.05/5.29 | ( B = one_one_real ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right1
% 5.05/5.29 thf(fact_2533_mult__cancel__right1,axiom,
% 5.05/5.29 ! [C: rat,B: rat] :
% 5.05/5.29 ( ( C
% 5.05/5.29 = ( times_times_rat @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_rat )
% 5.05/5.29 | ( B = one_one_rat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right1
% 5.05/5.29 thf(fact_2534_mult__cancel__right1,axiom,
% 5.05/5.29 ! [C: int,B: int] :
% 5.05/5.29 ( ( C
% 5.05/5.29 = ( times_times_int @ B @ C ) )
% 5.05/5.29 = ( ( C = zero_zero_int )
% 5.05/5.29 | ( B = one_one_int ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_right1
% 5.05/5.29 thf(fact_2535_mult__cancel__left2,axiom,
% 5.05/5.29 ! [C: complex,A: complex] :
% 5.05/5.29 ( ( ( times_times_complex @ C @ A )
% 5.05/5.29 = C )
% 5.05/5.29 = ( ( C = zero_zero_complex )
% 5.05/5.29 | ( A = one_one_complex ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left2
% 5.05/5.29 thf(fact_2536_mult__cancel__left2,axiom,
% 5.05/5.29 ! [C: real,A: real] :
% 5.05/5.29 ( ( ( times_times_real @ C @ A )
% 5.05/5.29 = C )
% 5.05/5.29 = ( ( C = zero_zero_real )
% 5.05/5.29 | ( A = one_one_real ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left2
% 5.05/5.29 thf(fact_2537_mult__cancel__left2,axiom,
% 5.05/5.29 ! [C: rat,A: rat] :
% 5.05/5.29 ( ( ( times_times_rat @ C @ A )
% 5.05/5.29 = C )
% 5.05/5.29 = ( ( C = zero_zero_rat )
% 5.05/5.29 | ( A = one_one_rat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left2
% 5.05/5.29 thf(fact_2538_mult__cancel__left2,axiom,
% 5.05/5.29 ! [C: int,A: int] :
% 5.05/5.29 ( ( ( times_times_int @ C @ A )
% 5.05/5.29 = C )
% 5.05/5.29 = ( ( C = zero_zero_int )
% 5.05/5.29 | ( A = one_one_int ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left2
% 5.05/5.29 thf(fact_2539_mult__cancel__left1,axiom,
% 5.05/5.29 ! [C: complex,B: complex] :
% 5.05/5.29 ( ( C
% 5.05/5.29 = ( times_times_complex @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_complex )
% 5.05/5.29 | ( B = one_one_complex ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left1
% 5.05/5.29 thf(fact_2540_mult__cancel__left1,axiom,
% 5.05/5.29 ! [C: real,B: real] :
% 5.05/5.29 ( ( C
% 5.05/5.29 = ( times_times_real @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_real )
% 5.05/5.29 | ( B = one_one_real ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left1
% 5.05/5.29 thf(fact_2541_mult__cancel__left1,axiom,
% 5.05/5.29 ! [C: rat,B: rat] :
% 5.05/5.29 ( ( C
% 5.05/5.29 = ( times_times_rat @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_rat )
% 5.05/5.29 | ( B = one_one_rat ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left1
% 5.05/5.29 thf(fact_2542_mult__cancel__left1,axiom,
% 5.05/5.29 ! [C: int,B: int] :
% 5.05/5.29 ( ( C
% 5.05/5.29 = ( times_times_int @ C @ B ) )
% 5.05/5.29 = ( ( C = zero_zero_int )
% 5.05/5.29 | ( B = one_one_int ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % mult_cancel_left1
% 5.05/5.29 thf(fact_2543_nonzero__mult__div__cancel__right,axiom,
% 5.05/5.29 ! [B: complex,A: complex] :
% 5.05/5.29 ( ( B != zero_zero_complex )
% 5.05/5.29 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.05/5.29 = A ) ) ).
% 5.05/5.29
% 5.05/5.29 % nonzero_mult_div_cancel_right
% 5.05/5.29 thf(fact_2544_nonzero__mult__div__cancel__right,axiom,
% 5.05/5.29 ! [B: real,A: real] :
% 5.05/5.29 ( ( B != zero_zero_real )
% 5.05/5.29 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.05/5.29 = A ) ) ).
% 5.05/5.29
% 5.05/5.29 % nonzero_mult_div_cancel_right
% 5.05/5.29 thf(fact_2545_nonzero__mult__div__cancel__right,axiom,
% 5.05/5.29 ! [B: rat,A: rat] :
% 5.05/5.29 ( ( B != zero_zero_rat )
% 5.05/5.29 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.05/5.29 = A ) ) ).
% 5.05/5.29
% 5.05/5.29 % nonzero_mult_div_cancel_right
% 5.05/5.29 thf(fact_2546_nonzero__mult__div__cancel__right,axiom,
% 5.05/5.29 ! [B: nat,A: nat] :
% 5.05/5.29 ( ( B != zero_zero_nat )
% 5.05/5.29 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.05/5.29 = A ) ) ).
% 5.05/5.29
% 5.05/5.29 % nonzero_mult_div_cancel_right
% 5.05/5.29 thf(fact_2547_nonzero__mult__div__cancel__right,axiom,
% 5.05/5.29 ! [B: int,A: int] :
% 5.05/5.29 ( ( B != zero_zero_int )
% 5.05/5.29 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.05/5.29 = A ) ) ).
% 5.05/5.29
% 5.05/5.29 % nonzero_mult_div_cancel_right
% 5.05/5.29 thf(fact_2548_nonzero__mult__div__cancel__left,axiom,
% 5.05/5.29 ! [A: complex,B: complex] :
% 5.05/5.29 ( ( A != zero_zero_complex )
% 5.05/5.29 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.05/5.29 = B ) ) ).
% 5.05/5.29
% 5.05/5.29 % nonzero_mult_div_cancel_left
% 5.05/5.29 thf(fact_2549_nonzero__mult__div__cancel__left,axiom,
% 5.05/5.29 ! [A: real,B: real] :
% 5.05/5.29 ( ( A != zero_zero_real )
% 5.05/5.29 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.05/5.29 = B ) ) ).
% 5.05/5.29
% 5.05/5.29 % nonzero_mult_div_cancel_left
% 5.05/5.29 thf(fact_2550_nonzero__mult__div__cancel__left,axiom,
% 5.05/5.29 ! [A: rat,B: rat] :
% 5.05/5.29 ( ( A != zero_zero_rat )
% 5.05/5.29 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.05/5.29 = B ) ) ).
% 5.05/5.29
% 5.05/5.29 % nonzero_mult_div_cancel_left
% 5.05/5.29 thf(fact_2551_nonzero__mult__div__cancel__left,axiom,
% 5.05/5.29 ! [A: nat,B: nat] :
% 5.05/5.29 ( ( A != zero_zero_nat )
% 5.05/5.29 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.05/5.29 = B ) ) ).
% 5.05/5.29
% 5.05/5.29 % nonzero_mult_div_cancel_left
% 5.05/5.29 thf(fact_2552_nonzero__mult__div__cancel__left,axiom,
% 5.05/5.29 ! [A: int,B: int] :
% 5.05/5.29 ( ( A != zero_zero_int )
% 5.05/5.29 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.05/5.29 = B ) ) ).
% 5.05/5.29
% 5.05/5.29 % nonzero_mult_div_cancel_left
% 5.05/5.29 thf(fact_2553_div__mult__mult1__if,axiom,
% 5.05/5.29 ! [C: nat,A: nat,B: nat] :
% 5.05/5.29 ( ( ( C = zero_zero_nat )
% 5.05/5.29 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.05/5.29 = zero_zero_nat ) )
% 5.05/5.29 & ( ( C != zero_zero_nat )
% 5.05/5.29 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.05/5.29 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.05/5.29
% 5.05/5.29 % div_mult_mult1_if
% 5.05/5.29 thf(fact_2554_div__mult__mult1__if,axiom,
% 5.05/5.29 ! [C: int,A: int,B: int] :
% 5.05/5.29 ( ( ( C = zero_zero_int )
% 5.05/5.29 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.05/5.29 = zero_zero_int ) )
% 5.05/5.29 & ( ( C != zero_zero_int )
% 5.05/5.29 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.05/5.30 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % div_mult_mult1_if
% 5.05/5.30 thf(fact_2555_div__mult__mult2,axiom,
% 5.05/5.30 ! [C: nat,A: nat,B: nat] :
% 5.05/5.30 ( ( C != zero_zero_nat )
% 5.05/5.30 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.05/5.30 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % div_mult_mult2
% 5.05/5.30 thf(fact_2556_div__mult__mult2,axiom,
% 5.05/5.30 ! [C: int,A: int,B: int] :
% 5.05/5.30 ( ( C != zero_zero_int )
% 5.05/5.30 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.05/5.30 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % div_mult_mult2
% 5.05/5.30 thf(fact_2557_div__mult__mult1,axiom,
% 5.05/5.30 ! [C: nat,A: nat,B: nat] :
% 5.05/5.30 ( ( C != zero_zero_nat )
% 5.05/5.30 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.05/5.30 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % div_mult_mult1
% 5.05/5.30 thf(fact_2558_div__mult__mult1,axiom,
% 5.05/5.30 ! [C: int,A: int,B: int] :
% 5.05/5.30 ( ( C != zero_zero_int )
% 5.05/5.30 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.05/5.30 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % div_mult_mult1
% 5.05/5.30 thf(fact_2559_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.05/5.30 ! [C: complex,A: complex,B: complex] :
% 5.05/5.30 ( ( C != zero_zero_complex )
% 5.05/5.30 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.05/5.30 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_right2
% 5.05/5.30 thf(fact_2560_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.05/5.30 ! [C: real,A: real,B: real] :
% 5.05/5.30 ( ( C != zero_zero_real )
% 5.05/5.30 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.05/5.30 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_right2
% 5.05/5.30 thf(fact_2561_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.05/5.30 ! [C: rat,A: rat,B: rat] :
% 5.05/5.30 ( ( C != zero_zero_rat )
% 5.05/5.30 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.05/5.30 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_right2
% 5.05/5.30 thf(fact_2562_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.05/5.30 ! [C: complex,A: complex,B: complex] :
% 5.05/5.30 ( ( C != zero_zero_complex )
% 5.05/5.30 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.05/5.30 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_right
% 5.05/5.30 thf(fact_2563_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.05/5.30 ! [C: real,A: real,B: real] :
% 5.05/5.30 ( ( C != zero_zero_real )
% 5.05/5.30 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.05/5.30 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_right
% 5.05/5.30 thf(fact_2564_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.05/5.30 ! [C: rat,A: rat,B: rat] :
% 5.05/5.30 ( ( C != zero_zero_rat )
% 5.05/5.30 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.05/5.30 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_right
% 5.05/5.30 thf(fact_2565_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.05/5.30 ! [C: complex,A: complex,B: complex] :
% 5.05/5.30 ( ( C != zero_zero_complex )
% 5.05/5.30 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.05/5.30 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_left2
% 5.05/5.30 thf(fact_2566_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.05/5.30 ! [C: real,A: real,B: real] :
% 5.05/5.30 ( ( C != zero_zero_real )
% 5.05/5.30 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.05/5.30 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_left2
% 5.05/5.30 thf(fact_2567_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.05/5.30 ! [C: rat,A: rat,B: rat] :
% 5.05/5.30 ( ( C != zero_zero_rat )
% 5.05/5.30 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.05/5.30 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_left2
% 5.05/5.30 thf(fact_2568_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.05/5.30 ! [C: complex,A: complex,B: complex] :
% 5.05/5.30 ( ( C != zero_zero_complex )
% 5.05/5.30 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.05/5.30 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_left
% 5.05/5.30 thf(fact_2569_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.05/5.30 ! [C: real,A: real,B: real] :
% 5.05/5.30 ( ( C != zero_zero_real )
% 5.05/5.30 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.05/5.30 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_left
% 5.05/5.30 thf(fact_2570_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.05/5.30 ! [C: rat,A: rat,B: rat] :
% 5.05/5.30 ( ( C != zero_zero_rat )
% 5.05/5.30 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.05/5.30 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % nonzero_mult_divide_mult_cancel_left
% 5.05/5.30 thf(fact_2571_mult__divide__mult__cancel__left__if,axiom,
% 5.05/5.30 ! [C: complex,A: complex,B: complex] :
% 5.05/5.30 ( ( ( C = zero_zero_complex )
% 5.05/5.30 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.05/5.30 = zero_zero_complex ) )
% 5.05/5.30 & ( ( C != zero_zero_complex )
% 5.05/5.30 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.05/5.30 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % mult_divide_mult_cancel_left_if
% 5.05/5.30 thf(fact_2572_mult__divide__mult__cancel__left__if,axiom,
% 5.05/5.30 ! [C: real,A: real,B: real] :
% 5.05/5.30 ( ( ( C = zero_zero_real )
% 5.05/5.30 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.05/5.30 = zero_zero_real ) )
% 5.05/5.30 & ( ( C != zero_zero_real )
% 5.05/5.30 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.05/5.30 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % mult_divide_mult_cancel_left_if
% 5.05/5.30 thf(fact_2573_mult__divide__mult__cancel__left__if,axiom,
% 5.05/5.30 ! [C: rat,A: rat,B: rat] :
% 5.05/5.30 ( ( ( C = zero_zero_rat )
% 5.05/5.30 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.05/5.30 = zero_zero_rat ) )
% 5.05/5.30 & ( ( C != zero_zero_rat )
% 5.05/5.30 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.05/5.30 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % mult_divide_mult_cancel_left_if
% 5.05/5.30 thf(fact_2574_diff__add__zero,axiom,
% 5.05/5.30 ! [A: nat,B: nat] :
% 5.05/5.30 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.05/5.30 = zero_zero_nat ) ).
% 5.05/5.30
% 5.05/5.30 % diff_add_zero
% 5.05/5.30 thf(fact_2575_diff__numeral__special_I9_J,axiom,
% 5.05/5.30 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.05/5.30 = zero_zero_complex ) ).
% 5.05/5.30
% 5.05/5.30 % diff_numeral_special(9)
% 5.05/5.30 thf(fact_2576_diff__numeral__special_I9_J,axiom,
% 5.05/5.30 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.05/5.30 = zero_zero_real ) ).
% 5.05/5.30
% 5.05/5.30 % diff_numeral_special(9)
% 5.05/5.30 thf(fact_2577_diff__numeral__special_I9_J,axiom,
% 5.05/5.30 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.05/5.30 = zero_zero_rat ) ).
% 5.05/5.30
% 5.05/5.30 % diff_numeral_special(9)
% 5.05/5.30 thf(fact_2578_diff__numeral__special_I9_J,axiom,
% 5.05/5.30 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.05/5.30 = zero_zero_int ) ).
% 5.05/5.30
% 5.05/5.30 % diff_numeral_special(9)
% 5.05/5.30 thf(fact_2579_div__self,axiom,
% 5.05/5.30 ! [A: complex] :
% 5.05/5.30 ( ( A != zero_zero_complex )
% 5.05/5.30 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.05/5.30 = one_one_complex ) ) ).
% 5.05/5.30
% 5.05/5.30 % div_self
% 5.05/5.30 thf(fact_2580_div__self,axiom,
% 5.05/5.30 ! [A: real] :
% 5.05/5.30 ( ( A != zero_zero_real )
% 5.05/5.30 => ( ( divide_divide_real @ A @ A )
% 5.05/5.30 = one_one_real ) ) ).
% 5.05/5.30
% 5.05/5.30 % div_self
% 5.05/5.30 thf(fact_2581_div__self,axiom,
% 5.05/5.30 ! [A: rat] :
% 5.05/5.30 ( ( A != zero_zero_rat )
% 5.05/5.30 => ( ( divide_divide_rat @ A @ A )
% 5.05/5.30 = one_one_rat ) ) ).
% 5.05/5.30
% 5.05/5.30 % div_self
% 5.05/5.30 thf(fact_2582_div__self,axiom,
% 5.05/5.30 ! [A: nat] :
% 5.05/5.30 ( ( A != zero_zero_nat )
% 5.05/5.30 => ( ( divide_divide_nat @ A @ A )
% 5.05/5.30 = one_one_nat ) ) ).
% 5.05/5.30
% 5.05/5.30 % div_self
% 5.05/5.30 thf(fact_2583_div__self,axiom,
% 5.05/5.30 ! [A: int] :
% 5.05/5.30 ( ( A != zero_zero_int )
% 5.05/5.30 => ( ( divide_divide_int @ A @ A )
% 5.05/5.30 = one_one_int ) ) ).
% 5.05/5.30
% 5.05/5.30 % div_self
% 5.05/5.30 thf(fact_2584_divide__eq__1__iff,axiom,
% 5.05/5.30 ! [A: complex,B: complex] :
% 5.05/5.30 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.05/5.30 = one_one_complex )
% 5.05/5.30 = ( ( B != zero_zero_complex )
% 5.05/5.30 & ( A = B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_eq_1_iff
% 5.05/5.30 thf(fact_2585_divide__eq__1__iff,axiom,
% 5.05/5.30 ! [A: real,B: real] :
% 5.05/5.30 ( ( ( divide_divide_real @ A @ B )
% 5.05/5.30 = one_one_real )
% 5.05/5.30 = ( ( B != zero_zero_real )
% 5.05/5.30 & ( A = B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_eq_1_iff
% 5.05/5.30 thf(fact_2586_divide__eq__1__iff,axiom,
% 5.05/5.30 ! [A: rat,B: rat] :
% 5.05/5.30 ( ( ( divide_divide_rat @ A @ B )
% 5.05/5.30 = one_one_rat )
% 5.05/5.30 = ( ( B != zero_zero_rat )
% 5.05/5.30 & ( A = B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_eq_1_iff
% 5.05/5.30 thf(fact_2587_one__eq__divide__iff,axiom,
% 5.05/5.30 ! [A: complex,B: complex] :
% 5.05/5.30 ( ( one_one_complex
% 5.05/5.30 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.05/5.30 = ( ( B != zero_zero_complex )
% 5.05/5.30 & ( A = B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % one_eq_divide_iff
% 5.05/5.30 thf(fact_2588_one__eq__divide__iff,axiom,
% 5.05/5.30 ! [A: real,B: real] :
% 5.05/5.30 ( ( one_one_real
% 5.05/5.30 = ( divide_divide_real @ A @ B ) )
% 5.05/5.30 = ( ( B != zero_zero_real )
% 5.05/5.30 & ( A = B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % one_eq_divide_iff
% 5.05/5.30 thf(fact_2589_one__eq__divide__iff,axiom,
% 5.05/5.30 ! [A: rat,B: rat] :
% 5.05/5.30 ( ( one_one_rat
% 5.05/5.30 = ( divide_divide_rat @ A @ B ) )
% 5.05/5.30 = ( ( B != zero_zero_rat )
% 5.05/5.30 & ( A = B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % one_eq_divide_iff
% 5.05/5.30 thf(fact_2590_divide__self,axiom,
% 5.05/5.30 ! [A: complex] :
% 5.05/5.30 ( ( A != zero_zero_complex )
% 5.05/5.30 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.05/5.30 = one_one_complex ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_self
% 5.05/5.30 thf(fact_2591_divide__self,axiom,
% 5.05/5.30 ! [A: real] :
% 5.05/5.30 ( ( A != zero_zero_real )
% 5.05/5.30 => ( ( divide_divide_real @ A @ A )
% 5.05/5.30 = one_one_real ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_self
% 5.05/5.30 thf(fact_2592_divide__self,axiom,
% 5.05/5.30 ! [A: rat] :
% 5.05/5.30 ( ( A != zero_zero_rat )
% 5.05/5.30 => ( ( divide_divide_rat @ A @ A )
% 5.05/5.30 = one_one_rat ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_self
% 5.05/5.30 thf(fact_2593_divide__self__if,axiom,
% 5.05/5.30 ! [A: complex] :
% 5.05/5.30 ( ( ( A = zero_zero_complex )
% 5.05/5.30 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.05/5.30 = zero_zero_complex ) )
% 5.05/5.30 & ( ( A != zero_zero_complex )
% 5.05/5.30 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.05/5.30 = one_one_complex ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_self_if
% 5.05/5.30 thf(fact_2594_divide__self__if,axiom,
% 5.05/5.30 ! [A: real] :
% 5.05/5.30 ( ( ( A = zero_zero_real )
% 5.05/5.30 => ( ( divide_divide_real @ A @ A )
% 5.05/5.30 = zero_zero_real ) )
% 5.05/5.30 & ( ( A != zero_zero_real )
% 5.05/5.30 => ( ( divide_divide_real @ A @ A )
% 5.05/5.30 = one_one_real ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_self_if
% 5.05/5.30 thf(fact_2595_divide__self__if,axiom,
% 5.05/5.30 ! [A: rat] :
% 5.05/5.30 ( ( ( A = zero_zero_rat )
% 5.05/5.30 => ( ( divide_divide_rat @ A @ A )
% 5.05/5.30 = zero_zero_rat ) )
% 5.05/5.30 & ( ( A != zero_zero_rat )
% 5.05/5.30 => ( ( divide_divide_rat @ A @ A )
% 5.05/5.30 = one_one_rat ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_self_if
% 5.05/5.30 thf(fact_2596_divide__eq__eq__1,axiom,
% 5.05/5.30 ! [B: real,A: real] :
% 5.05/5.30 ( ( ( divide_divide_real @ B @ A )
% 5.05/5.30 = one_one_real )
% 5.05/5.30 = ( ( A != zero_zero_real )
% 5.05/5.30 & ( A = B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_eq_eq_1
% 5.05/5.30 thf(fact_2597_divide__eq__eq__1,axiom,
% 5.05/5.30 ! [B: rat,A: rat] :
% 5.05/5.30 ( ( ( divide_divide_rat @ B @ A )
% 5.05/5.30 = one_one_rat )
% 5.05/5.30 = ( ( A != zero_zero_rat )
% 5.05/5.30 & ( A = B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % divide_eq_eq_1
% 5.05/5.30 thf(fact_2598_eq__divide__eq__1,axiom,
% 5.05/5.30 ! [B: real,A: real] :
% 5.05/5.30 ( ( one_one_real
% 5.05/5.30 = ( divide_divide_real @ B @ A ) )
% 5.05/5.30 = ( ( A != zero_zero_real )
% 5.05/5.30 & ( A = B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % eq_divide_eq_1
% 5.05/5.30 thf(fact_2599_eq__divide__eq__1,axiom,
% 5.05/5.30 ! [B: rat,A: rat] :
% 5.05/5.30 ( ( one_one_rat
% 5.05/5.30 = ( divide_divide_rat @ B @ A ) )
% 5.05/5.30 = ( ( A != zero_zero_rat )
% 5.05/5.30 & ( A = B ) ) ) ).
% 5.05/5.30
% 5.05/5.30 % eq_divide_eq_1
% 5.05/5.30 thf(fact_2600_one__divide__eq__0__iff,axiom,
% 5.05/5.30 ! [A: real] :
% 5.05/5.30 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.05/5.30 = zero_zero_real )
% 5.05/5.30 = ( A = zero_zero_real ) ) ).
% 5.05/5.30
% 5.05/5.30 % one_divide_eq_0_iff
% 5.05/5.30 thf(fact_2601_one__divide__eq__0__iff,axiom,
% 5.05/5.30 ! [A: rat] :
% 5.05/5.30 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.05/5.30 = zero_zero_rat )
% 5.05/5.30 = ( A = zero_zero_rat ) ) ).
% 5.05/5.30
% 5.05/5.30 % one_divide_eq_0_iff
% 5.05/5.30 thf(fact_2602_zero__eq__1__divide__iff,axiom,
% 5.05/5.30 ! [A: real] :
% 5.05/5.30 ( ( zero_zero_real
% 5.05/5.30 = ( divide_divide_real @ one_one_real @ A ) )
% 5.05/5.30 = ( A = zero_zero_real ) ) ).
% 5.05/5.30
% 5.05/5.30 % zero_eq_1_divide_iff
% 5.05/5.30 thf(fact_2603_zero__eq__1__divide__iff,axiom,
% 5.05/5.30 ! [A: rat] :
% 5.05/5.30 ( ( zero_zero_rat
% 5.05/5.30 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.05/5.30 = ( A = zero_zero_rat ) ) ).
% 5.05/5.30
% 5.05/5.30 % zero_eq_1_divide_iff
% 5.05/5.30 thf(fact_2604_power__0__Suc,axiom,
% 5.05/5.30 ! [N2: nat] :
% 5.05/5.30 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N2 ) )
% 5.05/5.30 = zero_zero_rat ) ).
% 5.05/5.30
% 5.05/5.30 % power_0_Suc
% 5.05/5.30 thf(fact_2605_power__0__Suc,axiom,
% 5.05/5.30 ! [N2: nat] :
% 5.05/5.30 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.05/5.30 = zero_zero_nat ) ).
% 5.05/5.30
% 5.05/5.30 % power_0_Suc
% 5.05/5.30 thf(fact_2606_power__0__Suc,axiom,
% 5.05/5.30 ! [N2: nat] :
% 5.05/5.30 ( ( power_power_real @ zero_zero_real @ ( suc @ N2 ) )
% 5.05/5.30 = zero_zero_real ) ).
% 5.05/5.30
% 5.05/5.30 % power_0_Suc
% 5.05/5.30 thf(fact_2607_power__0__Suc,axiom,
% 5.05/5.30 ! [N2: nat] :
% 5.05/5.30 ( ( power_power_int @ zero_zero_int @ ( suc @ N2 ) )
% 5.05/5.30 = zero_zero_int ) ).
% 5.05/5.30
% 5.05/5.30 % power_0_Suc
% 5.05/5.30 thf(fact_2608_power__0__Suc,axiom,
% 5.05/5.30 ! [N2: nat] :
% 5.05/5.30 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N2 ) )
% 5.05/5.30 = zero_zero_complex ) ).
% 5.05/5.30
% 5.05/5.30 % power_0_Suc
% 5.05/5.30 thf(fact_2609_power__zero__numeral,axiom,
% 5.05/5.30 ! [K: num] :
% 5.05/5.30 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.05/5.30 = zero_zero_rat ) ).
% 5.05/5.30
% 5.05/5.30 % power_zero_numeral
% 5.05/5.30 thf(fact_2610_power__zero__numeral,axiom,
% 5.05/5.30 ! [K: num] :
% 5.05/5.30 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.05/5.30 = zero_zero_nat ) ).
% 5.05/5.30
% 5.05/5.30 % power_zero_numeral
% 5.05/5.30 thf(fact_2611_power__zero__numeral,axiom,
% 5.05/5.30 ! [K: num] :
% 5.05/5.30 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.05/5.30 = zero_zero_real ) ).
% 5.05/5.30
% 5.05/5.30 % power_zero_numeral
% 5.05/5.30 thf(fact_2612_power__zero__numeral,axiom,
% 5.05/5.30 ! [K: num] :
% 5.05/5.30 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.05/5.30 = zero_zero_int ) ).
% 5.05/5.30
% 5.05/5.30 % power_zero_numeral
% 5.05/5.30 thf(fact_2613_power__zero__numeral,axiom,
% 5.05/5.30 ! [K: num] :
% 5.05/5.30 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.05/5.30 = zero_zero_complex ) ).
% 5.05/5.30
% 5.05/5.30 % power_zero_numeral
% 5.05/5.30 thf(fact_2614_mod__mult__self1__is__0,axiom,
% 5.06/5.30 ! [B: nat,A: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self1_is_0
% 5.06/5.30 thf(fact_2615_mod__mult__self1__is__0,axiom,
% 5.06/5.30 ! [B: int,A: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.06/5.30 = zero_zero_int ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self1_is_0
% 5.06/5.30 thf(fact_2616_mod__mult__self1__is__0,axiom,
% 5.06/5.30 ! [B: code_integer,A: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.06/5.30 = zero_z3403309356797280102nteger ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self1_is_0
% 5.06/5.30 thf(fact_2617_mod__mult__self2__is__0,axiom,
% 5.06/5.30 ! [A: nat,B: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self2_is_0
% 5.06/5.30 thf(fact_2618_mod__mult__self2__is__0,axiom,
% 5.06/5.30 ! [A: int,B: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.06/5.30 = zero_zero_int ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self2_is_0
% 5.06/5.30 thf(fact_2619_mod__mult__self2__is__0,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.06/5.30 = zero_z3403309356797280102nteger ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self2_is_0
% 5.06/5.30 thf(fact_2620_mod__by__1,axiom,
% 5.06/5.30 ! [A: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % mod_by_1
% 5.06/5.30 thf(fact_2621_mod__by__1,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.06/5.30 = zero_zero_int ) ).
% 5.06/5.30
% 5.06/5.30 % mod_by_1
% 5.06/5.30 thf(fact_2622_mod__by__1,axiom,
% 5.06/5.30 ! [A: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.06/5.30 = zero_z3403309356797280102nteger ) ).
% 5.06/5.30
% 5.06/5.30 % mod_by_1
% 5.06/5.30 thf(fact_2623_bits__mod__by__1,axiom,
% 5.06/5.30 ! [A: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % bits_mod_by_1
% 5.06/5.30 thf(fact_2624_bits__mod__by__1,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.06/5.30 = zero_zero_int ) ).
% 5.06/5.30
% 5.06/5.30 % bits_mod_by_1
% 5.06/5.30 thf(fact_2625_bits__mod__by__1,axiom,
% 5.06/5.30 ! [A: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.06/5.30 = zero_z3403309356797280102nteger ) ).
% 5.06/5.30
% 5.06/5.30 % bits_mod_by_1
% 5.06/5.30 thf(fact_2626_power__Suc0__right,axiom,
% 5.06/5.30 ! [A: nat] :
% 5.06/5.30 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % power_Suc0_right
% 5.06/5.30 thf(fact_2627_power__Suc0__right,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % power_Suc0_right
% 5.06/5.30 thf(fact_2628_power__Suc0__right,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % power_Suc0_right
% 5.06/5.30 thf(fact_2629_power__Suc0__right,axiom,
% 5.06/5.30 ! [A: complex] :
% 5.06/5.30 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % power_Suc0_right
% 5.06/5.30 thf(fact_2630_bits__mod__div__trivial,axiom,
% 5.06/5.30 ! [A: nat,B: nat] :
% 5.06/5.30 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % bits_mod_div_trivial
% 5.06/5.30 thf(fact_2631_bits__mod__div__trivial,axiom,
% 5.06/5.30 ! [A: int,B: int] :
% 5.06/5.30 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.06/5.30 = zero_zero_int ) ).
% 5.06/5.30
% 5.06/5.30 % bits_mod_div_trivial
% 5.06/5.30 thf(fact_2632_bits__mod__div__trivial,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer] :
% 5.06/5.30 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.06/5.30 = zero_z3403309356797280102nteger ) ).
% 5.06/5.30
% 5.06/5.30 % bits_mod_div_trivial
% 5.06/5.30 thf(fact_2633_mod__div__trivial,axiom,
% 5.06/5.30 ! [A: nat,B: nat] :
% 5.06/5.30 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % mod_div_trivial
% 5.06/5.30 thf(fact_2634_mod__div__trivial,axiom,
% 5.06/5.30 ! [A: int,B: int] :
% 5.06/5.30 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.06/5.30 = zero_zero_int ) ).
% 5.06/5.30
% 5.06/5.30 % mod_div_trivial
% 5.06/5.30 thf(fact_2635_mod__div__trivial,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer] :
% 5.06/5.30 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.06/5.30 = zero_z3403309356797280102nteger ) ).
% 5.06/5.30
% 5.06/5.30 % mod_div_trivial
% 5.06/5.30 thf(fact_2636_mod__mult__self4,axiom,
% 5.06/5.30 ! [B: nat,C: nat,A: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.06/5.30 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self4
% 5.06/5.30 thf(fact_2637_mod__mult__self4,axiom,
% 5.06/5.30 ! [B: int,C: int,A: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.06/5.30 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self4
% 5.06/5.30 thf(fact_2638_mod__mult__self4,axiom,
% 5.06/5.30 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.06/5.30 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self4
% 5.06/5.30 thf(fact_2639_mod__mult__self3,axiom,
% 5.06/5.30 ! [C: nat,B: nat,A: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.06/5.30 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self3
% 5.06/5.30 thf(fact_2640_mod__mult__self3,axiom,
% 5.06/5.30 ! [C: int,B: int,A: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.06/5.30 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self3
% 5.06/5.30 thf(fact_2641_mod__mult__self3,axiom,
% 5.06/5.30 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.06/5.30 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self3
% 5.06/5.30 thf(fact_2642_mod__mult__self2,axiom,
% 5.06/5.30 ! [A: nat,B: nat,C: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.06/5.30 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self2
% 5.06/5.30 thf(fact_2643_mod__mult__self2,axiom,
% 5.06/5.30 ! [A: int,B: int,C: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.06/5.30 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self2
% 5.06/5.30 thf(fact_2644_mod__mult__self2,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.06/5.30 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self2
% 5.06/5.30 thf(fact_2645_mod__mult__self1,axiom,
% 5.06/5.30 ! [A: nat,C: nat,B: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.06/5.30 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self1
% 5.06/5.30 thf(fact_2646_mod__mult__self1,axiom,
% 5.06/5.30 ! [A: int,C: int,B: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.06/5.30 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self1
% 5.06/5.30 thf(fact_2647_mod__mult__self1,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.06/5.30 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_self1
% 5.06/5.30 thf(fact_2648_zero__less__Suc,axiom,
% 5.06/5.30 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_less_Suc
% 5.06/5.30 thf(fact_2649_less__Suc0,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.06/5.30 = ( N2 = zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % less_Suc0
% 5.06/5.30 thf(fact_2650_max__0__1_I4_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 5.06/5.30 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(4)
% 5.06/5.30 thf(fact_2651_max__0__1_I4_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ zero_z3403309356797280102nteger )
% 5.06/5.30 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(4)
% 5.06/5.30 thf(fact_2652_max__0__1_I4_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 5.06/5.30 = ( numeral_numeral_real @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(4)
% 5.06/5.30 thf(fact_2653_max__0__1_I4_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 5.06/5.30 = ( numeral_numeral_rat @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(4)
% 5.06/5.30 thf(fact_2654_max__0__1_I4_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 5.06/5.30 = ( numeral_numeral_nat @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(4)
% 5.06/5.30 thf(fact_2655_max__0__1_I4_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 5.06/5.30 = ( numeral_numeral_int @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(4)
% 5.06/5.30 thf(fact_2656_max__0__1_I3_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.06/5.30 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(3)
% 5.06/5.30 thf(fact_2657_max__0__1_I3_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X ) )
% 5.06/5.30 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(3)
% 5.06/5.30 thf(fact_2658_max__0__1_I3_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 5.06/5.30 = ( numeral_numeral_real @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(3)
% 5.06/5.30 thf(fact_2659_max__0__1_I3_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 5.06/5.30 = ( numeral_numeral_rat @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(3)
% 5.06/5.30 thf(fact_2660_max__0__1_I3_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 5.06/5.30 = ( numeral_numeral_nat @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(3)
% 5.06/5.30 thf(fact_2661_max__0__1_I3_J,axiom,
% 5.06/5.30 ! [X: num] :
% 5.06/5.30 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 5.06/5.30 = ( numeral_numeral_int @ X ) ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(3)
% 5.06/5.30 thf(fact_2662_max__0__1_I1_J,axiom,
% 5.06/5.30 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.06/5.30 = one_one_real ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(1)
% 5.06/5.30 thf(fact_2663_max__0__1_I1_J,axiom,
% 5.06/5.30 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.06/5.30 = one_one_rat ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(1)
% 5.06/5.30 thf(fact_2664_max__0__1_I1_J,axiom,
% 5.06/5.30 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.06/5.30 = one_one_nat ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(1)
% 5.06/5.30 thf(fact_2665_max__0__1_I1_J,axiom,
% 5.06/5.30 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.06/5.30 = one_on7984719198319812577d_enat ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(1)
% 5.06/5.30 thf(fact_2666_max__0__1_I1_J,axiom,
% 5.06/5.30 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.06/5.30 = one_one_int ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(1)
% 5.06/5.30 thf(fact_2667_max__0__1_I1_J,axiom,
% 5.06/5.30 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 5.06/5.30 = one_one_Code_integer ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(1)
% 5.06/5.30 thf(fact_2668_max__0__1_I2_J,axiom,
% 5.06/5.30 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.06/5.30 = one_one_real ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(2)
% 5.06/5.30 thf(fact_2669_max__0__1_I2_J,axiom,
% 5.06/5.30 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.06/5.30 = one_one_rat ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(2)
% 5.06/5.30 thf(fact_2670_max__0__1_I2_J,axiom,
% 5.06/5.30 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.06/5.30 = one_one_nat ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(2)
% 5.06/5.30 thf(fact_2671_max__0__1_I2_J,axiom,
% 5.06/5.30 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.06/5.30 = one_on7984719198319812577d_enat ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(2)
% 5.06/5.30 thf(fact_2672_max__0__1_I2_J,axiom,
% 5.06/5.30 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.06/5.30 = one_one_int ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(2)
% 5.06/5.30 thf(fact_2673_max__0__1_I2_J,axiom,
% 5.06/5.30 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 5.06/5.30 = one_one_Code_integer ) ).
% 5.06/5.30
% 5.06/5.30 % max_0_1(2)
% 5.06/5.30 thf(fact_2674_add__gr__0,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.30 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.30 | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % add_gr_0
% 5.06/5.30 thf(fact_2675_one__eq__mult__iff,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( ( suc @ zero_zero_nat )
% 5.06/5.30 = ( times_times_nat @ M @ N2 ) )
% 5.06/5.30 = ( ( M
% 5.06/5.30 = ( suc @ zero_zero_nat ) )
% 5.06/5.30 & ( N2
% 5.06/5.30 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % one_eq_mult_iff
% 5.06/5.30 thf(fact_2676_mult__eq__1__iff,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( ( times_times_nat @ M @ N2 )
% 5.06/5.30 = ( suc @ zero_zero_nat ) )
% 5.06/5.30 = ( ( M
% 5.06/5.30 = ( suc @ zero_zero_nat ) )
% 5.06/5.30 & ( N2
% 5.06/5.30 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_eq_1_iff
% 5.06/5.30 thf(fact_2677_div__by__Suc__0,axiom,
% 5.06/5.30 ! [M: nat] :
% 5.06/5.30 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.06/5.30 = M ) ).
% 5.06/5.30
% 5.06/5.30 % div_by_Suc_0
% 5.06/5.30 thf(fact_2678_mult__less__cancel2,axiom,
% 5.06/5.30 ! [M: nat,K: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 5.06/5.30 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.30 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_less_cancel2
% 5.06/5.30 thf(fact_2679_nat__0__less__mult__iff,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 5.06/5.30 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.30 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nat_0_less_mult_iff
% 5.06/5.30 thf(fact_2680_nat__mult__less__cancel__disj,axiom,
% 5.06/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.06/5.30 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.30 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nat_mult_less_cancel_disj
% 5.06/5.30 thf(fact_2681_zero__less__diff,axiom,
% 5.06/5.30 ! [N2: nat,M: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 5.06/5.30 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_less_diff
% 5.06/5.30 thf(fact_2682_power__Suc__0,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.30 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_Suc_0
% 5.06/5.30 thf(fact_2683_nat__power__eq__Suc__0__iff,axiom,
% 5.06/5.30 ! [X: nat,M: nat] :
% 5.06/5.30 ( ( ( power_power_nat @ X @ M )
% 5.06/5.30 = ( suc @ zero_zero_nat ) )
% 5.06/5.30 = ( ( M = zero_zero_nat )
% 5.06/5.30 | ( X
% 5.06/5.30 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nat_power_eq_Suc_0_iff
% 5.06/5.30 thf(fact_2684_div__less,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ M @ N2 )
% 5.06/5.30 => ( ( divide_divide_nat @ M @ N2 )
% 5.06/5.30 = zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_less
% 5.06/5.30 thf(fact_2685_diff__is__0__eq,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( ( minus_minus_nat @ M @ N2 )
% 5.06/5.30 = zero_zero_nat )
% 5.06/5.30 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % diff_is_0_eq
% 5.06/5.30 thf(fact_2686_diff__is__0__eq_H,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.30 => ( ( minus_minus_nat @ M @ N2 )
% 5.06/5.30 = zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % diff_is_0_eq'
% 5.06/5.30 thf(fact_2687_less__one,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ N2 @ one_one_nat )
% 5.06/5.30 = ( N2 = zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % less_one
% 5.06/5.30 thf(fact_2688_nat__zero__less__power__iff,axiom,
% 5.06/5.30 ! [X: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N2 ) )
% 5.06/5.30 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.06/5.30 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nat_zero_less_power_iff
% 5.06/5.30 thf(fact_2689_nat__mult__div__cancel__disj,axiom,
% 5.06/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.30 ( ( ( K = zero_zero_nat )
% 5.06/5.30 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.06/5.30 = zero_zero_nat ) )
% 5.06/5.30 & ( ( K != zero_zero_nat )
% 5.06/5.30 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.06/5.30 = ( divide_divide_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nat_mult_div_cancel_disj
% 5.06/5.30 thf(fact_2690_mod__by__Suc__0,axiom,
% 5.06/5.30 ! [M: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % mod_by_Suc_0
% 5.06/5.30 thf(fact_2691_divide__le__0__1__iff,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.06/5.30 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_le_0_1_iff
% 5.06/5.30 thf(fact_2692_divide__le__0__1__iff,axiom,
% 5.06/5.30 ! [A: rat] :
% 5.06/5.30 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.06/5.30 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_le_0_1_iff
% 5.06/5.30 thf(fact_2693_zero__le__divide__1__iff,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.06/5.30 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_le_divide_1_iff
% 5.06/5.30 thf(fact_2694_zero__le__divide__1__iff,axiom,
% 5.06/5.30 ! [A: rat] :
% 5.06/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.06/5.30 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_le_divide_1_iff
% 5.06/5.30 thf(fact_2695_divide__less__0__1__iff,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.06/5.30 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_less_0_1_iff
% 5.06/5.30 thf(fact_2696_divide__less__0__1__iff,axiom,
% 5.06/5.30 ! [A: rat] :
% 5.06/5.30 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.06/5.30 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_less_0_1_iff
% 5.06/5.30 thf(fact_2697_divide__less__eq__1__neg,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.30 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.06/5.30 = ( ord_less_real @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_less_eq_1_neg
% 5.06/5.30 thf(fact_2698_divide__less__eq__1__neg,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.30 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.06/5.30 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_less_eq_1_neg
% 5.06/5.30 thf(fact_2699_divide__less__eq__1__pos,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.30 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.06/5.30 = ( ord_less_real @ B @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_less_eq_1_pos
% 5.06/5.30 thf(fact_2700_divide__less__eq__1__pos,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.30 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.06/5.30 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_less_eq_1_pos
% 5.06/5.30 thf(fact_2701_less__divide__eq__1__neg,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.30 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.06/5.30 = ( ord_less_real @ B @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % less_divide_eq_1_neg
% 5.06/5.30 thf(fact_2702_less__divide__eq__1__neg,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.30 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.06/5.30 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % less_divide_eq_1_neg
% 5.06/5.30 thf(fact_2703_less__divide__eq__1__pos,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.30 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.06/5.30 = ( ord_less_real @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % less_divide_eq_1_pos
% 5.06/5.30 thf(fact_2704_less__divide__eq__1__pos,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.30 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.06/5.30 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % less_divide_eq_1_pos
% 5.06/5.30 thf(fact_2705_zero__less__divide__1__iff,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.06/5.30 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_less_divide_1_iff
% 5.06/5.30 thf(fact_2706_zero__less__divide__1__iff,axiom,
% 5.06/5.30 ! [A: rat] :
% 5.06/5.30 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.06/5.30 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_less_divide_1_iff
% 5.06/5.30 thf(fact_2707_eq__divide__eq__numeral1_I1_J,axiom,
% 5.06/5.30 ! [A: complex,B: complex,W: num] :
% 5.06/5.30 ( ( A
% 5.06/5.30 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.30 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.06/5.30 != zero_zero_complex )
% 5.06/5.30 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.30 = B ) )
% 5.06/5.30 & ( ( ( numera6690914467698888265omplex @ W )
% 5.06/5.30 = zero_zero_complex )
% 5.06/5.30 => ( A = zero_zero_complex ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % eq_divide_eq_numeral1(1)
% 5.06/5.30 thf(fact_2708_eq__divide__eq__numeral1_I1_J,axiom,
% 5.06/5.30 ! [A: real,B: real,W: num] :
% 5.06/5.30 ( ( A
% 5.06/5.30 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.06/5.30 = ( ( ( ( numeral_numeral_real @ W )
% 5.06/5.30 != zero_zero_real )
% 5.06/5.30 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.06/5.30 = B ) )
% 5.06/5.30 & ( ( ( numeral_numeral_real @ W )
% 5.06/5.30 = zero_zero_real )
% 5.06/5.30 => ( A = zero_zero_real ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % eq_divide_eq_numeral1(1)
% 5.06/5.30 thf(fact_2709_eq__divide__eq__numeral1_I1_J,axiom,
% 5.06/5.30 ! [A: rat,B: rat,W: num] :
% 5.06/5.30 ( ( A
% 5.06/5.30 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.06/5.30 = ( ( ( ( numeral_numeral_rat @ W )
% 5.06/5.30 != zero_zero_rat )
% 5.06/5.30 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.06/5.30 = B ) )
% 5.06/5.30 & ( ( ( numeral_numeral_rat @ W )
% 5.06/5.30 = zero_zero_rat )
% 5.06/5.30 => ( A = zero_zero_rat ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % eq_divide_eq_numeral1(1)
% 5.06/5.30 thf(fact_2710_divide__eq__eq__numeral1_I1_J,axiom,
% 5.06/5.30 ! [B: complex,W: num,A: complex] :
% 5.06/5.30 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.30 = A )
% 5.06/5.30 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.06/5.30 != zero_zero_complex )
% 5.06/5.30 => ( B
% 5.06/5.30 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.06/5.30 & ( ( ( numera6690914467698888265omplex @ W )
% 5.06/5.30 = zero_zero_complex )
% 5.06/5.30 => ( A = zero_zero_complex ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_eq_eq_numeral1(1)
% 5.06/5.30 thf(fact_2711_divide__eq__eq__numeral1_I1_J,axiom,
% 5.06/5.30 ! [B: real,W: num,A: real] :
% 5.06/5.30 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.06/5.30 = A )
% 5.06/5.30 = ( ( ( ( numeral_numeral_real @ W )
% 5.06/5.30 != zero_zero_real )
% 5.06/5.30 => ( B
% 5.06/5.30 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.06/5.30 & ( ( ( numeral_numeral_real @ W )
% 5.06/5.30 = zero_zero_real )
% 5.06/5.30 => ( A = zero_zero_real ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_eq_eq_numeral1(1)
% 5.06/5.30 thf(fact_2712_divide__eq__eq__numeral1_I1_J,axiom,
% 5.06/5.30 ! [B: rat,W: num,A: rat] :
% 5.06/5.30 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.06/5.30 = A )
% 5.06/5.30 = ( ( ( ( numeral_numeral_rat @ W )
% 5.06/5.30 != zero_zero_rat )
% 5.06/5.30 => ( B
% 5.06/5.30 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.06/5.30 & ( ( ( numeral_numeral_rat @ W )
% 5.06/5.30 = zero_zero_rat )
% 5.06/5.30 => ( A = zero_zero_rat ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_eq_eq_numeral1(1)
% 5.06/5.30 thf(fact_2713_div__mult__self4,axiom,
% 5.06/5.30 ! [B: nat,C: nat,A: nat] :
% 5.06/5.30 ( ( B != zero_zero_nat )
% 5.06/5.30 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.06/5.30 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_mult_self4
% 5.06/5.30 thf(fact_2714_div__mult__self4,axiom,
% 5.06/5.30 ! [B: int,C: int,A: int] :
% 5.06/5.30 ( ( B != zero_zero_int )
% 5.06/5.30 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.06/5.30 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_mult_self4
% 5.06/5.30 thf(fact_2715_div__mult__self3,axiom,
% 5.06/5.30 ! [B: nat,C: nat,A: nat] :
% 5.06/5.30 ( ( B != zero_zero_nat )
% 5.06/5.30 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.06/5.30 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_mult_self3
% 5.06/5.30 thf(fact_2716_div__mult__self3,axiom,
% 5.06/5.30 ! [B: int,C: int,A: int] :
% 5.06/5.30 ( ( B != zero_zero_int )
% 5.06/5.30 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.06/5.30 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_mult_self3
% 5.06/5.30 thf(fact_2717_div__mult__self2,axiom,
% 5.06/5.30 ! [B: nat,A: nat,C: nat] :
% 5.06/5.30 ( ( B != zero_zero_nat )
% 5.06/5.30 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.06/5.30 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_mult_self2
% 5.06/5.30 thf(fact_2718_div__mult__self2,axiom,
% 5.06/5.30 ! [B: int,A: int,C: int] :
% 5.06/5.30 ( ( B != zero_zero_int )
% 5.06/5.30 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.06/5.30 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_mult_self2
% 5.06/5.30 thf(fact_2719_div__mult__self1,axiom,
% 5.06/5.30 ! [B: nat,A: nat,C: nat] :
% 5.06/5.30 ( ( B != zero_zero_nat )
% 5.06/5.30 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.06/5.30 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_mult_self1
% 5.06/5.30 thf(fact_2720_div__mult__self1,axiom,
% 5.06/5.30 ! [B: int,A: int,C: int] :
% 5.06/5.30 ( ( B != zero_zero_int )
% 5.06/5.30 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.06/5.30 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_mult_self1
% 5.06/5.30 thf(fact_2721_nonzero__divide__mult__cancel__right,axiom,
% 5.06/5.30 ! [B: complex,A: complex] :
% 5.06/5.30 ( ( B != zero_zero_complex )
% 5.06/5.30 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.06/5.30 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nonzero_divide_mult_cancel_right
% 5.06/5.30 thf(fact_2722_nonzero__divide__mult__cancel__right,axiom,
% 5.06/5.30 ! [B: real,A: real] :
% 5.06/5.30 ( ( B != zero_zero_real )
% 5.06/5.30 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.06/5.30 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nonzero_divide_mult_cancel_right
% 5.06/5.30 thf(fact_2723_nonzero__divide__mult__cancel__right,axiom,
% 5.06/5.30 ! [B: rat,A: rat] :
% 5.06/5.30 ( ( B != zero_zero_rat )
% 5.06/5.30 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.06/5.30 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nonzero_divide_mult_cancel_right
% 5.06/5.30 thf(fact_2724_nonzero__divide__mult__cancel__left,axiom,
% 5.06/5.30 ! [A: complex,B: complex] :
% 5.06/5.30 ( ( A != zero_zero_complex )
% 5.06/5.30 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.06/5.30 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nonzero_divide_mult_cancel_left
% 5.06/5.30 thf(fact_2725_nonzero__divide__mult__cancel__left,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( A != zero_zero_real )
% 5.06/5.30 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.06/5.30 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nonzero_divide_mult_cancel_left
% 5.06/5.30 thf(fact_2726_nonzero__divide__mult__cancel__left,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( A != zero_zero_rat )
% 5.06/5.30 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.06/5.30 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nonzero_divide_mult_cancel_left
% 5.06/5.30 thf(fact_2727_power__eq__0__iff,axiom,
% 5.06/5.30 ! [A: rat,N2: nat] :
% 5.06/5.30 ( ( ( power_power_rat @ A @ N2 )
% 5.06/5.30 = zero_zero_rat )
% 5.06/5.30 = ( ( A = zero_zero_rat )
% 5.06/5.30 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_eq_0_iff
% 5.06/5.30 thf(fact_2728_power__eq__0__iff,axiom,
% 5.06/5.30 ! [A: nat,N2: nat] :
% 5.06/5.30 ( ( ( power_power_nat @ A @ N2 )
% 5.06/5.30 = zero_zero_nat )
% 5.06/5.30 = ( ( A = zero_zero_nat )
% 5.06/5.30 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_eq_0_iff
% 5.06/5.30 thf(fact_2729_power__eq__0__iff,axiom,
% 5.06/5.30 ! [A: real,N2: nat] :
% 5.06/5.30 ( ( ( power_power_real @ A @ N2 )
% 5.06/5.30 = zero_zero_real )
% 5.06/5.30 = ( ( A = zero_zero_real )
% 5.06/5.30 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_eq_0_iff
% 5.06/5.30 thf(fact_2730_power__eq__0__iff,axiom,
% 5.06/5.30 ! [A: int,N2: nat] :
% 5.06/5.30 ( ( ( power_power_int @ A @ N2 )
% 5.06/5.30 = zero_zero_int )
% 5.06/5.30 = ( ( A = zero_zero_int )
% 5.06/5.30 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_eq_0_iff
% 5.06/5.30 thf(fact_2731_power__eq__0__iff,axiom,
% 5.06/5.30 ! [A: complex,N2: nat] :
% 5.06/5.30 ( ( ( power_power_complex @ A @ N2 )
% 5.06/5.30 = zero_zero_complex )
% 5.06/5.30 = ( ( A = zero_zero_complex )
% 5.06/5.30 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_eq_0_iff
% 5.06/5.30 thf(fact_2732_Suc__pred,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.06/5.30 = N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % Suc_pred
% 5.06/5.30 thf(fact_2733_one__le__mult__iff,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 5.06/5.30 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.06/5.30 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % one_le_mult_iff
% 5.06/5.30 thf(fact_2734_mult__le__cancel2,axiom,
% 5.06/5.30 ! [M: nat,K: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 5.06/5.30 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.30 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_le_cancel2
% 5.06/5.30 thf(fact_2735_nat__mult__le__cancel__disj,axiom,
% 5.06/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.06/5.30 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.30 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nat_mult_le_cancel_disj
% 5.06/5.30 thf(fact_2736_div__mult__self1__is__m,axiom,
% 5.06/5.30 ! [N2: nat,M: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 5.06/5.30 = M ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_mult_self1_is_m
% 5.06/5.30 thf(fact_2737_div__mult__self__is__m,axiom,
% 5.06/5.30 ! [N2: nat,M: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 5.06/5.30 = M ) ) ).
% 5.06/5.30
% 5.06/5.30 % div_mult_self_is_m
% 5.06/5.30 thf(fact_2738_Suc__mod__mult__self4,axiom,
% 5.06/5.30 ! [N2: nat,K: nat,M: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M ) ) @ N2 )
% 5.06/5.30 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % Suc_mod_mult_self4
% 5.06/5.30 thf(fact_2739_Suc__mod__mult__self3,axiom,
% 5.06/5.30 ! [K: nat,N2: nat,M: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M ) ) @ N2 )
% 5.06/5.30 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % Suc_mod_mult_self3
% 5.06/5.30 thf(fact_2740_Suc__mod__mult__self2,axiom,
% 5.06/5.30 ! [M: nat,N2: nat,K: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 5.06/5.30 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % Suc_mod_mult_self2
% 5.06/5.30 thf(fact_2741_Suc__mod__mult__self1,axiom,
% 5.06/5.30 ! [M: nat,K: nat,N2: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 5.06/5.30 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % Suc_mod_mult_self1
% 5.06/5.30 thf(fact_2742_divide__le__eq__1__neg,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.30 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.06/5.30 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_le_eq_1_neg
% 5.06/5.30 thf(fact_2743_divide__le__eq__1__neg,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.30 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.06/5.30 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_le_eq_1_neg
% 5.06/5.30 thf(fact_2744_divide__le__eq__1__pos,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.30 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.06/5.30 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_le_eq_1_pos
% 5.06/5.30 thf(fact_2745_divide__le__eq__1__pos,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.30 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.06/5.30 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divide_le_eq_1_pos
% 5.06/5.30 thf(fact_2746_le__divide__eq__1__neg,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.30 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.06/5.30 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % le_divide_eq_1_neg
% 5.06/5.30 thf(fact_2747_le__divide__eq__1__neg,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.30 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.06/5.30 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % le_divide_eq_1_neg
% 5.06/5.30 thf(fact_2748_le__divide__eq__1__pos,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.30 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.06/5.30 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % le_divide_eq_1_pos
% 5.06/5.30 thf(fact_2749_le__divide__eq__1__pos,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.30 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.06/5.30 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % le_divide_eq_1_pos
% 5.06/5.30 thf(fact_2750_power__strict__decreasing__iff,axiom,
% 5.06/5.30 ! [B: real,M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.30 => ( ( ord_less_real @ B @ one_one_real )
% 5.06/5.30 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_strict_decreasing_iff
% 5.06/5.30 thf(fact_2751_power__strict__decreasing__iff,axiom,
% 5.06/5.30 ! [B: rat,M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.06/5.30 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.06/5.30 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_strict_decreasing_iff
% 5.06/5.30 thf(fact_2752_power__strict__decreasing__iff,axiom,
% 5.06/5.30 ! [B: nat,M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.30 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.06/5.30 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_strict_decreasing_iff
% 5.06/5.30 thf(fact_2753_power__strict__decreasing__iff,axiom,
% 5.06/5.30 ! [B: int,M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.30 => ( ( ord_less_int @ B @ one_one_int )
% 5.06/5.30 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_strict_decreasing_iff
% 5.06/5.30 thf(fact_2754_zero__eq__power2,axiom,
% 5.06/5.30 ! [A: rat] :
% 5.06/5.30 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_rat )
% 5.06/5.30 = ( A = zero_zero_rat ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_eq_power2
% 5.06/5.30 thf(fact_2755_zero__eq__power2,axiom,
% 5.06/5.30 ! [A: nat] :
% 5.06/5.30 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_nat )
% 5.06/5.30 = ( A = zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_eq_power2
% 5.06/5.30 thf(fact_2756_zero__eq__power2,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_real )
% 5.06/5.30 = ( A = zero_zero_real ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_eq_power2
% 5.06/5.30 thf(fact_2757_zero__eq__power2,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_int )
% 5.06/5.30 = ( A = zero_zero_int ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_eq_power2
% 5.06/5.30 thf(fact_2758_zero__eq__power2,axiom,
% 5.06/5.30 ! [A: complex] :
% 5.06/5.30 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_complex )
% 5.06/5.30 = ( A = zero_zero_complex ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_eq_power2
% 5.06/5.30 thf(fact_2759_power__mono__iff,axiom,
% 5.06/5.30 ! [A: real,B: real,N2: nat] :
% 5.06/5.30 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_mono_iff
% 5.06/5.30 thf(fact_2760_power__mono__iff,axiom,
% 5.06/5.30 ! [A: rat,B: rat,N2: nat] :
% 5.06/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_mono_iff
% 5.06/5.30 thf(fact_2761_power__mono__iff,axiom,
% 5.06/5.30 ! [A: nat,B: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_mono_iff
% 5.06/5.30 thf(fact_2762_power__mono__iff,axiom,
% 5.06/5.30 ! [A: int,B: int,N2: nat] :
% 5.06/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.30 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_mono_iff
% 5.06/5.30 thf(fact_2763_bits__one__mod__two__eq__one,axiom,
% 5.06/5.30 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = one_one_nat ) ).
% 5.06/5.30
% 5.06/5.30 % bits_one_mod_two_eq_one
% 5.06/5.30 thf(fact_2764_bits__one__mod__two__eq__one,axiom,
% 5.06/5.30 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.30 = one_one_int ) ).
% 5.06/5.30
% 5.06/5.30 % bits_one_mod_two_eq_one
% 5.06/5.30 thf(fact_2765_bits__one__mod__two__eq__one,axiom,
% 5.06/5.30 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.30 = one_one_Code_integer ) ).
% 5.06/5.30
% 5.06/5.30 % bits_one_mod_two_eq_one
% 5.06/5.30 thf(fact_2766_one__mod__two__eq__one,axiom,
% 5.06/5.30 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = one_one_nat ) ).
% 5.06/5.30
% 5.06/5.30 % one_mod_two_eq_one
% 5.06/5.30 thf(fact_2767_one__mod__two__eq__one,axiom,
% 5.06/5.30 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.30 = one_one_int ) ).
% 5.06/5.30
% 5.06/5.30 % one_mod_two_eq_one
% 5.06/5.30 thf(fact_2768_one__mod__two__eq__one,axiom,
% 5.06/5.30 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.30 = one_one_Code_integer ) ).
% 5.06/5.30
% 5.06/5.30 % one_mod_two_eq_one
% 5.06/5.30 thf(fact_2769_mod2__Suc__Suc,axiom,
% 5.06/5.30 ! [M: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod2_Suc_Suc
% 5.06/5.30 thf(fact_2770_Suc__diff__1,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 5.06/5.30 = N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % Suc_diff_1
% 5.06/5.30 thf(fact_2771_Suc__times__numeral__mod__eq,axiom,
% 5.06/5.30 ! [K: num,N2: nat] :
% 5.06/5.30 ( ( ( numeral_numeral_nat @ K )
% 5.06/5.30 != one_one_nat )
% 5.06/5.30 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N2 ) ) @ ( numeral_numeral_nat @ K ) )
% 5.06/5.30 = one_one_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % Suc_times_numeral_mod_eq
% 5.06/5.30 thf(fact_2772_bits__1__div__2,axiom,
% 5.06/5.30 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % bits_1_div_2
% 5.06/5.30 thf(fact_2773_bits__1__div__2,axiom,
% 5.06/5.30 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_int ) ).
% 5.06/5.30
% 5.06/5.30 % bits_1_div_2
% 5.06/5.30 thf(fact_2774_one__div__two__eq__zero,axiom,
% 5.06/5.30 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % one_div_two_eq_zero
% 5.06/5.30 thf(fact_2775_one__div__two__eq__zero,axiom,
% 5.06/5.30 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_int ) ).
% 5.06/5.30
% 5.06/5.30 % one_div_two_eq_zero
% 5.06/5.30 thf(fact_2776_power2__eq__iff__nonneg,axiom,
% 5.06/5.30 ! [X: real,Y: real] :
% 5.06/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.30 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = ( X = Y ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power2_eq_iff_nonneg
% 5.06/5.30 thf(fact_2777_power2__eq__iff__nonneg,axiom,
% 5.06/5.30 ! [X: rat,Y: rat] :
% 5.06/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.30 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = ( X = Y ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power2_eq_iff_nonneg
% 5.06/5.30 thf(fact_2778_power2__eq__iff__nonneg,axiom,
% 5.06/5.30 ! [X: nat,Y: nat] :
% 5.06/5.30 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.06/5.30 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.06/5.30 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = ( X = Y ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power2_eq_iff_nonneg
% 5.06/5.30 thf(fact_2779_power2__eq__iff__nonneg,axiom,
% 5.06/5.30 ! [X: int,Y: int] :
% 5.06/5.30 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.30 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.30 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = ( X = Y ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power2_eq_iff_nonneg
% 5.06/5.30 thf(fact_2780_power2__less__eq__zero__iff,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.06/5.30 = ( A = zero_zero_real ) ) ).
% 5.06/5.30
% 5.06/5.30 % power2_less_eq_zero_iff
% 5.06/5.30 thf(fact_2781_power2__less__eq__zero__iff,axiom,
% 5.06/5.30 ! [A: rat] :
% 5.06/5.30 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.06/5.30 = ( A = zero_zero_rat ) ) ).
% 5.06/5.30
% 5.06/5.30 % power2_less_eq_zero_iff
% 5.06/5.30 thf(fact_2782_power2__less__eq__zero__iff,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.06/5.30 = ( A = zero_zero_int ) ) ).
% 5.06/5.30
% 5.06/5.30 % power2_less_eq_zero_iff
% 5.06/5.30 thf(fact_2783_power__decreasing__iff,axiom,
% 5.06/5.30 ! [B: real,M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.30 => ( ( ord_less_real @ B @ one_one_real )
% 5.06/5.30 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_decreasing_iff
% 5.06/5.30 thf(fact_2784_power__decreasing__iff,axiom,
% 5.06/5.30 ! [B: rat,M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.06/5.30 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.06/5.30 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_decreasing_iff
% 5.06/5.30 thf(fact_2785_power__decreasing__iff,axiom,
% 5.06/5.30 ! [B: nat,M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.30 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.06/5.30 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_decreasing_iff
% 5.06/5.30 thf(fact_2786_power__decreasing__iff,axiom,
% 5.06/5.30 ! [B: int,M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.30 => ( ( ord_less_int @ B @ one_one_int )
% 5.06/5.30 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 5.06/5.30 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_decreasing_iff
% 5.06/5.30 thf(fact_2787_zero__less__power2,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = ( A != zero_zero_real ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_less_power2
% 5.06/5.30 thf(fact_2788_zero__less__power2,axiom,
% 5.06/5.30 ! [A: rat] :
% 5.06/5.30 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = ( A != zero_zero_rat ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_less_power2
% 5.06/5.30 thf(fact_2789_zero__less__power2,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = ( A != zero_zero_int ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_less_power2
% 5.06/5.30 thf(fact_2790_sum__power2__eq__zero__iff,axiom,
% 5.06/5.30 ! [X: rat,Y: rat] :
% 5.06/5.30 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = zero_zero_rat )
% 5.06/5.30 = ( ( X = zero_zero_rat )
% 5.06/5.30 & ( Y = zero_zero_rat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % sum_power2_eq_zero_iff
% 5.06/5.30 thf(fact_2791_sum__power2__eq__zero__iff,axiom,
% 5.06/5.30 ! [X: real,Y: real] :
% 5.06/5.30 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = zero_zero_real )
% 5.06/5.30 = ( ( X = zero_zero_real )
% 5.06/5.30 & ( Y = zero_zero_real ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % sum_power2_eq_zero_iff
% 5.06/5.30 thf(fact_2792_sum__power2__eq__zero__iff,axiom,
% 5.06/5.30 ! [X: int,Y: int] :
% 5.06/5.30 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = zero_zero_int )
% 5.06/5.30 = ( ( X = zero_zero_int )
% 5.06/5.30 & ( Y = zero_zero_int ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % sum_power2_eq_zero_iff
% 5.06/5.30 thf(fact_2793_not__mod__2__eq__1__eq__0,axiom,
% 5.06/5.30 ! [A: nat] :
% 5.06/5.30 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 != one_one_nat )
% 5.06/5.30 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % not_mod_2_eq_1_eq_0
% 5.06/5.30 thf(fact_2794_not__mod__2__eq__1__eq__0,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.30 != one_one_int )
% 5.06/5.30 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_int ) ) ).
% 5.06/5.30
% 5.06/5.30 % not_mod_2_eq_1_eq_0
% 5.06/5.30 thf(fact_2795_not__mod__2__eq__1__eq__0,axiom,
% 5.06/5.30 ! [A: code_integer] :
% 5.06/5.30 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.30 != one_one_Code_integer )
% 5.06/5.30 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.30
% 5.06/5.30 % not_mod_2_eq_1_eq_0
% 5.06/5.30 thf(fact_2796_not__mod__2__eq__0__eq__1,axiom,
% 5.06/5.30 ! [A: nat] :
% 5.06/5.30 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 != zero_zero_nat )
% 5.06/5.30 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = one_one_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % not_mod_2_eq_0_eq_1
% 5.06/5.30 thf(fact_2797_not__mod__2__eq__0__eq__1,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.30 != zero_zero_int )
% 5.06/5.30 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.30 = one_one_int ) ) ).
% 5.06/5.30
% 5.06/5.30 % not_mod_2_eq_0_eq_1
% 5.06/5.30 thf(fact_2798_not__mod__2__eq__0__eq__1,axiom,
% 5.06/5.30 ! [A: code_integer] :
% 5.06/5.30 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.30 != zero_z3403309356797280102nteger )
% 5.06/5.30 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.30 = one_one_Code_integer ) ) ).
% 5.06/5.30
% 5.06/5.30 % not_mod_2_eq_0_eq_1
% 5.06/5.30 thf(fact_2799_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 != ( suc @ zero_zero_nat ) )
% 5.06/5.30 = ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % not_mod2_eq_Suc_0_eq_0
% 5.06/5.30 thf(fact_2800_add__self__mod__2,axiom,
% 5.06/5.30 ! [M: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % add_self_mod_2
% 5.06/5.30 thf(fact_2801_mod2__gr__0,axiom,
% 5.06/5.30 ! [M: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.30 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.30 = one_one_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod2_gr_0
% 5.06/5.30 thf(fact_2802_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.06/5.30 ! [B: nat,A: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.30 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.06/5.30 thf(fact_2803_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.06/5.30 ! [B: int,A: int] :
% 5.06/5.30 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.30 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.06/5.30 thf(fact_2804_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.06/5.30 ! [B: code_integer,A: code_integer] :
% 5.06/5.30 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.06/5.30 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.06/5.30 thf(fact_2805_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer] :
% 5.06/5.30 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.06/5.30 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.06/5.30 thf(fact_2806_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.06/5.30 ! [A: nat,B: nat] :
% 5.06/5.30 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.30 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.06/5.30 thf(fact_2807_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.06/5.30 ! [A: int,B: int] :
% 5.06/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.30 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.06/5.30 thf(fact_2808_mod__Suc,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.06/5.30 = N2 )
% 5.06/5.30 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 5.06/5.30 = zero_zero_nat ) )
% 5.06/5.30 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.06/5.30 != N2 )
% 5.06/5.30 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 5.06/5.30 = ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_Suc
% 5.06/5.30 thf(fact_2809_mod__less__divisor,axiom,
% 5.06/5.30 ! [N2: nat,M: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_less_divisor
% 5.06/5.30 thf(fact_2810_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.06/5.30 ! [A: $o,B: $o,X: nat] :
% 5.06/5.30 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.06/5.30 = ( ( ( X = zero_zero_nat )
% 5.06/5.30 => A )
% 5.06/5.30 & ( ( X != zero_zero_nat )
% 5.06/5.30 => ( ( ( X = one_one_nat )
% 5.06/5.30 => B )
% 5.06/5.30 & ( X = one_one_nat ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.naive_member.simps(1)
% 5.06/5.30 thf(fact_2811_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.06/5.30 ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.06/5.30 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.membermima.simps(1)
% 5.06/5.30 thf(fact_2812_VEBT_Osize_I4_J,axiom,
% 5.06/5.30 ! [X21: $o,X222: $o] :
% 5.06/5.30 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT.size(4)
% 5.06/5.30 thf(fact_2813_mod__eq__0D,axiom,
% 5.06/5.30 ! [M: nat,D: nat] :
% 5.06/5.30 ( ( ( modulo_modulo_nat @ M @ D )
% 5.06/5.30 = zero_zero_nat )
% 5.06/5.30 => ? [Q3: nat] :
% 5.06/5.30 ( M
% 5.06/5.30 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_eq_0D
% 5.06/5.30 thf(fact_2814_mod__eq__self__iff__div__eq__0,axiom,
% 5.06/5.30 ! [A: nat,B: nat] :
% 5.06/5.30 ( ( ( modulo_modulo_nat @ A @ B )
% 5.06/5.30 = A )
% 5.06/5.30 = ( ( divide_divide_nat @ A @ B )
% 5.06/5.30 = zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_eq_self_iff_div_eq_0
% 5.06/5.30 thf(fact_2815_mod__eq__self__iff__div__eq__0,axiom,
% 5.06/5.30 ! [A: int,B: int] :
% 5.06/5.30 ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.30 = A )
% 5.06/5.30 = ( ( divide_divide_int @ A @ B )
% 5.06/5.30 = zero_zero_int ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_eq_self_iff_div_eq_0
% 5.06/5.30 thf(fact_2816_mod__eq__self__iff__div__eq__0,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer] :
% 5.06/5.30 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.06/5.30 = A )
% 5.06/5.30 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.06/5.30 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_eq_self_iff_div_eq_0
% 5.06/5.30 thf(fact_2817_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.06/5.30 ! [X: produc9072475918466114483BT_nat] :
% 5.06/5.30 ( ! [Uu2: $o,Uv2: $o,D4: nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D4 ) )
% 5.06/5.30 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.valid'.cases
% 5.06/5.30 thf(fact_2818_bot__nat__def,axiom,
% 5.06/5.30 bot_bot_nat = zero_zero_nat ).
% 5.06/5.30
% 5.06/5.30 % bot_nat_def
% 5.06/5.30 thf(fact_2819_vebt__delete_Osimps_I1_J,axiom,
% 5.06/5.30 ! [A: $o,B: $o] :
% 5.06/5.30 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 5.06/5.30 = ( vEBT_Leaf @ $false @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % vebt_delete.simps(1)
% 5.06/5.30 thf(fact_2820_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.06/5.30 ! [X: produc9072475918466114483BT_nat] :
% 5.06/5.30 ( ! [A3: $o,B2: $o,X3: nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X3 ) )
% 5.06/5.30 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.06/5.30 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ X3 ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.naive_member.cases
% 5.06/5.30 thf(fact_2821_vebt__buildup_Osimps_I1_J,axiom,
% 5.06/5.30 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.06/5.30 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.06/5.30
% 5.06/5.30 % vebt_buildup.simps(1)
% 5.06/5.30 thf(fact_2822_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer] :
% 5.06/5.30 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.06/5.30 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.06/5.30 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.06/5.30 = A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.mod_less
% 5.06/5.30 thf(fact_2823_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.06/5.30 ! [A: nat,B: nat] :
% 5.06/5.30 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.30 => ( ( ord_less_nat @ A @ B )
% 5.06/5.30 => ( ( modulo_modulo_nat @ A @ B )
% 5.06/5.30 = A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.mod_less
% 5.06/5.30 thf(fact_2824_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.06/5.30 ! [A: int,B: int] :
% 5.06/5.30 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.30 => ( ( ord_less_int @ A @ B )
% 5.06/5.30 => ( ( modulo_modulo_int @ A @ B )
% 5.06/5.30 = A ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.mod_less
% 5.06/5.30 thf(fact_2825_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.06/5.30 ! [B: code_integer,A: code_integer] :
% 5.06/5.30 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.06/5.30 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.06/5.30 thf(fact_2826_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.06/5.30 ! [B: nat,A: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.30 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.06/5.30 thf(fact_2827_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.06/5.30 ! [B: int,A: int] :
% 5.06/5.30 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.30 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.06/5.30 thf(fact_2828_cong__exp__iff__simps_I2_J,axiom,
% 5.06/5.30 ! [N2: num,Q2: num] :
% 5.06/5.30 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.06/5.30 = zero_zero_nat )
% 5.06/5.30 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.06/5.30 = zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(2)
% 5.06/5.30 thf(fact_2829_cong__exp__iff__simps_I2_J,axiom,
% 5.06/5.30 ! [N2: num,Q2: num] :
% 5.06/5.30 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.06/5.30 = zero_zero_int )
% 5.06/5.30 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) )
% 5.06/5.30 = zero_zero_int ) ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(2)
% 5.06/5.30 thf(fact_2830_cong__exp__iff__simps_I2_J,axiom,
% 5.06/5.30 ! [N2: num,Q2: num] :
% 5.06/5.30 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.06/5.30 = zero_z3403309356797280102nteger )
% 5.06/5.30 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.06/5.30 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(2)
% 5.06/5.30 thf(fact_2831_cong__exp__iff__simps_I1_J,axiom,
% 5.06/5.30 ! [N2: num] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(1)
% 5.06/5.30 thf(fact_2832_cong__exp__iff__simps_I1_J,axiom,
% 5.06/5.30 ! [N2: num] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) )
% 5.06/5.30 = zero_zero_int ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(1)
% 5.06/5.30 thf(fact_2833_cong__exp__iff__simps_I1_J,axiom,
% 5.06/5.30 ! [N2: num] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) )
% 5.06/5.30 = zero_z3403309356797280102nteger ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(1)
% 5.06/5.30 thf(fact_2834_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.06/5.30 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.06/5.30 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.naive_member.simps(2)
% 5.06/5.30 thf(fact_2835_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.06/5.30 ! [X: produc5542196010084753463at_nat] :
% 5.06/5.30 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.06/5.30 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.06/5.30 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B2 ) ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.option_shift.cases
% 5.06/5.30 thf(fact_2836_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.06/5.30 ! [X: produc8306885398267862888on_nat] :
% 5.06/5.30 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.06/5.30 => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.06/5.30 => ~ ! [F2: nat > nat > nat,A3: nat,B2: nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B2 ) ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.option_shift.cases
% 5.06/5.30 thf(fact_2837_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.06/5.30 ! [X: produc1193250871479095198on_num] :
% 5.06/5.30 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.06/5.30 => ( ! [Uw2: num > num > num,V2: num] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.06/5.30 => ~ ! [F2: num > num > num,A3: num,B2: num] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A3 ) @ ( some_num @ B2 ) ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.option_shift.cases
% 5.06/5.30 thf(fact_2838_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.06/5.30 ! [X: produc5491161045314408544at_nat] :
% 5.06/5.30 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.06/5.30 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.06/5.30 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y5 ) ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.option_comp_shift.cases
% 5.06/5.30 thf(fact_2839_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.06/5.30 ! [X: produc2233624965454879586on_nat] :
% 5.06/5.30 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.06/5.30 => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.06/5.30 => ~ ! [F2: nat > nat > $o,X3: nat,Y5: nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y5 ) ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.option_comp_shift.cases
% 5.06/5.30 thf(fact_2840_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.06/5.30 ! [X: produc7036089656553540234on_num] :
% 5.06/5.30 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.06/5.30 => ( ! [Uw2: num > num > $o,V2: num] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.06/5.30 => ~ ! [F2: num > num > $o,X3: num,Y5: num] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y5 ) ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.option_comp_shift.cases
% 5.06/5.30 thf(fact_2841_mod__le__divisor,axiom,
% 5.06/5.30 ! [N2: nat,M: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_le_divisor
% 5.06/5.30 thf(fact_2842_invar__vebt_Ointros_I1_J,axiom,
% 5.06/5.30 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % invar_vebt.intros(1)
% 5.06/5.30 thf(fact_2843_power__0__left,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ( N2 = zero_zero_nat )
% 5.06/5.30 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 5.06/5.30 = one_one_rat ) )
% 5.06/5.30 & ( ( N2 != zero_zero_nat )
% 5.06/5.30 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 5.06/5.30 = zero_zero_rat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_0_left
% 5.06/5.30 thf(fact_2844_power__0__left,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ( N2 = zero_zero_nat )
% 5.06/5.30 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 = one_one_nat ) )
% 5.06/5.30 & ( ( N2 != zero_zero_nat )
% 5.06/5.30 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 = zero_zero_nat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_0_left
% 5.06/5.30 thf(fact_2845_power__0__left,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ( N2 = zero_zero_nat )
% 5.06/5.30 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.06/5.30 = one_one_real ) )
% 5.06/5.30 & ( ( N2 != zero_zero_nat )
% 5.06/5.30 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.06/5.30 = zero_zero_real ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_0_left
% 5.06/5.30 thf(fact_2846_power__0__left,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ( N2 = zero_zero_nat )
% 5.06/5.30 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.06/5.30 = one_one_int ) )
% 5.06/5.30 & ( ( N2 != zero_zero_nat )
% 5.06/5.30 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.06/5.30 = zero_zero_int ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_0_left
% 5.06/5.30 thf(fact_2847_power__0__left,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ( N2 = zero_zero_nat )
% 5.06/5.30 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.06/5.30 = one_one_complex ) )
% 5.06/5.30 & ( ( N2 != zero_zero_nat )
% 5.06/5.30 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.06/5.30 = zero_zero_complex ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_0_left
% 5.06/5.30 thf(fact_2848_vebt__delete_Osimps_I2_J,axiom,
% 5.06/5.30 ! [A: $o,B: $o] :
% 5.06/5.30 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 5.06/5.30 = ( vEBT_Leaf @ A @ $false ) ) ).
% 5.06/5.30
% 5.06/5.30 % vebt_delete.simps(2)
% 5.06/5.30 thf(fact_2849_zero__power,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 5.06/5.30 = zero_zero_rat ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_power
% 5.06/5.30 thf(fact_2850_zero__power,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 = zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_power
% 5.06/5.30 thf(fact_2851_zero__power,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.06/5.30 = zero_zero_real ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_power
% 5.06/5.30 thf(fact_2852_zero__power,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.06/5.30 = zero_zero_int ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_power
% 5.06/5.30 thf(fact_2853_zero__power,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.06/5.30 = zero_zero_complex ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_power
% 5.06/5.30 thf(fact_2854_mod__mult__right__eq,axiom,
% 5.06/5.30 ! [A: nat,B: nat,C: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_right_eq
% 5.06/5.30 thf(fact_2855_mod__mult__right__eq,axiom,
% 5.06/5.30 ! [A: int,B: int,C: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_right_eq
% 5.06/5.30 thf(fact_2856_mod__mult__right__eq,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_right_eq
% 5.06/5.30 thf(fact_2857_mod__mult__left__eq,axiom,
% 5.06/5.30 ! [A: nat,C: nat,B: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_left_eq
% 5.06/5.30 thf(fact_2858_mod__mult__left__eq,axiom,
% 5.06/5.30 ! [A: int,C: int,B: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_left_eq
% 5.06/5.30 thf(fact_2859_mod__mult__left__eq,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_left_eq
% 5.06/5.30 thf(fact_2860_mult__mod__right,axiom,
% 5.06/5.30 ! [C: nat,A: nat,B: nat] :
% 5.06/5.30 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.06/5.30 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_mod_right
% 5.06/5.30 thf(fact_2861_mult__mod__right,axiom,
% 5.06/5.30 ! [C: int,A: int,B: int] :
% 5.06/5.30 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.06/5.30 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_mod_right
% 5.06/5.30 thf(fact_2862_mult__mod__right,axiom,
% 5.06/5.30 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.06/5.30 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_mod_right
% 5.06/5.30 thf(fact_2863_mod__mult__mult2,axiom,
% 5.06/5.30 ! [A: nat,C: nat,B: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.06/5.30 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_mult2
% 5.06/5.30 thf(fact_2864_mod__mult__mult2,axiom,
% 5.06/5.30 ! [A: int,C: int,B: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.06/5.30 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_mult2
% 5.06/5.30 thf(fact_2865_mod__mult__mult2,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.06/5.30 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_mult2
% 5.06/5.30 thf(fact_2866_mod__mult__cong,axiom,
% 5.06/5.30 ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
% 5.06/5.30 ( ( ( modulo_modulo_nat @ A @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ A6 @ C ) )
% 5.06/5.30 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ B6 @ C ) )
% 5.06/5.30 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ ( times_times_nat @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_cong
% 5.06/5.30 thf(fact_2867_mod__mult__cong,axiom,
% 5.06/5.30 ! [A: int,C: int,A6: int,B: int,B6: int] :
% 5.06/5.30 ( ( ( modulo_modulo_int @ A @ C )
% 5.06/5.30 = ( modulo_modulo_int @ A6 @ C ) )
% 5.06/5.30 => ( ( ( modulo_modulo_int @ B @ C )
% 5.06/5.30 = ( modulo_modulo_int @ B6 @ C ) )
% 5.06/5.30 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( times_times_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_cong
% 5.06/5.30 thf(fact_2868_mod__mult__cong,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,A6: code_integer,B: code_integer,B6: code_integer] :
% 5.06/5.30 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ A6 @ C ) )
% 5.06/5.30 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ B6 @ C ) )
% 5.06/5.30 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_cong
% 5.06/5.30 thf(fact_2869_mod__mult__eq,axiom,
% 5.06/5.30 ! [A: nat,C: nat,B: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_eq
% 5.06/5.30 thf(fact_2870_mod__mult__eq,axiom,
% 5.06/5.30 ! [A: int,C: int,B: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_eq
% 5.06/5.30 thf(fact_2871_mod__mult__eq,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_mult_eq
% 5.06/5.30 thf(fact_2872_mod__add__right__eq,axiom,
% 5.06/5.30 ! [A: nat,B: nat,C: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_right_eq
% 5.06/5.30 thf(fact_2873_mod__add__right__eq,axiom,
% 5.06/5.30 ! [A: int,B: int,C: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_right_eq
% 5.06/5.30 thf(fact_2874_mod__add__right__eq,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_right_eq
% 5.06/5.30 thf(fact_2875_mod__add__left__eq,axiom,
% 5.06/5.30 ! [A: nat,C: nat,B: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_left_eq
% 5.06/5.30 thf(fact_2876_mod__add__left__eq,axiom,
% 5.06/5.30 ! [A: int,C: int,B: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_left_eq
% 5.06/5.30 thf(fact_2877_mod__add__left__eq,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_left_eq
% 5.06/5.30 thf(fact_2878_mod__add__cong,axiom,
% 5.06/5.30 ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
% 5.06/5.30 ( ( ( modulo_modulo_nat @ A @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ A6 @ C ) )
% 5.06/5.30 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ B6 @ C ) )
% 5.06/5.30 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ ( plus_plus_nat @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_cong
% 5.06/5.30 thf(fact_2879_mod__add__cong,axiom,
% 5.06/5.30 ! [A: int,C: int,A6: int,B: int,B6: int] :
% 5.06/5.30 ( ( ( modulo_modulo_int @ A @ C )
% 5.06/5.30 = ( modulo_modulo_int @ A6 @ C ) )
% 5.06/5.30 => ( ( ( modulo_modulo_int @ B @ C )
% 5.06/5.30 = ( modulo_modulo_int @ B6 @ C ) )
% 5.06/5.30 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( plus_plus_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_cong
% 5.06/5.30 thf(fact_2880_mod__add__cong,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,A6: code_integer,B: code_integer,B6: code_integer] :
% 5.06/5.30 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ A6 @ C ) )
% 5.06/5.30 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ B6 @ C ) )
% 5.06/5.30 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_cong
% 5.06/5.30 thf(fact_2881_mod__add__eq,axiom,
% 5.06/5.30 ! [A: nat,C: nat,B: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_eq
% 5.06/5.30 thf(fact_2882_mod__add__eq,axiom,
% 5.06/5.30 ! [A: int,C: int,B: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_eq
% 5.06/5.30 thf(fact_2883_mod__add__eq,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_add_eq
% 5.06/5.30 thf(fact_2884_mod__diff__right__eq,axiom,
% 5.06/5.30 ! [A: int,B: int,C: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_diff_right_eq
% 5.06/5.30 thf(fact_2885_mod__diff__right__eq,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_diff_right_eq
% 5.06/5.30 thf(fact_2886_mod__diff__left__eq,axiom,
% 5.06/5.30 ! [A: int,C: int,B: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_diff_left_eq
% 5.06/5.30 thf(fact_2887_mod__diff__left__eq,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_diff_left_eq
% 5.06/5.30 thf(fact_2888_mod__diff__cong,axiom,
% 5.06/5.30 ! [A: int,C: int,A6: int,B: int,B6: int] :
% 5.06/5.30 ( ( ( modulo_modulo_int @ A @ C )
% 5.06/5.30 = ( modulo_modulo_int @ A6 @ C ) )
% 5.06/5.30 => ( ( ( modulo_modulo_int @ B @ C )
% 5.06/5.30 = ( modulo_modulo_int @ B6 @ C ) )
% 5.06/5.30 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( minus_minus_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_diff_cong
% 5.06/5.30 thf(fact_2889_mod__diff__cong,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,A6: code_integer,B: code_integer,B6: code_integer] :
% 5.06/5.30 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ A6 @ C ) )
% 5.06/5.30 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ B6 @ C ) )
% 5.06/5.30 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_diff_cong
% 5.06/5.30 thf(fact_2890_mod__diff__eq,axiom,
% 5.06/5.30 ! [A: int,C: int,B: int] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_diff_eq
% 5.06/5.30 thf(fact_2891_mod__diff__eq,axiom,
% 5.06/5.30 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_diff_eq
% 5.06/5.30 thf(fact_2892_power__mod,axiom,
% 5.06/5.30 ! [A: nat,B: nat,N2: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N2 ) @ B )
% 5.06/5.30 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N2 ) @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_mod
% 5.06/5.30 thf(fact_2893_power__mod,axiom,
% 5.06/5.30 ! [A: int,B: int,N2: nat] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N2 ) @ B )
% 5.06/5.30 = ( modulo_modulo_int @ ( power_power_int @ A @ N2 ) @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_mod
% 5.06/5.30 thf(fact_2894_power__mod,axiom,
% 5.06/5.30 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N2 ) @ B )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ B ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_mod
% 5.06/5.30 thf(fact_2895_vebt__member_Osimps_I1_J,axiom,
% 5.06/5.30 ! [A: $o,B: $o,X: nat] :
% 5.06/5.30 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.06/5.30 = ( ( ( X = zero_zero_nat )
% 5.06/5.30 => A )
% 5.06/5.30 & ( ( X != zero_zero_nat )
% 5.06/5.30 => ( ( ( X = one_one_nat )
% 5.06/5.30 => B )
% 5.06/5.30 & ( X = one_one_nat ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % vebt_member.simps(1)
% 5.06/5.30 thf(fact_2896_mod__Suc__Suc__eq,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ N2 )
% 5.06/5.30 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_Suc_Suc_eq
% 5.06/5.30 thf(fact_2897_mod__Suc__eq,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) @ N2 )
% 5.06/5.30 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % mod_Suc_eq
% 5.06/5.30 thf(fact_2898_VEBT_Oexhaust,axiom,
% 5.06/5.30 ! [Y: vEBT_VEBT] :
% 5.06/5.30 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.06/5.30 ( Y
% 5.06/5.30 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.06/5.30 => ~ ! [X212: $o,X223: $o] :
% 5.06/5.30 ( Y
% 5.06/5.30 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT.exhaust
% 5.06/5.30 thf(fact_2899_VEBT_Odistinct_I1_J,axiom,
% 5.06/5.30 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.06/5.30 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.06/5.30 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT.distinct(1)
% 5.06/5.30 thf(fact_2900_vebt__buildup_Osimps_I2_J,axiom,
% 5.06/5.30 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.06/5.30 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.06/5.30
% 5.06/5.30 % vebt_buildup.simps(2)
% 5.06/5.30 thf(fact_2901_mod__less__eq__dividend,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 5.06/5.30
% 5.06/5.30 % mod_less_eq_dividend
% 5.06/5.30 thf(fact_2902_vebt__insert_Osimps_I1_J,axiom,
% 5.06/5.30 ! [X: nat,A: $o,B: $o] :
% 5.06/5.30 ( ( ( X = zero_zero_nat )
% 5.06/5.30 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.06/5.30 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.06/5.30 & ( ( X != zero_zero_nat )
% 5.06/5.30 => ( ( ( X = one_one_nat )
% 5.06/5.30 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.06/5.30 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.06/5.30 & ( ( X != one_one_nat )
% 5.06/5.30 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.06/5.30 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % vebt_insert.simps(1)
% 5.06/5.30 thf(fact_2903_vebt__pred_Osimps_I1_J,axiom,
% 5.06/5.30 ! [Uu: $o,Uv: $o] :
% 5.06/5.30 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.06/5.30 = none_nat ) ).
% 5.06/5.30
% 5.06/5.30 % vebt_pred.simps(1)
% 5.06/5.30 thf(fact_2904_le__numeral__extra_I3_J,axiom,
% 5.06/5.30 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.06/5.30
% 5.06/5.30 % le_numeral_extra(3)
% 5.06/5.30 thf(fact_2905_le__numeral__extra_I3_J,axiom,
% 5.06/5.30 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.06/5.30
% 5.06/5.30 % le_numeral_extra(3)
% 5.06/5.30 thf(fact_2906_le__numeral__extra_I3_J,axiom,
% 5.06/5.30 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.06/5.30
% 5.06/5.30 % le_numeral_extra(3)
% 5.06/5.30 thf(fact_2907_le__numeral__extra_I3_J,axiom,
% 5.06/5.30 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.06/5.30
% 5.06/5.30 % le_numeral_extra(3)
% 5.06/5.30 thf(fact_2908_zero__le,axiom,
% 5.06/5.30 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 5.06/5.30
% 5.06/5.30 % zero_le
% 5.06/5.30 thf(fact_2909_field__lbound__gt__zero,axiom,
% 5.06/5.30 ! [D1: real,D22: real] :
% 5.06/5.30 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.06/5.30 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.06/5.30 => ? [E2: real] :
% 5.06/5.30 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.06/5.30 & ( ord_less_real @ E2 @ D1 )
% 5.06/5.30 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % field_lbound_gt_zero
% 5.06/5.30 thf(fact_2910_field__lbound__gt__zero,axiom,
% 5.06/5.30 ! [D1: rat,D22: rat] :
% 5.06/5.30 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.06/5.30 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.06/5.30 => ? [E2: rat] :
% 5.06/5.30 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.06/5.30 & ( ord_less_rat @ E2 @ D1 )
% 5.06/5.30 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % field_lbound_gt_zero
% 5.06/5.30 thf(fact_2911_less__numeral__extra_I3_J,axiom,
% 5.06/5.30 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.06/5.30
% 5.06/5.30 % less_numeral_extra(3)
% 5.06/5.30 thf(fact_2912_less__numeral__extra_I3_J,axiom,
% 5.06/5.30 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.06/5.30
% 5.06/5.30 % less_numeral_extra(3)
% 5.06/5.30 thf(fact_2913_less__numeral__extra_I3_J,axiom,
% 5.06/5.30 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % less_numeral_extra(3)
% 5.06/5.30 thf(fact_2914_less__numeral__extra_I3_J,axiom,
% 5.06/5.30 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.06/5.30
% 5.06/5.30 % less_numeral_extra(3)
% 5.06/5.30 thf(fact_2915_gr__zeroI,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( N2 != zero_zero_nat )
% 5.06/5.30 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % gr_zeroI
% 5.06/5.30 thf(fact_2916_not__less__zero,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % not_less_zero
% 5.06/5.30 thf(fact_2917_gr__implies__not__zero,axiom,
% 5.06/5.30 ! [M: nat,N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ M @ N2 )
% 5.06/5.30 => ( N2 != zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % gr_implies_not_zero
% 5.06/5.30 thf(fact_2918_zero__less__iff__neq__zero,axiom,
% 5.06/5.30 ! [N2: nat] :
% 5.06/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.30 = ( N2 != zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_less_iff_neq_zero
% 5.06/5.30 thf(fact_2919_zero__neq__numeral,axiom,
% 5.06/5.30 ! [N2: num] :
% 5.06/5.30 ( zero_zero_complex
% 5.06/5.30 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_neq_numeral
% 5.06/5.30 thf(fact_2920_zero__neq__numeral,axiom,
% 5.06/5.30 ! [N2: num] :
% 5.06/5.30 ( zero_zero_real
% 5.06/5.30 != ( numeral_numeral_real @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_neq_numeral
% 5.06/5.30 thf(fact_2921_zero__neq__numeral,axiom,
% 5.06/5.30 ! [N2: num] :
% 5.06/5.30 ( zero_zero_rat
% 5.06/5.30 != ( numeral_numeral_rat @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_neq_numeral
% 5.06/5.30 thf(fact_2922_zero__neq__numeral,axiom,
% 5.06/5.30 ! [N2: num] :
% 5.06/5.30 ( zero_zero_nat
% 5.06/5.30 != ( numeral_numeral_nat @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_neq_numeral
% 5.06/5.30 thf(fact_2923_zero__neq__numeral,axiom,
% 5.06/5.30 ! [N2: num] :
% 5.06/5.30 ( zero_zero_int
% 5.06/5.30 != ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_neq_numeral
% 5.06/5.30 thf(fact_2924_cong__exp__iff__simps_I9_J,axiom,
% 5.06/5.30 ! [M: num,Q2: num,N2: num] :
% 5.06/5.30 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.06/5.30 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.30 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.06/5.30 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(9)
% 5.06/5.30 thf(fact_2925_cong__exp__iff__simps_I9_J,axiom,
% 5.06/5.30 ! [M: num,Q2: num,N2: num] :
% 5.06/5.30 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.06/5.30 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.30 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.06/5.30 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(9)
% 5.06/5.30 thf(fact_2926_cong__exp__iff__simps_I9_J,axiom,
% 5.06/5.30 ! [M: num,Q2: num,N2: num] :
% 5.06/5.30 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.30 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(9)
% 5.06/5.30 thf(fact_2927_cong__exp__iff__simps_I4_J,axiom,
% 5.06/5.30 ! [M: num,N2: num] :
% 5.06/5.30 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.06/5.30 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(4)
% 5.06/5.30 thf(fact_2928_cong__exp__iff__simps_I4_J,axiom,
% 5.06/5.30 ! [M: num,N2: num] :
% 5.06/5.30 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.06/5.30 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(4)
% 5.06/5.30 thf(fact_2929_cong__exp__iff__simps_I4_J,axiom,
% 5.06/5.30 ! [M: num,N2: num] :
% 5.06/5.30 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.06/5.30 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % cong_exp_iff_simps(4)
% 5.06/5.30 thf(fact_2930_mult__right__cancel,axiom,
% 5.06/5.30 ! [C: complex,A: complex,B: complex] :
% 5.06/5.30 ( ( C != zero_zero_complex )
% 5.06/5.30 => ( ( ( times_times_complex @ A @ C )
% 5.06/5.30 = ( times_times_complex @ B @ C ) )
% 5.06/5.30 = ( A = B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_right_cancel
% 5.06/5.30 thf(fact_2931_mult__right__cancel,axiom,
% 5.06/5.30 ! [C: real,A: real,B: real] :
% 5.06/5.30 ( ( C != zero_zero_real )
% 5.06/5.30 => ( ( ( times_times_real @ A @ C )
% 5.06/5.30 = ( times_times_real @ B @ C ) )
% 5.06/5.30 = ( A = B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_right_cancel
% 5.06/5.30 thf(fact_2932_mult__right__cancel,axiom,
% 5.06/5.30 ! [C: rat,A: rat,B: rat] :
% 5.06/5.30 ( ( C != zero_zero_rat )
% 5.06/5.30 => ( ( ( times_times_rat @ A @ C )
% 5.06/5.30 = ( times_times_rat @ B @ C ) )
% 5.06/5.30 = ( A = B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_right_cancel
% 5.06/5.30 thf(fact_2933_mult__right__cancel,axiom,
% 5.06/5.30 ! [C: nat,A: nat,B: nat] :
% 5.06/5.30 ( ( C != zero_zero_nat )
% 5.06/5.30 => ( ( ( times_times_nat @ A @ C )
% 5.06/5.30 = ( times_times_nat @ B @ C ) )
% 5.06/5.30 = ( A = B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_right_cancel
% 5.06/5.30 thf(fact_2934_mult__right__cancel,axiom,
% 5.06/5.30 ! [C: int,A: int,B: int] :
% 5.06/5.30 ( ( C != zero_zero_int )
% 5.06/5.30 => ( ( ( times_times_int @ A @ C )
% 5.06/5.30 = ( times_times_int @ B @ C ) )
% 5.06/5.30 = ( A = B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_right_cancel
% 5.06/5.30 thf(fact_2935_mult__left__cancel,axiom,
% 5.06/5.30 ! [C: complex,A: complex,B: complex] :
% 5.06/5.30 ( ( C != zero_zero_complex )
% 5.06/5.30 => ( ( ( times_times_complex @ C @ A )
% 5.06/5.30 = ( times_times_complex @ C @ B ) )
% 5.06/5.30 = ( A = B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_left_cancel
% 5.06/5.30 thf(fact_2936_mult__left__cancel,axiom,
% 5.06/5.30 ! [C: real,A: real,B: real] :
% 5.06/5.30 ( ( C != zero_zero_real )
% 5.06/5.30 => ( ( ( times_times_real @ C @ A )
% 5.06/5.30 = ( times_times_real @ C @ B ) )
% 5.06/5.30 = ( A = B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_left_cancel
% 5.06/5.30 thf(fact_2937_mult__left__cancel,axiom,
% 5.06/5.30 ! [C: rat,A: rat,B: rat] :
% 5.06/5.30 ( ( C != zero_zero_rat )
% 5.06/5.30 => ( ( ( times_times_rat @ C @ A )
% 5.06/5.30 = ( times_times_rat @ C @ B ) )
% 5.06/5.30 = ( A = B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_left_cancel
% 5.06/5.30 thf(fact_2938_mult__left__cancel,axiom,
% 5.06/5.30 ! [C: nat,A: nat,B: nat] :
% 5.06/5.30 ( ( C != zero_zero_nat )
% 5.06/5.30 => ( ( ( times_times_nat @ C @ A )
% 5.06/5.30 = ( times_times_nat @ C @ B ) )
% 5.06/5.30 = ( A = B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_left_cancel
% 5.06/5.30 thf(fact_2939_mult__left__cancel,axiom,
% 5.06/5.30 ! [C: int,A: int,B: int] :
% 5.06/5.30 ( ( C != zero_zero_int )
% 5.06/5.30 => ( ( ( times_times_int @ C @ A )
% 5.06/5.30 = ( times_times_int @ C @ B ) )
% 5.06/5.30 = ( A = B ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_left_cancel
% 5.06/5.30 thf(fact_2940_no__zero__divisors,axiom,
% 5.06/5.30 ! [A: complex,B: complex] :
% 5.06/5.30 ( ( A != zero_zero_complex )
% 5.06/5.30 => ( ( B != zero_zero_complex )
% 5.06/5.30 => ( ( times_times_complex @ A @ B )
% 5.06/5.30 != zero_zero_complex ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % no_zero_divisors
% 5.06/5.30 thf(fact_2941_no__zero__divisors,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( A != zero_zero_real )
% 5.06/5.30 => ( ( B != zero_zero_real )
% 5.06/5.30 => ( ( times_times_real @ A @ B )
% 5.06/5.30 != zero_zero_real ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % no_zero_divisors
% 5.06/5.30 thf(fact_2942_no__zero__divisors,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( A != zero_zero_rat )
% 5.06/5.30 => ( ( B != zero_zero_rat )
% 5.06/5.30 => ( ( times_times_rat @ A @ B )
% 5.06/5.30 != zero_zero_rat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % no_zero_divisors
% 5.06/5.30 thf(fact_2943_no__zero__divisors,axiom,
% 5.06/5.30 ! [A: nat,B: nat] :
% 5.06/5.30 ( ( A != zero_zero_nat )
% 5.06/5.30 => ( ( B != zero_zero_nat )
% 5.06/5.30 => ( ( times_times_nat @ A @ B )
% 5.06/5.30 != zero_zero_nat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % no_zero_divisors
% 5.06/5.30 thf(fact_2944_no__zero__divisors,axiom,
% 5.06/5.30 ! [A: int,B: int] :
% 5.06/5.30 ( ( A != zero_zero_int )
% 5.06/5.30 => ( ( B != zero_zero_int )
% 5.06/5.30 => ( ( times_times_int @ A @ B )
% 5.06/5.30 != zero_zero_int ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % no_zero_divisors
% 5.06/5.30 thf(fact_2945_divisors__zero,axiom,
% 5.06/5.30 ! [A: complex,B: complex] :
% 5.06/5.30 ( ( ( times_times_complex @ A @ B )
% 5.06/5.30 = zero_zero_complex )
% 5.06/5.30 => ( ( A = zero_zero_complex )
% 5.06/5.30 | ( B = zero_zero_complex ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divisors_zero
% 5.06/5.30 thf(fact_2946_divisors__zero,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( ( times_times_real @ A @ B )
% 5.06/5.30 = zero_zero_real )
% 5.06/5.30 => ( ( A = zero_zero_real )
% 5.06/5.30 | ( B = zero_zero_real ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divisors_zero
% 5.06/5.30 thf(fact_2947_divisors__zero,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( ( times_times_rat @ A @ B )
% 5.06/5.30 = zero_zero_rat )
% 5.06/5.30 => ( ( A = zero_zero_rat )
% 5.06/5.30 | ( B = zero_zero_rat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divisors_zero
% 5.06/5.30 thf(fact_2948_divisors__zero,axiom,
% 5.06/5.30 ! [A: nat,B: nat] :
% 5.06/5.30 ( ( ( times_times_nat @ A @ B )
% 5.06/5.30 = zero_zero_nat )
% 5.06/5.30 => ( ( A = zero_zero_nat )
% 5.06/5.30 | ( B = zero_zero_nat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divisors_zero
% 5.06/5.30 thf(fact_2949_divisors__zero,axiom,
% 5.06/5.30 ! [A: int,B: int] :
% 5.06/5.30 ( ( ( times_times_int @ A @ B )
% 5.06/5.30 = zero_zero_int )
% 5.06/5.30 => ( ( A = zero_zero_int )
% 5.06/5.30 | ( B = zero_zero_int ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % divisors_zero
% 5.06/5.30 thf(fact_2950_mult__not__zero,axiom,
% 5.06/5.30 ! [A: complex,B: complex] :
% 5.06/5.30 ( ( ( times_times_complex @ A @ B )
% 5.06/5.30 != zero_zero_complex )
% 5.06/5.30 => ( ( A != zero_zero_complex )
% 5.06/5.30 & ( B != zero_zero_complex ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_not_zero
% 5.06/5.30 thf(fact_2951_mult__not__zero,axiom,
% 5.06/5.30 ! [A: real,B: real] :
% 5.06/5.30 ( ( ( times_times_real @ A @ B )
% 5.06/5.30 != zero_zero_real )
% 5.06/5.30 => ( ( A != zero_zero_real )
% 5.06/5.30 & ( B != zero_zero_real ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_not_zero
% 5.06/5.30 thf(fact_2952_mult__not__zero,axiom,
% 5.06/5.30 ! [A: rat,B: rat] :
% 5.06/5.30 ( ( ( times_times_rat @ A @ B )
% 5.06/5.30 != zero_zero_rat )
% 5.06/5.30 => ( ( A != zero_zero_rat )
% 5.06/5.30 & ( B != zero_zero_rat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_not_zero
% 5.06/5.30 thf(fact_2953_mult__not__zero,axiom,
% 5.06/5.30 ! [A: nat,B: nat] :
% 5.06/5.30 ( ( ( times_times_nat @ A @ B )
% 5.06/5.30 != zero_zero_nat )
% 5.06/5.30 => ( ( A != zero_zero_nat )
% 5.06/5.30 & ( B != zero_zero_nat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_not_zero
% 5.06/5.30 thf(fact_2954_mult__not__zero,axiom,
% 5.06/5.30 ! [A: int,B: int] :
% 5.06/5.30 ( ( ( times_times_int @ A @ B )
% 5.06/5.30 != zero_zero_int )
% 5.06/5.30 => ( ( A != zero_zero_int )
% 5.06/5.30 & ( B != zero_zero_int ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % mult_not_zero
% 5.06/5.30 thf(fact_2955_add_Ogroup__left__neutral,axiom,
% 5.06/5.30 ! [A: complex] :
% 5.06/5.30 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % add.group_left_neutral
% 5.06/5.30 thf(fact_2956_add_Ogroup__left__neutral,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % add.group_left_neutral
% 5.06/5.30 thf(fact_2957_add_Ogroup__left__neutral,axiom,
% 5.06/5.30 ! [A: rat] :
% 5.06/5.30 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % add.group_left_neutral
% 5.06/5.30 thf(fact_2958_add_Ogroup__left__neutral,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % add.group_left_neutral
% 5.06/5.30 thf(fact_2959_add_Ocomm__neutral,axiom,
% 5.06/5.30 ! [A: complex] :
% 5.06/5.30 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % add.comm_neutral
% 5.06/5.30 thf(fact_2960_add_Ocomm__neutral,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % add.comm_neutral
% 5.06/5.30 thf(fact_2961_add_Ocomm__neutral,axiom,
% 5.06/5.30 ! [A: rat] :
% 5.06/5.30 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % add.comm_neutral
% 5.06/5.30 thf(fact_2962_add_Ocomm__neutral,axiom,
% 5.06/5.30 ! [A: nat] :
% 5.06/5.30 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % add.comm_neutral
% 5.06/5.30 thf(fact_2963_add_Ocomm__neutral,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % add.comm_neutral
% 5.06/5.30 thf(fact_2964_comm__monoid__add__class_Oadd__0,axiom,
% 5.06/5.30 ! [A: complex] :
% 5.06/5.30 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % comm_monoid_add_class.add_0
% 5.06/5.30 thf(fact_2965_comm__monoid__add__class_Oadd__0,axiom,
% 5.06/5.30 ! [A: real] :
% 5.06/5.30 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % comm_monoid_add_class.add_0
% 5.06/5.30 thf(fact_2966_comm__monoid__add__class_Oadd__0,axiom,
% 5.06/5.30 ! [A: rat] :
% 5.06/5.30 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % comm_monoid_add_class.add_0
% 5.06/5.30 thf(fact_2967_comm__monoid__add__class_Oadd__0,axiom,
% 5.06/5.30 ! [A: nat] :
% 5.06/5.30 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % comm_monoid_add_class.add_0
% 5.06/5.30 thf(fact_2968_comm__monoid__add__class_Oadd__0,axiom,
% 5.06/5.30 ! [A: int] :
% 5.06/5.30 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.06/5.30 = A ) ).
% 5.06/5.30
% 5.06/5.30 % comm_monoid_add_class.add_0
% 5.06/5.30 thf(fact_2969_zero__neq__one,axiom,
% 5.06/5.30 zero_zero_complex != one_one_complex ).
% 5.06/5.30
% 5.06/5.30 % zero_neq_one
% 5.06/5.30 thf(fact_2970_zero__neq__one,axiom,
% 5.06/5.30 zero_zero_real != one_one_real ).
% 5.06/5.30
% 5.06/5.30 % zero_neq_one
% 5.06/5.30 thf(fact_2971_zero__neq__one,axiom,
% 5.06/5.30 zero_zero_rat != one_one_rat ).
% 5.06/5.30
% 5.06/5.30 % zero_neq_one
% 5.06/5.30 thf(fact_2972_zero__neq__one,axiom,
% 5.06/5.30 zero_zero_nat != one_one_nat ).
% 5.06/5.30
% 5.06/5.30 % zero_neq_one
% 5.06/5.30 thf(fact_2973_zero__neq__one,axiom,
% 5.06/5.30 zero_zero_int != one_one_int ).
% 5.06/5.30
% 5.06/5.30 % zero_neq_one
% 5.06/5.30 thf(fact_2974_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.06/5.30 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.06/5.30 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.membermima.simps(2)
% 5.06/5.30 thf(fact_2975_eq__iff__diff__eq__0,axiom,
% 5.06/5.30 ( ( ^ [Y4: complex,Z3: complex] : ( Y4 = Z3 ) )
% 5.06/5.30 = ( ^ [A4: complex,B4: complex] :
% 5.06/5.30 ( ( minus_minus_complex @ A4 @ B4 )
% 5.06/5.30 = zero_zero_complex ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % eq_iff_diff_eq_0
% 5.06/5.30 thf(fact_2976_eq__iff__diff__eq__0,axiom,
% 5.06/5.30 ( ( ^ [Y4: real,Z3: real] : ( Y4 = Z3 ) )
% 5.06/5.30 = ( ^ [A4: real,B4: real] :
% 5.06/5.30 ( ( minus_minus_real @ A4 @ B4 )
% 5.06/5.30 = zero_zero_real ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % eq_iff_diff_eq_0
% 5.06/5.30 thf(fact_2977_eq__iff__diff__eq__0,axiom,
% 5.06/5.30 ( ( ^ [Y4: rat,Z3: rat] : ( Y4 = Z3 ) )
% 5.06/5.30 = ( ^ [A4: rat,B4: rat] :
% 5.06/5.30 ( ( minus_minus_rat @ A4 @ B4 )
% 5.06/5.30 = zero_zero_rat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % eq_iff_diff_eq_0
% 5.06/5.30 thf(fact_2978_eq__iff__diff__eq__0,axiom,
% 5.06/5.30 ( ( ^ [Y4: int,Z3: int] : ( Y4 = Z3 ) )
% 5.06/5.30 = ( ^ [A4: int,B4: int] :
% 5.06/5.30 ( ( minus_minus_int @ A4 @ B4 )
% 5.06/5.30 = zero_zero_int ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % eq_iff_diff_eq_0
% 5.06/5.30 thf(fact_2979_power__not__zero,axiom,
% 5.06/5.30 ! [A: rat,N2: nat] :
% 5.06/5.30 ( ( A != zero_zero_rat )
% 5.06/5.30 => ( ( power_power_rat @ A @ N2 )
% 5.06/5.30 != zero_zero_rat ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_not_zero
% 5.06/5.30 thf(fact_2980_power__not__zero,axiom,
% 5.06/5.30 ! [A: nat,N2: nat] :
% 5.06/5.30 ( ( A != zero_zero_nat )
% 5.06/5.30 => ( ( power_power_nat @ A @ N2 )
% 5.06/5.30 != zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_not_zero
% 5.06/5.30 thf(fact_2981_power__not__zero,axiom,
% 5.06/5.30 ! [A: real,N2: nat] :
% 5.06/5.30 ( ( A != zero_zero_real )
% 5.06/5.30 => ( ( power_power_real @ A @ N2 )
% 5.06/5.30 != zero_zero_real ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_not_zero
% 5.06/5.30 thf(fact_2982_power__not__zero,axiom,
% 5.06/5.30 ! [A: int,N2: nat] :
% 5.06/5.30 ( ( A != zero_zero_int )
% 5.06/5.30 => ( ( power_power_int @ A @ N2 )
% 5.06/5.30 != zero_zero_int ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_not_zero
% 5.06/5.30 thf(fact_2983_power__not__zero,axiom,
% 5.06/5.30 ! [A: complex,N2: nat] :
% 5.06/5.30 ( ( A != zero_zero_complex )
% 5.06/5.30 => ( ( power_power_complex @ A @ N2 )
% 5.06/5.30 != zero_zero_complex ) ) ).
% 5.06/5.30
% 5.06/5.30 % power_not_zero
% 5.06/5.30 thf(fact_2984_num_Osize_I4_J,axiom,
% 5.06/5.30 ( ( size_size_num @ one )
% 5.06/5.30 = zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % num.size(4)
% 5.06/5.30 thf(fact_2985_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.06/5.30 ! [Uu: $o] :
% 5.06/5.30 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.minNull.simps(3)
% 5.06/5.30 thf(fact_2986_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.06/5.30 ! [Uv: $o] :
% 5.06/5.30 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.minNull.simps(2)
% 5.06/5.30 thf(fact_2987_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.06/5.30 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.06/5.30
% 5.06/5.30 % VEBT_internal.minNull.simps(1)
% 5.06/5.30 thf(fact_2988_vebt__buildup_Ocases,axiom,
% 5.06/5.30 ! [X: nat] :
% 5.06/5.30 ( ( X != zero_zero_nat )
% 5.06/5.30 => ( ( X
% 5.06/5.30 != ( suc @ zero_zero_nat ) )
% 5.06/5.30 => ~ ! [Va2: nat] :
% 5.06/5.30 ( X
% 5.06/5.30 != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % vebt_buildup.cases
% 5.06/5.30 thf(fact_2989_nat_Odistinct_I1_J,axiom,
% 5.06/5.30 ! [X22: nat] :
% 5.06/5.30 ( zero_zero_nat
% 5.06/5.30 != ( suc @ X22 ) ) ).
% 5.06/5.30
% 5.06/5.30 % nat.distinct(1)
% 5.06/5.30 thf(fact_2990_old_Onat_Odistinct_I2_J,axiom,
% 5.06/5.30 ! [Nat2: nat] :
% 5.06/5.30 ( ( suc @ Nat2 )
% 5.06/5.30 != zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % old.nat.distinct(2)
% 5.06/5.30 thf(fact_2991_old_Onat_Odistinct_I1_J,axiom,
% 5.06/5.30 ! [Nat2: nat] :
% 5.06/5.30 ( zero_zero_nat
% 5.06/5.30 != ( suc @ Nat2 ) ) ).
% 5.06/5.30
% 5.06/5.30 % old.nat.distinct(1)
% 5.06/5.30 thf(fact_2992_nat_OdiscI,axiom,
% 5.06/5.30 ! [Nat: nat,X22: nat] :
% 5.06/5.30 ( ( Nat
% 5.06/5.30 = ( suc @ X22 ) )
% 5.06/5.30 => ( Nat != zero_zero_nat ) ) ).
% 5.06/5.30
% 5.06/5.30 % nat.discI
% 5.06/5.30 thf(fact_2993_old_Onat_Oexhaust,axiom,
% 5.06/5.30 ! [Y: nat] :
% 5.06/5.30 ( ( Y != zero_zero_nat )
% 5.06/5.30 => ~ ! [Nat3: nat] :
% 5.06/5.30 ( Y
% 5.06/5.30 != ( suc @ Nat3 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % old.nat.exhaust
% 5.06/5.30 thf(fact_2994_nat__induct,axiom,
% 5.06/5.30 ! [P: nat > $o,N2: nat] :
% 5.06/5.30 ( ( P @ zero_zero_nat )
% 5.06/5.30 => ( ! [N3: nat] :
% 5.06/5.30 ( ( P @ N3 )
% 5.06/5.30 => ( P @ ( suc @ N3 ) ) )
% 5.06/5.30 => ( P @ N2 ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % nat_induct
% 5.06/5.30 thf(fact_2995_diff__induct,axiom,
% 5.06/5.30 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 5.06/5.30 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 5.06/5.30 => ( ! [Y5: nat] : ( P @ zero_zero_nat @ ( suc @ Y5 ) )
% 5.06/5.30 => ( ! [X3: nat,Y5: nat] :
% 5.06/5.30 ( ( P @ X3 @ Y5 )
% 5.06/5.30 => ( P @ ( suc @ X3 ) @ ( suc @ Y5 ) ) )
% 5.06/5.30 => ( P @ M @ N2 ) ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % diff_induct
% 5.06/5.30 thf(fact_2996_zero__induct,axiom,
% 5.06/5.30 ! [P: nat > $o,K: nat] :
% 5.06/5.30 ( ( P @ K )
% 5.06/5.30 => ( ! [N3: nat] :
% 5.06/5.30 ( ( P @ ( suc @ N3 ) )
% 5.06/5.30 => ( P @ N3 ) )
% 5.06/5.30 => ( P @ zero_zero_nat ) ) ) ).
% 5.06/5.30
% 5.06/5.30 % zero_induct
% 5.06/5.30 thf(fact_2997_Suc__neq__Zero,axiom,
% 5.06/5.30 ! [M: nat] :
% 5.06/5.30 ( ( suc @ M )
% 5.06/5.30 != zero_zero_nat ) ).
% 5.06/5.30
% 5.06/5.30 % Suc_neq_Zero
% 5.06/5.30 thf(fact_2998_Zero__neq__Suc,axiom,
% 5.06/5.31 ! [M: nat] :
% 5.06/5.31 ( zero_zero_nat
% 5.06/5.31 != ( suc @ M ) ) ).
% 5.06/5.31
% 5.06/5.31 % Zero_neq_Suc
% 5.06/5.31 thf(fact_2999_Zero__not__Suc,axiom,
% 5.06/5.31 ! [M: nat] :
% 5.06/5.31 ( zero_zero_nat
% 5.06/5.31 != ( suc @ M ) ) ).
% 5.06/5.31
% 5.06/5.31 % Zero_not_Suc
% 5.06/5.31 thf(fact_3000_not0__implies__Suc,axiom,
% 5.06/5.31 ! [N2: nat] :
% 5.06/5.31 ( ( N2 != zero_zero_nat )
% 5.06/5.31 => ? [M2: nat] :
% 5.06/5.31 ( N2
% 5.06/5.31 = ( suc @ M2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % not0_implies_Suc
% 5.06/5.31 thf(fact_3001_bot__nat__0_Oextremum__strict,axiom,
% 5.06/5.31 ! [A: nat] :
% 5.06/5.31 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.06/5.31
% 5.06/5.31 % bot_nat_0.extremum_strict
% 5.06/5.31 thf(fact_3002_gr0I,axiom,
% 5.06/5.31 ! [N2: nat] :
% 5.06/5.31 ( ( N2 != zero_zero_nat )
% 5.06/5.31 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.06/5.31
% 5.06/5.31 % gr0I
% 5.06/5.31 thf(fact_3003_not__gr0,axiom,
% 5.06/5.31 ! [N2: nat] :
% 5.06/5.31 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.31 = ( N2 = zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % not_gr0
% 5.06/5.31 thf(fact_3004_not__less0,axiom,
% 5.06/5.31 ! [N2: nat] :
% 5.06/5.31 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.06/5.31
% 5.06/5.31 % not_less0
% 5.06/5.31 thf(fact_3005_less__zeroE,axiom,
% 5.06/5.31 ! [N2: nat] :
% 5.06/5.31 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.06/5.31
% 5.06/5.31 % less_zeroE
% 5.06/5.31 thf(fact_3006_gr__implies__not0,axiom,
% 5.06/5.31 ! [M: nat,N2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ M @ N2 )
% 5.06/5.31 => ( N2 != zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % gr_implies_not0
% 5.06/5.31 thf(fact_3007_infinite__descent0,axiom,
% 5.06/5.31 ! [P: nat > $o,N2: nat] :
% 5.06/5.31 ( ( P @ zero_zero_nat )
% 5.06/5.31 => ( ! [N3: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.06/5.31 => ( ~ ( P @ N3 )
% 5.06/5.31 => ? [M3: nat] :
% 5.06/5.31 ( ( ord_less_nat @ M3 @ N3 )
% 5.06/5.31 & ~ ( P @ M3 ) ) ) )
% 5.06/5.31 => ( P @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % infinite_descent0
% 5.06/5.31 thf(fact_3008_less__eq__nat_Osimps_I1_J,axiom,
% 5.06/5.31 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 5.06/5.31
% 5.06/5.31 % less_eq_nat.simps(1)
% 5.06/5.31 thf(fact_3009_bot__nat__0_Oextremum__unique,axiom,
% 5.06/5.31 ! [A: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.06/5.31 = ( A = zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % bot_nat_0.extremum_unique
% 5.06/5.31 thf(fact_3010_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.06/5.31 ! [A: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.06/5.31 => ( A = zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % bot_nat_0.extremum_uniqueI
% 5.06/5.31 thf(fact_3011_le__0__eq,axiom,
% 5.06/5.31 ! [N2: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 5.06/5.31 = ( N2 = zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % le_0_eq
% 5.06/5.31 thf(fact_3012_add__eq__self__zero,axiom,
% 5.06/5.31 ! [M: nat,N2: nat] :
% 5.06/5.31 ( ( ( plus_plus_nat @ M @ N2 )
% 5.06/5.31 = M )
% 5.06/5.31 => ( N2 = zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_eq_self_zero
% 5.06/5.31 thf(fact_3013_plus__nat_Oadd__0,axiom,
% 5.06/5.31 ! [N2: nat] :
% 5.06/5.31 ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 = N2 ) ).
% 5.06/5.31
% 5.06/5.31 % plus_nat.add_0
% 5.06/5.31 thf(fact_3014_nat__mult__eq__cancel__disj,axiom,
% 5.06/5.31 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.31 ( ( ( times_times_nat @ K @ M )
% 5.06/5.31 = ( times_times_nat @ K @ N2 ) )
% 5.06/5.31 = ( ( K = zero_zero_nat )
% 5.06/5.31 | ( M = N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nat_mult_eq_cancel_disj
% 5.06/5.31 thf(fact_3015_mult__0,axiom,
% 5.06/5.31 ! [N2: nat] :
% 5.06/5.31 ( ( times_times_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 = zero_zero_nat ) ).
% 5.06/5.31
% 5.06/5.31 % mult_0
% 5.06/5.31 thf(fact_3016_minus__nat_Odiff__0,axiom,
% 5.06/5.31 ! [M: nat] :
% 5.06/5.31 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.06/5.31 = M ) ).
% 5.06/5.31
% 5.06/5.31 % minus_nat.diff_0
% 5.06/5.31 thf(fact_3017_diffs0__imp__equal,axiom,
% 5.06/5.31 ! [M: nat,N2: nat] :
% 5.06/5.31 ( ( ( minus_minus_nat @ M @ N2 )
% 5.06/5.31 = zero_zero_nat )
% 5.06/5.31 => ( ( ( minus_minus_nat @ N2 @ M )
% 5.06/5.31 = zero_zero_nat )
% 5.06/5.31 => ( M = N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % diffs0_imp_equal
% 5.06/5.31 thf(fact_3018_mod__geq,axiom,
% 5.06/5.31 ! [M: nat,N2: nat] :
% 5.06/5.31 ( ~ ( ord_less_nat @ M @ N2 )
% 5.06/5.31 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.06/5.31 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mod_geq
% 5.06/5.31 thf(fact_3019_nat__mod__eq__iff,axiom,
% 5.06/5.31 ! [X: nat,N2: nat,Y: nat] :
% 5.06/5.31 ( ( ( modulo_modulo_nat @ X @ N2 )
% 5.06/5.31 = ( modulo_modulo_nat @ Y @ N2 ) )
% 5.06/5.31 = ( ? [Q1: nat,Q22: nat] :
% 5.06/5.31 ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
% 5.06/5.31 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nat_mod_eq_iff
% 5.06/5.31 thf(fact_3020_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.06/5.31 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.06/5.31 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.06/5.31 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.06/5.31 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.06/5.31 thf(fact_3021_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.06/5.31 ! [C: nat,A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.06/5.31 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.06/5.31 thf(fact_3022_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.06/5.31 ! [C: int,A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.06/5.31 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.06/5.31 thf(fact_3023_split__mod,axiom,
% 5.06/5.31 ! [P: nat > $o,M: nat,N2: nat] :
% 5.06/5.31 ( ( P @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.06/5.31 = ( ( ( N2 = zero_zero_nat )
% 5.06/5.31 => ( P @ M ) )
% 5.06/5.31 & ( ( N2 != zero_zero_nat )
% 5.06/5.31 => ! [I5: nat,J3: nat] :
% 5.06/5.31 ( ( ord_less_nat @ J3 @ N2 )
% 5.06/5.31 => ( ( M
% 5.06/5.31 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I5 ) @ J3 ) )
% 5.06/5.31 => ( P @ J3 ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % split_mod
% 5.06/5.31 thf(fact_3024_power__eq__iff__eq__base,axiom,
% 5.06/5.31 ! [N2: nat,A: real,B: real] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.31 => ( ( ( power_power_real @ A @ N2 )
% 5.06/5.31 = ( power_power_real @ B @ N2 ) )
% 5.06/5.31 = ( A = B ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_eq_iff_eq_base
% 5.06/5.31 thf(fact_3025_power__eq__iff__eq__base,axiom,
% 5.06/5.31 ! [N2: nat,A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.31 => ( ( ( power_power_rat @ A @ N2 )
% 5.06/5.31 = ( power_power_rat @ B @ N2 ) )
% 5.06/5.31 = ( A = B ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_eq_iff_eq_base
% 5.06/5.31 thf(fact_3026_power__eq__iff__eq__base,axiom,
% 5.06/5.31 ! [N2: nat,A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ( ( power_power_nat @ A @ N2 )
% 5.06/5.31 = ( power_power_nat @ B @ N2 ) )
% 5.06/5.31 = ( A = B ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_eq_iff_eq_base
% 5.06/5.31 thf(fact_3027_power__eq__iff__eq__base,axiom,
% 5.06/5.31 ! [N2: nat,A: int,B: int] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ( ( power_power_int @ A @ N2 )
% 5.06/5.31 = ( power_power_int @ B @ N2 ) )
% 5.06/5.31 = ( A = B ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_eq_iff_eq_base
% 5.06/5.31 thf(fact_3028_power__eq__imp__eq__base,axiom,
% 5.06/5.31 ! [A: real,N2: nat,B: real] :
% 5.06/5.31 ( ( ( power_power_real @ A @ N2 )
% 5.06/5.31 = ( power_power_real @ B @ N2 ) )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( A = B ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_eq_imp_eq_base
% 5.06/5.31 thf(fact_3029_power__eq__imp__eq__base,axiom,
% 5.06/5.31 ! [A: rat,N2: nat,B: rat] :
% 5.06/5.31 ( ( ( power_power_rat @ A @ N2 )
% 5.06/5.31 = ( power_power_rat @ B @ N2 ) )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( A = B ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_eq_imp_eq_base
% 5.06/5.31 thf(fact_3030_power__eq__imp__eq__base,axiom,
% 5.06/5.31 ! [A: nat,N2: nat,B: nat] :
% 5.06/5.31 ( ( ( power_power_nat @ A @ N2 )
% 5.06/5.31 = ( power_power_nat @ B @ N2 ) )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( A = B ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_eq_imp_eq_base
% 5.06/5.31 thf(fact_3031_power__eq__imp__eq__base,axiom,
% 5.06/5.31 ! [A: int,N2: nat,B: int] :
% 5.06/5.31 ( ( ( power_power_int @ A @ N2 )
% 5.06/5.31 = ( power_power_int @ B @ N2 ) )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( A = B ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_eq_imp_eq_base
% 5.06/5.31 thf(fact_3032_lambda__zero,axiom,
% 5.06/5.31 ( ( ^ [H: complex] : zero_zero_complex )
% 5.06/5.31 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.06/5.31
% 5.06/5.31 % lambda_zero
% 5.06/5.31 thf(fact_3033_lambda__zero,axiom,
% 5.06/5.31 ( ( ^ [H: real] : zero_zero_real )
% 5.06/5.31 = ( times_times_real @ zero_zero_real ) ) ).
% 5.06/5.31
% 5.06/5.31 % lambda_zero
% 5.06/5.31 thf(fact_3034_lambda__zero,axiom,
% 5.06/5.31 ( ( ^ [H: rat] : zero_zero_rat )
% 5.06/5.31 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.06/5.31
% 5.06/5.31 % lambda_zero
% 5.06/5.31 thf(fact_3035_lambda__zero,axiom,
% 5.06/5.31 ( ( ^ [H: nat] : zero_zero_nat )
% 5.06/5.31 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % lambda_zero
% 5.06/5.31 thf(fact_3036_lambda__zero,axiom,
% 5.06/5.31 ( ( ^ [H: int] : zero_zero_int )
% 5.06/5.31 = ( times_times_int @ zero_zero_int ) ) ).
% 5.06/5.31
% 5.06/5.31 % lambda_zero
% 5.06/5.31 thf(fact_3037_VEBT__internal_Omembermima_Ocases,axiom,
% 5.06/5.31 ! [X: produc9072475918466114483BT_nat] :
% 5.06/5.31 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.06/5.31 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.06/5.31 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X3 ) )
% 5.06/5.31 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X3 ) )
% 5.06/5.31 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ X3 ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % VEBT_internal.membermima.cases
% 5.06/5.31 thf(fact_3038_vebt__member_Ocases,axiom,
% 5.06/5.31 ! [X: produc9072475918466114483BT_nat] :
% 5.06/5.31 ( ! [A3: $o,B2: $o,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X3 ) )
% 5.06/5.31 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X3 ) )
% 5.06/5.31 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X3 ) )
% 5.06/5.31 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 5.06/5.31 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % vebt_member.cases
% 5.06/5.31 thf(fact_3039_vebt__delete_Ocases,axiom,
% 5.06/5.31 ! [X: produc9072475918466114483BT_nat] :
% 5.06/5.31 ( ! [A3: $o,B2: $o] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ zero_zero_nat ) )
% 5.06/5.31 => ( ! [A3: $o,B2: $o] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.06/5.31 => ( ! [A3: $o,B2: $o,N3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ ( suc @ N3 ) ) ) )
% 5.06/5.31 => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Uu2 ) )
% 5.06/5.31 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X3 ) )
% 5.06/5.31 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X3 ) )
% 5.06/5.31 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % vebt_delete.cases
% 5.06/5.31 thf(fact_3040_vebt__insert_Ocases,axiom,
% 5.06/5.31 ! [X: produc9072475918466114483BT_nat] :
% 5.06/5.31 ( ! [A3: $o,B2: $o,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X3 ) )
% 5.06/5.31 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) @ X3 ) )
% 5.06/5.31 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X3 ) )
% 5.06/5.31 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X3 ) )
% 5.06/5.31 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % vebt_insert.cases
% 5.06/5.31 thf(fact_3041_vebt__succ_Ocases,axiom,
% 5.06/5.31 ! [X: produc9072475918466114483BT_nat] :
% 5.06/5.31 ( ! [Uu2: $o,B2: $o] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B2 ) @ zero_zero_nat ) )
% 5.06/5.31 => ( ! [Uv2: $o,Uw2: $o,N3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) )
% 5.06/5.31 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 5.06/5.31 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve ) )
% 5.06/5.31 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 5.06/5.31 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % vebt_succ.cases
% 5.06/5.31 thf(fact_3042_vebt__pred_Ocases,axiom,
% 5.06/5.31 ! [X: produc9072475918466114483BT_nat] :
% 5.06/5.31 ( ! [Uu2: $o,Uv2: $o] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 5.06/5.31 => ( ! [A3: $o,Uw2: $o] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.06/5.31 => ( ! [A3: $o,B2: $o,Va2: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ ( suc @ Va2 ) ) ) )
% 5.06/5.31 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 5.06/5.31 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Vf ) )
% 5.06/5.31 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 5.06/5.31 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % vebt_pred.cases
% 5.06/5.31 thf(fact_3043_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.06/5.31 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 5.06/5.31 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X )
% 5.06/5.31 = ( ( X = Mi )
% 5.06/5.31 | ( X = Ma ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % VEBT_internal.membermima.simps(3)
% 5.06/5.31 thf(fact_3044_divmod__digit__0_I2_J,axiom,
% 5.06/5.31 ! [B: nat,A: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.06/5.31 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.06/5.31 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divmod_digit_0(2)
% 5.06/5.31 thf(fact_3045_divmod__digit__0_I2_J,axiom,
% 5.06/5.31 ! [B: int,A: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.06/5.31 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.06/5.31 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divmod_digit_0(2)
% 5.06/5.31 thf(fact_3046_divmod__digit__0_I2_J,axiom,
% 5.06/5.31 ! [B: code_integer,A: code_integer] :
% 5.06/5.31 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.06/5.31 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.06/5.31 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.06/5.31 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divmod_digit_0(2)
% 5.06/5.31 thf(fact_3047_cong__exp__iff__simps_I6_J,axiom,
% 5.06/5.31 ! [Q2: num,N2: num] :
% 5.06/5.31 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.06/5.31 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % cong_exp_iff_simps(6)
% 5.06/5.31 thf(fact_3048_cong__exp__iff__simps_I6_J,axiom,
% 5.06/5.31 ! [Q2: num,N2: num] :
% 5.06/5.31 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.06/5.31 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % cong_exp_iff_simps(6)
% 5.06/5.31 thf(fact_3049_cong__exp__iff__simps_I6_J,axiom,
% 5.06/5.31 ! [Q2: num,N2: num] :
% 5.06/5.31 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.06/5.31 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % cong_exp_iff_simps(6)
% 5.06/5.31 thf(fact_3050_cong__exp__iff__simps_I8_J,axiom,
% 5.06/5.31 ! [M: num,Q2: num] :
% 5.06/5.31 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.06/5.31 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % cong_exp_iff_simps(8)
% 5.06/5.31 thf(fact_3051_cong__exp__iff__simps_I8_J,axiom,
% 5.06/5.31 ! [M: num,Q2: num] :
% 5.06/5.31 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.06/5.31 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % cong_exp_iff_simps(8)
% 5.06/5.31 thf(fact_3052_cong__exp__iff__simps_I8_J,axiom,
% 5.06/5.31 ! [M: num,Q2: num] :
% 5.06/5.31 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.06/5.31 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % cong_exp_iff_simps(8)
% 5.06/5.31 thf(fact_3053_mod__eqE,axiom,
% 5.06/5.31 ! [A: int,C: int,B: int] :
% 5.06/5.31 ( ( ( modulo_modulo_int @ A @ C )
% 5.06/5.31 = ( modulo_modulo_int @ B @ C ) )
% 5.06/5.31 => ~ ! [D4: int] :
% 5.06/5.31 ( B
% 5.06/5.31 != ( plus_plus_int @ A @ ( times_times_int @ C @ D4 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mod_eqE
% 5.06/5.31 thf(fact_3054_mod__eqE,axiom,
% 5.06/5.31 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.31 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.06/5.31 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.06/5.31 => ~ ! [D4: code_integer] :
% 5.06/5.31 ( B
% 5.06/5.31 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D4 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mod_eqE
% 5.06/5.31 thf(fact_3055_div__add1__eq,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat] :
% 5.06/5.31 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.06/5.31 = ( 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 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % div_add1_eq
% 5.06/5.31 thf(fact_3056_div__add1__eq,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int] :
% 5.06/5.31 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.06/5.31 = ( 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 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % div_add1_eq
% 5.06/5.31 thf(fact_3057_div__add1__eq,axiom,
% 5.06/5.31 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.31 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.06/5.31 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % div_add1_eq
% 5.06/5.31 thf(fact_3058_Suc__times__mod__eq,axiom,
% 5.06/5.31 ! [M: nat,N2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.06/5.31 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 5.06/5.31 = one_one_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % Suc_times_mod_eq
% 5.06/5.31 thf(fact_3059_mod__induct,axiom,
% 5.06/5.31 ! [P: nat > $o,N2: nat,P4: nat,M: nat] :
% 5.06/5.31 ( ( P @ N2 )
% 5.06/5.31 => ( ( ord_less_nat @ N2 @ P4 )
% 5.06/5.31 => ( ( ord_less_nat @ M @ P4 )
% 5.06/5.31 => ( ! [N3: nat] :
% 5.06/5.31 ( ( ord_less_nat @ N3 @ P4 )
% 5.06/5.31 => ( ( P @ N3 )
% 5.06/5.31 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P4 ) ) ) )
% 5.06/5.31 => ( P @ M ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mod_induct
% 5.06/5.31 thf(fact_3060_mod__Suc__le__divisor,axiom,
% 5.06/5.31 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 5.06/5.31
% 5.06/5.31 % mod_Suc_le_divisor
% 5.06/5.31 thf(fact_3061_power__strict__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,N2: nat] :
% 5.06/5.31 ( ( ord_less_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_strict_mono
% 5.06/5.31 thf(fact_3062_power__strict__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,N2: nat] :
% 5.06/5.31 ( ( ord_less_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_strict_mono
% 5.06/5.31 thf(fact_3063_power__strict__mono,axiom,
% 5.06/5.31 ! [A: nat,B: nat,N2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_strict_mono
% 5.06/5.31 thf(fact_3064_power__strict__mono,axiom,
% 5.06/5.31 ! [A: int,B: int,N2: nat] :
% 5.06/5.31 ( ( ord_less_int @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_strict_mono
% 5.06/5.31 thf(fact_3065_nat__mod__eq__lemma,axiom,
% 5.06/5.31 ! [X: nat,N2: nat,Y: nat] :
% 5.06/5.31 ( ( ( modulo_modulo_nat @ X @ N2 )
% 5.06/5.31 = ( modulo_modulo_nat @ Y @ N2 ) )
% 5.06/5.31 => ( ( ord_less_eq_nat @ Y @ X )
% 5.06/5.31 => ? [Q3: nat] :
% 5.06/5.31 ( X
% 5.06/5.31 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q3 ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nat_mod_eq_lemma
% 5.06/5.31 thf(fact_3066_mod__eq__nat2E,axiom,
% 5.06/5.31 ! [M: nat,Q2: nat,N2: nat] :
% 5.06/5.31 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.06/5.31 = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 5.06/5.31 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.31 => ~ ! [S: nat] :
% 5.06/5.31 ( N2
% 5.06/5.31 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mod_eq_nat2E
% 5.06/5.31 thf(fact_3067_mod__eq__nat1E,axiom,
% 5.06/5.31 ! [M: nat,Q2: nat,N2: nat] :
% 5.06/5.31 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.06/5.31 = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 5.06/5.31 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.31 => ~ ! [S: nat] :
% 5.06/5.31 ( M
% 5.06/5.31 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mod_eq_nat1E
% 5.06/5.31 thf(fact_3068_mod__if,axiom,
% 5.06/5.31 ( modulo_modulo_nat
% 5.06/5.31 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mod_if
% 5.06/5.31 thf(fact_3069_le__mod__geq,axiom,
% 5.06/5.31 ! [N2: nat,M: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.31 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.06/5.31 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % le_mod_geq
% 5.06/5.31 thf(fact_3070_vebt__delete_Osimps_I3_J,axiom,
% 5.06/5.31 ! [A: $o,B: $o,N2: nat] :
% 5.06/5.31 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N2 ) ) )
% 5.06/5.31 = ( vEBT_Leaf @ A @ B ) ) ).
% 5.06/5.31
% 5.06/5.31 % vebt_delete.simps(3)
% 5.06/5.31 thf(fact_3071_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_nat @ A @ B )
% 5.06/5.31 => ( ( divide_divide_nat @ A @ B )
% 5.06/5.31 = zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % unique_euclidean_semiring_numeral_class.div_less
% 5.06/5.31 thf(fact_3072_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_int @ A @ B )
% 5.06/5.31 => ( ( divide_divide_int @ A @ B )
% 5.06/5.31 = zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % unique_euclidean_semiring_numeral_class.div_less
% 5.06/5.31 thf(fact_3073_div__positive,axiom,
% 5.06/5.31 ! [B: nat,A: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ( ord_less_eq_nat @ B @ A )
% 5.06/5.31 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % div_positive
% 5.06/5.31 thf(fact_3074_div__positive,axiom,
% 5.06/5.31 ! [B: int,A: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ( ord_less_eq_int @ B @ A )
% 5.06/5.31 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % div_positive
% 5.06/5.31 thf(fact_3075_vebt__mint_Osimps_I1_J,axiom,
% 5.06/5.31 ! [A: $o,B: $o] :
% 5.06/5.31 ( ( A
% 5.06/5.31 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.06/5.31 = ( some_nat @ zero_zero_nat ) ) )
% 5.06/5.31 & ( ~ A
% 5.06/5.31 => ( ( B
% 5.06/5.31 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.06/5.31 = ( some_nat @ one_one_nat ) ) )
% 5.06/5.31 & ( ~ B
% 5.06/5.31 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.06/5.31 = none_nat ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % vebt_mint.simps(1)
% 5.06/5.31 thf(fact_3076_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.06/5.31 ! [C: nat,A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.06/5.31 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.06/5.31 thf(fact_3077_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.06/5.31 ! [C: int,A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.06/5.31 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.06/5.31 thf(fact_3078_vebt__maxt_Osimps_I1_J,axiom,
% 5.06/5.31 ! [B: $o,A: $o] :
% 5.06/5.31 ( ( B
% 5.06/5.31 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.06/5.31 = ( some_nat @ one_one_nat ) ) )
% 5.06/5.31 & ( ~ B
% 5.06/5.31 => ( ( A
% 5.06/5.31 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.06/5.31 = ( some_nat @ zero_zero_nat ) ) )
% 5.06/5.31 & ( ~ A
% 5.06/5.31 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.06/5.31 = none_nat ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % vebt_maxt.simps(1)
% 5.06/5.31 thf(fact_3079_vebt__pred_Osimps_I2_J,axiom,
% 5.06/5.31 ! [A: $o,Uw: $o] :
% 5.06/5.31 ( ( A
% 5.06/5.31 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.06/5.31 = ( some_nat @ zero_zero_nat ) ) )
% 5.06/5.31 & ( ~ A
% 5.06/5.31 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.06/5.31 = none_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % vebt_pred.simps(2)
% 5.06/5.31 thf(fact_3080_vebt__succ_Osimps_I1_J,axiom,
% 5.06/5.31 ! [B: $o,Uu: $o] :
% 5.06/5.31 ( ( B
% 5.06/5.31 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.06/5.31 = ( some_nat @ one_one_nat ) ) )
% 5.06/5.31 & ( ~ B
% 5.06/5.31 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.06/5.31 = none_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % vebt_succ.simps(1)
% 5.06/5.31 thf(fact_3081_zero__le__numeral,axiom,
% 5.06/5.31 ! [N2: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_numeral
% 5.06/5.31 thf(fact_3082_zero__le__numeral,axiom,
% 5.06/5.31 ! [N2: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_numeral
% 5.06/5.31 thf(fact_3083_zero__le__numeral,axiom,
% 5.06/5.31 ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_numeral
% 5.06/5.31 thf(fact_3084_zero__le__numeral,axiom,
% 5.06/5.31 ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_numeral
% 5.06/5.31 thf(fact_3085_not__numeral__le__zero,axiom,
% 5.06/5.31 ! [N2: num] :
% 5.06/5.31 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 5.06/5.31
% 5.06/5.31 % not_numeral_le_zero
% 5.06/5.31 thf(fact_3086_not__numeral__le__zero,axiom,
% 5.06/5.31 ! [N2: num] :
% 5.06/5.31 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 5.06/5.31
% 5.06/5.31 % not_numeral_le_zero
% 5.06/5.31 thf(fact_3087_not__numeral__le__zero,axiom,
% 5.06/5.31 ! [N2: num] :
% 5.06/5.31 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 5.06/5.31
% 5.06/5.31 % not_numeral_le_zero
% 5.06/5.31 thf(fact_3088_not__numeral__le__zero,axiom,
% 5.06/5.31 ! [N2: num] :
% 5.06/5.31 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 5.06/5.31
% 5.06/5.31 % not_numeral_le_zero
% 5.06/5.31 thf(fact_3089_mult__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_real @ C @ D )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_mono
% 5.06/5.31 thf(fact_3090_mult__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_rat @ C @ D )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_mono
% 5.06/5.31 thf(fact_3091_mult__mono,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_nat @ C @ D )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_mono
% 5.06/5.31 thf(fact_3092_mult__mono,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_int @ C @ D )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_mono
% 5.06/5.31 thf(fact_3093_mult__mono_H,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_real @ C @ D )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_mono'
% 5.06/5.31 thf(fact_3094_mult__mono_H,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_rat @ C @ D )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_mono'
% 5.06/5.31 thf(fact_3095_mult__mono_H,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_nat @ C @ D )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_mono'
% 5.06/5.31 thf(fact_3096_mult__mono_H,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_int @ C @ D )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_mono'
% 5.06/5.31 thf(fact_3097_zero__le__square,axiom,
% 5.06/5.31 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_square
% 5.06/5.31 thf(fact_3098_zero__le__square,axiom,
% 5.06/5.31 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_square
% 5.06/5.31 thf(fact_3099_zero__le__square,axiom,
% 5.06/5.31 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_square
% 5.06/5.31 thf(fact_3100_split__mult__pos__le,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.06/5.31 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.31 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.06/5.31 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % split_mult_pos_le
% 5.06/5.31 thf(fact_3101_split__mult__pos__le,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.06/5.31 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.06/5.31 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % split_mult_pos_le
% 5.06/5.31 thf(fact_3102_split__mult__pos__le,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.06/5.31 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.31 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.06/5.31 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % split_mult_pos_le
% 5.06/5.31 thf(fact_3103_mult__left__mono__neg,axiom,
% 5.06/5.31 ! [B: real,A: real,C: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ B @ A )
% 5.06/5.31 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_left_mono_neg
% 5.06/5.31 thf(fact_3104_mult__left__mono__neg,axiom,
% 5.06/5.31 ! [B: rat,A: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ B @ A )
% 5.06/5.31 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_left_mono_neg
% 5.06/5.31 thf(fact_3105_mult__left__mono__neg,axiom,
% 5.06/5.31 ! [B: int,A: int,C: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ B @ A )
% 5.06/5.31 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_left_mono_neg
% 5.06/5.31 thf(fact_3106_mult__nonpos__nonpos,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.06/5.31 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonpos_nonpos
% 5.06/5.31 thf(fact_3107_mult__nonpos__nonpos,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonpos_nonpos
% 5.06/5.31 thf(fact_3108_mult__nonpos__nonpos,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.06/5.31 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonpos_nonpos
% 5.06/5.31 thf(fact_3109_mult__left__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_left_mono
% 5.06/5.31 thf(fact_3110_mult__left__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_left_mono
% 5.06/5.31 thf(fact_3111_mult__left__mono,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_left_mono
% 5.06/5.31 thf(fact_3112_mult__left__mono,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_left_mono
% 5.06/5.31 thf(fact_3113_mult__right__mono__neg,axiom,
% 5.06/5.31 ! [B: real,A: real,C: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ B @ A )
% 5.06/5.31 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_right_mono_neg
% 5.06/5.31 thf(fact_3114_mult__right__mono__neg,axiom,
% 5.06/5.31 ! [B: rat,A: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ B @ A )
% 5.06/5.31 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_right_mono_neg
% 5.06/5.31 thf(fact_3115_mult__right__mono__neg,axiom,
% 5.06/5.31 ! [B: int,A: int,C: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ B @ A )
% 5.06/5.31 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_right_mono_neg
% 5.06/5.31 thf(fact_3116_mult__right__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_right_mono
% 5.06/5.31 thf(fact_3117_mult__right__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_right_mono
% 5.06/5.31 thf(fact_3118_mult__right__mono,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_right_mono
% 5.06/5.31 thf(fact_3119_mult__right__mono,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_right_mono
% 5.06/5.31 thf(fact_3120_mult__le__0__iff,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.06/5.31 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.06/5.31 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.31 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_le_0_iff
% 5.06/5.31 thf(fact_3121_mult__le__0__iff,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.06/5.31 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.06/5.31 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_le_0_iff
% 5.06/5.31 thf(fact_3122_mult__le__0__iff,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.06/5.31 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.06/5.31 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.31 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_le_0_iff
% 5.06/5.31 thf(fact_3123_split__mult__neg__le,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.06/5.31 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.31 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.06/5.31
% 5.06/5.31 % split_mult_neg_le
% 5.06/5.31 thf(fact_3124_split__mult__neg__le,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.06/5.31 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.06/5.31
% 5.06/5.31 % split_mult_neg_le
% 5.06/5.31 thf(fact_3125_split__mult__neg__le,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.06/5.31 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.06/5.31 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.06/5.31 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % split_mult_neg_le
% 5.06/5.31 thf(fact_3126_split__mult__neg__le,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.06/5.31 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.31 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.06/5.31
% 5.06/5.31 % split_mult_neg_le
% 5.06/5.31 thf(fact_3127_mult__nonneg__nonneg,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.31 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonneg
% 5.06/5.31 thf(fact_3128_mult__nonneg__nonneg,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.31 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonneg
% 5.06/5.31 thf(fact_3129_mult__nonneg__nonneg,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonneg
% 5.06/5.31 thf(fact_3130_mult__nonneg__nonneg,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonneg
% 5.06/5.31 thf(fact_3131_mult__nonneg__nonpos,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonpos
% 5.06/5.31 thf(fact_3132_mult__nonneg__nonpos,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonpos
% 5.06/5.31 thf(fact_3133_mult__nonneg__nonpos,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.06/5.31 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonpos
% 5.06/5.31 thf(fact_3134_mult__nonneg__nonpos,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonpos
% 5.06/5.31 thf(fact_3135_mult__nonpos__nonneg,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonpos_nonneg
% 5.06/5.31 thf(fact_3136_mult__nonpos__nonneg,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonpos_nonneg
% 5.06/5.31 thf(fact_3137_mult__nonpos__nonneg,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonpos_nonneg
% 5.06/5.31 thf(fact_3138_mult__nonpos__nonneg,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonpos_nonneg
% 5.06/5.31 thf(fact_3139_mult__nonneg__nonpos2,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonpos2
% 5.06/5.31 thf(fact_3140_mult__nonneg__nonpos2,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonpos2
% 5.06/5.31 thf(fact_3141_mult__nonneg__nonpos2,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.06/5.31 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonpos2
% 5.06/5.31 thf(fact_3142_mult__nonneg__nonpos2,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_nonneg_nonpos2
% 5.06/5.31 thf(fact_3143_zero__le__mult__iff,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.06/5.31 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.06/5.31 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.31 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_mult_iff
% 5.06/5.31 thf(fact_3144_zero__le__mult__iff,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.06/5.31 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.06/5.31 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_mult_iff
% 5.06/5.31 thf(fact_3145_zero__le__mult__iff,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.06/5.31 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.06/5.31 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.31 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_mult_iff
% 5.06/5.31 thf(fact_3146_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.06/5.31 thf(fact_3147_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.06/5.31 thf(fact_3148_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.06/5.31 thf(fact_3149_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.06/5.31 thf(fact_3150_zero__less__numeral,axiom,
% 5.06/5.31 ! [N2: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_numeral
% 5.06/5.31 thf(fact_3151_zero__less__numeral,axiom,
% 5.06/5.31 ! [N2: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_numeral
% 5.06/5.31 thf(fact_3152_zero__less__numeral,axiom,
% 5.06/5.31 ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_numeral
% 5.06/5.31 thf(fact_3153_zero__less__numeral,axiom,
% 5.06/5.31 ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_numeral
% 5.06/5.31 thf(fact_3154_not__numeral__less__zero,axiom,
% 5.06/5.31 ! [N2: num] :
% 5.06/5.31 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 5.06/5.31
% 5.06/5.31 % not_numeral_less_zero
% 5.06/5.31 thf(fact_3155_not__numeral__less__zero,axiom,
% 5.06/5.31 ! [N2: num] :
% 5.06/5.31 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 5.06/5.31
% 5.06/5.31 % not_numeral_less_zero
% 5.06/5.31 thf(fact_3156_not__numeral__less__zero,axiom,
% 5.06/5.31 ! [N2: num] :
% 5.06/5.31 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 5.06/5.31
% 5.06/5.31 % not_numeral_less_zero
% 5.06/5.31 thf(fact_3157_not__numeral__less__zero,axiom,
% 5.06/5.31 ! [N2: num] :
% 5.06/5.31 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 5.06/5.31
% 5.06/5.31 % not_numeral_less_zero
% 5.06/5.31 thf(fact_3158_add__decreasing,axiom,
% 5.06/5.31 ! [A: real,C: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_eq_real @ C @ B )
% 5.06/5.31 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_decreasing
% 5.06/5.31 thf(fact_3159_add__decreasing,axiom,
% 5.06/5.31 ! [A: rat,C: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_eq_rat @ C @ B )
% 5.06/5.31 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_decreasing
% 5.06/5.31 thf(fact_3160_add__decreasing,axiom,
% 5.06/5.31 ! [A: nat,C: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.06/5.31 => ( ( ord_less_eq_nat @ C @ B )
% 5.06/5.31 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_decreasing
% 5.06/5.31 thf(fact_3161_add__decreasing,axiom,
% 5.06/5.31 ! [A: int,C: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_eq_int @ C @ B )
% 5.06/5.31 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_decreasing
% 5.06/5.31 thf(fact_3162_add__increasing,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_eq_real @ B @ C )
% 5.06/5.31 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_increasing
% 5.06/5.31 thf(fact_3163_add__increasing,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.06/5.31 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_increasing
% 5.06/5.31 thf(fact_3164_add__increasing,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_eq_nat @ B @ C )
% 5.06/5.31 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_increasing
% 5.06/5.31 thf(fact_3165_add__increasing,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_eq_int @ B @ C )
% 5.06/5.31 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_increasing
% 5.06/5.31 thf(fact_3166_add__decreasing2,axiom,
% 5.06/5.31 ! [C: real,A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_eq_real @ A @ B )
% 5.06/5.31 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_decreasing2
% 5.06/5.31 thf(fact_3167_add__decreasing2,axiom,
% 5.06/5.31 ! [C: rat,A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.31 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_decreasing2
% 5.06/5.31 thf(fact_3168_add__decreasing2,axiom,
% 5.06/5.31 ! [C: nat,A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.06/5.31 => ( ( ord_less_eq_nat @ A @ B )
% 5.06/5.31 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_decreasing2
% 5.06/5.31 thf(fact_3169_add__decreasing2,axiom,
% 5.06/5.31 ! [C: int,A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_eq_int @ A @ B )
% 5.06/5.31 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_decreasing2
% 5.06/5.31 thf(fact_3170_add__increasing2,axiom,
% 5.06/5.31 ! [C: real,B: real,A: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ( ord_less_eq_real @ B @ A )
% 5.06/5.31 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_increasing2
% 5.06/5.31 thf(fact_3171_add__increasing2,axiom,
% 5.06/5.31 ! [C: rat,B: rat,A: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ( ord_less_eq_rat @ B @ A )
% 5.06/5.31 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_increasing2
% 5.06/5.31 thf(fact_3172_add__increasing2,axiom,
% 5.06/5.31 ! [C: nat,B: nat,A: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ( ord_less_eq_nat @ B @ A )
% 5.06/5.31 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_increasing2
% 5.06/5.31 thf(fact_3173_add__increasing2,axiom,
% 5.06/5.31 ! [C: int,B: int,A: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ( ord_less_eq_int @ B @ A )
% 5.06/5.31 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_increasing2
% 5.06/5.31 thf(fact_3174_add__nonneg__nonneg,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.31 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonneg_nonneg
% 5.06/5.31 thf(fact_3175_add__nonneg__nonneg,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.31 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonneg_nonneg
% 5.06/5.31 thf(fact_3176_add__nonneg__nonneg,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonneg_nonneg
% 5.06/5.31 thf(fact_3177_add__nonneg__nonneg,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonneg_nonneg
% 5.06/5.31 thf(fact_3178_add__nonpos__nonpos,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.06/5.31 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonpos_nonpos
% 5.06/5.31 thf(fact_3179_add__nonpos__nonpos,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonpos_nonpos
% 5.06/5.31 thf(fact_3180_add__nonpos__nonpos,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.06/5.31 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.06/5.31 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonpos_nonpos
% 5.06/5.31 thf(fact_3181_add__nonpos__nonpos,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.06/5.31 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonpos_nonpos
% 5.06/5.31 thf(fact_3182_add__nonneg__eq__0__iff,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.31 => ( ( ( plus_plus_real @ X @ Y )
% 5.06/5.31 = zero_zero_real )
% 5.06/5.31 = ( ( X = zero_zero_real )
% 5.06/5.31 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonneg_eq_0_iff
% 5.06/5.31 thf(fact_3183_add__nonneg__eq__0__iff,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.31 => ( ( ( plus_plus_rat @ X @ Y )
% 5.06/5.31 = zero_zero_rat )
% 5.06/5.31 = ( ( X = zero_zero_rat )
% 5.06/5.31 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonneg_eq_0_iff
% 5.06/5.31 thf(fact_3184_add__nonneg__eq__0__iff,axiom,
% 5.06/5.31 ! [X: nat,Y: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.06/5.31 => ( ( ( plus_plus_nat @ X @ Y )
% 5.06/5.31 = zero_zero_nat )
% 5.06/5.31 = ( ( X = zero_zero_nat )
% 5.06/5.31 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonneg_eq_0_iff
% 5.06/5.31 thf(fact_3185_add__nonneg__eq__0__iff,axiom,
% 5.06/5.31 ! [X: int,Y: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.31 => ( ( ( plus_plus_int @ X @ Y )
% 5.06/5.31 = zero_zero_int )
% 5.06/5.31 = ( ( X = zero_zero_int )
% 5.06/5.31 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonneg_eq_0_iff
% 5.06/5.31 thf(fact_3186_add__nonpos__eq__0__iff,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.06/5.31 => ( ( ( plus_plus_real @ X @ Y )
% 5.06/5.31 = zero_zero_real )
% 5.06/5.31 = ( ( X = zero_zero_real )
% 5.06/5.31 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonpos_eq_0_iff
% 5.06/5.31 thf(fact_3187_add__nonpos__eq__0__iff,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.06/5.31 => ( ( ( plus_plus_rat @ X @ Y )
% 5.06/5.31 = zero_zero_rat )
% 5.06/5.31 = ( ( X = zero_zero_rat )
% 5.06/5.31 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonpos_eq_0_iff
% 5.06/5.31 thf(fact_3188_add__nonpos__eq__0__iff,axiom,
% 5.06/5.31 ! [X: nat,Y: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 5.06/5.31 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 5.06/5.31 => ( ( ( plus_plus_nat @ X @ Y )
% 5.06/5.31 = zero_zero_nat )
% 5.06/5.31 = ( ( X = zero_zero_nat )
% 5.06/5.31 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonpos_eq_0_iff
% 5.06/5.31 thf(fact_3189_add__nonpos__eq__0__iff,axiom,
% 5.06/5.31 ! [X: int,Y: int] :
% 5.06/5.31 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.06/5.31 => ( ( ( plus_plus_int @ X @ Y )
% 5.06/5.31 = zero_zero_int )
% 5.06/5.31 = ( ( X = zero_zero_int )
% 5.06/5.31 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_nonpos_eq_0_iff
% 5.06/5.31 thf(fact_3190_not__one__le__zero,axiom,
% 5.06/5.31 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.06/5.31
% 5.06/5.31 % not_one_le_zero
% 5.06/5.31 thf(fact_3191_not__one__le__zero,axiom,
% 5.06/5.31 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.06/5.31
% 5.06/5.31 % not_one_le_zero
% 5.06/5.31 thf(fact_3192_not__one__le__zero,axiom,
% 5.06/5.31 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.06/5.31
% 5.06/5.31 % not_one_le_zero
% 5.06/5.31 thf(fact_3193_not__one__le__zero,axiom,
% 5.06/5.31 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.06/5.31
% 5.06/5.31 % not_one_le_zero
% 5.06/5.31 thf(fact_3194_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.06/5.31 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.06/5.31
% 5.06/5.31 % linordered_nonzero_semiring_class.zero_le_one
% 5.06/5.31 thf(fact_3195_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.06/5.31 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.06/5.31
% 5.06/5.31 % linordered_nonzero_semiring_class.zero_le_one
% 5.06/5.31 thf(fact_3196_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.06/5.31 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.06/5.31
% 5.06/5.31 % linordered_nonzero_semiring_class.zero_le_one
% 5.06/5.31 thf(fact_3197_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.06/5.31 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.06/5.31
% 5.06/5.31 % linordered_nonzero_semiring_class.zero_le_one
% 5.06/5.31 thf(fact_3198_zero__less__one__class_Ozero__le__one,axiom,
% 5.06/5.31 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.06/5.31
% 5.06/5.31 % zero_less_one_class.zero_le_one
% 5.06/5.31 thf(fact_3199_zero__less__one__class_Ozero__le__one,axiom,
% 5.06/5.31 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.06/5.31
% 5.06/5.31 % zero_less_one_class.zero_le_one
% 5.06/5.31 thf(fact_3200_zero__less__one__class_Ozero__le__one,axiom,
% 5.06/5.31 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.06/5.31
% 5.06/5.31 % zero_less_one_class.zero_le_one
% 5.06/5.31 thf(fact_3201_zero__less__one__class_Ozero__le__one,axiom,
% 5.06/5.31 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.06/5.31
% 5.06/5.31 % zero_less_one_class.zero_le_one
% 5.06/5.31 thf(fact_3202_mult__neg__neg,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.06/5.31 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_neg_neg
% 5.06/5.31 thf(fact_3203_mult__neg__neg,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_neg_neg
% 5.06/5.31 thf(fact_3204_mult__neg__neg,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ A @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.06/5.31 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_neg_neg
% 5.06/5.31 thf(fact_3205_not__square__less__zero,axiom,
% 5.06/5.31 ! [A: real] :
% 5.06/5.31 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.06/5.31
% 5.06/5.31 % not_square_less_zero
% 5.06/5.31 thf(fact_3206_not__square__less__zero,axiom,
% 5.06/5.31 ! [A: rat] :
% 5.06/5.31 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.06/5.31
% 5.06/5.31 % not_square_less_zero
% 5.06/5.31 thf(fact_3207_not__square__less__zero,axiom,
% 5.06/5.31 ! [A: int] :
% 5.06/5.31 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.06/5.31
% 5.06/5.31 % not_square_less_zero
% 5.06/5.31 thf(fact_3208_mult__less__0__iff,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.06/5.31 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.06/5.31 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.31 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_0_iff
% 5.06/5.31 thf(fact_3209_mult__less__0__iff,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.06/5.31 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.06/5.31 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_0_iff
% 5.06/5.31 thf(fact_3210_mult__less__0__iff,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.06/5.31 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.31 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.06/5.31 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.06/5.31 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_0_iff
% 5.06/5.31 thf(fact_3211_mult__neg__pos,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.31 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_neg_pos
% 5.06/5.31 thf(fact_3212_mult__neg__pos,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.06/5.31 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_neg_pos
% 5.06/5.31 thf(fact_3213_mult__neg__pos,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_neg_pos
% 5.06/5.31 thf(fact_3214_mult__neg__pos,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ A @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_neg_pos
% 5.06/5.31 thf(fact_3215_mult__pos__neg,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.06/5.31 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_neg
% 5.06/5.31 thf(fact_3216_mult__pos__neg,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_neg
% 5.06/5.31 thf(fact_3217_mult__pos__neg,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.06/5.31 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_neg
% 5.06/5.31 thf(fact_3218_mult__pos__neg,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.06/5.31 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_neg
% 5.06/5.31 thf(fact_3219_mult__pos__pos,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.31 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_pos
% 5.06/5.31 thf(fact_3220_mult__pos__pos,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.06/5.31 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_pos
% 5.06/5.31 thf(fact_3221_mult__pos__pos,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_pos
% 5.06/5.31 thf(fact_3222_mult__pos__pos,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_pos
% 5.06/5.31 thf(fact_3223_mult__pos__neg2,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.06/5.31 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_neg2
% 5.06/5.31 thf(fact_3224_mult__pos__neg2,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_neg2
% 5.06/5.31 thf(fact_3225_mult__pos__neg2,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.06/5.31 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_neg2
% 5.06/5.31 thf(fact_3226_mult__pos__neg2,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.06/5.31 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_pos_neg2
% 5.06/5.31 thf(fact_3227_zero__less__mult__iff,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.06/5.31 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.06/5.31 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.31 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_iff
% 5.06/5.31 thf(fact_3228_zero__less__mult__iff,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.06/5.31 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.06/5.31 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_iff
% 5.06/5.31 thf(fact_3229_zero__less__mult__iff,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.06/5.31 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.31 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.06/5.31 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.06/5.31 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_iff
% 5.06/5.31 thf(fact_3230_zero__less__mult__pos,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_pos
% 5.06/5.31 thf(fact_3231_zero__less__mult__pos,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_pos
% 5.06/5.31 thf(fact_3232_zero__less__mult__pos,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_pos
% 5.06/5.31 thf(fact_3233_zero__less__mult__pos,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.06/5.31 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_pos
% 5.06/5.31 thf(fact_3234_zero__less__mult__pos2,axiom,
% 5.06/5.31 ! [B: real,A: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_pos2
% 5.06/5.31 thf(fact_3235_zero__less__mult__pos2,axiom,
% 5.06/5.31 ! [B: rat,A: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_pos2
% 5.06/5.31 thf(fact_3236_zero__less__mult__pos2,axiom,
% 5.06/5.31 ! [B: nat,A: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_pos2
% 5.06/5.31 thf(fact_3237_zero__less__mult__pos2,axiom,
% 5.06/5.31 ! [B: int,A: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.06/5.31 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_mult_pos2
% 5.06/5.31 thf(fact_3238_mult__less__cancel__left__neg,axiom,
% 5.06/5.31 ! [C: real,A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.06/5.31 = ( ord_less_real @ B @ A ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_left_neg
% 5.06/5.31 thf(fact_3239_mult__less__cancel__left__neg,axiom,
% 5.06/5.31 ! [C: rat,A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.06/5.31 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_left_neg
% 5.06/5.31 thf(fact_3240_mult__less__cancel__left__neg,axiom,
% 5.06/5.31 ! [C: int,A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.31 = ( ord_less_int @ B @ A ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_left_neg
% 5.06/5.31 thf(fact_3241_mult__less__cancel__left__pos,axiom,
% 5.06/5.31 ! [C: real,A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.06/5.31 = ( ord_less_real @ A @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_left_pos
% 5.06/5.31 thf(fact_3242_mult__less__cancel__left__pos,axiom,
% 5.06/5.31 ! [C: rat,A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.06/5.31 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_left_pos
% 5.06/5.31 thf(fact_3243_mult__less__cancel__left__pos,axiom,
% 5.06/5.31 ! [C: int,A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.31 = ( ord_less_int @ A @ B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_left_pos
% 5.06/5.31 thf(fact_3244_mult__strict__left__mono__neg,axiom,
% 5.06/5.31 ! [B: real,A: real,C: real] :
% 5.06/5.31 ( ( ord_less_real @ B @ A )
% 5.06/5.31 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.31 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_left_mono_neg
% 5.06/5.31 thf(fact_3245_mult__strict__left__mono__neg,axiom,
% 5.06/5.31 ! [B: rat,A: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_rat @ B @ A )
% 5.06/5.31 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_left_mono_neg
% 5.06/5.31 thf(fact_3246_mult__strict__left__mono__neg,axiom,
% 5.06/5.31 ! [B: int,A: int,C: int] :
% 5.06/5.31 ( ( ord_less_int @ B @ A )
% 5.06/5.31 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.31 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_left_mono_neg
% 5.06/5.31 thf(fact_3247_mult__strict__left__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_left_mono
% 5.06/5.31 thf(fact_3248_mult__strict__left__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_left_mono
% 5.06/5.31 thf(fact_3249_mult__strict__left__mono,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat] :
% 5.06/5.31 ( ( ord_less_nat @ A @ B )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_left_mono
% 5.06/5.31 thf(fact_3250_mult__strict__left__mono,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int] :
% 5.06/5.31 ( ( ord_less_int @ A @ B )
% 5.06/5.31 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_left_mono
% 5.06/5.31 thf(fact_3251_mult__less__cancel__left__disj,axiom,
% 5.06/5.31 ! [C: real,A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.06/5.31 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.31 & ( ord_less_real @ A @ B ) )
% 5.06/5.31 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.31 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_left_disj
% 5.06/5.31 thf(fact_3252_mult__less__cancel__left__disj,axiom,
% 5.06/5.31 ! [C: rat,A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.06/5.31 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.31 & ( ord_less_rat @ A @ B ) )
% 5.06/5.31 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_left_disj
% 5.06/5.31 thf(fact_3253_mult__less__cancel__left__disj,axiom,
% 5.06/5.31 ! [C: int,A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.31 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.31 & ( ord_less_int @ A @ B ) )
% 5.06/5.31 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.31 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_left_disj
% 5.06/5.31 thf(fact_3254_mult__strict__right__mono__neg,axiom,
% 5.06/5.31 ! [B: real,A: real,C: real] :
% 5.06/5.31 ( ( ord_less_real @ B @ A )
% 5.06/5.31 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.31 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_right_mono_neg
% 5.06/5.31 thf(fact_3255_mult__strict__right__mono__neg,axiom,
% 5.06/5.31 ! [B: rat,A: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_rat @ B @ A )
% 5.06/5.31 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_right_mono_neg
% 5.06/5.31 thf(fact_3256_mult__strict__right__mono__neg,axiom,
% 5.06/5.31 ! [B: int,A: int,C: int] :
% 5.06/5.31 ( ( ord_less_int @ B @ A )
% 5.06/5.31 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.31 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_right_mono_neg
% 5.06/5.31 thf(fact_3257_mult__strict__right__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_right_mono
% 5.06/5.31 thf(fact_3258_mult__strict__right__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_right_mono
% 5.06/5.31 thf(fact_3259_mult__strict__right__mono,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat] :
% 5.06/5.31 ( ( ord_less_nat @ A @ B )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_right_mono
% 5.06/5.31 thf(fact_3260_mult__strict__right__mono,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int] :
% 5.06/5.31 ( ( ord_less_int @ A @ B )
% 5.06/5.31 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_strict_right_mono
% 5.06/5.31 thf(fact_3261_mult__less__cancel__right__disj,axiom,
% 5.06/5.31 ! [A: real,C: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.06/5.31 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.31 & ( ord_less_real @ A @ B ) )
% 5.06/5.31 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.31 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_right_disj
% 5.06/5.31 thf(fact_3262_mult__less__cancel__right__disj,axiom,
% 5.06/5.31 ! [A: rat,C: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.06/5.31 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.31 & ( ord_less_rat @ A @ B ) )
% 5.06/5.31 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_right_disj
% 5.06/5.31 thf(fact_3263_mult__less__cancel__right__disj,axiom,
% 5.06/5.31 ! [A: int,C: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.06/5.31 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.31 & ( ord_less_int @ A @ B ) )
% 5.06/5.31 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.31 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_cancel_right_disj
% 5.06/5.31 thf(fact_3264_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.06/5.31 thf(fact_3265_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.06/5.31 thf(fact_3266_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat] :
% 5.06/5.31 ( ( ord_less_nat @ A @ B )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.06/5.31 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.06/5.31 thf(fact_3267_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int] :
% 5.06/5.31 ( ( ord_less_int @ A @ B )
% 5.06/5.31 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.31 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.06/5.31 thf(fact_3268_add__less__zeroD,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.06/5.31 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_less_zeroD
% 5.06/5.31 thf(fact_3269_add__less__zeroD,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.06/5.31 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_less_zeroD
% 5.06/5.31 thf(fact_3270_add__less__zeroD,axiom,
% 5.06/5.31 ! [X: int,Y: int] :
% 5.06/5.31 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_int @ X @ zero_zero_int )
% 5.06/5.31 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_less_zeroD
% 5.06/5.31 thf(fact_3271_add__neg__neg,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.06/5.31 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_neg_neg
% 5.06/5.31 thf(fact_3272_add__neg__neg,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_neg_neg
% 5.06/5.31 thf(fact_3273_add__neg__neg,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.06/5.31 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.06/5.31 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_neg_neg
% 5.06/5.31 thf(fact_3274_add__neg__neg,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ A @ zero_zero_int )
% 5.06/5.31 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.06/5.31 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_neg_neg
% 5.06/5.31 thf(fact_3275_add__pos__pos,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.31 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_pos_pos
% 5.06/5.31 thf(fact_3276_add__pos__pos,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.06/5.31 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_pos_pos
% 5.06/5.31 thf(fact_3277_add__pos__pos,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_pos_pos
% 5.06/5.31 thf(fact_3278_add__pos__pos,axiom,
% 5.06/5.31 ! [A: int,B: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_pos_pos
% 5.06/5.31 thf(fact_3279_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.06/5.31 ! [A: nat,B: nat] :
% 5.06/5.31 ( ( ord_less_nat @ A @ B )
% 5.06/5.31 => ~ ! [C3: nat] :
% 5.06/5.31 ( ( B
% 5.06/5.31 = ( plus_plus_nat @ A @ C3 ) )
% 5.06/5.31 => ( C3 = zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % canonically_ordered_monoid_add_class.lessE
% 5.06/5.31 thf(fact_3280_pos__add__strict,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ( ord_less_real @ B @ C )
% 5.06/5.31 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % pos_add_strict
% 5.06/5.31 thf(fact_3281_pos__add__strict,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ( ord_less_rat @ B @ C )
% 5.06/5.31 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % pos_add_strict
% 5.06/5.31 thf(fact_3282_pos__add__strict,axiom,
% 5.06/5.31 ! [A: nat,B: nat,C: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ( ord_less_nat @ B @ C )
% 5.06/5.31 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % pos_add_strict
% 5.06/5.31 thf(fact_3283_pos__add__strict,axiom,
% 5.06/5.31 ! [A: int,B: int,C: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ( ord_less_int @ B @ C )
% 5.06/5.31 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % pos_add_strict
% 5.06/5.31 thf(fact_3284_not__one__less__zero,axiom,
% 5.06/5.31 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.06/5.31
% 5.06/5.31 % not_one_less_zero
% 5.06/5.31 thf(fact_3285_not__one__less__zero,axiom,
% 5.06/5.31 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.06/5.31
% 5.06/5.31 % not_one_less_zero
% 5.06/5.31 thf(fact_3286_not__one__less__zero,axiom,
% 5.06/5.31 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.06/5.31
% 5.06/5.31 % not_one_less_zero
% 5.06/5.31 thf(fact_3287_not__one__less__zero,axiom,
% 5.06/5.31 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.06/5.31
% 5.06/5.31 % not_one_less_zero
% 5.06/5.31 thf(fact_3288_zero__less__one,axiom,
% 5.06/5.31 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.06/5.31
% 5.06/5.31 % zero_less_one
% 5.06/5.31 thf(fact_3289_zero__less__one,axiom,
% 5.06/5.31 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.06/5.31
% 5.06/5.31 % zero_less_one
% 5.06/5.31 thf(fact_3290_zero__less__one,axiom,
% 5.06/5.31 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.06/5.31
% 5.06/5.31 % zero_less_one
% 5.06/5.31 thf(fact_3291_zero__less__one,axiom,
% 5.06/5.31 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.06/5.31
% 5.06/5.31 % zero_less_one
% 5.06/5.31 thf(fact_3292_less__numeral__extra_I1_J,axiom,
% 5.06/5.31 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.06/5.31
% 5.06/5.31 % less_numeral_extra(1)
% 5.06/5.31 thf(fact_3293_less__numeral__extra_I1_J,axiom,
% 5.06/5.31 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.06/5.31
% 5.06/5.31 % less_numeral_extra(1)
% 5.06/5.31 thf(fact_3294_less__numeral__extra_I1_J,axiom,
% 5.06/5.31 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.06/5.31
% 5.06/5.31 % less_numeral_extra(1)
% 5.06/5.31 thf(fact_3295_less__numeral__extra_I1_J,axiom,
% 5.06/5.31 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.06/5.31
% 5.06/5.31 % less_numeral_extra(1)
% 5.06/5.31 thf(fact_3296_le__iff__diff__le__0,axiom,
% 5.06/5.31 ( ord_less_eq_real
% 5.06/5.31 = ( ^ [A4: real,B4: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B4 ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % le_iff_diff_le_0
% 5.06/5.31 thf(fact_3297_le__iff__diff__le__0,axiom,
% 5.06/5.31 ( ord_less_eq_rat
% 5.06/5.31 = ( ^ [A4: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A4 @ B4 ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % le_iff_diff_le_0
% 5.06/5.31 thf(fact_3298_le__iff__diff__le__0,axiom,
% 5.06/5.31 ( ord_less_eq_int
% 5.06/5.31 = ( ^ [A4: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B4 ) @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % le_iff_diff_le_0
% 5.06/5.31 thf(fact_3299_divide__le__0__iff,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.06/5.31 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.06/5.31 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.31 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_le_0_iff
% 5.06/5.31 thf(fact_3300_divide__le__0__iff,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.06/5.31 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.06/5.31 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_le_0_iff
% 5.06/5.31 thf(fact_3301_divide__right__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_right_mono
% 5.06/5.31 thf(fact_3302_divide__right__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_right_mono
% 5.06/5.31 thf(fact_3303_zero__le__divide__iff,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.31 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.06/5.31 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.31 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_divide_iff
% 5.06/5.31 thf(fact_3304_zero__le__divide__iff,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.06/5.31 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.06/5.31 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_divide_iff
% 5.06/5.31 thf(fact_3305_divide__nonneg__nonneg,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.31 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_nonneg_nonneg
% 5.06/5.31 thf(fact_3306_divide__nonneg__nonneg,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.31 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_nonneg_nonneg
% 5.06/5.31 thf(fact_3307_divide__nonneg__nonpos,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.31 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.06/5.31 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_nonneg_nonpos
% 5.06/5.31 thf(fact_3308_divide__nonneg__nonpos,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.31 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_nonneg_nonpos
% 5.06/5.31 thf(fact_3309_divide__nonpos__nonneg,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.31 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_nonpos_nonneg
% 5.06/5.31 thf(fact_3310_divide__nonpos__nonneg,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.31 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_nonpos_nonneg
% 5.06/5.31 thf(fact_3311_divide__nonpos__nonpos,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.06/5.31 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_nonpos_nonpos
% 5.06/5.31 thf(fact_3312_divide__nonpos__nonpos,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_nonpos_nonpos
% 5.06/5.31 thf(fact_3313_divide__right__mono__neg,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.31 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_right_mono_neg
% 5.06/5.31 thf(fact_3314_divide__right__mono__neg,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_right_mono_neg
% 5.06/5.31 thf(fact_3315_less__iff__diff__less__0,axiom,
% 5.06/5.31 ( ord_less_real
% 5.06/5.31 = ( ^ [A4: real,B4: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B4 ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % less_iff_diff_less_0
% 5.06/5.31 thf(fact_3316_less__iff__diff__less__0,axiom,
% 5.06/5.31 ( ord_less_rat
% 5.06/5.31 = ( ^ [A4: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A4 @ B4 ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % less_iff_diff_less_0
% 5.06/5.31 thf(fact_3317_less__iff__diff__less__0,axiom,
% 5.06/5.31 ( ord_less_int
% 5.06/5.31 = ( ^ [A4: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B4 ) @ zero_zero_int ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % less_iff_diff_less_0
% 5.06/5.31 thf(fact_3318_divide__neg__neg,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_real @ X @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.06/5.31 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_neg_neg
% 5.06/5.31 thf(fact_3319_divide__neg__neg,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_neg_neg
% 5.06/5.31 thf(fact_3320_divide__neg__pos,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_real @ X @ zero_zero_real )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.31 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_neg_pos
% 5.06/5.31 thf(fact_3321_divide__neg__pos,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.06/5.31 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_neg_pos
% 5.06/5.31 thf(fact_3322_divide__pos__neg,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.31 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.06/5.31 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_pos_neg
% 5.06/5.31 thf(fact_3323_divide__pos__neg,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.06/5.31 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_pos_neg
% 5.06/5.31 thf(fact_3324_divide__pos__pos,axiom,
% 5.06/5.31 ! [X: real,Y: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.31 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_pos_pos
% 5.06/5.31 thf(fact_3325_divide__pos__pos,axiom,
% 5.06/5.31 ! [X: rat,Y: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.06/5.31 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_pos_pos
% 5.06/5.31 thf(fact_3326_divide__less__0__iff,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.06/5.31 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.06/5.31 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.31 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_less_0_iff
% 5.06/5.31 thf(fact_3327_divide__less__0__iff,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.06/5.31 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.06/5.31 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_less_0_iff
% 5.06/5.31 thf(fact_3328_divide__less__cancel,axiom,
% 5.06/5.31 ! [A: real,C: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.06/5.31 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_real @ A @ B ) )
% 5.06/5.31 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.31 => ( ord_less_real @ B @ A ) )
% 5.06/5.31 & ( C != zero_zero_real ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_less_cancel
% 5.06/5.31 thf(fact_3329_divide__less__cancel,axiom,
% 5.06/5.31 ! [A: rat,C: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.31 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_rat @ A @ B ) )
% 5.06/5.31 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_rat @ B @ A ) )
% 5.06/5.31 & ( C != zero_zero_rat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_less_cancel
% 5.06/5.31 thf(fact_3330_zero__less__divide__iff,axiom,
% 5.06/5.31 ! [A: real,B: real] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.31 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.06/5.31 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.31 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_divide_iff
% 5.06/5.31 thf(fact_3331_zero__less__divide__iff,axiom,
% 5.06/5.31 ! [A: rat,B: rat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.06/5.31 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.06/5.31 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.31 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_divide_iff
% 5.06/5.31 thf(fact_3332_divide__strict__right__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( ord_less_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.31 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_strict_right_mono
% 5.06/5.31 thf(fact_3333_divide__strict__right__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.31 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_strict_right_mono
% 5.06/5.31 thf(fact_3334_divide__strict__right__mono__neg,axiom,
% 5.06/5.31 ! [B: real,A: real,C: real] :
% 5.06/5.31 ( ( ord_less_real @ B @ A )
% 5.06/5.31 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.31 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_strict_right_mono_neg
% 5.06/5.31 thf(fact_3335_divide__strict__right__mono__neg,axiom,
% 5.06/5.31 ! [B: rat,A: rat,C: rat] :
% 5.06/5.31 ( ( ord_less_rat @ B @ A )
% 5.06/5.31 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.31 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_strict_right_mono_neg
% 5.06/5.31 thf(fact_3336_power__mono,axiom,
% 5.06/5.31 ! [A: real,B: real,N2: nat] :
% 5.06/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_mono
% 5.06/5.31 thf(fact_3337_power__mono,axiom,
% 5.06/5.31 ! [A: rat,B: rat,N2: nat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_mono
% 5.06/5.31 thf(fact_3338_power__mono,axiom,
% 5.06/5.31 ! [A: nat,B: nat,N2: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_mono
% 5.06/5.31 thf(fact_3339_power__mono,axiom,
% 5.06/5.31 ! [A: int,B: int,N2: nat] :
% 5.06/5.31 ( ( ord_less_eq_int @ A @ B )
% 5.06/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % power_mono
% 5.06/5.31 thf(fact_3340_zero__le__power,axiom,
% 5.06/5.31 ! [A: real,N2: nat] :
% 5.06/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_power
% 5.06/5.31 thf(fact_3341_zero__le__power,axiom,
% 5.06/5.31 ! [A: rat,N2: nat] :
% 5.06/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_power
% 5.06/5.31 thf(fact_3342_zero__le__power,axiom,
% 5.06/5.31 ! [A: nat,N2: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_power
% 5.06/5.31 thf(fact_3343_zero__le__power,axiom,
% 5.06/5.31 ! [A: int,N2: nat] :
% 5.06/5.31 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_le_power
% 5.06/5.31 thf(fact_3344_zero__less__power,axiom,
% 5.06/5.31 ! [A: real,N2: nat] :
% 5.06/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.31 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_power
% 5.06/5.31 thf(fact_3345_zero__less__power,axiom,
% 5.06/5.31 ! [A: rat,N2: nat] :
% 5.06/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.31 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_power
% 5.06/5.31 thf(fact_3346_zero__less__power,axiom,
% 5.06/5.31 ! [A: nat,N2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.31 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_power
% 5.06/5.31 thf(fact_3347_zero__less__power,axiom,
% 5.06/5.31 ! [A: int,N2: nat] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.31 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % zero_less_power
% 5.06/5.31 thf(fact_3348_nonzero__eq__divide__eq,axiom,
% 5.06/5.31 ! [C: complex,A: complex,B: complex] :
% 5.06/5.31 ( ( C != zero_zero_complex )
% 5.06/5.31 => ( ( A
% 5.06/5.31 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.06/5.31 = ( ( times_times_complex @ A @ C )
% 5.06/5.31 = B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nonzero_eq_divide_eq
% 5.06/5.31 thf(fact_3349_nonzero__eq__divide__eq,axiom,
% 5.06/5.31 ! [C: real,A: real,B: real] :
% 5.06/5.31 ( ( C != zero_zero_real )
% 5.06/5.31 => ( ( A
% 5.06/5.31 = ( divide_divide_real @ B @ C ) )
% 5.06/5.31 = ( ( times_times_real @ A @ C )
% 5.06/5.31 = B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nonzero_eq_divide_eq
% 5.06/5.31 thf(fact_3350_nonzero__eq__divide__eq,axiom,
% 5.06/5.31 ! [C: rat,A: rat,B: rat] :
% 5.06/5.31 ( ( C != zero_zero_rat )
% 5.06/5.31 => ( ( A
% 5.06/5.31 = ( divide_divide_rat @ B @ C ) )
% 5.06/5.31 = ( ( times_times_rat @ A @ C )
% 5.06/5.31 = B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nonzero_eq_divide_eq
% 5.06/5.31 thf(fact_3351_nonzero__divide__eq__eq,axiom,
% 5.06/5.31 ! [C: complex,B: complex,A: complex] :
% 5.06/5.31 ( ( C != zero_zero_complex )
% 5.06/5.31 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.06/5.31 = A )
% 5.06/5.31 = ( B
% 5.06/5.31 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nonzero_divide_eq_eq
% 5.06/5.31 thf(fact_3352_nonzero__divide__eq__eq,axiom,
% 5.06/5.31 ! [C: real,B: real,A: real] :
% 5.06/5.31 ( ( C != zero_zero_real )
% 5.06/5.31 => ( ( ( divide_divide_real @ B @ C )
% 5.06/5.31 = A )
% 5.06/5.31 = ( B
% 5.06/5.31 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nonzero_divide_eq_eq
% 5.06/5.31 thf(fact_3353_nonzero__divide__eq__eq,axiom,
% 5.06/5.31 ! [C: rat,B: rat,A: rat] :
% 5.06/5.31 ( ( C != zero_zero_rat )
% 5.06/5.31 => ( ( ( divide_divide_rat @ B @ C )
% 5.06/5.31 = A )
% 5.06/5.31 = ( B
% 5.06/5.31 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nonzero_divide_eq_eq
% 5.06/5.31 thf(fact_3354_eq__divide__imp,axiom,
% 5.06/5.31 ! [C: complex,A: complex,B: complex] :
% 5.06/5.31 ( ( C != zero_zero_complex )
% 5.06/5.31 => ( ( ( times_times_complex @ A @ C )
% 5.06/5.31 = B )
% 5.06/5.31 => ( A
% 5.06/5.31 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % eq_divide_imp
% 5.06/5.31 thf(fact_3355_eq__divide__imp,axiom,
% 5.06/5.31 ! [C: real,A: real,B: real] :
% 5.06/5.31 ( ( C != zero_zero_real )
% 5.06/5.31 => ( ( ( times_times_real @ A @ C )
% 5.06/5.31 = B )
% 5.06/5.31 => ( A
% 5.06/5.31 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % eq_divide_imp
% 5.06/5.31 thf(fact_3356_eq__divide__imp,axiom,
% 5.06/5.31 ! [C: rat,A: rat,B: rat] :
% 5.06/5.31 ( ( C != zero_zero_rat )
% 5.06/5.31 => ( ( ( times_times_rat @ A @ C )
% 5.06/5.31 = B )
% 5.06/5.31 => ( A
% 5.06/5.31 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % eq_divide_imp
% 5.06/5.31 thf(fact_3357_divide__eq__imp,axiom,
% 5.06/5.31 ! [C: complex,B: complex,A: complex] :
% 5.06/5.31 ( ( C != zero_zero_complex )
% 5.06/5.31 => ( ( B
% 5.06/5.31 = ( times_times_complex @ A @ C ) )
% 5.06/5.31 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.06/5.31 = A ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_eq_imp
% 5.06/5.31 thf(fact_3358_divide__eq__imp,axiom,
% 5.06/5.31 ! [C: real,B: real,A: real] :
% 5.06/5.31 ( ( C != zero_zero_real )
% 5.06/5.31 => ( ( B
% 5.06/5.31 = ( times_times_real @ A @ C ) )
% 5.06/5.31 => ( ( divide_divide_real @ B @ C )
% 5.06/5.31 = A ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_eq_imp
% 5.06/5.31 thf(fact_3359_divide__eq__imp,axiom,
% 5.06/5.31 ! [C: rat,B: rat,A: rat] :
% 5.06/5.31 ( ( C != zero_zero_rat )
% 5.06/5.31 => ( ( B
% 5.06/5.31 = ( times_times_rat @ A @ C ) )
% 5.06/5.31 => ( ( divide_divide_rat @ B @ C )
% 5.06/5.31 = A ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_eq_imp
% 5.06/5.31 thf(fact_3360_eq__divide__eq,axiom,
% 5.06/5.31 ! [A: complex,B: complex,C: complex] :
% 5.06/5.31 ( ( A
% 5.06/5.31 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.06/5.31 = ( ( ( C != zero_zero_complex )
% 5.06/5.31 => ( ( times_times_complex @ A @ C )
% 5.06/5.31 = B ) )
% 5.06/5.31 & ( ( C = zero_zero_complex )
% 5.06/5.31 => ( A = zero_zero_complex ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % eq_divide_eq
% 5.06/5.31 thf(fact_3361_eq__divide__eq,axiom,
% 5.06/5.31 ! [A: real,B: real,C: real] :
% 5.06/5.31 ( ( A
% 5.06/5.31 = ( divide_divide_real @ B @ C ) )
% 5.06/5.31 = ( ( ( C != zero_zero_real )
% 5.06/5.31 => ( ( times_times_real @ A @ C )
% 5.06/5.31 = B ) )
% 5.06/5.31 & ( ( C = zero_zero_real )
% 5.06/5.31 => ( A = zero_zero_real ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % eq_divide_eq
% 5.06/5.31 thf(fact_3362_eq__divide__eq,axiom,
% 5.06/5.31 ! [A: rat,B: rat,C: rat] :
% 5.06/5.31 ( ( A
% 5.06/5.31 = ( divide_divide_rat @ B @ C ) )
% 5.06/5.31 = ( ( ( C != zero_zero_rat )
% 5.06/5.31 => ( ( times_times_rat @ A @ C )
% 5.06/5.31 = B ) )
% 5.06/5.31 & ( ( C = zero_zero_rat )
% 5.06/5.31 => ( A = zero_zero_rat ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % eq_divide_eq
% 5.06/5.31 thf(fact_3363_divide__eq__eq,axiom,
% 5.06/5.31 ! [B: complex,C: complex,A: complex] :
% 5.06/5.31 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.06/5.31 = A )
% 5.06/5.31 = ( ( ( C != zero_zero_complex )
% 5.06/5.31 => ( B
% 5.06/5.31 = ( times_times_complex @ A @ C ) ) )
% 5.06/5.31 & ( ( C = zero_zero_complex )
% 5.06/5.31 => ( A = zero_zero_complex ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_eq_eq
% 5.06/5.31 thf(fact_3364_divide__eq__eq,axiom,
% 5.06/5.31 ! [B: real,C: real,A: real] :
% 5.06/5.31 ( ( ( divide_divide_real @ B @ C )
% 5.06/5.31 = A )
% 5.06/5.31 = ( ( ( C != zero_zero_real )
% 5.06/5.31 => ( B
% 5.06/5.31 = ( times_times_real @ A @ C ) ) )
% 5.06/5.31 & ( ( C = zero_zero_real )
% 5.06/5.31 => ( A = zero_zero_real ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_eq_eq
% 5.06/5.31 thf(fact_3365_divide__eq__eq,axiom,
% 5.06/5.31 ! [B: rat,C: rat,A: rat] :
% 5.06/5.31 ( ( ( divide_divide_rat @ B @ C )
% 5.06/5.31 = A )
% 5.06/5.31 = ( ( ( C != zero_zero_rat )
% 5.06/5.31 => ( B
% 5.06/5.31 = ( times_times_rat @ A @ C ) ) )
% 5.06/5.31 & ( ( C = zero_zero_rat )
% 5.06/5.31 => ( A = zero_zero_rat ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divide_eq_eq
% 5.06/5.31 thf(fact_3366_frac__eq__eq,axiom,
% 5.06/5.31 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.06/5.31 ( ( Y != zero_zero_complex )
% 5.06/5.31 => ( ( Z != zero_zero_complex )
% 5.06/5.31 => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 5.06/5.31 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.06/5.31 = ( ( times_times_complex @ X @ Z )
% 5.06/5.31 = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % frac_eq_eq
% 5.06/5.31 thf(fact_3367_frac__eq__eq,axiom,
% 5.06/5.31 ! [Y: real,Z: real,X: real,W: real] :
% 5.06/5.31 ( ( Y != zero_zero_real )
% 5.06/5.31 => ( ( Z != zero_zero_real )
% 5.06/5.31 => ( ( ( divide_divide_real @ X @ Y )
% 5.06/5.31 = ( divide_divide_real @ W @ Z ) )
% 5.06/5.31 = ( ( times_times_real @ X @ Z )
% 5.06/5.31 = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % frac_eq_eq
% 5.06/5.31 thf(fact_3368_frac__eq__eq,axiom,
% 5.06/5.31 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.06/5.31 ( ( Y != zero_zero_rat )
% 5.06/5.31 => ( ( Z != zero_zero_rat )
% 5.06/5.31 => ( ( ( divide_divide_rat @ X @ Y )
% 5.06/5.31 = ( divide_divide_rat @ W @ Z ) )
% 5.06/5.31 = ( ( times_times_rat @ X @ Z )
% 5.06/5.31 = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % frac_eq_eq
% 5.06/5.31 thf(fact_3369_right__inverse__eq,axiom,
% 5.06/5.31 ! [B: complex,A: complex] :
% 5.06/5.31 ( ( B != zero_zero_complex )
% 5.06/5.31 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.06/5.31 = one_one_complex )
% 5.06/5.31 = ( A = B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % right_inverse_eq
% 5.06/5.31 thf(fact_3370_right__inverse__eq,axiom,
% 5.06/5.31 ! [B: real,A: real] :
% 5.06/5.31 ( ( B != zero_zero_real )
% 5.06/5.31 => ( ( ( divide_divide_real @ A @ B )
% 5.06/5.31 = one_one_real )
% 5.06/5.31 = ( A = B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % right_inverse_eq
% 5.06/5.31 thf(fact_3371_right__inverse__eq,axiom,
% 5.06/5.31 ! [B: rat,A: rat] :
% 5.06/5.31 ( ( B != zero_zero_rat )
% 5.06/5.31 => ( ( ( divide_divide_rat @ A @ B )
% 5.06/5.31 = one_one_rat )
% 5.06/5.31 = ( A = B ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % right_inverse_eq
% 5.06/5.31 thf(fact_3372_power__0,axiom,
% 5.06/5.31 ! [A: rat] :
% 5.06/5.31 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.06/5.31 = one_one_rat ) ).
% 5.06/5.31
% 5.06/5.31 % power_0
% 5.06/5.31 thf(fact_3373_power__0,axiom,
% 5.06/5.31 ! [A: nat] :
% 5.06/5.31 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.06/5.31 = one_one_nat ) ).
% 5.06/5.31
% 5.06/5.31 % power_0
% 5.06/5.31 thf(fact_3374_power__0,axiom,
% 5.06/5.31 ! [A: real] :
% 5.06/5.31 ( ( power_power_real @ A @ zero_zero_nat )
% 5.06/5.31 = one_one_real ) ).
% 5.06/5.31
% 5.06/5.31 % power_0
% 5.06/5.31 thf(fact_3375_power__0,axiom,
% 5.06/5.31 ! [A: int] :
% 5.06/5.31 ( ( power_power_int @ A @ zero_zero_nat )
% 5.06/5.31 = one_one_int ) ).
% 5.06/5.31
% 5.06/5.31 % power_0
% 5.06/5.31 thf(fact_3376_power__0,axiom,
% 5.06/5.31 ! [A: complex] :
% 5.06/5.31 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.06/5.31 = one_one_complex ) ).
% 5.06/5.31
% 5.06/5.31 % power_0
% 5.06/5.31 thf(fact_3377_divmod__digit__0_I1_J,axiom,
% 5.06/5.31 ! [B: nat,A: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.31 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.06/5.31 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.06/5.31 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divmod_digit_0(1)
% 5.06/5.31 thf(fact_3378_divmod__digit__0_I1_J,axiom,
% 5.06/5.31 ! [B: int,A: int] :
% 5.06/5.31 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.31 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.06/5.31 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.06/5.31 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divmod_digit_0(1)
% 5.06/5.31 thf(fact_3379_divmod__digit__0_I1_J,axiom,
% 5.06/5.31 ! [B: code_integer,A: code_integer] :
% 5.06/5.31 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.06/5.31 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.06/5.31 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.06/5.31 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % divmod_digit_0(1)
% 5.06/5.31 thf(fact_3380_less__Suc__eq__0__disj,axiom,
% 5.06/5.31 ! [M: nat,N2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.06/5.31 = ( ( M = zero_zero_nat )
% 5.06/5.31 | ? [J3: nat] :
% 5.06/5.31 ( ( M
% 5.06/5.31 = ( suc @ J3 ) )
% 5.06/5.31 & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % less_Suc_eq_0_disj
% 5.06/5.31 thf(fact_3381_gr0__implies__Suc,axiom,
% 5.06/5.31 ! [N2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ? [M2: nat] :
% 5.06/5.31 ( N2
% 5.06/5.31 = ( suc @ M2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % gr0_implies_Suc
% 5.06/5.31 thf(fact_3382_All__less__Suc2,axiom,
% 5.06/5.31 ! [N2: nat,P: nat > $o] :
% 5.06/5.31 ( ( ! [I5: nat] :
% 5.06/5.31 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 5.06/5.31 => ( P @ I5 ) ) )
% 5.06/5.31 = ( ( P @ zero_zero_nat )
% 5.06/5.31 & ! [I5: nat] :
% 5.06/5.31 ( ( ord_less_nat @ I5 @ N2 )
% 5.06/5.31 => ( P @ ( suc @ I5 ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % All_less_Suc2
% 5.06/5.31 thf(fact_3383_gr0__conv__Suc,axiom,
% 5.06/5.31 ! [N2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 = ( ? [M6: nat] :
% 5.06/5.31 ( N2
% 5.06/5.31 = ( suc @ M6 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % gr0_conv_Suc
% 5.06/5.31 thf(fact_3384_Ex__less__Suc2,axiom,
% 5.06/5.31 ! [N2: nat,P: nat > $o] :
% 5.06/5.31 ( ( ? [I5: nat] :
% 5.06/5.31 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 5.06/5.31 & ( P @ I5 ) ) )
% 5.06/5.31 = ( ( P @ zero_zero_nat )
% 5.06/5.31 | ? [I5: nat] :
% 5.06/5.31 ( ( ord_less_nat @ I5 @ N2 )
% 5.06/5.31 & ( P @ ( suc @ I5 ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % Ex_less_Suc2
% 5.06/5.31 thf(fact_3385_one__is__add,axiom,
% 5.06/5.31 ! [M: nat,N2: nat] :
% 5.06/5.31 ( ( ( suc @ zero_zero_nat )
% 5.06/5.31 = ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.31 = ( ( ( M
% 5.06/5.31 = ( suc @ zero_zero_nat ) )
% 5.06/5.31 & ( N2 = zero_zero_nat ) )
% 5.06/5.31 | ( ( M = zero_zero_nat )
% 5.06/5.31 & ( N2
% 5.06/5.31 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % one_is_add
% 5.06/5.31 thf(fact_3386_add__is__1,axiom,
% 5.06/5.31 ! [M: nat,N2: nat] :
% 5.06/5.31 ( ( ( plus_plus_nat @ M @ N2 )
% 5.06/5.31 = ( suc @ zero_zero_nat ) )
% 5.06/5.31 = ( ( ( M
% 5.06/5.31 = ( suc @ zero_zero_nat ) )
% 5.06/5.31 & ( N2 = zero_zero_nat ) )
% 5.06/5.31 | ( ( M = zero_zero_nat )
% 5.06/5.31 & ( N2
% 5.06/5.31 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % add_is_1
% 5.06/5.31 thf(fact_3387_option_Osize_I4_J,axiom,
% 5.06/5.31 ! [X22: product_prod_nat_nat] :
% 5.06/5.31 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.06/5.31 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % option.size(4)
% 5.06/5.31 thf(fact_3388_option_Osize_I4_J,axiom,
% 5.06/5.31 ! [X22: nat] :
% 5.06/5.31 ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 5.06/5.31 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % option.size(4)
% 5.06/5.31 thf(fact_3389_option_Osize_I4_J,axiom,
% 5.06/5.31 ! [X22: num] :
% 5.06/5.31 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 5.06/5.31 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % option.size(4)
% 5.06/5.31 thf(fact_3390_ex__least__nat__le,axiom,
% 5.06/5.31 ! [P: nat > $o,N2: nat] :
% 5.06/5.31 ( ( P @ N2 )
% 5.06/5.31 => ( ~ ( P @ zero_zero_nat )
% 5.06/5.31 => ? [K2: nat] :
% 5.06/5.31 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.06/5.31 & ! [I: nat] :
% 5.06/5.31 ( ( ord_less_nat @ I @ K2 )
% 5.06/5.31 => ~ ( P @ I ) )
% 5.06/5.31 & ( P @ K2 ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % ex_least_nat_le
% 5.06/5.31 thf(fact_3391_less__imp__add__positive,axiom,
% 5.06/5.31 ! [I2: nat,J: nat] :
% 5.06/5.31 ( ( ord_less_nat @ I2 @ J )
% 5.06/5.31 => ? [K2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.06/5.31 & ( ( plus_plus_nat @ I2 @ K2 )
% 5.06/5.31 = J ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % less_imp_add_positive
% 5.06/5.31 thf(fact_3392_option_Osize_I3_J,axiom,
% 5.06/5.31 ( ( size_size_option_nat @ none_nat )
% 5.06/5.31 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % option.size(3)
% 5.06/5.31 thf(fact_3393_option_Osize_I3_J,axiom,
% 5.06/5.31 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.06/5.31 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % option.size(3)
% 5.06/5.31 thf(fact_3394_option_Osize_I3_J,axiom,
% 5.06/5.31 ( ( size_size_option_num @ none_num )
% 5.06/5.31 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % option.size(3)
% 5.06/5.31 thf(fact_3395_mult__less__mono1,axiom,
% 5.06/5.31 ! [I2: nat,J: nat,K: nat] :
% 5.06/5.31 ( ( ord_less_nat @ I2 @ J )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.31 => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_mono1
% 5.06/5.31 thf(fact_3396_mult__less__mono2,axiom,
% 5.06/5.31 ! [I2: nat,J: nat,K: nat] :
% 5.06/5.31 ( ( ord_less_nat @ I2 @ J )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.31 => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % mult_less_mono2
% 5.06/5.31 thf(fact_3397_nat__mult__eq__cancel1,axiom,
% 5.06/5.31 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.31 => ( ( ( times_times_nat @ K @ M )
% 5.06/5.31 = ( times_times_nat @ K @ N2 ) )
% 5.06/5.31 = ( M = N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nat_mult_eq_cancel1
% 5.06/5.31 thf(fact_3398_nat__mult__less__cancel1,axiom,
% 5.06/5.31 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.31 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.06/5.31 = ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nat_mult_less_cancel1
% 5.06/5.31 thf(fact_3399_diff__less,axiom,
% 5.06/5.31 ! [N2: nat,M: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.31 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.31 => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % diff_less
% 5.06/5.31 thf(fact_3400_One__nat__def,axiom,
% 5.06/5.31 ( one_one_nat
% 5.06/5.31 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % One_nat_def
% 5.06/5.31 thf(fact_3401_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.06/5.31 ! [M: nat,N2: nat] :
% 5.06/5.31 ( ( ( divide_divide_nat @ M @ N2 )
% 5.06/5.31 = zero_zero_nat )
% 5.06/5.31 = ( ( ord_less_nat @ M @ N2 )
% 5.06/5.31 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % Euclidean_Division.div_eq_0_iff
% 5.06/5.31 thf(fact_3402_nat__power__less__imp__less,axiom,
% 5.06/5.31 ! [I2: nat,M: nat,N2: nat] :
% 5.06/5.31 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 5.06/5.31 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 5.06/5.31 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.06/5.31
% 5.06/5.31 % nat_power_less_imp_less
% 5.06/5.31 thf(fact_3403_diff__add__0,axiom,
% 5.06/5.31 ! [N2: nat,M: nat] :
% 5.06/5.31 ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 5.06/5.31 = zero_zero_nat ) ).
% 5.06/5.31
% 5.06/5.31 % diff_add_0
% 5.06/5.31 thf(fact_3404_bits__stable__imp__add__self,axiom,
% 5.06/5.31 ! [A: nat] :
% 5.06/5.31 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.31 = A )
% 5.06/5.31 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.31 = zero_zero_nat ) ) ).
% 5.06/5.31
% 5.06/5.31 % bits_stable_imp_add_self
% 5.06/5.31 thf(fact_3405_bits__stable__imp__add__self,axiom,
% 5.06/5.31 ! [A: int] :
% 5.06/5.31 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.31 = A )
% 5.06/5.31 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.06/5.31 = zero_zero_int ) ) ).
% 5.06/5.31
% 5.06/5.31 % bits_stable_imp_add_self
% 5.06/5.31 thf(fact_3406_bits__stable__imp__add__self,axiom,
% 5.06/5.31 ! [A: code_integer] :
% 5.06/5.31 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.31 = A )
% 5.06/5.31 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.06/5.31 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.31
% 5.06/5.31 % bits_stable_imp_add_self
% 5.06/5.32 thf(fact_3407_mult__eq__self__implies__10,axiom,
% 5.06/5.32 ! [M: nat,N2: nat] :
% 5.06/5.32 ( ( M
% 5.06/5.32 = ( times_times_nat @ M @ N2 ) )
% 5.06/5.32 => ( ( N2 = one_one_nat )
% 5.06/5.32 | ( M = zero_zero_nat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_eq_self_implies_10
% 5.06/5.32 thf(fact_3408_vebt__insert_Osimps_I2_J,axiom,
% 5.06/5.32 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.06/5.32 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S2 ) @ X )
% 5.06/5.32 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S2 ) ) ).
% 5.06/5.32
% 5.06/5.32 % vebt_insert.simps(2)
% 5.06/5.32 thf(fact_3409_vebt__pred_Osimps_I3_J,axiom,
% 5.06/5.32 ! [B: $o,A: $o,Va: nat] :
% 5.06/5.32 ( ( B
% 5.06/5.32 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.06/5.32 = ( some_nat @ one_one_nat ) ) )
% 5.06/5.32 & ( ~ B
% 5.06/5.32 => ( ( A
% 5.06/5.32 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.06/5.32 = ( some_nat @ zero_zero_nat ) ) )
% 5.06/5.32 & ( ~ A
% 5.06/5.32 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.06/5.32 = none_nat ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % vebt_pred.simps(3)
% 5.06/5.32 thf(fact_3410_mod__double__modulus,axiom,
% 5.06/5.32 ! [M: code_integer,X: code_integer] :
% 5.06/5.32 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.06/5.32 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.06/5.32 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.06/5.32 = ( modulo364778990260209775nteger @ X @ M ) )
% 5.06/5.32 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.06/5.32 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mod_double_modulus
% 5.06/5.32 thf(fact_3411_mod__double__modulus,axiom,
% 5.06/5.32 ! [M: nat,X: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.06/5.32 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.06/5.32 = ( modulo_modulo_nat @ X @ M ) )
% 5.06/5.32 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.06/5.32 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mod_double_modulus
% 5.06/5.32 thf(fact_3412_mod__double__modulus,axiom,
% 5.06/5.32 ! [M: int,X: int] :
% 5.06/5.32 ( ( ord_less_int @ zero_zero_int @ M )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.32 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.06/5.32 = ( modulo_modulo_int @ X @ M ) )
% 5.06/5.32 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.06/5.32 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mod_double_modulus
% 5.06/5.32 thf(fact_3413_divmod__digit__1_I2_J,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer] :
% 5.06/5.32 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.06/5.32 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.06/5.32 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.06/5.32 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.06/5.32 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divmod_digit_1(2)
% 5.06/5.32 thf(fact_3414_divmod__digit__1_I2_J,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.32 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.06/5.32 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.06/5.32 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divmod_digit_1(2)
% 5.06/5.32 thf(fact_3415_divmod__digit__1_I2_J,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.32 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.06/5.32 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.06/5.32 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divmod_digit_1(2)
% 5.06/5.32 thf(fact_3416_mult__div__mod__eq,axiom,
% 5.06/5.32 ! [B: nat,A: nat] :
% 5.06/5.32 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % mult_div_mod_eq
% 5.06/5.32 thf(fact_3417_mult__div__mod__eq,axiom,
% 5.06/5.32 ! [B: int,A: int] :
% 5.06/5.32 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % mult_div_mod_eq
% 5.06/5.32 thf(fact_3418_mult__div__mod__eq,axiom,
% 5.06/5.32 ! [B: code_integer,A: code_integer] :
% 5.06/5.32 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % mult_div_mod_eq
% 5.06/5.32 thf(fact_3419_mod__mult__div__eq,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % mod_mult_div_eq
% 5.06/5.32 thf(fact_3420_mod__mult__div__eq,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % mod_mult_div_eq
% 5.06/5.32 thf(fact_3421_mod__mult__div__eq,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer] :
% 5.06/5.32 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % mod_mult_div_eq
% 5.06/5.32 thf(fact_3422_mod__div__mult__eq,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % mod_div_mult_eq
% 5.06/5.32 thf(fact_3423_mod__div__mult__eq,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % mod_div_mult_eq
% 5.06/5.32 thf(fact_3424_mod__div__mult__eq,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer] :
% 5.06/5.32 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % mod_div_mult_eq
% 5.06/5.32 thf(fact_3425_div__mult__mod__eq,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % div_mult_mod_eq
% 5.06/5.32 thf(fact_3426_div__mult__mod__eq,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % div_mult_mod_eq
% 5.06/5.32 thf(fact_3427_div__mult__mod__eq,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer] :
% 5.06/5.32 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.06/5.32 = A ) ).
% 5.06/5.32
% 5.06/5.32 % div_mult_mod_eq
% 5.06/5.32 thf(fact_3428_mod__div__decomp,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( A
% 5.06/5.32 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mod_div_decomp
% 5.06/5.32 thf(fact_3429_mod__div__decomp,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( A
% 5.06/5.32 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mod_div_decomp
% 5.06/5.32 thf(fact_3430_mod__div__decomp,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer] :
% 5.06/5.32 ( A
% 5.06/5.32 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mod_div_decomp
% 5.06/5.32 thf(fact_3431_cancel__div__mod__rules_I1_J,axiom,
% 5.06/5.32 ! [A: nat,B: nat,C: nat] :
% 5.06/5.32 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.06/5.32 = ( plus_plus_nat @ A @ C ) ) ).
% 5.06/5.32
% 5.06/5.32 % cancel_div_mod_rules(1)
% 5.06/5.32 thf(fact_3432_cancel__div__mod__rules_I1_J,axiom,
% 5.06/5.32 ! [A: int,B: int,C: int] :
% 5.06/5.32 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.06/5.32 = ( plus_plus_int @ A @ C ) ) ).
% 5.06/5.32
% 5.06/5.32 % cancel_div_mod_rules(1)
% 5.06/5.32 thf(fact_3433_cancel__div__mod__rules_I1_J,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.32 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.06/5.32 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.06/5.32
% 5.06/5.32 % cancel_div_mod_rules(1)
% 5.06/5.32 thf(fact_3434_cancel__div__mod__rules_I2_J,axiom,
% 5.06/5.32 ! [B: nat,A: nat,C: nat] :
% 5.06/5.32 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.06/5.32 = ( plus_plus_nat @ A @ C ) ) ).
% 5.06/5.32
% 5.06/5.32 % cancel_div_mod_rules(2)
% 5.06/5.32 thf(fact_3435_cancel__div__mod__rules_I2_J,axiom,
% 5.06/5.32 ! [B: int,A: int,C: int] :
% 5.06/5.32 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.06/5.32 = ( plus_plus_int @ A @ C ) ) ).
% 5.06/5.32
% 5.06/5.32 % cancel_div_mod_rules(2)
% 5.06/5.32 thf(fact_3436_cancel__div__mod__rules_I2_J,axiom,
% 5.06/5.32 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.06/5.32 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.06/5.32 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.06/5.32
% 5.06/5.32 % cancel_div_mod_rules(2)
% 5.06/5.32 thf(fact_3437_div__mult1__eq,axiom,
% 5.06/5.32 ! [A: nat,B: nat,C: nat] :
% 5.06/5.32 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.06/5.32 = ( 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 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_mult1_eq
% 5.06/5.32 thf(fact_3438_div__mult1__eq,axiom,
% 5.06/5.32 ! [A: int,B: int,C: int] :
% 5.06/5.32 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.06/5.32 = ( 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 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_mult1_eq
% 5.06/5.32 thf(fact_3439_div__mult1__eq,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.32 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.06/5.32 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_mult1_eq
% 5.06/5.32 thf(fact_3440_minus__mult__div__eq__mod,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.06/5.32 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_mult_div_eq_mod
% 5.06/5.32 thf(fact_3441_minus__mult__div__eq__mod,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.06/5.32 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_mult_div_eq_mod
% 5.06/5.32 thf(fact_3442_minus__mult__div__eq__mod,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer] :
% 5.06/5.32 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.06/5.32 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_mult_div_eq_mod
% 5.06/5.32 thf(fact_3443_minus__mod__eq__mult__div,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.06/5.32 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_mod_eq_mult_div
% 5.06/5.32 thf(fact_3444_minus__mod__eq__mult__div,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.06/5.32 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_mod_eq_mult_div
% 5.06/5.32 thf(fact_3445_minus__mod__eq__mult__div,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer] :
% 5.06/5.32 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.06/5.32 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_mod_eq_mult_div
% 5.06/5.32 thf(fact_3446_minus__mod__eq__div__mult,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.06/5.32 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_mod_eq_div_mult
% 5.06/5.32 thf(fact_3447_minus__mod__eq__div__mult,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.06/5.32 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_mod_eq_div_mult
% 5.06/5.32 thf(fact_3448_minus__mod__eq__div__mult,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer] :
% 5.06/5.32 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.06/5.32 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_mod_eq_div_mult
% 5.06/5.32 thf(fact_3449_minus__div__mult__eq__mod,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.06/5.32 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_div_mult_eq_mod
% 5.06/5.32 thf(fact_3450_minus__div__mult__eq__mod,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.06/5.32 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_div_mult_eq_mod
% 5.06/5.32 thf(fact_3451_minus__div__mult__eq__mod,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer] :
% 5.06/5.32 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.06/5.32 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.06/5.32
% 5.06/5.32 % minus_div_mult_eq_mod
% 5.06/5.32 thf(fact_3452_mod__mult2__eq,axiom,
% 5.06/5.32 ! [M: nat,N2: nat,Q2: nat] :
% 5.06/5.32 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
% 5.06/5.32 = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mod_mult2_eq
% 5.06/5.32 thf(fact_3453_modulo__nat__def,axiom,
% 5.06/5.32 ( modulo_modulo_nat
% 5.06/5.32 = ( ^ [M6: nat,N: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N ) @ N ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % modulo_nat_def
% 5.06/5.32 thf(fact_3454_VEBT__internal_OminNull_Ocases,axiom,
% 5.06/5.32 ! [X: vEBT_VEBT] :
% 5.06/5.32 ( ( X
% 5.06/5.32 != ( vEBT_Leaf @ $false @ $false ) )
% 5.06/5.32 => ( ! [Uv2: $o] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.06/5.32 => ( ! [Uu2: $o] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.06/5.32 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.06/5.32 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % VEBT_internal.minNull.cases
% 5.06/5.32 thf(fact_3455_div__geq,axiom,
% 5.06/5.32 ! [N2: nat,M: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.32 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.06/5.32 => ( ( divide_divide_nat @ M @ N2 )
% 5.06/5.32 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_geq
% 5.06/5.32 thf(fact_3456_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.06/5.32 ! [X: vEBT_VEBT] :
% 5.06/5.32 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.06/5.32 => ( ! [Uv2: $o] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.06/5.32 => ( ! [Uu2: $o] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.06/5.32 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % VEBT_internal.minNull.elims(3)
% 5.06/5.32 thf(fact_3457_vebt__succ_Osimps_I2_J,axiom,
% 5.06/5.32 ! [Uv: $o,Uw: $o,N2: nat] :
% 5.06/5.32 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) )
% 5.06/5.32 = none_nat ) ).
% 5.06/5.32
% 5.06/5.32 % vebt_succ.simps(2)
% 5.06/5.32 thf(fact_3458_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.06/5.32 ! [X: vEBT_VEBT] :
% 5.06/5.32 ( ( vEBT_VEBT_minNull @ X )
% 5.06/5.32 => ( ( X
% 5.06/5.32 != ( vEBT_Leaf @ $false @ $false ) )
% 5.06/5.32 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % VEBT_internal.minNull.elims(2)
% 5.06/5.32 thf(fact_3459_mult__le__cancel__left,axiom,
% 5.06/5.32 ! [C: real,A: real,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left
% 5.06/5.32 thf(fact_3460_mult__le__cancel__left,axiom,
% 5.06/5.32 ! [C: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left
% 5.06/5.32 thf(fact_3461_mult__le__cancel__left,axiom,
% 5.06/5.32 ! [C: int,A: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_eq_int @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left
% 5.06/5.32 thf(fact_3462_mult__le__cancel__right,axiom,
% 5.06/5.32 ! [A: real,C: real,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_right
% 5.06/5.32 thf(fact_3463_mult__le__cancel__right,axiom,
% 5.06/5.32 ! [A: rat,C: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_right
% 5.06/5.32 thf(fact_3464_mult__le__cancel__right,axiom,
% 5.06/5.32 ! [A: int,C: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_eq_int @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_right
% 5.06/5.32 thf(fact_3465_mult__left__less__imp__less,axiom,
% 5.06/5.32 ! [C: real,A: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_less_imp_less
% 5.06/5.32 thf(fact_3466_mult__left__less__imp__less,axiom,
% 5.06/5.32 ! [C: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_less_imp_less
% 5.06/5.32 thf(fact_3467_mult__left__less__imp__less,axiom,
% 5.06/5.32 ! [C: nat,A: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.32 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_less_imp_less
% 5.06/5.32 thf(fact_3468_mult__left__less__imp__less,axiom,
% 5.06/5.32 ! [C: int,A: int,B: int] :
% 5.06/5.32 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_less_imp_less
% 5.06/5.32 thf(fact_3469_mult__strict__mono,axiom,
% 5.06/5.32 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.32 ( ( ord_less_real @ A @ B )
% 5.06/5.32 => ( ( ord_less_real @ C @ D )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_strict_mono
% 5.06/5.32 thf(fact_3470_mult__strict__mono,axiom,
% 5.06/5.32 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.32 ( ( ord_less_rat @ A @ B )
% 5.06/5.32 => ( ( ord_less_rat @ C @ D )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_strict_mono
% 5.06/5.32 thf(fact_3471_mult__strict__mono,axiom,
% 5.06/5.32 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.32 ( ( ord_less_nat @ A @ B )
% 5.06/5.32 => ( ( ord_less_nat @ C @ D )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.32 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_strict_mono
% 5.06/5.32 thf(fact_3472_mult__strict__mono,axiom,
% 5.06/5.32 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.32 ( ( ord_less_int @ A @ B )
% 5.06/5.32 => ( ( ord_less_int @ C @ D )
% 5.06/5.32 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_strict_mono
% 5.06/5.32 thf(fact_3473_mult__less__cancel__left,axiom,
% 5.06/5.32 ! [C: real,A: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_left
% 5.06/5.32 thf(fact_3474_mult__less__cancel__left,axiom,
% 5.06/5.32 ! [C: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_left
% 5.06/5.32 thf(fact_3475_mult__less__cancel__left,axiom,
% 5.06/5.32 ! [C: int,A: int,B: int] :
% 5.06/5.32 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_left
% 5.06/5.32 thf(fact_3476_mult__right__less__imp__less,axiom,
% 5.06/5.32 ! [A: real,C: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_less_imp_less
% 5.06/5.32 thf(fact_3477_mult__right__less__imp__less,axiom,
% 5.06/5.32 ! [A: rat,C: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_less_imp_less
% 5.06/5.32 thf(fact_3478_mult__right__less__imp__less,axiom,
% 5.06/5.32 ! [A: nat,C: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.32 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_less_imp_less
% 5.06/5.32 thf(fact_3479_mult__right__less__imp__less,axiom,
% 5.06/5.32 ! [A: int,C: int,B: int] :
% 5.06/5.32 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_less_imp_less
% 5.06/5.32 thf(fact_3480_mult__strict__mono_H,axiom,
% 5.06/5.32 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.32 ( ( ord_less_real @ A @ B )
% 5.06/5.32 => ( ( ord_less_real @ C @ D )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_strict_mono'
% 5.06/5.32 thf(fact_3481_mult__strict__mono_H,axiom,
% 5.06/5.32 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.32 ( ( ord_less_rat @ A @ B )
% 5.06/5.32 => ( ( ord_less_rat @ C @ D )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_strict_mono'
% 5.06/5.32 thf(fact_3482_mult__strict__mono_H,axiom,
% 5.06/5.32 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.32 ( ( ord_less_nat @ A @ B )
% 5.06/5.32 => ( ( ord_less_nat @ C @ D )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.32 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_strict_mono'
% 5.06/5.32 thf(fact_3483_mult__strict__mono_H,axiom,
% 5.06/5.32 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.32 ( ( ord_less_int @ A @ B )
% 5.06/5.32 => ( ( ord_less_int @ C @ D )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_strict_mono'
% 5.06/5.32 thf(fact_3484_mult__less__cancel__right,axiom,
% 5.06/5.32 ! [A: real,C: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_right
% 5.06/5.32 thf(fact_3485_mult__less__cancel__right,axiom,
% 5.06/5.32 ! [A: rat,C: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_right
% 5.06/5.32 thf(fact_3486_mult__less__cancel__right,axiom,
% 5.06/5.32 ! [A: int,C: int,B: int] :
% 5.06/5.32 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_right
% 5.06/5.32 thf(fact_3487_mult__le__cancel__left__neg,axiom,
% 5.06/5.32 ! [C: real,A: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.06/5.32 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left_neg
% 5.06/5.32 thf(fact_3488_mult__le__cancel__left__neg,axiom,
% 5.06/5.32 ! [C: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.06/5.32 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left_neg
% 5.06/5.32 thf(fact_3489_mult__le__cancel__left__neg,axiom,
% 5.06/5.32 ! [C: int,A: int,B: int] :
% 5.06/5.32 ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.32 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left_neg
% 5.06/5.32 thf(fact_3490_mult__le__cancel__left__pos,axiom,
% 5.06/5.32 ! [C: real,A: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.06/5.32 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left_pos
% 5.06/5.32 thf(fact_3491_mult__le__cancel__left__pos,axiom,
% 5.06/5.32 ! [C: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.06/5.32 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left_pos
% 5.06/5.32 thf(fact_3492_mult__le__cancel__left__pos,axiom,
% 5.06/5.32 ! [C: int,A: int,B: int] :
% 5.06/5.32 ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.32 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left_pos
% 5.06/5.32 thf(fact_3493_mult__left__le__imp__le,axiom,
% 5.06/5.32 ! [C: real,A: real,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le_imp_le
% 5.06/5.32 thf(fact_3494_mult__left__le__imp__le,axiom,
% 5.06/5.32 ! [C: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le_imp_le
% 5.06/5.32 thf(fact_3495_mult__left__le__imp__le,axiom,
% 5.06/5.32 ! [C: nat,A: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.06/5.32 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le_imp_le
% 5.06/5.32 thf(fact_3496_mult__left__le__imp__le,axiom,
% 5.06/5.32 ! [C: int,A: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.32 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le_imp_le
% 5.06/5.32 thf(fact_3497_mult__right__le__imp__le,axiom,
% 5.06/5.32 ! [A: real,C: real,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_le_imp_le
% 5.06/5.32 thf(fact_3498_mult__right__le__imp__le,axiom,
% 5.06/5.32 ! [A: rat,C: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_le_imp_le
% 5.06/5.32 thf(fact_3499_mult__right__le__imp__le,axiom,
% 5.06/5.32 ! [A: nat,C: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.06/5.32 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_le_imp_le
% 5.06/5.32 thf(fact_3500_mult__right__le__imp__le,axiom,
% 5.06/5.32 ! [A: int,C: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.06/5.32 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_le_imp_le
% 5.06/5.32 thf(fact_3501_mult__le__less__imp__less,axiom,
% 5.06/5.32 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.32 => ( ( ord_less_real @ C @ D )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_less_imp_less
% 5.06/5.32 thf(fact_3502_mult__le__less__imp__less,axiom,
% 5.06/5.32 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.32 => ( ( ord_less_rat @ C @ D )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_less_imp_less
% 5.06/5.32 thf(fact_3503_mult__le__less__imp__less,axiom,
% 5.06/5.32 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ A @ B )
% 5.06/5.32 => ( ( ord_less_nat @ C @ D )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.06/5.32 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_less_imp_less
% 5.06/5.32 thf(fact_3504_mult__le__less__imp__less,axiom,
% 5.06/5.32 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ A @ B )
% 5.06/5.32 => ( ( ord_less_int @ C @ D )
% 5.06/5.32 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_less_imp_less
% 5.06/5.32 thf(fact_3505_mult__less__le__imp__less,axiom,
% 5.06/5.32 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.32 ( ( ord_less_real @ A @ B )
% 5.06/5.32 => ( ( ord_less_eq_real @ C @ D )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_le_imp_less
% 5.06/5.32 thf(fact_3506_mult__less__le__imp__less,axiom,
% 5.06/5.32 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.32 ( ( ord_less_rat @ A @ B )
% 5.06/5.32 => ( ( ord_less_eq_rat @ C @ D )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_le_imp_less
% 5.06/5.32 thf(fact_3507_mult__less__le__imp__less,axiom,
% 5.06/5.32 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.32 ( ( ord_less_nat @ A @ B )
% 5.06/5.32 => ( ( ord_less_eq_nat @ C @ D )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.06/5.32 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_le_imp_less
% 5.06/5.32 thf(fact_3508_mult__less__le__imp__less,axiom,
% 5.06/5.32 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.32 ( ( ord_less_int @ A @ B )
% 5.06/5.32 => ( ( ord_less_eq_int @ C @ D )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_le_imp_less
% 5.06/5.32 thf(fact_3509_field__le__epsilon,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ( ! [E2: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.06/5.32 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E2 ) ) )
% 5.06/5.32 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.06/5.32
% 5.06/5.32 % field_le_epsilon
% 5.06/5.32 thf(fact_3510_field__le__epsilon,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ( ! [E2: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.06/5.32 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 5.06/5.32 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.06/5.32
% 5.06/5.32 % field_le_epsilon
% 5.06/5.32 thf(fact_3511_add__neg__nonpos,axiom,
% 5.06/5.32 ! [A: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_neg_nonpos
% 5.06/5.32 thf(fact_3512_add__neg__nonpos,axiom,
% 5.06/5.32 ! [A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_neg_nonpos
% 5.06/5.32 thf(fact_3513_add__neg__nonpos,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.06/5.32 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.06/5.32 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_neg_nonpos
% 5.06/5.32 thf(fact_3514_add__neg__nonpos,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( ord_less_int @ A @ zero_zero_int )
% 5.06/5.32 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.06/5.32 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_neg_nonpos
% 5.06/5.32 thf(fact_3515_add__nonneg__pos,axiom,
% 5.06/5.32 ! [A: real,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.32 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_nonneg_pos
% 5.06/5.32 thf(fact_3516_add__nonneg__pos,axiom,
% 5.06/5.32 ! [A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.06/5.32 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_nonneg_pos
% 5.06/5.32 thf(fact_3517_add__nonneg__pos,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.32 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_nonneg_pos
% 5.06/5.32 thf(fact_3518_add__nonneg__pos,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.32 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_nonneg_pos
% 5.06/5.32 thf(fact_3519_add__nonpos__neg,axiom,
% 5.06/5.32 ! [A: real,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_nonpos_neg
% 5.06/5.32 thf(fact_3520_add__nonpos__neg,axiom,
% 5.06/5.32 ! [A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_nonpos_neg
% 5.06/5.32 thf(fact_3521_add__nonpos__neg,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.06/5.32 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.06/5.32 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_nonpos_neg
% 5.06/5.32 thf(fact_3522_add__nonpos__neg,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.32 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.06/5.32 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_nonpos_neg
% 5.06/5.32 thf(fact_3523_add__pos__nonneg,axiom,
% 5.06/5.32 ! [A: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.32 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_pos_nonneg
% 5.06/5.32 thf(fact_3524_add__pos__nonneg,axiom,
% 5.06/5.32 ! [A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.32 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_pos_nonneg
% 5.06/5.32 thf(fact_3525_add__pos__nonneg,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.32 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_pos_nonneg
% 5.06/5.32 thf(fact_3526_add__pos__nonneg,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.32 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_pos_nonneg
% 5.06/5.32 thf(fact_3527_add__strict__increasing,axiom,
% 5.06/5.32 ! [A: real,B: real,C: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ B @ C )
% 5.06/5.32 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_strict_increasing
% 5.06/5.32 thf(fact_3528_add__strict__increasing,axiom,
% 5.06/5.32 ! [A: rat,B: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.06/5.32 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_strict_increasing
% 5.06/5.32 thf(fact_3529_add__strict__increasing,axiom,
% 5.06/5.32 ! [A: nat,B: nat,C: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_eq_nat @ B @ C )
% 5.06/5.32 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_strict_increasing
% 5.06/5.32 thf(fact_3530_add__strict__increasing,axiom,
% 5.06/5.32 ! [A: int,B: int,C: int] :
% 5.06/5.32 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_eq_int @ B @ C )
% 5.06/5.32 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_strict_increasing
% 5.06/5.32 thf(fact_3531_add__strict__increasing2,axiom,
% 5.06/5.32 ! [A: real,B: real,C: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_real @ B @ C )
% 5.06/5.32 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_strict_increasing2
% 5.06/5.32 thf(fact_3532_add__strict__increasing2,axiom,
% 5.06/5.32 ! [A: rat,B: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_rat @ B @ C )
% 5.06/5.32 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_strict_increasing2
% 5.06/5.32 thf(fact_3533_add__strict__increasing2,axiom,
% 5.06/5.32 ! [A: nat,B: nat,C: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_nat @ B @ C )
% 5.06/5.32 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_strict_increasing2
% 5.06/5.32 thf(fact_3534_add__strict__increasing2,axiom,
% 5.06/5.32 ! [A: int,B: int,C: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_int @ B @ C )
% 5.06/5.32 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_strict_increasing2
% 5.06/5.32 thf(fact_3535_frac__le,axiom,
% 5.06/5.32 ! [Y: real,X: real,W: real,Z: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.32 => ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.06/5.32 => ( ( ord_less_eq_real @ W @ Z )
% 5.06/5.32 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % frac_le
% 5.06/5.32 thf(fact_3536_frac__le,axiom,
% 5.06/5.32 ! [Y: rat,X: rat,W: rat,Z: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.32 => ( ( ord_less_eq_rat @ X @ Y )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.06/5.32 => ( ( ord_less_eq_rat @ W @ Z )
% 5.06/5.32 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % frac_le
% 5.06/5.32 thf(fact_3537_frac__less,axiom,
% 5.06/5.32 ! [X: real,Y: real,W: real,Z: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.32 => ( ( ord_less_real @ X @ Y )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.06/5.32 => ( ( ord_less_eq_real @ W @ Z )
% 5.06/5.32 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % frac_less
% 5.06/5.32 thf(fact_3538_frac__less,axiom,
% 5.06/5.32 ! [X: rat,Y: rat,W: rat,Z: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.32 => ( ( ord_less_rat @ X @ Y )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.06/5.32 => ( ( ord_less_eq_rat @ W @ Z )
% 5.06/5.32 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % frac_less
% 5.06/5.32 thf(fact_3539_frac__less2,axiom,
% 5.06/5.32 ! [X: real,Y: real,W: real,Z: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.32 => ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.06/5.32 => ( ( ord_less_real @ W @ Z )
% 5.06/5.32 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % frac_less2
% 5.06/5.32 thf(fact_3540_frac__less2,axiom,
% 5.06/5.32 ! [X: rat,Y: rat,W: rat,Z: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.06/5.32 => ( ( ord_less_eq_rat @ X @ Y )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.06/5.32 => ( ( ord_less_rat @ W @ Z )
% 5.06/5.32 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % frac_less2
% 5.06/5.32 thf(fact_3541_divide__le__cancel,axiom,
% 5.06/5.32 ! [A: real,C: real,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_le_cancel
% 5.06/5.32 thf(fact_3542_divide__le__cancel,axiom,
% 5.06/5.32 ! [A: rat,C: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ A @ B ) )
% 5.06/5.32 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_le_cancel
% 5.06/5.32 thf(fact_3543_divide__nonneg__neg,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.32 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_nonneg_neg
% 5.06/5.32 thf(fact_3544_divide__nonneg__neg,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.32 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_nonneg_neg
% 5.06/5.32 thf(fact_3545_divide__nonneg__pos,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.32 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_nonneg_pos
% 5.06/5.32 thf(fact_3546_divide__nonneg__pos,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.06/5.32 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_nonneg_pos
% 5.06/5.32 thf(fact_3547_divide__nonpos__neg,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_nonpos_neg
% 5.06/5.32 thf(fact_3548_divide__nonpos__neg,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_nonpos_neg
% 5.06/5.32 thf(fact_3549_divide__nonpos__pos,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.32 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_nonpos_pos
% 5.06/5.32 thf(fact_3550_divide__nonpos__pos,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.06/5.32 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_nonpos_pos
% 5.06/5.32 thf(fact_3551_sum__squares__ge__zero,axiom,
% 5.06/5.32 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % sum_squares_ge_zero
% 5.06/5.32 thf(fact_3552_sum__squares__ge__zero,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % sum_squares_ge_zero
% 5.06/5.32 thf(fact_3553_sum__squares__ge__zero,axiom,
% 5.06/5.32 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % sum_squares_ge_zero
% 5.06/5.32 thf(fact_3554_sum__squares__le__zero__iff,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 5.06/5.32 = ( ( X = zero_zero_real )
% 5.06/5.32 & ( Y = zero_zero_real ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % sum_squares_le_zero_iff
% 5.06/5.32 thf(fact_3555_sum__squares__le__zero__iff,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 5.06/5.32 = ( ( X = zero_zero_rat )
% 5.06/5.32 & ( Y = zero_zero_rat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % sum_squares_le_zero_iff
% 5.06/5.32 thf(fact_3556_sum__squares__le__zero__iff,axiom,
% 5.06/5.32 ! [X: int,Y: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 5.06/5.32 = ( ( X = zero_zero_int )
% 5.06/5.32 & ( Y = zero_zero_int ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % sum_squares_le_zero_iff
% 5.06/5.32 thf(fact_3557_mult__left__le__one__le,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.32 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.32 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le_one_le
% 5.06/5.32 thf(fact_3558_mult__left__le__one__le,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.32 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le_one_le
% 5.06/5.32 thf(fact_3559_mult__left__le__one__le,axiom,
% 5.06/5.32 ! [X: int,Y: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.32 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.06/5.32 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le_one_le
% 5.06/5.32 thf(fact_3560_mult__right__le__one__le,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.32 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.32 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_le_one_le
% 5.06/5.32 thf(fact_3561_mult__right__le__one__le,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.32 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_le_one_le
% 5.06/5.32 thf(fact_3562_mult__right__le__one__le,axiom,
% 5.06/5.32 ! [X: int,Y: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.32 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.06/5.32 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_right_le_one_le
% 5.06/5.32 thf(fact_3563_mult__le__one,axiom,
% 5.06/5.32 ! [A: real,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.32 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.06/5.32 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_one
% 5.06/5.32 thf(fact_3564_mult__le__one,axiom,
% 5.06/5.32 ! [A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.32 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_one
% 5.06/5.32 thf(fact_3565_mult__le__one,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.32 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.06/5.32 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_one
% 5.06/5.32 thf(fact_3566_mult__le__one,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.32 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.06/5.32 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_one
% 5.06/5.32 thf(fact_3567_mult__left__le,axiom,
% 5.06/5.32 ! [C: real,A: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le
% 5.06/5.32 thf(fact_3568_mult__left__le,axiom,
% 5.06/5.32 ! [C: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le
% 5.06/5.32 thf(fact_3569_mult__left__le,axiom,
% 5.06/5.32 ! [C: nat,A: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le
% 5.06/5.32 thf(fact_3570_mult__left__le,axiom,
% 5.06/5.32 ! [C: int,A: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_left_le
% 5.06/5.32 thf(fact_3571_power__less__imp__less__base,axiom,
% 5.06/5.32 ! [A: real,N2: nat,B: real] :
% 5.06/5.32 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.32 => ( ord_less_real @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_less_imp_less_base
% 5.06/5.32 thf(fact_3572_power__less__imp__less__base,axiom,
% 5.06/5.32 ! [A: rat,N2: nat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.32 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_less_imp_less_base
% 5.06/5.32 thf(fact_3573_power__less__imp__less__base,axiom,
% 5.06/5.32 ! [A: nat,N2: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.32 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_less_imp_less_base
% 5.06/5.32 thf(fact_3574_power__less__imp__less__base,axiom,
% 5.06/5.32 ! [A: int,N2: nat,B: int] :
% 5.06/5.32 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.32 => ( ord_less_int @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_less_imp_less_base
% 5.06/5.32 thf(fact_3575_not__sum__squares__lt__zero,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 5.06/5.32
% 5.06/5.32 % not_sum_squares_lt_zero
% 5.06/5.32 thf(fact_3576_not__sum__squares__lt__zero,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 5.06/5.32
% 5.06/5.32 % not_sum_squares_lt_zero
% 5.06/5.32 thf(fact_3577_not__sum__squares__lt__zero,axiom,
% 5.06/5.32 ! [X: int,Y: int] :
% 5.06/5.32 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 5.06/5.32
% 5.06/5.32 % not_sum_squares_lt_zero
% 5.06/5.32 thf(fact_3578_sum__squares__gt__zero__iff,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 5.06/5.32 = ( ( X != zero_zero_real )
% 5.06/5.32 | ( Y != zero_zero_real ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % sum_squares_gt_zero_iff
% 5.06/5.32 thf(fact_3579_sum__squares__gt__zero__iff,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 5.06/5.32 = ( ( X != zero_zero_rat )
% 5.06/5.32 | ( Y != zero_zero_rat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % sum_squares_gt_zero_iff
% 5.06/5.32 thf(fact_3580_sum__squares__gt__zero__iff,axiom,
% 5.06/5.32 ! [X: int,Y: int] :
% 5.06/5.32 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 5.06/5.32 = ( ( X != zero_zero_int )
% 5.06/5.32 | ( Y != zero_zero_int ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % sum_squares_gt_zero_iff
% 5.06/5.32 thf(fact_3581_zero__less__two,axiom,
% 5.06/5.32 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.06/5.32
% 5.06/5.32 % zero_less_two
% 5.06/5.32 thf(fact_3582_zero__less__two,axiom,
% 5.06/5.32 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.06/5.32
% 5.06/5.32 % zero_less_two
% 5.06/5.32 thf(fact_3583_zero__less__two,axiom,
% 5.06/5.32 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.06/5.32
% 5.06/5.32 % zero_less_two
% 5.06/5.32 thf(fact_3584_zero__less__two,axiom,
% 5.06/5.32 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.06/5.32
% 5.06/5.32 % zero_less_two
% 5.06/5.32 thf(fact_3585_divide__strict__left__mono__neg,axiom,
% 5.06/5.32 ! [A: real,B: real,C: real] :
% 5.06/5.32 ( ( ord_less_real @ A @ B )
% 5.06/5.32 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.06/5.32 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_strict_left_mono_neg
% 5.06/5.32 thf(fact_3586_divide__strict__left__mono__neg,axiom,
% 5.06/5.32 ! [A: rat,B: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_rat @ A @ B )
% 5.06/5.32 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.06/5.32 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_strict_left_mono_neg
% 5.06/5.32 thf(fact_3587_divide__strict__left__mono,axiom,
% 5.06/5.32 ! [B: real,A: real,C: real] :
% 5.06/5.32 ( ( ord_less_real @ B @ A )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.06/5.32 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_strict_left_mono
% 5.06/5.32 thf(fact_3588_divide__strict__left__mono,axiom,
% 5.06/5.32 ! [B: rat,A: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_rat @ B @ A )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.06/5.32 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_strict_left_mono
% 5.06/5.32 thf(fact_3589_mult__imp__less__div__pos,axiom,
% 5.06/5.32 ! [Y: real,Z: real,X: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.32 => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X )
% 5.06/5.32 => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_imp_less_div_pos
% 5.06/5.32 thf(fact_3590_mult__imp__less__div__pos,axiom,
% 5.06/5.32 ! [Y: rat,Z: rat,X: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.06/5.32 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 5.06/5.32 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_imp_less_div_pos
% 5.06/5.32 thf(fact_3591_mult__imp__div__pos__less,axiom,
% 5.06/5.32 ! [Y: real,X: real,Z: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.32 => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y ) )
% 5.06/5.32 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_imp_div_pos_less
% 5.06/5.32 thf(fact_3592_mult__imp__div__pos__less,axiom,
% 5.06/5.32 ! [Y: rat,X: rat,Z: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.06/5.32 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 5.06/5.32 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_imp_div_pos_less
% 5.06/5.32 thf(fact_3593_pos__less__divide__eq,axiom,
% 5.06/5.32 ! [C: real,A: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.06/5.32 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % pos_less_divide_eq
% 5.06/5.32 thf(fact_3594_pos__less__divide__eq,axiom,
% 5.06/5.32 ! [C: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.32 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % pos_less_divide_eq
% 5.06/5.32 thf(fact_3595_pos__divide__less__eq,axiom,
% 5.06/5.32 ! [C: real,B: real,A: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.06/5.32 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % pos_divide_less_eq
% 5.06/5.32 thf(fact_3596_pos__divide__less__eq,axiom,
% 5.06/5.32 ! [C: rat,B: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.06/5.32 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % pos_divide_less_eq
% 5.06/5.32 thf(fact_3597_neg__less__divide__eq,axiom,
% 5.06/5.32 ! [C: real,A: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.06/5.32 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % neg_less_divide_eq
% 5.06/5.32 thf(fact_3598_neg__less__divide__eq,axiom,
% 5.06/5.32 ! [C: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.32 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % neg_less_divide_eq
% 5.06/5.32 thf(fact_3599_neg__divide__less__eq,axiom,
% 5.06/5.32 ! [C: real,B: real,A: real] :
% 5.06/5.32 ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.06/5.32 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % neg_divide_less_eq
% 5.06/5.32 thf(fact_3600_neg__divide__less__eq,axiom,
% 5.06/5.32 ! [C: rat,B: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.06/5.32 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % neg_divide_less_eq
% 5.06/5.32 thf(fact_3601_less__divide__eq,axiom,
% 5.06/5.32 ! [A: real,B: real,C: real] :
% 5.06/5.32 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % less_divide_eq
% 5.06/5.32 thf(fact_3602_less__divide__eq,axiom,
% 5.06/5.32 ! [A: rat,B: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % less_divide_eq
% 5.06/5.32 thf(fact_3603_divide__less__eq,axiom,
% 5.06/5.32 ! [B: real,C: real,A: real] :
% 5.06/5.32 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_less_eq
% 5.06/5.32 thf(fact_3604_divide__less__eq,axiom,
% 5.06/5.32 ! [B: rat,C: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_less_eq
% 5.06/5.32 thf(fact_3605_divide__less__eq__1,axiom,
% 5.06/5.32 ! [B: real,A: real] :
% 5.06/5.32 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.32 & ( ord_less_real @ B @ A ) )
% 5.06/5.32 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.32 & ( ord_less_real @ A @ B ) )
% 5.06/5.32 | ( A = zero_zero_real ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_less_eq_1
% 5.06/5.32 thf(fact_3606_divide__less__eq__1,axiom,
% 5.06/5.32 ! [B: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.32 & ( ord_less_rat @ B @ A ) )
% 5.06/5.32 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.32 & ( ord_less_rat @ A @ B ) )
% 5.06/5.32 | ( A = zero_zero_rat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_less_eq_1
% 5.06/5.32 thf(fact_3607_less__divide__eq__1,axiom,
% 5.06/5.32 ! [B: real,A: real] :
% 5.06/5.32 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.32 & ( ord_less_real @ A @ B ) )
% 5.06/5.32 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.32 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % less_divide_eq_1
% 5.06/5.32 thf(fact_3608_less__divide__eq__1,axiom,
% 5.06/5.32 ! [B: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.32 & ( ord_less_rat @ A @ B ) )
% 5.06/5.32 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.32 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % less_divide_eq_1
% 5.06/5.32 thf(fact_3609_power__le__one,axiom,
% 5.06/5.32 ! [A: real,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.06/5.32 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ one_one_real ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_le_one
% 5.06/5.32 thf(fact_3610_power__le__one,axiom,
% 5.06/5.32 ! [A: rat,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_le_one
% 5.06/5.32 thf(fact_3611_power__le__one,axiom,
% 5.06/5.32 ! [A: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.06/5.32 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_le_one
% 5.06/5.32 thf(fact_3612_power__le__one,axiom,
% 5.06/5.32 ! [A: int,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.06/5.32 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_le_one
% 5.06/5.32 thf(fact_3613_eq__divide__eq__numeral_I1_J,axiom,
% 5.06/5.32 ! [W: num,B: complex,C: complex] :
% 5.06/5.32 ( ( ( numera6690914467698888265omplex @ W )
% 5.06/5.32 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.06/5.32 = ( ( ( C != zero_zero_complex )
% 5.06/5.32 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.06/5.32 = B ) )
% 5.06/5.32 & ( ( C = zero_zero_complex )
% 5.06/5.32 => ( ( numera6690914467698888265omplex @ W )
% 5.06/5.32 = zero_zero_complex ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % eq_divide_eq_numeral(1)
% 5.06/5.32 thf(fact_3614_eq__divide__eq__numeral_I1_J,axiom,
% 5.06/5.32 ! [W: num,B: real,C: real] :
% 5.06/5.32 ( ( ( numeral_numeral_real @ W )
% 5.06/5.32 = ( divide_divide_real @ B @ C ) )
% 5.06/5.32 = ( ( ( C != zero_zero_real )
% 5.06/5.32 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.06/5.32 = B ) )
% 5.06/5.32 & ( ( C = zero_zero_real )
% 5.06/5.32 => ( ( numeral_numeral_real @ W )
% 5.06/5.32 = zero_zero_real ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % eq_divide_eq_numeral(1)
% 5.06/5.32 thf(fact_3615_eq__divide__eq__numeral_I1_J,axiom,
% 5.06/5.32 ! [W: num,B: rat,C: rat] :
% 5.06/5.32 ( ( ( numeral_numeral_rat @ W )
% 5.06/5.32 = ( divide_divide_rat @ B @ C ) )
% 5.06/5.32 = ( ( ( C != zero_zero_rat )
% 5.06/5.32 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.06/5.32 = B ) )
% 5.06/5.32 & ( ( C = zero_zero_rat )
% 5.06/5.32 => ( ( numeral_numeral_rat @ W )
% 5.06/5.32 = zero_zero_rat ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % eq_divide_eq_numeral(1)
% 5.06/5.32 thf(fact_3616_divide__eq__eq__numeral_I1_J,axiom,
% 5.06/5.32 ! [B: complex,C: complex,W: num] :
% 5.06/5.32 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.06/5.32 = ( numera6690914467698888265omplex @ W ) )
% 5.06/5.32 = ( ( ( C != zero_zero_complex )
% 5.06/5.32 => ( B
% 5.06/5.32 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.06/5.32 & ( ( C = zero_zero_complex )
% 5.06/5.32 => ( ( numera6690914467698888265omplex @ W )
% 5.06/5.32 = zero_zero_complex ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_eq_eq_numeral(1)
% 5.06/5.32 thf(fact_3617_divide__eq__eq__numeral_I1_J,axiom,
% 5.06/5.32 ! [B: real,C: real,W: num] :
% 5.06/5.32 ( ( ( divide_divide_real @ B @ C )
% 5.06/5.32 = ( numeral_numeral_real @ W ) )
% 5.06/5.32 = ( ( ( C != zero_zero_real )
% 5.06/5.32 => ( B
% 5.06/5.32 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.06/5.32 & ( ( C = zero_zero_real )
% 5.06/5.32 => ( ( numeral_numeral_real @ W )
% 5.06/5.32 = zero_zero_real ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_eq_eq_numeral(1)
% 5.06/5.32 thf(fact_3618_divide__eq__eq__numeral_I1_J,axiom,
% 5.06/5.32 ! [B: rat,C: rat,W: num] :
% 5.06/5.32 ( ( ( divide_divide_rat @ B @ C )
% 5.06/5.32 = ( numeral_numeral_rat @ W ) )
% 5.06/5.32 = ( ( ( C != zero_zero_rat )
% 5.06/5.32 => ( B
% 5.06/5.32 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.06/5.32 & ( ( C = zero_zero_rat )
% 5.06/5.32 => ( ( numeral_numeral_rat @ W )
% 5.06/5.32 = zero_zero_rat ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_eq_eq_numeral(1)
% 5.06/5.32 thf(fact_3619_divide__add__eq__iff,axiom,
% 5.06/5.32 ! [Z: complex,X: complex,Y: complex] :
% 5.06/5.32 ( ( Z != zero_zero_complex )
% 5.06/5.32 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_add_eq_iff
% 5.06/5.32 thf(fact_3620_divide__add__eq__iff,axiom,
% 5.06/5.32 ! [Z: real,X: real,Y: real] :
% 5.06/5.32 ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 5.06/5.32 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_add_eq_iff
% 5.06/5.32 thf(fact_3621_divide__add__eq__iff,axiom,
% 5.06/5.32 ! [Z: rat,X: rat,Y: rat] :
% 5.06/5.32 ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 5.06/5.32 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_add_eq_iff
% 5.06/5.32 thf(fact_3622_add__divide__eq__iff,axiom,
% 5.06/5.32 ! [Z: complex,X: complex,Y: complex] :
% 5.06/5.32 ( ( Z != zero_zero_complex )
% 5.06/5.32 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_iff
% 5.06/5.32 thf(fact_3623_add__divide__eq__iff,axiom,
% 5.06/5.32 ! [Z: real,X: real,Y: real] :
% 5.06/5.32 ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 5.06/5.32 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_iff
% 5.06/5.32 thf(fact_3624_add__divide__eq__iff,axiom,
% 5.06/5.32 ! [Z: rat,X: rat,Y: rat] :
% 5.06/5.32 ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 5.06/5.32 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_iff
% 5.06/5.32 thf(fact_3625_add__num__frac,axiom,
% 5.06/5.32 ! [Y: complex,Z: complex,X: complex] :
% 5.06/5.32 ( ( Y != zero_zero_complex )
% 5.06/5.32 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_num_frac
% 5.06/5.32 thf(fact_3626_add__num__frac,axiom,
% 5.06/5.32 ! [Y: real,Z: real,X: real] :
% 5.06/5.32 ( ( Y != zero_zero_real )
% 5.06/5.32 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y ) )
% 5.06/5.32 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_num_frac
% 5.06/5.32 thf(fact_3627_add__num__frac,axiom,
% 5.06/5.32 ! [Y: rat,Z: rat,X: rat] :
% 5.06/5.32 ( ( Y != zero_zero_rat )
% 5.06/5.32 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 5.06/5.32 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_num_frac
% 5.06/5.32 thf(fact_3628_add__frac__num,axiom,
% 5.06/5.32 ! [Y: complex,X: complex,Z: complex] :
% 5.06/5.32 ( ( Y != zero_zero_complex )
% 5.06/5.32 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_frac_num
% 5.06/5.32 thf(fact_3629_add__frac__num,axiom,
% 5.06/5.32 ! [Y: real,X: real,Z: real] :
% 5.06/5.32 ( ( Y != zero_zero_real )
% 5.06/5.32 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z )
% 5.06/5.32 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_frac_num
% 5.06/5.32 thf(fact_3630_add__frac__num,axiom,
% 5.06/5.32 ! [Y: rat,X: rat,Z: rat] :
% 5.06/5.32 ( ( Y != zero_zero_rat )
% 5.06/5.32 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 5.06/5.32 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_frac_num
% 5.06/5.32 thf(fact_3631_add__frac__eq,axiom,
% 5.06/5.32 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.06/5.32 ( ( Y != zero_zero_complex )
% 5.06/5.32 => ( ( Z != zero_zero_complex )
% 5.06/5.32 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_frac_eq
% 5.06/5.32 thf(fact_3632_add__frac__eq,axiom,
% 5.06/5.32 ! [Y: real,Z: real,X: real,W: real] :
% 5.06/5.32 ( ( Y != zero_zero_real )
% 5.06/5.32 => ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.06/5.32 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_frac_eq
% 5.06/5.32 thf(fact_3633_add__frac__eq,axiom,
% 5.06/5.32 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.06/5.32 ( ( Y != zero_zero_rat )
% 5.06/5.32 => ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.06/5.32 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_frac_eq
% 5.06/5.32 thf(fact_3634_add__divide__eq__if__simps_I1_J,axiom,
% 5.06/5.32 ! [Z: complex,A: complex,B: complex] :
% 5.06/5.32 ( ( ( Z = zero_zero_complex )
% 5.06/5.32 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.06/5.32 = A ) )
% 5.06/5.32 & ( ( Z != zero_zero_complex )
% 5.06/5.32 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_if_simps(1)
% 5.06/5.32 thf(fact_3635_add__divide__eq__if__simps_I1_J,axiom,
% 5.06/5.32 ! [Z: real,A: real,B: real] :
% 5.06/5.32 ( ( ( Z = zero_zero_real )
% 5.06/5.32 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.06/5.32 = A ) )
% 5.06/5.32 & ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.06/5.32 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_if_simps(1)
% 5.06/5.32 thf(fact_3636_add__divide__eq__if__simps_I1_J,axiom,
% 5.06/5.32 ! [Z: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ( Z = zero_zero_rat )
% 5.06/5.32 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.06/5.32 = A ) )
% 5.06/5.32 & ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.06/5.32 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_if_simps(1)
% 5.06/5.32 thf(fact_3637_add__divide__eq__if__simps_I2_J,axiom,
% 5.06/5.32 ! [Z: complex,A: complex,B: complex] :
% 5.06/5.32 ( ( ( Z = zero_zero_complex )
% 5.06/5.32 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.06/5.32 = B ) )
% 5.06/5.32 & ( ( Z != zero_zero_complex )
% 5.06/5.32 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_if_simps(2)
% 5.06/5.32 thf(fact_3638_add__divide__eq__if__simps_I2_J,axiom,
% 5.06/5.32 ! [Z: real,A: real,B: real] :
% 5.06/5.32 ( ( ( Z = zero_zero_real )
% 5.06/5.32 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.06/5.32 = B ) )
% 5.06/5.32 & ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.06/5.32 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_if_simps(2)
% 5.06/5.32 thf(fact_3639_add__divide__eq__if__simps_I2_J,axiom,
% 5.06/5.32 ! [Z: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ( Z = zero_zero_rat )
% 5.06/5.32 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.06/5.32 = B ) )
% 5.06/5.32 & ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.06/5.32 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_if_simps(2)
% 5.06/5.32 thf(fact_3640_power__inject__base,axiom,
% 5.06/5.32 ! [A: real,N2: nat,B: real] :
% 5.06/5.32 ( ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.06/5.32 = ( power_power_real @ B @ ( suc @ N2 ) ) )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.32 => ( A = B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_inject_base
% 5.06/5.32 thf(fact_3641_power__inject__base,axiom,
% 5.06/5.32 ! [A: rat,N2: nat,B: rat] :
% 5.06/5.32 ( ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 5.06/5.32 = ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.32 => ( A = B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_inject_base
% 5.06/5.32 thf(fact_3642_power__inject__base,axiom,
% 5.06/5.32 ! [A: nat,N2: nat,B: nat] :
% 5.06/5.32 ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.06/5.32 = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.32 => ( A = B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_inject_base
% 5.06/5.32 thf(fact_3643_power__inject__base,axiom,
% 5.06/5.32 ! [A: int,N2: nat,B: int] :
% 5.06/5.32 ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.06/5.32 = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.32 => ( A = B ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_inject_base
% 5.06/5.32 thf(fact_3644_power__le__imp__le__base,axiom,
% 5.06/5.32 ! [A: real,N2: nat,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ ( power_power_real @ B @ ( suc @ N2 ) ) )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.32 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_le_imp_le_base
% 5.06/5.32 thf(fact_3645_power__le__imp__le__base,axiom,
% 5.06/5.32 ! [A: rat,N2: nat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.32 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_le_imp_le_base
% 5.06/5.32 thf(fact_3646_power__le__imp__le__base,axiom,
% 5.06/5.32 ! [A: nat,N2: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.06/5.32 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_le_imp_le_base
% 5.06/5.32 thf(fact_3647_power__le__imp__le__base,axiom,
% 5.06/5.32 ! [A: int,N2: nat,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.32 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_le_imp_le_base
% 5.06/5.32 thf(fact_3648_div__add__self2,axiom,
% 5.06/5.32 ! [B: nat,A: nat] :
% 5.06/5.32 ( ( B != zero_zero_nat )
% 5.06/5.32 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.06/5.32 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_add_self2
% 5.06/5.32 thf(fact_3649_div__add__self2,axiom,
% 5.06/5.32 ! [B: int,A: int] :
% 5.06/5.32 ( ( B != zero_zero_int )
% 5.06/5.32 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.06/5.32 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_add_self2
% 5.06/5.32 thf(fact_3650_div__add__self1,axiom,
% 5.06/5.32 ! [B: nat,A: nat] :
% 5.06/5.32 ( ( B != zero_zero_nat )
% 5.06/5.32 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.06/5.32 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_add_self1
% 5.06/5.32 thf(fact_3651_div__add__self1,axiom,
% 5.06/5.32 ! [B: int,A: int] :
% 5.06/5.32 ( ( B != zero_zero_int )
% 5.06/5.32 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.06/5.32 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_add_self1
% 5.06/5.32 thf(fact_3652_divide__diff__eq__iff,axiom,
% 5.06/5.32 ! [Z: complex,X: complex,Y: complex] :
% 5.06/5.32 ( ( Z != zero_zero_complex )
% 5.06/5.32 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_diff_eq_iff
% 5.06/5.32 thf(fact_3653_divide__diff__eq__iff,axiom,
% 5.06/5.32 ! [Z: real,X: real,Y: real] :
% 5.06/5.32 ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 5.06/5.32 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_diff_eq_iff
% 5.06/5.32 thf(fact_3654_divide__diff__eq__iff,axiom,
% 5.06/5.32 ! [Z: rat,X: rat,Y: rat] :
% 5.06/5.32 ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 5.06/5.32 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_diff_eq_iff
% 5.06/5.32 thf(fact_3655_diff__divide__eq__iff,axiom,
% 5.06/5.32 ! [Z: complex,X: complex,Y: complex] :
% 5.06/5.32 ( ( Z != zero_zero_complex )
% 5.06/5.32 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % diff_divide_eq_iff
% 5.06/5.32 thf(fact_3656_diff__divide__eq__iff,axiom,
% 5.06/5.32 ! [Z: real,X: real,Y: real] :
% 5.06/5.32 ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 5.06/5.32 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % diff_divide_eq_iff
% 5.06/5.32 thf(fact_3657_diff__divide__eq__iff,axiom,
% 5.06/5.32 ! [Z: rat,X: rat,Y: rat] :
% 5.06/5.32 ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 5.06/5.32 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % diff_divide_eq_iff
% 5.06/5.32 thf(fact_3658_diff__frac__eq,axiom,
% 5.06/5.32 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.06/5.32 ( ( Y != zero_zero_complex )
% 5.06/5.32 => ( ( Z != zero_zero_complex )
% 5.06/5.32 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % diff_frac_eq
% 5.06/5.32 thf(fact_3659_diff__frac__eq,axiom,
% 5.06/5.32 ! [Y: real,Z: real,X: real,W: real] :
% 5.06/5.32 ( ( Y != zero_zero_real )
% 5.06/5.32 => ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.06/5.32 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % diff_frac_eq
% 5.06/5.32 thf(fact_3660_diff__frac__eq,axiom,
% 5.06/5.32 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.06/5.32 ( ( Y != zero_zero_rat )
% 5.06/5.32 => ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.06/5.32 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % diff_frac_eq
% 5.06/5.32 thf(fact_3661_add__divide__eq__if__simps_I4_J,axiom,
% 5.06/5.32 ! [Z: complex,A: complex,B: complex] :
% 5.06/5.32 ( ( ( Z = zero_zero_complex )
% 5.06/5.32 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.06/5.32 = A ) )
% 5.06/5.32 & ( ( Z != zero_zero_complex )
% 5.06/5.32 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.06/5.32 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_if_simps(4)
% 5.06/5.32 thf(fact_3662_add__divide__eq__if__simps_I4_J,axiom,
% 5.06/5.32 ! [Z: real,A: real,B: real] :
% 5.06/5.32 ( ( ( Z = zero_zero_real )
% 5.06/5.32 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.06/5.32 = A ) )
% 5.06/5.32 & ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.06/5.32 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_if_simps(4)
% 5.06/5.32 thf(fact_3663_add__divide__eq__if__simps_I4_J,axiom,
% 5.06/5.32 ! [Z: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ( Z = zero_zero_rat )
% 5.06/5.32 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.06/5.32 = A ) )
% 5.06/5.32 & ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.06/5.32 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % add_divide_eq_if_simps(4)
% 5.06/5.32 thf(fact_3664_numeral__1__eq__Suc__0,axiom,
% 5.06/5.32 ( ( numeral_numeral_nat @ one )
% 5.06/5.32 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.32
% 5.06/5.32 % numeral_1_eq_Suc_0
% 5.06/5.32 thf(fact_3665_num_Osize_I5_J,axiom,
% 5.06/5.32 ! [X22: num] :
% 5.06/5.32 ( ( size_size_num @ ( bit0 @ X22 ) )
% 5.06/5.32 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % num.size(5)
% 5.06/5.32 thf(fact_3666_ex__least__nat__less,axiom,
% 5.06/5.32 ! [P: nat > $o,N2: nat] :
% 5.06/5.32 ( ( P @ N2 )
% 5.06/5.32 => ( ~ ( P @ zero_zero_nat )
% 5.06/5.32 => ? [K2: nat] :
% 5.06/5.32 ( ( ord_less_nat @ K2 @ N2 )
% 5.06/5.32 & ! [I: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ I @ K2 )
% 5.06/5.32 => ~ ( P @ I ) )
% 5.06/5.32 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % ex_least_nat_less
% 5.06/5.32 thf(fact_3667_one__less__mult,axiom,
% 5.06/5.32 ! [N2: nat,M: nat] :
% 5.06/5.32 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.32 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.06/5.32 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % one_less_mult
% 5.06/5.32 thf(fact_3668_n__less__m__mult__n,axiom,
% 5.06/5.32 ! [N2: nat,M: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.32 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.06/5.32 => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % n_less_m_mult_n
% 5.06/5.32 thf(fact_3669_n__less__n__mult__m,axiom,
% 5.06/5.32 ! [N2: nat,M: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.32 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.06/5.32 => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % n_less_n_mult_m
% 5.06/5.32 thf(fact_3670_diff__Suc__less,axiom,
% 5.06/5.32 ! [N2: nat,I2: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.32 => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I2 ) ) @ N2 ) ) ).
% 5.06/5.32
% 5.06/5.32 % diff_Suc_less
% 5.06/5.32 thf(fact_3671_nat__induct__non__zero,axiom,
% 5.06/5.32 ! [N2: nat,P: nat > $o] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.32 => ( ( P @ one_one_nat )
% 5.06/5.32 => ( ! [N3: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.06/5.32 => ( ( P @ N3 )
% 5.06/5.32 => ( P @ ( suc @ N3 ) ) ) )
% 5.06/5.32 => ( P @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % nat_induct_non_zero
% 5.06/5.32 thf(fact_3672_length__pos__if__in__set,axiom,
% 5.06/5.32 ! [X: complex,Xs2: list_complex] :
% 5.06/5.32 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.06/5.32 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % length_pos_if_in_set
% 5.06/5.32 thf(fact_3673_length__pos__if__in__set,axiom,
% 5.06/5.32 ! [X: real,Xs2: list_real] :
% 5.06/5.32 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.06/5.32 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % length_pos_if_in_set
% 5.06/5.32 thf(fact_3674_length__pos__if__in__set,axiom,
% 5.06/5.32 ! [X: set_nat,Xs2: list_set_nat] :
% 5.06/5.32 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 5.06/5.32 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % length_pos_if_in_set
% 5.06/5.32 thf(fact_3675_length__pos__if__in__set,axiom,
% 5.06/5.32 ! [X: nat,Xs2: list_nat] :
% 5.06/5.32 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.06/5.32 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % length_pos_if_in_set
% 5.06/5.32 thf(fact_3676_length__pos__if__in__set,axiom,
% 5.06/5.32 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.06/5.32 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.06/5.32 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % length_pos_if_in_set
% 5.06/5.32 thf(fact_3677_length__pos__if__in__set,axiom,
% 5.06/5.32 ! [X: $o,Xs2: list_o] :
% 5.06/5.32 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.06/5.32 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % length_pos_if_in_set
% 5.06/5.32 thf(fact_3678_length__pos__if__in__set,axiom,
% 5.06/5.32 ! [X: int,Xs2: list_int] :
% 5.06/5.32 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.06/5.32 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % length_pos_if_in_set
% 5.06/5.32 thf(fact_3679_power__gt__expt,axiom,
% 5.06/5.32 ! [N2: nat,K: nat] :
% 5.06/5.32 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.32 => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_gt_expt
% 5.06/5.32 thf(fact_3680_nat__mult__le__cancel1,axiom,
% 5.06/5.32 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.32 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.06/5.32 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % nat_mult_le_cancel1
% 5.06/5.32 thf(fact_3681_nat__one__le__power,axiom,
% 5.06/5.32 ! [I2: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 5.06/5.32 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % nat_one_le_power
% 5.06/5.32 thf(fact_3682_div__le__mono2,axiom,
% 5.06/5.32 ! [M: nat,N2: nat,K: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.32 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.32 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_le_mono2
% 5.06/5.32 thf(fact_3683_div__greater__zero__iff,axiom,
% 5.06/5.32 ! [M: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 5.06/5.32 = ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.32 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_greater_zero_iff
% 5.06/5.32 thf(fact_3684_nat__diff__split,axiom,
% 5.06/5.32 ! [P: nat > $o,A: nat,B: nat] :
% 5.06/5.32 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.06/5.32 = ( ( ( ord_less_nat @ A @ B )
% 5.06/5.32 => ( P @ zero_zero_nat ) )
% 5.06/5.32 & ! [D2: nat] :
% 5.06/5.32 ( ( A
% 5.06/5.32 = ( plus_plus_nat @ B @ D2 ) )
% 5.06/5.32 => ( P @ D2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % nat_diff_split
% 5.06/5.32 thf(fact_3685_nat__diff__split__asm,axiom,
% 5.06/5.32 ! [P: nat > $o,A: nat,B: nat] :
% 5.06/5.32 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.06/5.32 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.06/5.32 & ~ ( P @ zero_zero_nat ) )
% 5.06/5.32 | ? [D2: nat] :
% 5.06/5.32 ( ( A
% 5.06/5.32 = ( plus_plus_nat @ B @ D2 ) )
% 5.06/5.32 & ~ ( P @ D2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % nat_diff_split_asm
% 5.06/5.32 thf(fact_3686_div__less__iff__less__mult,axiom,
% 5.06/5.32 ! [Q2: nat,M: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.06/5.32 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N2 )
% 5.06/5.32 = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_less_iff_less_mult
% 5.06/5.32 thf(fact_3687_nat__mult__div__cancel1,axiom,
% 5.06/5.32 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.32 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.06/5.32 = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % nat_mult_div_cancel1
% 5.06/5.32 thf(fact_3688_div__less__dividend,axiom,
% 5.06/5.32 ! [N2: nat,M: nat] :
% 5.06/5.32 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.32 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_less_dividend
% 5.06/5.32 thf(fact_3689_div__eq__dividend__iff,axiom,
% 5.06/5.32 ! [M: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.32 => ( ( ( divide_divide_nat @ M @ N2 )
% 5.06/5.32 = M )
% 5.06/5.32 = ( N2 = one_one_nat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % div_eq_dividend_iff
% 5.06/5.32 thf(fact_3690_divmod__digit__1_I1_J,axiom,
% 5.06/5.32 ! [A: code_integer,B: code_integer] :
% 5.06/5.32 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.06/5.32 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.06/5.32 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.06/5.32 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.06/5.32 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divmod_digit_1(1)
% 5.06/5.32 thf(fact_3691_divmod__digit__1_I1_J,axiom,
% 5.06/5.32 ! [A: nat,B: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.06/5.32 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.06/5.32 => ( ( 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 )
% 5.06/5.32 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divmod_digit_1(1)
% 5.06/5.32 thf(fact_3692_divmod__digit__1_I1_J,axiom,
% 5.06/5.32 ! [A: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.32 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.06/5.32 => ( ( 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 )
% 5.06/5.32 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divmod_digit_1(1)
% 5.06/5.32 thf(fact_3693_vebt__insert_Osimps_I3_J,axiom,
% 5.06/5.32 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.06/5.32 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X )
% 5.06/5.32 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) ).
% 5.06/5.32
% 5.06/5.32 % vebt_insert.simps(3)
% 5.06/5.32 thf(fact_3694_vebt__member_Osimps_I3_J,axiom,
% 5.06/5.32 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 5.06/5.32 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 5.06/5.32
% 5.06/5.32 % vebt_member.simps(3)
% 5.06/5.32 thf(fact_3695_vebt__mint_Ocases,axiom,
% 5.06/5.32 ! [X: vEBT_VEBT] :
% 5.06/5.32 ( ! [A3: $o,B2: $o] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.32 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.06/5.32 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % vebt_mint.cases
% 5.06/5.32 thf(fact_3696_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.06/5.32 ! [X: vEBT_VEBT,Y: $o] :
% 5.06/5.32 ( ( ( vEBT_VEBT_minNull @ X )
% 5.06/5.32 = Y )
% 5.06/5.32 => ( ( ( X
% 5.06/5.32 = ( vEBT_Leaf @ $false @ $false ) )
% 5.06/5.32 => ~ Y )
% 5.06/5.32 => ( ( ? [Uv2: $o] :
% 5.06/5.32 ( X
% 5.06/5.32 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.06/5.32 => Y )
% 5.06/5.32 => ( ( ? [Uu2: $o] :
% 5.06/5.32 ( X
% 5.06/5.32 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.06/5.32 => Y )
% 5.06/5.32 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.06/5.32 => ~ Y )
% 5.06/5.32 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.06/5.32 => Y ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % VEBT_internal.minNull.elims(1)
% 5.06/5.32 thf(fact_3697_vebt__mint_Oelims,axiom,
% 5.06/5.32 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.06/5.32 ( ( ( vEBT_vebt_mint @ X )
% 5.06/5.32 = Y )
% 5.06/5.32 => ( ! [A3: $o,B2: $o] :
% 5.06/5.32 ( ( X
% 5.06/5.32 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.32 => ~ ( ( A3
% 5.06/5.32 => ( Y
% 5.06/5.32 = ( some_nat @ zero_zero_nat ) ) )
% 5.06/5.32 & ( ~ A3
% 5.06/5.32 => ( ( B2
% 5.06/5.32 => ( Y
% 5.06/5.32 = ( some_nat @ one_one_nat ) ) )
% 5.06/5.32 & ( ~ B2
% 5.06/5.32 => ( Y = none_nat ) ) ) ) ) )
% 5.06/5.32 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.06/5.32 => ( Y != none_nat ) )
% 5.06/5.32 => ~ ! [Mi2: nat] :
% 5.06/5.32 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.06/5.32 => ( Y
% 5.06/5.32 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % vebt_mint.elims
% 5.06/5.32 thf(fact_3698_vebt__maxt_Oelims,axiom,
% 5.06/5.32 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.06/5.32 ( ( ( vEBT_vebt_maxt @ X )
% 5.06/5.32 = Y )
% 5.06/5.32 => ( ! [A3: $o,B2: $o] :
% 5.06/5.32 ( ( X
% 5.06/5.32 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.32 => ~ ( ( B2
% 5.06/5.32 => ( Y
% 5.06/5.32 = ( some_nat @ one_one_nat ) ) )
% 5.06/5.32 & ( ~ B2
% 5.06/5.32 => ( ( A3
% 5.06/5.32 => ( Y
% 5.06/5.32 = ( some_nat @ zero_zero_nat ) ) )
% 5.06/5.32 & ( ~ A3
% 5.06/5.32 => ( Y = none_nat ) ) ) ) ) )
% 5.06/5.32 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.06/5.32 => ( Y != none_nat ) )
% 5.06/5.32 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.06/5.32 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.06/5.32 ( X
% 5.06/5.32 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.06/5.32 => ( Y
% 5.06/5.32 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % vebt_maxt.elims
% 5.06/5.32 thf(fact_3699_mult__le__cancel__left1,axiom,
% 5.06/5.32 ! [C: real,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.06/5.32 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left1
% 5.06/5.32 thf(fact_3700_mult__le__cancel__left1,axiom,
% 5.06/5.32 ! [C: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.06/5.32 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left1
% 5.06/5.32 thf(fact_3701_mult__le__cancel__left1,axiom,
% 5.06/5.32 ! [C: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.06/5.32 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left1
% 5.06/5.32 thf(fact_3702_mult__le__cancel__left2,axiom,
% 5.06/5.32 ! [C: real,A: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.06/5.32 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left2
% 5.06/5.32 thf(fact_3703_mult__le__cancel__left2,axiom,
% 5.06/5.32 ! [C: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.06/5.32 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left2
% 5.06/5.32 thf(fact_3704_mult__le__cancel__left2,axiom,
% 5.06/5.32 ! [C: int,A: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.06/5.32 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.06/5.32 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_left2
% 5.06/5.32 thf(fact_3705_mult__le__cancel__right1,axiom,
% 5.06/5.32 ! [C: real,B: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.06/5.32 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_right1
% 5.06/5.32 thf(fact_3706_mult__le__cancel__right1,axiom,
% 5.06/5.32 ! [C: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.06/5.32 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_right1
% 5.06/5.32 thf(fact_3707_mult__le__cancel__right1,axiom,
% 5.06/5.32 ! [C: int,B: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.06/5.32 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_right1
% 5.06/5.32 thf(fact_3708_mult__le__cancel__right2,axiom,
% 5.06/5.32 ! [A: real,C: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.06/5.32 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_right2
% 5.06/5.32 thf(fact_3709_mult__le__cancel__right2,axiom,
% 5.06/5.32 ! [A: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.06/5.32 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_right2
% 5.06/5.32 thf(fact_3710_mult__le__cancel__right2,axiom,
% 5.06/5.32 ! [A: int,C: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.06/5.32 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.06/5.32 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_le_cancel_right2
% 5.06/5.32 thf(fact_3711_mult__less__cancel__left1,axiom,
% 5.06/5.32 ! [C: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ one_one_real @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_left1
% 5.06/5.32 thf(fact_3712_mult__less__cancel__left1,axiom,
% 5.06/5.32 ! [C: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_left1
% 5.06/5.32 thf(fact_3713_mult__less__cancel__left1,axiom,
% 5.06/5.32 ! [C: int,B: int] :
% 5.06/5.32 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.06/5.32 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ one_one_int @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_left1
% 5.06/5.32 thf(fact_3714_mult__less__cancel__left2,axiom,
% 5.06/5.32 ! [C: real,A: real] :
% 5.06/5.32 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.06/5.32 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ A @ one_one_real ) )
% 5.06/5.32 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_left2
% 5.06/5.32 thf(fact_3715_mult__less__cancel__left2,axiom,
% 5.06/5.32 ! [C: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.06/5.32 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.06/5.32 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_left2
% 5.06/5.32 thf(fact_3716_mult__less__cancel__left2,axiom,
% 5.06/5.32 ! [C: int,A: int] :
% 5.06/5.32 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.06/5.32 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ A @ one_one_int ) )
% 5.06/5.32 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_left2
% 5.06/5.32 thf(fact_3717_mult__less__cancel__right1,axiom,
% 5.06/5.32 ! [C: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ one_one_real @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_right1
% 5.06/5.32 thf(fact_3718_mult__less__cancel__right1,axiom,
% 5.06/5.32 ! [C: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_right1
% 5.06/5.32 thf(fact_3719_mult__less__cancel__right1,axiom,
% 5.06/5.32 ! [C: int,B: int] :
% 5.06/5.32 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ one_one_int @ B ) )
% 5.06/5.32 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_right1
% 5.06/5.32 thf(fact_3720_mult__less__cancel__right2,axiom,
% 5.06/5.32 ! [A: real,C: real] :
% 5.06/5.32 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.06/5.32 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ A @ one_one_real ) )
% 5.06/5.32 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_right2
% 5.06/5.32 thf(fact_3721_mult__less__cancel__right2,axiom,
% 5.06/5.32 ! [A: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.06/5.32 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.06/5.32 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_right2
% 5.06/5.32 thf(fact_3722_mult__less__cancel__right2,axiom,
% 5.06/5.32 ! [A: int,C: int] :
% 5.06/5.32 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.06/5.32 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.32 => ( ord_less_int @ A @ one_one_int ) )
% 5.06/5.32 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.06/5.32 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_less_cancel_right2
% 5.06/5.32 thf(fact_3723_field__le__mult__one__interval,axiom,
% 5.06/5.32 ! [X: real,Y: real] :
% 5.06/5.32 ( ! [Z4: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ Z4 )
% 5.06/5.32 => ( ( ord_less_real @ Z4 @ one_one_real )
% 5.06/5.32 => ( ord_less_eq_real @ ( times_times_real @ Z4 @ X ) @ Y ) ) )
% 5.06/5.32 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.06/5.32
% 5.06/5.32 % field_le_mult_one_interval
% 5.06/5.32 thf(fact_3724_field__le__mult__one__interval,axiom,
% 5.06/5.32 ! [X: rat,Y: rat] :
% 5.06/5.32 ( ! [Z4: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ Z4 )
% 5.06/5.32 => ( ( ord_less_rat @ Z4 @ one_one_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ Z4 @ X ) @ Y ) ) )
% 5.06/5.32 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.06/5.32
% 5.06/5.32 % field_le_mult_one_interval
% 5.06/5.32 thf(fact_3725_divide__left__mono__neg,axiom,
% 5.06/5.32 ! [A: real,B: real,C: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.32 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.06/5.32 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_left_mono_neg
% 5.06/5.32 thf(fact_3726_divide__left__mono__neg,axiom,
% 5.06/5.32 ! [A: rat,B: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.32 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.06/5.32 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_left_mono_neg
% 5.06/5.32 thf(fact_3727_mult__imp__le__div__pos,axiom,
% 5.06/5.32 ! [Y: real,Z: real,X: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.32 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X )
% 5.06/5.32 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_imp_le_div_pos
% 5.06/5.32 thf(fact_3728_mult__imp__le__div__pos,axiom,
% 5.06/5.32 ! [Y: rat,Z: rat,X: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.06/5.32 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 5.06/5.32 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_imp_le_div_pos
% 5.06/5.32 thf(fact_3729_mult__imp__div__pos__le,axiom,
% 5.06/5.32 ! [Y: real,X: real,Z: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.32 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y ) )
% 5.06/5.32 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_imp_div_pos_le
% 5.06/5.32 thf(fact_3730_mult__imp__div__pos__le,axiom,
% 5.06/5.32 ! [Y: rat,X: rat,Z: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.06/5.32 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 5.06/5.32 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % mult_imp_div_pos_le
% 5.06/5.32 thf(fact_3731_pos__le__divide__eq,axiom,
% 5.06/5.32 ! [C: real,A: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.06/5.32 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % pos_le_divide_eq
% 5.06/5.32 thf(fact_3732_pos__le__divide__eq,axiom,
% 5.06/5.32 ! [C: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.32 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % pos_le_divide_eq
% 5.06/5.32 thf(fact_3733_pos__divide__le__eq,axiom,
% 5.06/5.32 ! [C: real,B: real,A: real] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.06/5.32 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % pos_divide_le_eq
% 5.06/5.32 thf(fact_3734_pos__divide__le__eq,axiom,
% 5.06/5.32 ! [C: rat,B: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.06/5.32 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % pos_divide_le_eq
% 5.06/5.32 thf(fact_3735_neg__le__divide__eq,axiom,
% 5.06/5.32 ! [C: real,A: real,B: real] :
% 5.06/5.32 ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.06/5.32 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % neg_le_divide_eq
% 5.06/5.32 thf(fact_3736_neg__le__divide__eq,axiom,
% 5.06/5.32 ! [C: rat,A: rat,B: rat] :
% 5.06/5.32 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.32 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % neg_le_divide_eq
% 5.06/5.32 thf(fact_3737_neg__divide__le__eq,axiom,
% 5.06/5.32 ! [C: real,B: real,A: real] :
% 5.06/5.32 ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.06/5.32 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % neg_divide_le_eq
% 5.06/5.32 thf(fact_3738_neg__divide__le__eq,axiom,
% 5.06/5.32 ! [C: rat,B: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.06/5.32 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % neg_divide_le_eq
% 5.06/5.32 thf(fact_3739_divide__left__mono,axiom,
% 5.06/5.32 ! [B: real,A: real,C: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ B @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.06/5.32 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_left_mono
% 5.06/5.32 thf(fact_3740_divide__left__mono,axiom,
% 5.06/5.32 ! [B: rat,A: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ B @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.06/5.32 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_left_mono
% 5.06/5.32 thf(fact_3741_le__divide__eq,axiom,
% 5.06/5.32 ! [A: real,B: real,C: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % le_divide_eq
% 5.06/5.32 thf(fact_3742_le__divide__eq,axiom,
% 5.06/5.32 ! [A: rat,B: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % le_divide_eq
% 5.06/5.32 thf(fact_3743_divide__le__eq,axiom,
% 5.06/5.32 ! [B: real,C: real,A: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_le_eq
% 5.06/5.32 thf(fact_3744_divide__le__eq,axiom,
% 5.06/5.32 ! [B: rat,C: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_le_eq
% 5.06/5.32 thf(fact_3745_divide__le__eq__1,axiom,
% 5.06/5.32 ! [B: real,A: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.32 & ( ord_less_eq_real @ B @ A ) )
% 5.06/5.32 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.32 & ( ord_less_eq_real @ A @ B ) )
% 5.06/5.32 | ( A = zero_zero_real ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_le_eq_1
% 5.06/5.32 thf(fact_3746_divide__le__eq__1,axiom,
% 5.06/5.32 ! [B: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.32 & ( ord_less_eq_rat @ B @ A ) )
% 5.06/5.32 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.32 & ( ord_less_eq_rat @ A @ B ) )
% 5.06/5.32 | ( A = zero_zero_rat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_le_eq_1
% 5.06/5.32 thf(fact_3747_le__divide__eq__1,axiom,
% 5.06/5.32 ! [B: real,A: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.32 & ( ord_less_eq_real @ A @ B ) )
% 5.06/5.32 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.32 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % le_divide_eq_1
% 5.06/5.32 thf(fact_3748_le__divide__eq__1,axiom,
% 5.06/5.32 ! [B: rat,A: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.32 & ( ord_less_eq_rat @ A @ B ) )
% 5.06/5.32 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.32 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % le_divide_eq_1
% 5.06/5.32 thf(fact_3749_convex__bound__le,axiom,
% 5.06/5.32 ! [X: real,A: real,Y: real,U: real,V: real] :
% 5.06/5.32 ( ( ord_less_eq_real @ X @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ Y @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.06/5.32 => ( ( ( plus_plus_real @ U @ V )
% 5.06/5.32 = one_one_real )
% 5.06/5.32 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % convex_bound_le
% 5.06/5.32 thf(fact_3750_convex__bound__le,axiom,
% 5.06/5.32 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ X @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ Y @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.06/5.32 => ( ( ( plus_plus_rat @ U @ V )
% 5.06/5.32 = one_one_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % convex_bound_le
% 5.06/5.32 thf(fact_3751_convex__bound__le,axiom,
% 5.06/5.32 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.06/5.32 ( ( ord_less_eq_int @ X @ A )
% 5.06/5.32 => ( ( ord_less_eq_int @ Y @ A )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.06/5.32 => ( ( ( plus_plus_int @ U @ V )
% 5.06/5.32 = one_one_int )
% 5.06/5.32 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % convex_bound_le
% 5.06/5.32 thf(fact_3752_less__divide__eq__numeral_I1_J,axiom,
% 5.06/5.32 ! [W: num,B: real,C: real] :
% 5.06/5.32 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % less_divide_eq_numeral(1)
% 5.06/5.32 thf(fact_3753_less__divide__eq__numeral_I1_J,axiom,
% 5.06/5.32 ! [W: num,B: rat,C: rat] :
% 5.06/5.32 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % less_divide_eq_numeral(1)
% 5.06/5.32 thf(fact_3754_divide__less__eq__numeral_I1_J,axiom,
% 5.06/5.32 ! [B: real,C: real,W: num] :
% 5.06/5.32 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.06/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.32 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_less_eq_numeral(1)
% 5.06/5.32 thf(fact_3755_divide__less__eq__numeral_I1_J,axiom,
% 5.06/5.32 ! [B: rat,C: rat,W: num] :
% 5.06/5.32 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.06/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.06/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.32 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % divide_less_eq_numeral(1)
% 5.06/5.32 thf(fact_3756_frac__le__eq,axiom,
% 5.06/5.32 ! [Y: real,Z: real,X: real,W: real] :
% 5.06/5.32 ( ( Y != zero_zero_real )
% 5.06/5.32 => ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.06/5.32 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % frac_le_eq
% 5.06/5.32 thf(fact_3757_frac__le__eq,axiom,
% 5.06/5.32 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.06/5.32 ( ( Y != zero_zero_rat )
% 5.06/5.32 => ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.06/5.32 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % frac_le_eq
% 5.06/5.32 thf(fact_3758_frac__less__eq,axiom,
% 5.06/5.32 ! [Y: real,Z: real,X: real,W: real] :
% 5.06/5.32 ( ( Y != zero_zero_real )
% 5.06/5.32 => ( ( Z != zero_zero_real )
% 5.06/5.32 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.06/5.32 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % frac_less_eq
% 5.06/5.32 thf(fact_3759_frac__less__eq,axiom,
% 5.06/5.32 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.06/5.32 ( ( Y != zero_zero_rat )
% 5.06/5.32 => ( ( Z != zero_zero_rat )
% 5.06/5.32 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.06/5.32 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % frac_less_eq
% 5.06/5.32 thf(fact_3760_power__Suc__less,axiom,
% 5.06/5.32 ! [A: real,N2: nat] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_real @ A @ one_one_real )
% 5.06/5.32 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_less
% 5.06/5.32 thf(fact_3761_power__Suc__less,axiom,
% 5.06/5.32 ! [A: rat,N2: nat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.06/5.32 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_less
% 5.06/5.32 thf(fact_3762_power__Suc__less,axiom,
% 5.06/5.32 ! [A: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.06/5.32 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_less
% 5.06/5.32 thf(fact_3763_power__Suc__less,axiom,
% 5.06/5.32 ! [A: int,N2: nat] :
% 5.06/5.32 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_int @ A @ one_one_int )
% 5.06/5.32 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_less
% 5.06/5.32 thf(fact_3764_power__Suc__le__self,axiom,
% 5.06/5.32 ! [A: real,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.06/5.32 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_le_self
% 5.06/5.32 thf(fact_3765_power__Suc__le__self,axiom,
% 5.06/5.32 ! [A: rat,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_le_self
% 5.06/5.32 thf(fact_3766_power__Suc__le__self,axiom,
% 5.06/5.32 ! [A: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.06/5.32 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_le_self
% 5.06/5.32 thf(fact_3767_power__Suc__le__self,axiom,
% 5.06/5.32 ! [A: int,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.06/5.32 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_le_self
% 5.06/5.32 thf(fact_3768_power__Suc__less__one,axiom,
% 5.06/5.32 ! [A: real,N2: nat] :
% 5.06/5.32 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_real @ A @ one_one_real )
% 5.06/5.32 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ one_one_real ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_less_one
% 5.06/5.32 thf(fact_3769_power__Suc__less__one,axiom,
% 5.06/5.32 ! [A: rat,N2: nat] :
% 5.06/5.32 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.06/5.32 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_less_one
% 5.06/5.32 thf(fact_3770_power__Suc__less__one,axiom,
% 5.06/5.32 ! [A: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.06/5.32 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_less_one
% 5.06/5.32 thf(fact_3771_power__Suc__less__one,axiom,
% 5.06/5.32 ! [A: int,N2: nat] :
% 5.06/5.32 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_int @ A @ one_one_int )
% 5.06/5.32 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_Suc_less_one
% 5.06/5.32 thf(fact_3772_power__strict__decreasing,axiom,
% 5.06/5.32 ! [N2: nat,N4: nat,A: real] :
% 5.06/5.32 ( ( ord_less_nat @ N2 @ N4 )
% 5.06/5.32 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_real @ A @ one_one_real )
% 5.06/5.32 => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_strict_decreasing
% 5.06/5.32 thf(fact_3773_power__strict__decreasing,axiom,
% 5.06/5.32 ! [N2: nat,N4: nat,A: rat] :
% 5.06/5.32 ( ( ord_less_nat @ N2 @ N4 )
% 5.06/5.32 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.06/5.32 => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_strict_decreasing
% 5.06/5.32 thf(fact_3774_power__strict__decreasing,axiom,
% 5.06/5.32 ! [N2: nat,N4: nat,A: nat] :
% 5.06/5.32 ( ( ord_less_nat @ N2 @ N4 )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.06/5.32 => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_strict_decreasing
% 5.06/5.32 thf(fact_3775_power__strict__decreasing,axiom,
% 5.06/5.32 ! [N2: nat,N4: nat,A: int] :
% 5.06/5.32 ( ( ord_less_nat @ N2 @ N4 )
% 5.06/5.32 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_int @ A @ one_one_int )
% 5.06/5.32 => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_strict_decreasing
% 5.06/5.32 thf(fact_3776_power__decreasing,axiom,
% 5.06/5.32 ! [N2: nat,N4: nat,A: real] :
% 5.06/5.32 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.06/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.32 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.06/5.32 => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_decreasing
% 5.06/5.32 thf(fact_3777_power__decreasing,axiom,
% 5.06/5.32 ! [N2: nat,N4: nat,A: rat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.06/5.32 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.32 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.06/5.32 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_decreasing
% 5.06/5.32 thf(fact_3778_power__decreasing,axiom,
% 5.06/5.32 ! [N2: nat,N4: nat,A: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.06/5.32 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.06/5.32 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.06/5.32 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_decreasing
% 5.06/5.32 thf(fact_3779_power__decreasing,axiom,
% 5.06/5.32 ! [N2: nat,N4: nat,A: int] :
% 5.06/5.32 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.06/5.32 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.32 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.06/5.32 => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % power_decreasing
% 5.06/5.32 thf(fact_3780_zero__power2,axiom,
% 5.06/5.32 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.32 = zero_zero_rat ) ).
% 5.06/5.32
% 5.06/5.32 % zero_power2
% 5.06/5.32 thf(fact_3781_zero__power2,axiom,
% 5.06/5.32 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.32 = zero_zero_nat ) ).
% 5.06/5.32
% 5.06/5.32 % zero_power2
% 5.06/5.32 thf(fact_3782_zero__power2,axiom,
% 5.06/5.32 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.32 = zero_zero_real ) ).
% 5.06/5.32
% 5.06/5.32 % zero_power2
% 5.06/5.32 thf(fact_3783_zero__power2,axiom,
% 5.06/5.32 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.32 = zero_zero_int ) ).
% 5.06/5.32
% 5.06/5.32 % zero_power2
% 5.06/5.32 thf(fact_3784_zero__power2,axiom,
% 5.06/5.32 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.32 = zero_zero_complex ) ).
% 5.06/5.32
% 5.06/5.32 % zero_power2
% 5.06/5.32 thf(fact_3785_self__le__power,axiom,
% 5.06/5.32 ! [A: real,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.32 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % self_le_power
% 5.06/5.32 thf(fact_3786_self__le__power,axiom,
% 5.06/5.32 ! [A: rat,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.32 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % self_le_power
% 5.06/5.32 thf(fact_3787_self__le__power,axiom,
% 5.06/5.32 ! [A: nat,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.32 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % self_le_power
% 5.06/5.32 thf(fact_3788_self__le__power,axiom,
% 5.06/5.32 ! [A: int,N2: nat] :
% 5.06/5.32 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.32 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.06/5.32
% 5.06/5.32 % self_le_power
% 5.06/5.32 thf(fact_3789_one__less__power,axiom,
% 5.06/5.32 ! [A: real,N2: nat] :
% 5.06/5.32 ( ( ord_less_real @ one_one_real @ A )
% 5.06/5.32 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % one_less_power
% 5.06/5.33 thf(fact_3790_one__less__power,axiom,
% 5.06/5.33 ! [A: rat,N2: nat] :
% 5.06/5.33 ( ( ord_less_rat @ one_one_rat @ A )
% 5.06/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % one_less_power
% 5.06/5.33 thf(fact_3791_one__less__power,axiom,
% 5.06/5.33 ! [A: nat,N2: nat] :
% 5.06/5.33 ( ( ord_less_nat @ one_one_nat @ A )
% 5.06/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % one_less_power
% 5.06/5.33 thf(fact_3792_one__less__power,axiom,
% 5.06/5.33 ! [A: int,N2: nat] :
% 5.06/5.33 ( ( ord_less_int @ one_one_int @ A )
% 5.06/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % one_less_power
% 5.06/5.33 thf(fact_3793_numeral__2__eq__2,axiom,
% 5.06/5.33 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.06/5.33 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % numeral_2_eq_2
% 5.06/5.33 thf(fact_3794_pos2,axiom,
% 5.06/5.33 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.06/5.33
% 5.06/5.33 % pos2
% 5.06/5.33 thf(fact_3795_power__diff,axiom,
% 5.06/5.33 ! [A: complex,N2: nat,M: nat] :
% 5.06/5.33 ( ( A != zero_zero_complex )
% 5.06/5.33 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.33 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.33 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_diff
% 5.06/5.33 thf(fact_3796_power__diff,axiom,
% 5.06/5.33 ! [A: real,N2: nat,M: nat] :
% 5.06/5.33 ( ( A != zero_zero_real )
% 5.06/5.33 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.33 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.33 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_diff
% 5.06/5.33 thf(fact_3797_power__diff,axiom,
% 5.06/5.33 ! [A: rat,N2: nat,M: nat] :
% 5.06/5.33 ( ( A != zero_zero_rat )
% 5.06/5.33 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.33 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.33 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_diff
% 5.06/5.33 thf(fact_3798_power__diff,axiom,
% 5.06/5.33 ! [A: nat,N2: nat,M: nat] :
% 5.06/5.33 ( ( A != zero_zero_nat )
% 5.06/5.33 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.33 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.33 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_diff
% 5.06/5.33 thf(fact_3799_power__diff,axiom,
% 5.06/5.33 ! [A: int,N2: nat,M: nat] :
% 5.06/5.33 ( ( A != zero_zero_int )
% 5.06/5.33 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.33 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.33 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_diff
% 5.06/5.33 thf(fact_3800_div__if,axiom,
% 5.06/5.33 ( divide_divide_nat
% 5.06/5.33 = ( ^ [M6: nat,N: nat] :
% 5.06/5.33 ( if_nat
% 5.06/5.33 @ ( ( ord_less_nat @ M6 @ N )
% 5.06/5.33 | ( N = zero_zero_nat ) )
% 5.06/5.33 @ zero_zero_nat
% 5.06/5.33 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_if
% 5.06/5.33 thf(fact_3801_Suc__diff__eq__diff__pred,axiom,
% 5.06/5.33 ! [N2: nat,M: nat] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.06/5.33 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % Suc_diff_eq_diff_pred
% 5.06/5.33 thf(fact_3802_Suc__pred_H,axiom,
% 5.06/5.33 ! [N2: nat] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( N2
% 5.06/5.33 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % Suc_pred'
% 5.06/5.33 thf(fact_3803_less__eq__div__iff__mult__less__eq,axiom,
% 5.06/5.33 ! [Q2: nat,M: nat,N2: nat] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.06/5.33 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q2 ) )
% 5.06/5.33 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % less_eq_div_iff_mult_less_eq
% 5.06/5.33 thf(fact_3804_dividend__less__times__div,axiom,
% 5.06/5.33 ! [N2: nat,M: nat] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % dividend_less_times_div
% 5.06/5.33 thf(fact_3805_dividend__less__div__times,axiom,
% 5.06/5.33 ! [N2: nat,M: nat] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % dividend_less_div_times
% 5.06/5.33 thf(fact_3806_split__div,axiom,
% 5.06/5.33 ! [P: nat > $o,M: nat,N2: nat] :
% 5.06/5.33 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 5.06/5.33 = ( ( ( N2 = zero_zero_nat )
% 5.06/5.33 => ( P @ zero_zero_nat ) )
% 5.06/5.33 & ( ( N2 != zero_zero_nat )
% 5.06/5.33 => ! [I5: nat,J3: nat] :
% 5.06/5.33 ( ( ord_less_nat @ J3 @ N2 )
% 5.06/5.33 => ( ( M
% 5.06/5.33 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I5 ) @ J3 ) )
% 5.06/5.33 => ( P @ I5 ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % split_div
% 5.06/5.33 thf(fact_3807_add__eq__if,axiom,
% 5.06/5.33 ( plus_plus_nat
% 5.06/5.33 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % add_eq_if
% 5.06/5.33 thf(fact_3808_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.06/5.33 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.06/5.33 = Y )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.06/5.33 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.06/5.33 => Y )
% 5.06/5.33 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [S: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.naive_member.elims(1)
% 5.06/5.33 thf(fact_3809_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.06/5.33 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [S: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.06/5.33 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.naive_member.elims(2)
% 5.06/5.33 thf(fact_3810_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.06/5.33 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.06/5.33 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [S: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.06/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.naive_member.elims(3)
% 5.06/5.33 thf(fact_3811_mult__eq__if,axiom,
% 5.06/5.33 ( times_times_nat
% 5.06/5.33 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % mult_eq_if
% 5.06/5.33 thf(fact_3812_vebt__member_Osimps_I4_J,axiom,
% 5.06/5.33 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.06/5.33 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_member.simps(4)
% 5.06/5.33 thf(fact_3813_vebt__delete_Osimps_I5_J,axiom,
% 5.06/5.33 ! [Mi: nat,Ma: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT,X: nat] :
% 5.06/5.33 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ X )
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_delete.simps(5)
% 5.06/5.33 thf(fact_3814_vebt__succ_Osimps_I4_J,axiom,
% 5.06/5.33 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve2: nat] :
% 5.06/5.33 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve2 )
% 5.06/5.33 = none_nat ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_succ.simps(4)
% 5.06/5.33 thf(fact_3815_vebt__pred_Osimps_I5_J,axiom,
% 5.06/5.33 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.06/5.33 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve2 ) @ Vf2 )
% 5.06/5.33 = none_nat ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_pred.simps(5)
% 5.06/5.33 thf(fact_3816_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.06/5.33 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.06/5.33 = Y )
% 5.06/5.33 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.33 => Y )
% 5.06/5.33 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.06/5.33 => Y )
% 5.06/5.33 => ( ! [Mi2: nat,Ma2: nat] :
% 5.06/5.33 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( ~ ( ( Xa2 = Mi2 )
% 5.06/5.33 | ( Xa2 = Ma2 ) ) ) ) )
% 5.06/5.33 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [Vc2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( ~ ( ( Xa2 = Mi2 )
% 5.06/5.33 | ( Xa2 = Ma2 )
% 5.06/5.33 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 5.06/5.33 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [Vd2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.membermima.elims(1)
% 5.06/5.33 thf(fact_3817_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.06/5.33 => ( ! [Uu2: $o,Uv2: $o] :
% 5.06/5.33 ( X
% 5.06/5.33 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.33 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.06/5.33 => ( ! [Mi2: nat,Ma2: nat] :
% 5.06/5.33 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.06/5.33 => ( ( Xa2 = Mi2 )
% 5.06/5.33 | ( Xa2 = Ma2 ) ) )
% 5.06/5.33 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [Vc2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.06/5.33 => ( ( Xa2 = Mi2 )
% 5.06/5.33 | ( Xa2 = Ma2 )
% 5.06/5.33 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.06/5.33 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [Vd2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.06/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.membermima.elims(3)
% 5.06/5.33 thf(fact_3818_le__divide__eq__numeral_I1_J,axiom,
% 5.06/5.33 ! [W: num,B: real,C: real] :
% 5.06/5.33 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.06/5.33 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.33 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.06/5.33 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.33 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.33 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.06/5.33 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.33 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % le_divide_eq_numeral(1)
% 5.06/5.33 thf(fact_3819_le__divide__eq__numeral_I1_J,axiom,
% 5.06/5.33 ! [W: num,B: rat,C: rat] :
% 5.06/5.33 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.33 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.33 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.06/5.33 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.33 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.33 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.06/5.33 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.33 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % le_divide_eq_numeral(1)
% 5.06/5.33 thf(fact_3820_divide__le__eq__numeral_I1_J,axiom,
% 5.06/5.33 ! [B: real,C: real,W: num] :
% 5.06/5.33 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.06/5.33 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.33 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.06/5.33 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.33 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.33 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.06/5.33 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.33 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % divide_le_eq_numeral(1)
% 5.06/5.33 thf(fact_3821_divide__le__eq__numeral_I1_J,axiom,
% 5.06/5.33 ! [B: rat,C: rat,W: num] :
% 5.06/5.33 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.06/5.33 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.33 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.06/5.33 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.33 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.33 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.06/5.33 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.33 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % divide_le_eq_numeral(1)
% 5.06/5.33 thf(fact_3822_convex__bound__lt,axiom,
% 5.06/5.33 ! [X: real,A: real,Y: real,U: real,V: real] :
% 5.06/5.33 ( ( ord_less_real @ X @ A )
% 5.06/5.33 => ( ( ord_less_real @ Y @ A )
% 5.06/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.06/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.06/5.33 => ( ( ( plus_plus_real @ U @ V )
% 5.06/5.33 = one_one_real )
% 5.06/5.33 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % convex_bound_lt
% 5.06/5.33 thf(fact_3823_convex__bound__lt,axiom,
% 5.06/5.33 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.06/5.33 ( ( ord_less_rat @ X @ A )
% 5.06/5.33 => ( ( ord_less_rat @ Y @ A )
% 5.06/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.06/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.06/5.33 => ( ( ( plus_plus_rat @ U @ V )
% 5.06/5.33 = one_one_rat )
% 5.06/5.33 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % convex_bound_lt
% 5.06/5.33 thf(fact_3824_convex__bound__lt,axiom,
% 5.06/5.33 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.06/5.33 ( ( ord_less_int @ X @ A )
% 5.06/5.33 => ( ( ord_less_int @ Y @ A )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.06/5.33 => ( ( ( plus_plus_int @ U @ V )
% 5.06/5.33 = one_one_int )
% 5.06/5.33 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % convex_bound_lt
% 5.06/5.33 thf(fact_3825_half__gt__zero__iff,axiom,
% 5.06/5.33 ! [A: real] :
% 5.06/5.33 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.33 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.06/5.33
% 5.06/5.33 % half_gt_zero_iff
% 5.06/5.33 thf(fact_3826_half__gt__zero__iff,axiom,
% 5.06/5.33 ! [A: rat] :
% 5.06/5.33 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.06/5.33
% 5.06/5.33 % half_gt_zero_iff
% 5.06/5.33 thf(fact_3827_half__gt__zero,axiom,
% 5.06/5.33 ! [A: real] :
% 5.06/5.33 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.33 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % half_gt_zero
% 5.06/5.33 thf(fact_3828_half__gt__zero,axiom,
% 5.06/5.33 ! [A: rat] :
% 5.06/5.33 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.33 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % half_gt_zero
% 5.06/5.33 thf(fact_3829_scaling__mono,axiom,
% 5.06/5.33 ! [U: real,V: real,R2: real,S2: real] :
% 5.06/5.33 ( ( ord_less_eq_real @ U @ V )
% 5.06/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.06/5.33 => ( ( ord_less_eq_real @ R2 @ S2 )
% 5.06/5.33 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % scaling_mono
% 5.06/5.33 thf(fact_3830_scaling__mono,axiom,
% 5.06/5.33 ! [U: rat,V: rat,R2: rat,S2: rat] :
% 5.06/5.33 ( ( ord_less_eq_rat @ U @ V )
% 5.06/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.06/5.33 => ( ( ord_less_eq_rat @ R2 @ S2 )
% 5.06/5.33 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % scaling_mono
% 5.06/5.33 thf(fact_3831_power2__le__imp__le,axiom,
% 5.06/5.33 ! [X: real,Y: real] :
% 5.06/5.33 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.33 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_le_imp_le
% 5.06/5.33 thf(fact_3832_power2__le__imp__le,axiom,
% 5.06/5.33 ! [X: rat,Y: rat] :
% 5.06/5.33 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.33 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_le_imp_le
% 5.06/5.33 thf(fact_3833_power2__le__imp__le,axiom,
% 5.06/5.33 ! [X: nat,Y: nat] :
% 5.06/5.33 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.06/5.33 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_le_imp_le
% 5.06/5.33 thf(fact_3834_power2__le__imp__le,axiom,
% 5.06/5.33 ! [X: int,Y: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.33 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_le_imp_le
% 5.06/5.33 thf(fact_3835_power2__eq__imp__eq,axiom,
% 5.06/5.33 ! [X: real,Y: real] :
% 5.06/5.33 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.33 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.33 => ( X = Y ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_eq_imp_eq
% 5.06/5.33 thf(fact_3836_power2__eq__imp__eq,axiom,
% 5.06/5.33 ! [X: rat,Y: rat] :
% 5.06/5.33 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.33 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.33 => ( X = Y ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_eq_imp_eq
% 5.06/5.33 thf(fact_3837_power2__eq__imp__eq,axiom,
% 5.06/5.33 ! [X: nat,Y: nat] :
% 5.06/5.33 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.33 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.06/5.33 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.06/5.33 => ( X = Y ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_eq_imp_eq
% 5.06/5.33 thf(fact_3838_power2__eq__imp__eq,axiom,
% 5.06/5.33 ! [X: int,Y: int] :
% 5.06/5.33 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.33 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.33 => ( X = Y ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_eq_imp_eq
% 5.06/5.33 thf(fact_3839_zero__le__power2,axiom,
% 5.06/5.33 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zero_le_power2
% 5.06/5.33 thf(fact_3840_zero__le__power2,axiom,
% 5.06/5.33 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zero_le_power2
% 5.06/5.33 thf(fact_3841_zero__le__power2,axiom,
% 5.06/5.33 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zero_le_power2
% 5.06/5.33 thf(fact_3842_power2__less__0,axiom,
% 5.06/5.33 ! [A: real] :
% 5.06/5.33 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.06/5.33
% 5.06/5.33 % power2_less_0
% 5.06/5.33 thf(fact_3843_power2__less__0,axiom,
% 5.06/5.33 ! [A: rat] :
% 5.06/5.33 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.06/5.33
% 5.06/5.33 % power2_less_0
% 5.06/5.33 thf(fact_3844_power2__less__0,axiom,
% 5.06/5.33 ! [A: int] :
% 5.06/5.33 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.06/5.33
% 5.06/5.33 % power2_less_0
% 5.06/5.33 thf(fact_3845_exp__add__not__zero__imp__right,axiom,
% 5.06/5.33 ! [M: nat,N2: nat] :
% 5.06/5.33 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.33 != zero_zero_nat )
% 5.06/5.33 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.33 != zero_zero_nat ) ) ).
% 5.06/5.33
% 5.06/5.33 % exp_add_not_zero_imp_right
% 5.06/5.33 thf(fact_3846_exp__add__not__zero__imp__right,axiom,
% 5.06/5.33 ! [M: nat,N2: nat] :
% 5.06/5.33 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.33 != zero_zero_int )
% 5.06/5.33 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.33 != zero_zero_int ) ) ).
% 5.06/5.33
% 5.06/5.33 % exp_add_not_zero_imp_right
% 5.06/5.33 thf(fact_3847_exp__add__not__zero__imp__left,axiom,
% 5.06/5.33 ! [M: nat,N2: nat] :
% 5.06/5.33 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.33 != zero_zero_nat )
% 5.06/5.33 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.06/5.33 != zero_zero_nat ) ) ).
% 5.06/5.33
% 5.06/5.33 % exp_add_not_zero_imp_left
% 5.06/5.33 thf(fact_3848_exp__add__not__zero__imp__left,axiom,
% 5.06/5.33 ! [M: nat,N2: nat] :
% 5.06/5.33 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.33 != zero_zero_int )
% 5.06/5.33 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.06/5.33 != zero_zero_int ) ) ).
% 5.06/5.33
% 5.06/5.33 % exp_add_not_zero_imp_left
% 5.06/5.33 thf(fact_3849_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.06/5.33 ! [N2: nat,M: nat] :
% 5.06/5.33 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.33 != zero_zero_nat )
% 5.06/5.33 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 5.06/5.33 != zero_zero_nat ) ) ).
% 5.06/5.33
% 5.06/5.33 % exp_not_zero_imp_exp_diff_not_zero
% 5.06/5.33 thf(fact_3850_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.06/5.33 ! [N2: nat,M: nat] :
% 5.06/5.33 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.33 != zero_zero_int )
% 5.06/5.33 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 5.06/5.33 != zero_zero_int ) ) ).
% 5.06/5.33
% 5.06/5.33 % exp_not_zero_imp_exp_diff_not_zero
% 5.06/5.33 thf(fact_3851_power__diff__power__eq,axiom,
% 5.06/5.33 ! [A: nat,N2: nat,M: nat] :
% 5.06/5.33 ( ( A != zero_zero_nat )
% 5.06/5.33 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.33 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.06/5.33 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.06/5.33 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.33 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.06/5.33 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_diff_power_eq
% 5.06/5.33 thf(fact_3852_power__diff__power__eq,axiom,
% 5.06/5.33 ! [A: int,N2: nat,M: nat] :
% 5.06/5.33 ( ( A != zero_zero_int )
% 5.06/5.33 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.33 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.06/5.33 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.06/5.33 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.33 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.06/5.33 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_diff_power_eq
% 5.06/5.33 thf(fact_3853_less__2__cases__iff,axiom,
% 5.06/5.33 ! [N2: nat] :
% 5.06/5.33 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.33 = ( ( N2 = zero_zero_nat )
% 5.06/5.33 | ( N2
% 5.06/5.33 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % less_2_cases_iff
% 5.06/5.33 thf(fact_3854_less__2__cases,axiom,
% 5.06/5.33 ! [N2: nat] :
% 5.06/5.33 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.33 => ( ( N2 = zero_zero_nat )
% 5.06/5.33 | ( N2
% 5.06/5.33 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % less_2_cases
% 5.06/5.33 thf(fact_3855_nat__induct2,axiom,
% 5.06/5.33 ! [P: nat > $o,N2: nat] :
% 5.06/5.33 ( ( P @ zero_zero_nat )
% 5.06/5.33 => ( ( P @ one_one_nat )
% 5.06/5.33 => ( ! [N3: nat] :
% 5.06/5.33 ( ( P @ N3 )
% 5.06/5.33 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.33 => ( P @ N2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % nat_induct2
% 5.06/5.33 thf(fact_3856_power__eq__if,axiom,
% 5.06/5.33 ( power_power_complex
% 5.06/5.33 = ( ^ [P5: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_eq_if
% 5.06/5.33 thf(fact_3857_power__eq__if,axiom,
% 5.06/5.33 ( power_power_real
% 5.06/5.33 = ( ^ [P5: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_eq_if
% 5.06/5.33 thf(fact_3858_power__eq__if,axiom,
% 5.06/5.33 ( power_power_rat
% 5.06/5.33 = ( ^ [P5: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_eq_if
% 5.06/5.33 thf(fact_3859_power__eq__if,axiom,
% 5.06/5.33 ( power_power_nat
% 5.06/5.33 = ( ^ [P5: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_eq_if
% 5.06/5.33 thf(fact_3860_power__eq__if,axiom,
% 5.06/5.33 ( power_power_int
% 5.06/5.33 = ( ^ [P5: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_eq_if
% 5.06/5.33 thf(fact_3861_power__minus__mult,axiom,
% 5.06/5.33 ! [N2: nat,A: complex] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.06/5.33 = ( power_power_complex @ A @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_minus_mult
% 5.06/5.33 thf(fact_3862_power__minus__mult,axiom,
% 5.06/5.33 ! [N2: nat,A: real] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.06/5.33 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_minus_mult
% 5.06/5.33 thf(fact_3863_power__minus__mult,axiom,
% 5.06/5.33 ! [N2: nat,A: rat] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.06/5.33 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_minus_mult
% 5.06/5.33 thf(fact_3864_power__minus__mult,axiom,
% 5.06/5.33 ! [N2: nat,A: nat] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.06/5.33 = ( power_power_nat @ A @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_minus_mult
% 5.06/5.33 thf(fact_3865_power__minus__mult,axiom,
% 5.06/5.33 ! [N2: nat,A: int] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.06/5.33 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power_minus_mult
% 5.06/5.33 thf(fact_3866_split__div_H,axiom,
% 5.06/5.33 ! [P: nat > $o,M: nat,N2: nat] :
% 5.06/5.33 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 5.06/5.33 = ( ( ( N2 = zero_zero_nat )
% 5.06/5.33 & ( P @ zero_zero_nat ) )
% 5.06/5.33 | ? [Q4: nat] :
% 5.06/5.33 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q4 ) @ M )
% 5.06/5.33 & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q4 ) ) )
% 5.06/5.33 & ( P @ Q4 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % split_div'
% 5.06/5.33 thf(fact_3867_le__div__geq,axiom,
% 5.06/5.33 ! [N2: nat,M: nat] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.33 => ( ( divide_divide_nat @ M @ N2 )
% 5.06/5.33 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % le_div_geq
% 5.06/5.33 thf(fact_3868_div__exp__mod__exp__eq,axiom,
% 5.06/5.33 ! [A: nat,N2: nat,M: nat] :
% 5.06/5.33 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.06/5.33 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_exp_mod_exp_eq
% 5.06/5.33 thf(fact_3869_div__exp__mod__exp__eq,axiom,
% 5.06/5.33 ! [A: int,N2: nat,M: nat] :
% 5.06/5.33 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.06/5.33 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_exp_mod_exp_eq
% 5.06/5.33 thf(fact_3870_div__exp__mod__exp__eq,axiom,
% 5.06/5.33 ! [A: code_integer,N2: nat,M: nat] :
% 5.06/5.33 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.06/5.33 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_exp_mod_exp_eq
% 5.06/5.33 thf(fact_3871_vebt__delete_Osimps_I6_J,axiom,
% 5.06/5.33 ! [Mi: nat,Ma: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT,X: nat] :
% 5.06/5.33 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ X )
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_delete.simps(6)
% 5.06/5.33 thf(fact_3872_vebt__succ_Osimps_I5_J,axiom,
% 5.06/5.33 ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.06/5.33 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.06/5.33 = none_nat ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_succ.simps(5)
% 5.06/5.33 thf(fact_3873_vebt__pred_Osimps_I6_J,axiom,
% 5.06/5.33 ! [V: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.06/5.33 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 5.06/5.33 = none_nat ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_pred.simps(6)
% 5.06/5.33 thf(fact_3874_power2__less__imp__less,axiom,
% 5.06/5.33 ! [X: real,Y: real] :
% 5.06/5.33 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.33 => ( ord_less_real @ X @ Y ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_less_imp_less
% 5.06/5.33 thf(fact_3875_power2__less__imp__less,axiom,
% 5.06/5.33 ! [X: rat,Y: rat] :
% 5.06/5.33 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.33 => ( ord_less_rat @ X @ Y ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_less_imp_less
% 5.06/5.33 thf(fact_3876_power2__less__imp__less,axiom,
% 5.06/5.33 ! [X: nat,Y: nat] :
% 5.06/5.33 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.06/5.33 => ( ord_less_nat @ X @ Y ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_less_imp_less
% 5.06/5.33 thf(fact_3877_power2__less__imp__less,axiom,
% 5.06/5.33 ! [X: int,Y: int] :
% 5.06/5.33 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.33 => ( ord_less_int @ X @ Y ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % power2_less_imp_less
% 5.06/5.33 thf(fact_3878_sum__power2__le__zero__iff,axiom,
% 5.06/5.33 ! [X: real,Y: real] :
% 5.06/5.33 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.06/5.33 = ( ( X = zero_zero_real )
% 5.06/5.33 & ( Y = zero_zero_real ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % sum_power2_le_zero_iff
% 5.06/5.33 thf(fact_3879_sum__power2__le__zero__iff,axiom,
% 5.06/5.33 ! [X: rat,Y: rat] :
% 5.06/5.33 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.06/5.33 = ( ( X = zero_zero_rat )
% 5.06/5.33 & ( Y = zero_zero_rat ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % sum_power2_le_zero_iff
% 5.06/5.33 thf(fact_3880_sum__power2__le__zero__iff,axiom,
% 5.06/5.33 ! [X: int,Y: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.06/5.33 = ( ( X = zero_zero_int )
% 5.06/5.33 & ( Y = zero_zero_int ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % sum_power2_le_zero_iff
% 5.06/5.33 thf(fact_3881_sum__power2__ge__zero,axiom,
% 5.06/5.33 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % sum_power2_ge_zero
% 5.06/5.33 thf(fact_3882_sum__power2__ge__zero,axiom,
% 5.06/5.33 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % sum_power2_ge_zero
% 5.06/5.33 thf(fact_3883_sum__power2__ge__zero,axiom,
% 5.06/5.33 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % sum_power2_ge_zero
% 5.06/5.33 thf(fact_3884_sum__power2__gt__zero__iff,axiom,
% 5.06/5.33 ! [X: real,Y: real] :
% 5.06/5.33 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.33 = ( ( X != zero_zero_real )
% 5.06/5.33 | ( Y != zero_zero_real ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % sum_power2_gt_zero_iff
% 5.06/5.33 thf(fact_3885_sum__power2__gt__zero__iff,axiom,
% 5.06/5.33 ! [X: rat,Y: rat] :
% 5.06/5.33 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.33 = ( ( X != zero_zero_rat )
% 5.06/5.33 | ( Y != zero_zero_rat ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % sum_power2_gt_zero_iff
% 5.06/5.33 thf(fact_3886_sum__power2__gt__zero__iff,axiom,
% 5.06/5.33 ! [X: int,Y: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.33 = ( ( X != zero_zero_int )
% 5.06/5.33 | ( Y != zero_zero_int ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % sum_power2_gt_zero_iff
% 5.06/5.33 thf(fact_3887_not__sum__power2__lt__zero,axiom,
% 5.06/5.33 ! [X: real,Y: real] :
% 5.06/5.33 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.06/5.33
% 5.06/5.33 % not_sum_power2_lt_zero
% 5.06/5.33 thf(fact_3888_not__sum__power2__lt__zero,axiom,
% 5.06/5.33 ! [X: rat,Y: rat] :
% 5.06/5.33 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.06/5.33
% 5.06/5.33 % not_sum_power2_lt_zero
% 5.06/5.33 thf(fact_3889_not__sum__power2__lt__zero,axiom,
% 5.06/5.33 ! [X: int,Y: int] :
% 5.06/5.33 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.06/5.33
% 5.06/5.33 % not_sum_power2_lt_zero
% 5.06/5.33 thf(fact_3890_zero__le__even__power_H,axiom,
% 5.06/5.33 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zero_le_even_power'
% 5.06/5.33 thf(fact_3891_zero__le__even__power_H,axiom,
% 5.06/5.33 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zero_le_even_power'
% 5.06/5.33 thf(fact_3892_zero__le__even__power_H,axiom,
% 5.06/5.33 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zero_le_even_power'
% 5.06/5.33 thf(fact_3893_nat__bit__induct,axiom,
% 5.06/5.33 ! [P: nat > $o,N2: nat] :
% 5.06/5.33 ( ( P @ zero_zero_nat )
% 5.06/5.33 => ( ! [N3: nat] :
% 5.06/5.33 ( ( P @ N3 )
% 5.06/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.06/5.33 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.06/5.33 => ( ! [N3: nat] :
% 5.06/5.33 ( ( P @ N3 )
% 5.06/5.33 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.06/5.33 => ( P @ N2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % nat_bit_induct
% 5.06/5.33 thf(fact_3894_Suc__n__div__2__gt__zero,axiom,
% 5.06/5.33 ! [N2: nat] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % Suc_n_div_2_gt_zero
% 5.06/5.33 thf(fact_3895_div__2__gt__zero,axiom,
% 5.06/5.33 ! [N2: nat] :
% 5.06/5.33 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.33 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_2_gt_zero
% 5.06/5.33 thf(fact_3896_mult__exp__mod__exp__eq,axiom,
% 5.06/5.33 ! [M: nat,N2: nat,A: nat] :
% 5.06/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.33 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.33 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % mult_exp_mod_exp_eq
% 5.06/5.33 thf(fact_3897_mult__exp__mod__exp__eq,axiom,
% 5.06/5.33 ! [M: nat,N2: nat,A: int] :
% 5.06/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.33 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.33 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % mult_exp_mod_exp_eq
% 5.06/5.33 thf(fact_3898_mult__exp__mod__exp__eq,axiom,
% 5.06/5.33 ! [M: nat,N2: nat,A: code_integer] :
% 5.06/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.33 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.33 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % mult_exp_mod_exp_eq
% 5.06/5.33 thf(fact_3899_odd__0__le__power__imp__0__le,axiom,
% 5.06/5.33 ! [A: real,N2: nat] :
% 5.06/5.33 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.33 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.06/5.33
% 5.06/5.33 % odd_0_le_power_imp_0_le
% 5.06/5.33 thf(fact_3900_odd__0__le__power__imp__0__le,axiom,
% 5.06/5.33 ! [A: rat,N2: nat] :
% 5.06/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.33 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.06/5.33
% 5.06/5.33 % odd_0_le_power_imp_0_le
% 5.06/5.33 thf(fact_3901_odd__0__le__power__imp__0__le,axiom,
% 5.06/5.33 ! [A: int,N2: nat] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.33 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.06/5.33
% 5.06/5.33 % odd_0_le_power_imp_0_le
% 5.06/5.33 thf(fact_3902_odd__power__less__zero,axiom,
% 5.06/5.33 ! [A: real,N2: nat] :
% 5.06/5.33 ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.33 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_real ) ) ).
% 5.06/5.33
% 5.06/5.33 % odd_power_less_zero
% 5.06/5.33 thf(fact_3903_odd__power__less__zero,axiom,
% 5.06/5.33 ! [A: rat,N2: nat] :
% 5.06/5.33 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.33 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_rat ) ) ).
% 5.06/5.33
% 5.06/5.33 % odd_power_less_zero
% 5.06/5.33 thf(fact_3904_odd__power__less__zero,axiom,
% 5.06/5.33 ! [A: int,N2: nat] :
% 5.06/5.33 ( ( ord_less_int @ A @ zero_zero_int )
% 5.06/5.33 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 5.06/5.33
% 5.06/5.33 % odd_power_less_zero
% 5.06/5.33 thf(fact_3905_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.06/5.33 ! [X: nat,N2: nat,M: nat] :
% 5.06/5.33 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 5.06/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.33 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.exp_split_high_low(1)
% 5.06/5.33 thf(fact_3906_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.06/5.33 ! [X: nat,N2: nat,M: nat] :
% 5.06/5.33 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 5.06/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.33 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.exp_split_high_low(2)
% 5.06/5.33 thf(fact_3907_vebt__member_Oelims_I2_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [Summary2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ~ ( ( Xa2 != Mi2 )
% 5.06/5.33 => ( ( Xa2 != Ma2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_member.elims(2)
% 5.06/5.33 thf(fact_3908_vebt__member_Oelims_I1_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.06/5.33 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.06/5.33 = Y )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.06/5.33 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.06/5.33 => Y )
% 5.06/5.33 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.06/5.33 => Y )
% 5.06/5.33 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.06/5.33 => Y )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [Summary2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( ~ ( ( Xa2 != Mi2 )
% 5.06/5.33 => ( ( Xa2 != Ma2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_member.elims(1)
% 5.06/5.33 thf(fact_3909_vebt__member_Oelims_I3_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.06/5.33 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.06/5.33 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.06/5.33 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [Summary2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( Xa2 != Mi2 )
% 5.06/5.33 => ( ( Xa2 != Ma2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_member.elims(3)
% 5.06/5.33 thf(fact_3910_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.06/5.33 => ( ! [Mi2: nat,Ma2: nat] :
% 5.06/5.33 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.06/5.33 => ~ ( ( Xa2 = Mi2 )
% 5.06/5.33 | ( Xa2 = Ma2 ) ) )
% 5.06/5.33 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [Vc2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.06/5.33 => ~ ( ( Xa2 = Mi2 )
% 5.06/5.33 | ( Xa2 = Ma2 )
% 5.06/5.33 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.06/5.33 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.06/5.33 ( ? [Vd2: vEBT_VEBT] :
% 5.06/5.33 ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.06/5.33 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.membermima.elims(2)
% 5.06/5.33 thf(fact_3911_arith__geo__mean,axiom,
% 5.06/5.33 ! [U: real,X: real,Y: real] :
% 5.06/5.33 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.33 = ( times_times_real @ X @ Y ) )
% 5.06/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.33 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % arith_geo_mean
% 5.06/5.33 thf(fact_3912_arith__geo__mean,axiom,
% 5.06/5.33 ! [U: rat,X: rat,Y: rat] :
% 5.06/5.33 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.33 = ( times_times_rat @ X @ Y ) )
% 5.06/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.33 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.33 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % arith_geo_mean
% 5.06/5.33 thf(fact_3913_invar__vebt_Osimps,axiom,
% 5.06/5.33 ( vEBT_invar_vebt
% 5.06/5.33 = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 5.06/5.33 ( ( ? [A4: $o,B4: $o] :
% 5.06/5.33 ( A1
% 5.06/5.33 = ( vEBT_Leaf @ A4 @ B4 ) )
% 5.06/5.33 & ( A22
% 5.06/5.33 = ( suc @ zero_zero_nat ) ) )
% 5.06/5.33 | ? [TreeList2: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT] :
% 5.06/5.33 ( ( A1
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList2 @ Summary3 ) )
% 5.06/5.33 & ! [X2: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.06/5.33 => ( vEBT_invar_vebt @ X2 @ N ) )
% 5.06/5.33 & ( vEBT_invar_vebt @ Summary3 @ N )
% 5.06/5.33 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.06/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.06/5.33 & ( A22
% 5.06/5.33 = ( plus_plus_nat @ N @ N ) )
% 5.06/5.33 & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 5.06/5.33 & ! [X2: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.06/5.33 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.33 | ? [TreeList2: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT] :
% 5.06/5.33 ( ( A1
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList2 @ Summary3 ) )
% 5.06/5.33 & ! [X2: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.06/5.33 => ( vEBT_invar_vebt @ X2 @ N ) )
% 5.06/5.33 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N ) )
% 5.06/5.33 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.06/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.06/5.33 & ( A22
% 5.06/5.33 = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 5.06/5.33 & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 5.06/5.33 & ! [X2: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.06/5.33 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.33 | ? [TreeList2: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.06/5.33 ( ( A1
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList2 @ Summary3 ) )
% 5.06/5.33 & ! [X2: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.06/5.33 => ( vEBT_invar_vebt @ X2 @ N ) )
% 5.06/5.33 & ( vEBT_invar_vebt @ Summary3 @ N )
% 5.06/5.33 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.06/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.06/5.33 & ( A22
% 5.06/5.33 = ( plus_plus_nat @ N @ N ) )
% 5.06/5.33 & ! [I5: nat] :
% 5.06/5.33 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.06/5.33 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X4 ) )
% 5.06/5.33 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 5.06/5.33 & ( ( Mi3 = Ma3 )
% 5.06/5.33 => ! [X2: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.06/5.33 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.33 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.06/5.33 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.06/5.33 & ( ( Mi3 != Ma3 )
% 5.06/5.33 => ! [I5: nat] :
% 5.06/5.33 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.06/5.33 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N )
% 5.06/5.33 = I5 )
% 5.06/5.33 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N ) ) )
% 5.06/5.33 & ! [X2: nat] :
% 5.06/5.33 ( ( ( ( vEBT_VEBT_high @ X2 @ N )
% 5.06/5.33 = I5 )
% 5.06/5.33 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ ( vEBT_VEBT_low @ X2 @ N ) ) )
% 5.06/5.33 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.06/5.33 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 5.06/5.33 | ? [TreeList2: list_VEBT_VEBT,N: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.06/5.33 ( ( A1
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList2 @ Summary3 ) )
% 5.06/5.33 & ! [X2: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.06/5.33 => ( vEBT_invar_vebt @ X2 @ N ) )
% 5.06/5.33 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N ) )
% 5.06/5.33 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.06/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.06/5.33 & ( A22
% 5.06/5.33 = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 5.06/5.33 & ! [I5: nat] :
% 5.06/5.33 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.06/5.33 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X4 ) )
% 5.06/5.33 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 5.06/5.33 & ( ( Mi3 = Ma3 )
% 5.06/5.33 => ! [X2: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.06/5.33 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.33 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.06/5.33 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.06/5.33 & ( ( Mi3 != Ma3 )
% 5.06/5.33 => ! [I5: nat] :
% 5.06/5.33 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.06/5.33 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N )
% 5.06/5.33 = I5 )
% 5.06/5.33 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N ) ) )
% 5.06/5.33 & ! [X2: nat] :
% 5.06/5.33 ( ( ( ( vEBT_VEBT_high @ X2 @ N )
% 5.06/5.33 = I5 )
% 5.06/5.33 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ ( vEBT_VEBT_low @ X2 @ N ) ) )
% 5.06/5.33 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.06/5.33 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % invar_vebt.simps
% 5.06/5.33 thf(fact_3914_invar__vebt_Ocases,axiom,
% 5.06/5.33 ! [A12: vEBT_VEBT,A23: nat] :
% 5.06/5.33 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 5.06/5.33 => ( ( ? [A3: $o,B2: $o] :
% 5.06/5.33 ( A12
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( A23
% 5.06/5.33 != ( suc @ zero_zero_nat ) ) )
% 5.06/5.33 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M2: nat,Deg2: nat] :
% 5.06/5.33 ( ( A12
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( A23 = Deg2 )
% 5.06/5.33 => ( ! [X5: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.06/5.33 => ( ( vEBT_invar_vebt @ Summary2 @ M2 )
% 5.06/5.33 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.06/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.06/5.33 => ( ( M2 = N3 )
% 5.06/5.33 => ( ( Deg2
% 5.06/5.33 = ( plus_plus_nat @ N3 @ M2 ) )
% 5.06/5.33 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.06/5.33 => ~ ! [X5: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.33 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.06/5.33 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M2: nat,Deg2: nat] :
% 5.06/5.33 ( ( A12
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( A23 = Deg2 )
% 5.06/5.33 => ( ! [X5: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.06/5.33 => ( ( vEBT_invar_vebt @ Summary2 @ M2 )
% 5.06/5.33 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.06/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.06/5.33 => ( ( M2
% 5.06/5.33 = ( suc @ N3 ) )
% 5.06/5.33 => ( ( Deg2
% 5.06/5.33 = ( plus_plus_nat @ N3 @ M2 ) )
% 5.06/5.33 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.06/5.33 => ~ ! [X5: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.33 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.06/5.33 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M2: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.06/5.33 ( ( A12
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( A23 = Deg2 )
% 5.06/5.33 => ( ! [X5: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.06/5.33 => ( ( vEBT_invar_vebt @ Summary2 @ M2 )
% 5.06/5.33 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.06/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.06/5.33 => ( ( M2 = N3 )
% 5.06/5.33 => ( ( Deg2
% 5.06/5.33 = ( plus_plus_nat @ N3 @ M2 ) )
% 5.06/5.33 => ( ! [I: nat] :
% 5.06/5.33 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.06/5.33 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X4 ) )
% 5.06/5.33 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.06/5.33 => ( ( ( Mi2 = Ma2 )
% 5.06/5.33 => ! [X5: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.33 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.06/5.33 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.06/5.33 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.33 => ~ ( ( Mi2 != Ma2 )
% 5.06/5.33 => ! [I: nat] :
% 5.06/5.33 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.06/5.33 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.06/5.33 = I )
% 5.06/5.33 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.06/5.33 & ! [X5: nat] :
% 5.06/5.33 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 5.06/5.33 = I )
% 5.06/5.33 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 5.06/5.33 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.06/5.33 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.06/5.33 => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M2: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.06/5.33 ( ( A12
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( A23 = Deg2 )
% 5.06/5.33 => ( ! [X5: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 5.06/5.33 => ( ( vEBT_invar_vebt @ Summary2 @ M2 )
% 5.06/5.33 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.06/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.06/5.33 => ( ( M2
% 5.06/5.33 = ( suc @ N3 ) )
% 5.06/5.33 => ( ( Deg2
% 5.06/5.33 = ( plus_plus_nat @ N3 @ M2 ) )
% 5.06/5.33 => ( ! [I: nat] :
% 5.06/5.33 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.06/5.33 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X4 ) )
% 5.06/5.33 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 5.06/5.33 => ( ( ( Mi2 = Ma2 )
% 5.06/5.33 => ! [X5: vEBT_VEBT] :
% 5.06/5.33 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.33 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.06/5.33 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.06/5.33 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.33 => ~ ( ( Mi2 != Ma2 )
% 5.06/5.33 => ! [I: nat] :
% 5.06/5.33 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.06/5.33 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.06/5.33 = I )
% 5.06/5.33 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.06/5.33 & ! [X5: nat] :
% 5.06/5.33 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 5.06/5.33 = I )
% 5.06/5.33 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 5.06/5.33 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.06/5.33 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % invar_vebt.cases
% 5.06/5.33 thf(fact_3915_vebt__insert_Oelims,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.06/5.33 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.06/5.33 = Y )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.06/5.33 & ( ( Xa2 != one_one_nat )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ) ) )
% 5.06/5.33 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) ) )
% 5.06/5.33 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) )
% 5.06/5.33 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 != ( if_VEBT_VEBT
% 5.06/5.33 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 & ~ ( ( Xa2 = Mi2 )
% 5.06/5.33 | ( Xa2 = Ma2 ) ) )
% 5.06/5.33 @ ( 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 @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.06/5.33 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_insert.elims
% 5.06/5.33 thf(fact_3916_verit__le__mono__div,axiom,
% 5.06/5.33 ! [A2: nat,B3: nat,N2: nat] :
% 5.06/5.33 ( ( ord_less_nat @ A2 @ B3 )
% 5.06/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ord_less_eq_nat
% 5.06/5.33 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 5.06/5.33 @ ( if_nat
% 5.06/5.33 @ ( ( modulo_modulo_nat @ B3 @ N2 )
% 5.06/5.33 = zero_zero_nat )
% 5.06/5.33 @ one_one_nat
% 5.06/5.33 @ zero_zero_nat ) )
% 5.06/5.33 @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_le_mono_div
% 5.06/5.33 thf(fact_3917_inrange,axiom,
% 5.06/5.33 ! [T: vEBT_VEBT,N2: nat] :
% 5.06/5.33 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.06/5.33 => ( 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 ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % inrange
% 5.06/5.33 thf(fact_3918_set__bit__0,axiom,
% 5.06/5.33 ! [A: int] :
% 5.06/5.33 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.06/5.33 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % set_bit_0
% 5.06/5.33 thf(fact_3919_set__bit__0,axiom,
% 5.06/5.33 ! [A: nat] :
% 5.06/5.33 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.06/5.33 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % set_bit_0
% 5.06/5.33 thf(fact_3920_vebt__succ_Opelims,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.06/5.33 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 5.06/5.33 = Y )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [Uu2: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 5.06/5.33 => ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => ( ( ( B2
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( some_nat @ one_one_nat ) ) )
% 5.06/5.33 & ( ~ B2
% 5.06/5.33 => ( Y = none_nat ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 5.06/5.33 => ( ! [Uv2: $o,Uw2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.06/5.33 => ! [N3: nat] :
% 5.06/5.33 ( ( Xa2
% 5.06/5.33 = ( suc @ N3 ) )
% 5.06/5.33 => ( ( Y = none_nat )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 5.06/5.33 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.06/5.33 => ( ( Y = none_nat )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.06/5.33 => ( ( Y = none_nat )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.06/5.33 => ( ( Y = none_nat )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( some_nat @ Mi2 ) ) )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 @ ( if_option_nat
% 5.06/5.33 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 != none_nat )
% 5.06/5.33 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.06/5.33 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 @ ( if_option_nat
% 5.06/5.33 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.33 = none_nat )
% 5.06/5.33 @ none_nat
% 5.06/5.33 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.06/5.33 @ none_nat ) ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_succ.pelims
% 5.06/5.33 thf(fact_3921_vebt__pred_Opelims,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.06/5.33 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.06/5.33 = Y )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [Uu2: $o,Uv2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.33 => ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => ( ( Y = none_nat )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.06/5.33 => ( ! [A3: $o,Uw2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ Uw2 ) )
% 5.06/5.33 => ( ( Xa2
% 5.06/5.33 = ( suc @ zero_zero_nat ) )
% 5.06/5.33 => ( ( ( A3
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( some_nat @ zero_zero_nat ) ) )
% 5.06/5.33 & ( ~ A3
% 5.06/5.33 => ( Y = none_nat ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ! [Va2: nat] :
% 5.06/5.33 ( ( Xa2
% 5.06/5.33 = ( suc @ ( suc @ Va2 ) ) )
% 5.06/5.33 => ( ( ( B2
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( some_nat @ one_one_nat ) ) )
% 5.06/5.33 & ( ~ B2
% 5.06/5.33 => ( ( A3
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( some_nat @ zero_zero_nat ) ) )
% 5.06/5.33 & ( ~ A3
% 5.06/5.33 => ( Y = none_nat ) ) ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 5.06/5.33 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 5.06/5.33 => ( ( Y = none_nat )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.06/5.33 => ( ( Y = none_nat )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.06/5.33 => ( ( Y = none_nat )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( some_nat @ Ma2 ) ) )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 @ ( if_option_nat
% 5.06/5.33 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 != none_nat )
% 5.06/5.33 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.06/5.33 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 @ ( if_option_nat
% 5.06/5.33 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.33 = none_nat )
% 5.06/5.33 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.06/5.33 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.06/5.33 @ none_nat ) ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_pred.pelims
% 5.06/5.33 thf(fact_3922_double__eq__0__iff,axiom,
% 5.06/5.33 ! [A: real] :
% 5.06/5.33 ( ( ( plus_plus_real @ A @ A )
% 5.06/5.33 = zero_zero_real )
% 5.06/5.33 = ( A = zero_zero_real ) ) ).
% 5.06/5.33
% 5.06/5.33 % double_eq_0_iff
% 5.06/5.33 thf(fact_3923_double__eq__0__iff,axiom,
% 5.06/5.33 ! [A: rat] :
% 5.06/5.33 ( ( ( plus_plus_rat @ A @ A )
% 5.06/5.33 = zero_zero_rat )
% 5.06/5.33 = ( A = zero_zero_rat ) ) ).
% 5.06/5.33
% 5.06/5.33 % double_eq_0_iff
% 5.06/5.33 thf(fact_3924_double__eq__0__iff,axiom,
% 5.06/5.33 ! [A: int] :
% 5.06/5.33 ( ( ( plus_plus_int @ A @ A )
% 5.06/5.33 = zero_zero_int )
% 5.06/5.33 = ( A = zero_zero_int ) ) ).
% 5.06/5.33
% 5.06/5.33 % double_eq_0_iff
% 5.06/5.33 thf(fact_3925_vebt__delete_Opelims,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.06/5.33 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 5.06/5.33 = Y )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( vEBT_Leaf @ $false @ B2 ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( Xa2
% 5.06/5.33 = ( suc @ zero_zero_nat ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ $false ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ! [N3: nat] :
% 5.06/5.33 ( ( Xa2
% 5.06/5.33 = ( suc @ ( suc @ N3 ) ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 5.06/5.33 => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ Xa2 ) ) ) )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.06/5.33 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.06/5.33 => ( ( ( ( Xa2 = Mi2 )
% 5.06/5.33 & ( Xa2 = Ma2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.06/5.33 & ( ~ ( ( Xa2 = Mi2 )
% 5.06/5.33 & ( Xa2 = Ma2 ) )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 @ ( vEBT_Node
% 5.06/5.33 @ ( some_P7363390416028606310at_nat
% 5.06/5.33 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.06/5.33 @ ( if_nat
% 5.06/5.33 @ ( ( ( Xa2 = Mi2 )
% 5.06/5.33 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.06/5.33 = Ma2 ) )
% 5.06/5.33 & ( ( Xa2 != Mi2 )
% 5.06/5.33 => ( Xa2 = Ma2 ) ) )
% 5.06/5.33 @ ( if_nat
% 5.06/5.33 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 = none_nat )
% 5.06/5.33 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.06/5.33 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.06/5.33 @ Ma2 ) ) )
% 5.06/5.33 @ ( suc @ ( suc @ Va2 ) )
% 5.06/5.33 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 @ ( vEBT_Node
% 5.06/5.33 @ ( some_P7363390416028606310at_nat
% 5.06/5.33 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.06/5.33 @ ( if_nat
% 5.06/5.33 @ ( ( ( Xa2 = Mi2 )
% 5.06/5.33 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.06/5.33 = Ma2 ) )
% 5.06/5.33 & ( ( Xa2 != Mi2 )
% 5.06/5.33 => ( Xa2 = Ma2 ) ) )
% 5.06/5.33 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.06/5.33 @ Ma2 ) ) )
% 5.06/5.33 @ ( suc @ ( suc @ Va2 ) )
% 5.06/5.33 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 @ Summary2 ) )
% 5.06/5.33 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_delete.pelims
% 5.06/5.33 thf(fact_3926_unset__bit__0,axiom,
% 5.06/5.33 ! [A: int] :
% 5.06/5.33 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.06/5.33 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % unset_bit_0
% 5.06/5.33 thf(fact_3927_unset__bit__0,axiom,
% 5.06/5.33 ! [A: nat] :
% 5.06/5.33 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.06/5.33 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % unset_bit_0
% 5.06/5.33 thf(fact_3928_div__mod__decomp,axiom,
% 5.06/5.33 ! [A2: nat,N2: nat] :
% 5.06/5.33 ( A2
% 5.06/5.33 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_mod_decomp
% 5.06/5.33 thf(fact_3929_verit__eq__simplify_I8_J,axiom,
% 5.06/5.33 ! [X22: num,Y22: num] :
% 5.06/5.33 ( ( ( bit0 @ X22 )
% 5.06/5.33 = ( bit0 @ Y22 ) )
% 5.06/5.33 = ( X22 = Y22 ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_eq_simplify(8)
% 5.06/5.33 thf(fact_3930_div__pos__pos__trivial,axiom,
% 5.06/5.33 ! [K: int,L2: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.33 => ( ( ord_less_int @ K @ L2 )
% 5.06/5.33 => ( ( divide_divide_int @ K @ L2 )
% 5.06/5.33 = zero_zero_int ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_pos_pos_trivial
% 5.06/5.33 thf(fact_3931_div__neg__neg__trivial,axiom,
% 5.06/5.33 ! [K: int,L2: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.06/5.33 => ( ( ord_less_int @ L2 @ K )
% 5.06/5.33 => ( ( divide_divide_int @ K @ L2 )
% 5.06/5.33 = zero_zero_int ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_neg_neg_trivial
% 5.06/5.33 thf(fact_3932_idiff__0__right,axiom,
% 5.06/5.33 ! [N2: extended_enat] :
% 5.06/5.33 ( ( minus_3235023915231533773d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 5.06/5.33 = N2 ) ).
% 5.06/5.33
% 5.06/5.33 % idiff_0_right
% 5.06/5.33 thf(fact_3933_idiff__0,axiom,
% 5.06/5.33 ! [N2: extended_enat] :
% 5.06/5.33 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.06/5.33 = zero_z5237406670263579293d_enat ) ).
% 5.06/5.33
% 5.06/5.33 % idiff_0
% 5.06/5.33 thf(fact_3934_not__real__square__gt__zero,axiom,
% 5.06/5.33 ! [X: real] :
% 5.06/5.33 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 5.06/5.33 = ( X = zero_zero_real ) ) ).
% 5.06/5.33
% 5.06/5.33 % not_real_square_gt_zero
% 5.06/5.33 thf(fact_3935_zmod__numeral__Bit0,axiom,
% 5.06/5.33 ! [V: num,W: num] :
% 5.06/5.33 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.06/5.33 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zmod_numeral_Bit0
% 5.06/5.33 thf(fact_3936_half__negative__int__iff,axiom,
% 5.06/5.33 ! [K: int] :
% 5.06/5.33 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.06/5.33 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.06/5.33
% 5.06/5.33 % half_negative_int_iff
% 5.06/5.33 thf(fact_3937_half__nonnegative__int__iff,axiom,
% 5.06/5.33 ! [K: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.06/5.33 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.06/5.33
% 5.06/5.33 % half_nonnegative_int_iff
% 5.06/5.33 thf(fact_3938_div__pos__geq,axiom,
% 5.06/5.33 ! [L2: int,K: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.06/5.33 => ( ( ord_less_eq_int @ L2 @ K )
% 5.06/5.33 => ( ( divide_divide_int @ K @ L2 )
% 5.06/5.33 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_pos_geq
% 5.06/5.33 thf(fact_3939_verit__le__mono__div__int,axiom,
% 5.06/5.33 ! [A2: int,B3: int,N2: int] :
% 5.06/5.33 ( ( ord_less_int @ A2 @ B3 )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.06/5.33 => ( ord_less_eq_int
% 5.06/5.33 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N2 )
% 5.06/5.33 @ ( if_int
% 5.06/5.33 @ ( ( modulo_modulo_int @ B3 @ N2 )
% 5.06/5.33 = zero_zero_int )
% 5.06/5.33 @ one_one_int
% 5.06/5.33 @ zero_zero_int ) )
% 5.06/5.33 @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_le_mono_div_int
% 5.06/5.33 thf(fact_3940_zmod__zmult2__eq,axiom,
% 5.06/5.33 ! [C: int,A: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.33 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zmod_zmult2_eq
% 5.06/5.33 thf(fact_3941_zdiv__zmult2__eq,axiom,
% 5.06/5.33 ! [C: int,A: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.06/5.33 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.06/5.33 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zdiv_zmult2_eq
% 5.06/5.33 thf(fact_3942_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.06/5.33 ! [A: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.06/5.33 = ( ( ord_less_eq_int @ B @ A )
% 5.06/5.33 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % nonneg1_imp_zdiv_pos_iff
% 5.06/5.33 thf(fact_3943_pos__imp__zdiv__nonneg__iff,axiom,
% 5.06/5.33 ! [B: int,A: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.06/5.33 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % pos_imp_zdiv_nonneg_iff
% 5.06/5.33 thf(fact_3944_neg__imp__zdiv__nonneg__iff,axiom,
% 5.06/5.33 ! [B: int,A: int] :
% 5.06/5.33 ( ( ord_less_int @ B @ zero_zero_int )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.06/5.33 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % neg_imp_zdiv_nonneg_iff
% 5.06/5.33 thf(fact_3945_pos__imp__zdiv__pos__iff,axiom,
% 5.06/5.33 ! [K: int,I2: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 5.06/5.33 = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % pos_imp_zdiv_pos_iff
% 5.06/5.33 thf(fact_3946_div__nonpos__pos__le0,axiom,
% 5.06/5.33 ! [A: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.33 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_nonpos_pos_le0
% 5.06/5.33 thf(fact_3947_div__nonneg__neg__le0,axiom,
% 5.06/5.33 ! [A: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.33 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.06/5.33 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_nonneg_neg_le0
% 5.06/5.33 thf(fact_3948_div__positive__int,axiom,
% 5.06/5.33 ! [L2: int,K: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ L2 @ K )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.06/5.33 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_positive_int
% 5.06/5.33 thf(fact_3949_split__pos__lemma,axiom,
% 5.06/5.33 ! [K: int,P: int > int > $o,N2: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.33 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 5.06/5.33 = ( ! [I5: int,J3: int] :
% 5.06/5.33 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.06/5.33 & ( ord_less_int @ J3 @ K )
% 5.06/5.33 & ( N2
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.06/5.33 => ( P @ I5 @ J3 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % split_pos_lemma
% 5.06/5.33 thf(fact_3950_split__neg__lemma,axiom,
% 5.06/5.33 ! [K: int,P: int > int > $o,N2: int] :
% 5.06/5.33 ( ( ord_less_int @ K @ zero_zero_int )
% 5.06/5.33 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 5.06/5.33 = ( ! [I5: int,J3: int] :
% 5.06/5.33 ( ( ( ord_less_int @ K @ J3 )
% 5.06/5.33 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.06/5.33 & ( N2
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.06/5.33 => ( P @ I5 @ J3 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % split_neg_lemma
% 5.06/5.33 thf(fact_3951_div__int__pos__iff,axiom,
% 5.06/5.33 ! [K: int,L2: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 5.06/5.33 = ( ( K = zero_zero_int )
% 5.06/5.33 | ( L2 = zero_zero_int )
% 5.06/5.33 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.33 & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 5.06/5.33 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.06/5.33 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_int_pos_iff
% 5.06/5.33 thf(fact_3952_zdiv__mono2__neg,axiom,
% 5.06/5.33 ! [A: int,B6: int,B: int] :
% 5.06/5.33 ( ( ord_less_int @ A @ zero_zero_int )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 5.06/5.33 => ( ( ord_less_eq_int @ B6 @ B )
% 5.06/5.33 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B6 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zdiv_mono2_neg
% 5.06/5.33 thf(fact_3953_zdiv__mono1__neg,axiom,
% 5.06/5.33 ! [A: int,A6: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ A @ A6 )
% 5.06/5.33 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.06/5.33 => ( ord_less_eq_int @ ( divide_divide_int @ A6 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zdiv_mono1_neg
% 5.06/5.33 thf(fact_3954_int__div__pos__eq,axiom,
% 5.06/5.33 ! [A: int,B: int,Q2: int,R2: int] :
% 5.06/5.33 ( ( A
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.06/5.33 => ( ( ord_less_int @ R2 @ B )
% 5.06/5.33 => ( ( divide_divide_int @ A @ B )
% 5.06/5.33 = Q2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % int_div_pos_eq
% 5.06/5.33 thf(fact_3955_int__div__neg__eq,axiom,
% 5.06/5.33 ! [A: int,B: int,Q2: int,R2: int] :
% 5.06/5.33 ( ( A
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.06/5.33 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.06/5.33 => ( ( ord_less_int @ B @ R2 )
% 5.06/5.33 => ( ( divide_divide_int @ A @ B )
% 5.06/5.33 = Q2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % int_div_neg_eq
% 5.06/5.33 thf(fact_3956_zdiv__eq__0__iff,axiom,
% 5.06/5.33 ! [I2: int,K: int] :
% 5.06/5.33 ( ( ( divide_divide_int @ I2 @ K )
% 5.06/5.33 = zero_zero_int )
% 5.06/5.33 = ( ( K = zero_zero_int )
% 5.06/5.33 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.06/5.33 & ( ord_less_int @ I2 @ K ) )
% 5.06/5.33 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.06/5.33 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zdiv_eq_0_iff
% 5.06/5.33 thf(fact_3957_zdiv__mono2,axiom,
% 5.06/5.33 ! [A: int,B6: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 5.06/5.33 => ( ( ord_less_eq_int @ B6 @ B )
% 5.06/5.33 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B6 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zdiv_mono2
% 5.06/5.33 thf(fact_3958_zdiv__mono1,axiom,
% 5.06/5.33 ! [A: int,A6: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ A @ A6 )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.33 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A6 @ B ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zdiv_mono1
% 5.06/5.33 thf(fact_3959_split__zdiv,axiom,
% 5.06/5.33 ! [P: int > $o,N2: int,K: int] :
% 5.06/5.33 ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 5.06/5.33 = ( ( ( K = zero_zero_int )
% 5.06/5.33 => ( P @ zero_zero_int ) )
% 5.06/5.33 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.33 => ! [I5: int,J3: int] :
% 5.06/5.33 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.06/5.33 & ( ord_less_int @ J3 @ K )
% 5.06/5.33 & ( N2
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.06/5.33 => ( P @ I5 ) ) )
% 5.06/5.33 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.06/5.33 => ! [I5: int,J3: int] :
% 5.06/5.33 ( ( ( ord_less_int @ K @ J3 )
% 5.06/5.33 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.06/5.33 & ( N2
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.06/5.33 => ( P @ I5 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % split_zdiv
% 5.06/5.33 thf(fact_3960_div__mod__decomp__int,axiom,
% 5.06/5.33 ! [A2: int,N2: int] :
% 5.06/5.33 ( A2
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A2 @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_mod_decomp_int
% 5.06/5.33 thf(fact_3961_pos__zmod__mult__2,axiom,
% 5.06/5.33 ! [A: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.33 => ( ( 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 ) )
% 5.06/5.33 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % pos_zmod_mult_2
% 5.06/5.33 thf(fact_3962_neg__zmod__mult__2,axiom,
% 5.06/5.33 ! [A: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.33 => ( ( 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 ) )
% 5.06/5.33 = ( 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 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % neg_zmod_mult_2
% 5.06/5.33 thf(fact_3963_enat__0__less__mult__iff,axiom,
% 5.06/5.33 ! [M: extended_enat,N2: extended_enat] :
% 5.06/5.33 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N2 ) )
% 5.06/5.33 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.06/5.33 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % enat_0_less_mult_iff
% 5.06/5.33 thf(fact_3964_iadd__is__0,axiom,
% 5.06/5.33 ! [M: extended_enat,N2: extended_enat] :
% 5.06/5.33 ( ( ( plus_p3455044024723400733d_enat @ M @ N2 )
% 5.06/5.33 = zero_z5237406670263579293d_enat )
% 5.06/5.33 = ( ( M = zero_z5237406670263579293d_enat )
% 5.06/5.33 & ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % iadd_is_0
% 5.06/5.33 thf(fact_3965_ile0__eq,axiom,
% 5.06/5.33 ! [N2: extended_enat] :
% 5.06/5.33 ( ( ord_le2932123472753598470d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 5.06/5.33 = ( N2 = zero_z5237406670263579293d_enat ) ) ).
% 5.06/5.33
% 5.06/5.33 % ile0_eq
% 5.06/5.33 thf(fact_3966_i0__lb,axiom,
% 5.06/5.33 ! [N2: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N2 ) ).
% 5.06/5.33
% 5.06/5.33 % i0_lb
% 5.06/5.33 thf(fact_3967_ex__nat__less,axiom,
% 5.06/5.33 ! [N2: nat,P: nat > $o] :
% 5.06/5.33 ( ( ? [M6: nat] :
% 5.06/5.33 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.06/5.33 & ( P @ M6 ) ) )
% 5.06/5.33 = ( ? [X2: nat] :
% 5.06/5.33 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.33 & ( P @ X2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % ex_nat_less
% 5.06/5.33 thf(fact_3968_all__nat__less,axiom,
% 5.06/5.33 ! [N2: nat,P: nat > $o] :
% 5.06/5.33 ( ( ! [M6: nat] :
% 5.06/5.33 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.06/5.33 => ( P @ M6 ) ) )
% 5.06/5.33 = ( ! [X2: nat] :
% 5.06/5.33 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.33 => ( P @ X2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % all_nat_less
% 5.06/5.33 thf(fact_3969_not__exp__less__eq__0__int,axiom,
% 5.06/5.33 ! [N2: nat] :
% 5.06/5.33 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_int ) ).
% 5.06/5.33
% 5.06/5.33 % not_exp_less_eq_0_int
% 5.06/5.33 thf(fact_3970_neg__zdiv__mult__2,axiom,
% 5.06/5.33 ! [A: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.33 => ( ( 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 ) )
% 5.06/5.33 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % neg_zdiv_mult_2
% 5.06/5.33 thf(fact_3971_pos__zdiv__mult__2,axiom,
% 5.06/5.33 ! [A: int,B: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.33 => ( ( 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 ) )
% 5.06/5.33 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % pos_zdiv_mult_2
% 5.06/5.33 thf(fact_3972_verit__la__disequality,axiom,
% 5.06/5.33 ! [A: rat,B: rat] :
% 5.06/5.33 ( ( A = B )
% 5.06/5.33 | ~ ( ord_less_eq_rat @ A @ B )
% 5.06/5.33 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_la_disequality
% 5.06/5.33 thf(fact_3973_verit__la__disequality,axiom,
% 5.06/5.33 ! [A: num,B: num] :
% 5.06/5.33 ( ( A = B )
% 5.06/5.33 | ~ ( ord_less_eq_num @ A @ B )
% 5.06/5.33 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_la_disequality
% 5.06/5.33 thf(fact_3974_verit__la__disequality,axiom,
% 5.06/5.33 ! [A: nat,B: nat] :
% 5.06/5.33 ( ( A = B )
% 5.06/5.33 | ~ ( ord_less_eq_nat @ A @ B )
% 5.06/5.33 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_la_disequality
% 5.06/5.33 thf(fact_3975_verit__la__disequality,axiom,
% 5.06/5.33 ! [A: int,B: int] :
% 5.06/5.33 ( ( A = B )
% 5.06/5.33 | ~ ( ord_less_eq_int @ A @ B )
% 5.06/5.33 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_la_disequality
% 5.06/5.33 thf(fact_3976_verit__comp__simplify1_I2_J,axiom,
% 5.06/5.33 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(2)
% 5.06/5.33 thf(fact_3977_verit__comp__simplify1_I2_J,axiom,
% 5.06/5.33 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(2)
% 5.06/5.33 thf(fact_3978_verit__comp__simplify1_I2_J,axiom,
% 5.06/5.33 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(2)
% 5.06/5.33 thf(fact_3979_verit__comp__simplify1_I2_J,axiom,
% 5.06/5.33 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(2)
% 5.06/5.33 thf(fact_3980_verit__comp__simplify1_I2_J,axiom,
% 5.06/5.33 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(2)
% 5.06/5.33 thf(fact_3981_verit__comp__simplify1_I1_J,axiom,
% 5.06/5.33 ! [A: real] :
% 5.06/5.33 ~ ( ord_less_real @ A @ A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(1)
% 5.06/5.33 thf(fact_3982_verit__comp__simplify1_I1_J,axiom,
% 5.06/5.33 ! [A: rat] :
% 5.06/5.33 ~ ( ord_less_rat @ A @ A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(1)
% 5.06/5.33 thf(fact_3983_verit__comp__simplify1_I1_J,axiom,
% 5.06/5.33 ! [A: num] :
% 5.06/5.33 ~ ( ord_less_num @ A @ A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(1)
% 5.06/5.33 thf(fact_3984_verit__comp__simplify1_I1_J,axiom,
% 5.06/5.33 ! [A: nat] :
% 5.06/5.33 ~ ( ord_less_nat @ A @ A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(1)
% 5.06/5.33 thf(fact_3985_verit__comp__simplify1_I1_J,axiom,
% 5.06/5.33 ! [A: int] :
% 5.06/5.33 ~ ( ord_less_int @ A @ A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(1)
% 5.06/5.33 thf(fact_3986_realpow__pos__nth2,axiom,
% 5.06/5.33 ! [A: real,N2: nat] :
% 5.06/5.33 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.33 => ? [R3: real] :
% 5.06/5.33 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.06/5.33 & ( ( power_power_real @ R3 @ ( suc @ N2 ) )
% 5.06/5.33 = A ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % realpow_pos_nth2
% 5.06/5.33 thf(fact_3987_real__arch__pow__inv,axiom,
% 5.06/5.33 ! [Y: real,X: real] :
% 5.06/5.33 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.33 => ( ( ord_less_real @ X @ one_one_real )
% 5.06/5.33 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X @ N3 ) @ Y ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % real_arch_pow_inv
% 5.06/5.33 thf(fact_3988_int__power__div__base,axiom,
% 5.06/5.33 ! [M: nat,K: int] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.33 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.06/5.33 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % int_power_div_base
% 5.06/5.33 thf(fact_3989_realpow__pos__nth,axiom,
% 5.06/5.33 ! [N2: nat,A: real] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.33 => ? [R3: real] :
% 5.06/5.33 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.06/5.33 & ( ( power_power_real @ R3 @ N2 )
% 5.06/5.33 = A ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % realpow_pos_nth
% 5.06/5.33 thf(fact_3990_realpow__pos__nth__unique,axiom,
% 5.06/5.33 ! [N2: nat,A: real] :
% 5.06/5.33 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.33 => ? [X3: real] :
% 5.06/5.33 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.06/5.33 & ( ( power_power_real @ X3 @ N2 )
% 5.06/5.33 = A )
% 5.06/5.33 & ! [Y3: real] :
% 5.06/5.33 ( ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.06/5.33 & ( ( power_power_real @ Y3 @ N2 )
% 5.06/5.33 = A ) )
% 5.06/5.33 => ( Y3 = X3 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % realpow_pos_nth_unique
% 5.06/5.33 thf(fact_3991_verit__comp__simplify1_I3_J,axiom,
% 5.06/5.33 ! [B6: real,A6: real] :
% 5.06/5.33 ( ( ~ ( ord_less_eq_real @ B6 @ A6 ) )
% 5.06/5.33 = ( ord_less_real @ A6 @ B6 ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(3)
% 5.06/5.33 thf(fact_3992_verit__comp__simplify1_I3_J,axiom,
% 5.06/5.33 ! [B6: rat,A6: rat] :
% 5.06/5.33 ( ( ~ ( ord_less_eq_rat @ B6 @ A6 ) )
% 5.06/5.33 = ( ord_less_rat @ A6 @ B6 ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(3)
% 5.06/5.33 thf(fact_3993_verit__comp__simplify1_I3_J,axiom,
% 5.06/5.33 ! [B6: num,A6: num] :
% 5.06/5.33 ( ( ~ ( ord_less_eq_num @ B6 @ A6 ) )
% 5.06/5.33 = ( ord_less_num @ A6 @ B6 ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(3)
% 5.06/5.33 thf(fact_3994_verit__comp__simplify1_I3_J,axiom,
% 5.06/5.33 ! [B6: nat,A6: nat] :
% 5.06/5.33 ( ( ~ ( ord_less_eq_nat @ B6 @ A6 ) )
% 5.06/5.33 = ( ord_less_nat @ A6 @ B6 ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(3)
% 5.06/5.33 thf(fact_3995_verit__comp__simplify1_I3_J,axiom,
% 5.06/5.33 ! [B6: int,A6: int] :
% 5.06/5.33 ( ( ~ ( ord_less_eq_int @ B6 @ A6 ) )
% 5.06/5.33 = ( ord_less_int @ A6 @ B6 ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_comp_simplify1(3)
% 5.06/5.33 thf(fact_3996_verit__sum__simplify,axiom,
% 5.06/5.33 ! [A: complex] :
% 5.06/5.33 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.06/5.33 = A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_sum_simplify
% 5.06/5.33 thf(fact_3997_verit__sum__simplify,axiom,
% 5.06/5.33 ! [A: real] :
% 5.06/5.33 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.06/5.33 = A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_sum_simplify
% 5.06/5.33 thf(fact_3998_verit__sum__simplify,axiom,
% 5.06/5.33 ! [A: rat] :
% 5.06/5.33 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.06/5.33 = A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_sum_simplify
% 5.06/5.33 thf(fact_3999_verit__sum__simplify,axiom,
% 5.06/5.33 ! [A: nat] :
% 5.06/5.33 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.06/5.33 = A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_sum_simplify
% 5.06/5.33 thf(fact_4000_verit__sum__simplify,axiom,
% 5.06/5.33 ! [A: int] :
% 5.06/5.33 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.06/5.33 = A ) ).
% 5.06/5.33
% 5.06/5.33 % verit_sum_simplify
% 5.06/5.33 thf(fact_4001_verit__eq__simplify_I10_J,axiom,
% 5.06/5.33 ! [X22: num] :
% 5.06/5.33 ( one
% 5.06/5.33 != ( bit0 @ X22 ) ) ).
% 5.06/5.33
% 5.06/5.33 % verit_eq_simplify(10)
% 5.06/5.33 thf(fact_4002_max__def__raw,axiom,
% 5.06/5.33 ( ord_ma741700101516333627d_enat
% 5.06/5.33 = ( ^ [A4: extended_enat,B4: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % max_def_raw
% 5.06/5.33 thf(fact_4003_max__def__raw,axiom,
% 5.06/5.33 ( ord_max_Code_integer
% 5.06/5.33 = ( ^ [A4: code_integer,B4: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % max_def_raw
% 5.06/5.33 thf(fact_4004_max__def__raw,axiom,
% 5.06/5.33 ( ord_max_set_int
% 5.06/5.33 = ( ^ [A4: set_int,B4: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % max_def_raw
% 5.06/5.33 thf(fact_4005_max__def__raw,axiom,
% 5.06/5.33 ( ord_max_rat
% 5.06/5.33 = ( ^ [A4: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % max_def_raw
% 5.06/5.33 thf(fact_4006_max__def__raw,axiom,
% 5.06/5.33 ( ord_max_num
% 5.06/5.33 = ( ^ [A4: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % max_def_raw
% 5.06/5.33 thf(fact_4007_max__def__raw,axiom,
% 5.06/5.33 ( ord_max_nat
% 5.06/5.33 = ( ^ [A4: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % max_def_raw
% 5.06/5.33 thf(fact_4008_max__def__raw,axiom,
% 5.06/5.33 ( ord_max_int
% 5.06/5.33 = ( ^ [A4: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A4 @ B4 ) @ B4 @ A4 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % max_def_raw
% 5.06/5.33 thf(fact_4009_div__less__mono,axiom,
% 5.06/5.33 ! [A2: nat,B3: nat,N2: nat] :
% 5.06/5.33 ( ( ord_less_nat @ A2 @ B3 )
% 5.06/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.33 => ( ( ( modulo_modulo_nat @ A2 @ N2 )
% 5.06/5.33 = zero_zero_nat )
% 5.06/5.33 => ( ( ( modulo_modulo_nat @ B3 @ N2 )
% 5.06/5.33 = zero_zero_nat )
% 5.06/5.33 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N2 ) @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % div_less_mono
% 5.06/5.33 thf(fact_4010_set__bit__Suc,axiom,
% 5.06/5.33 ! [N2: nat,A: code_integer] :
% 5.06/5.33 ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 5.06/5.33 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % set_bit_Suc
% 5.06/5.33 thf(fact_4011_set__bit__Suc,axiom,
% 5.06/5.33 ! [N2: nat,A: int] :
% 5.06/5.33 ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 5.06/5.33 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % set_bit_Suc
% 5.06/5.33 thf(fact_4012_set__bit__Suc,axiom,
% 5.06/5.33 ! [N2: nat,A: nat] :
% 5.06/5.33 ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 5.06/5.33 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % set_bit_Suc
% 5.06/5.33 thf(fact_4013_unset__bit__Suc,axiom,
% 5.06/5.33 ! [N2: nat,A: code_integer] :
% 5.06/5.33 ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 5.06/5.33 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % unset_bit_Suc
% 5.06/5.33 thf(fact_4014_unset__bit__Suc,axiom,
% 5.06/5.33 ! [N2: nat,A: int] :
% 5.06/5.33 ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 5.06/5.33 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % unset_bit_Suc
% 5.06/5.33 thf(fact_4015_unset__bit__Suc,axiom,
% 5.06/5.33 ! [N2: nat,A: nat] :
% 5.06/5.33 ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 5.06/5.33 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % unset_bit_Suc
% 5.06/5.33 thf(fact_4016_vebt__insert_Opelims,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.06/5.33 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.06/5.33 = Y )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 5.06/5.33 & ( ( Xa2 != one_one_nat )
% 5.06/5.33 => ( Y
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( if_VEBT_VEBT
% 5.06/5.33 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 & ~ ( ( Xa2 = Mi2 )
% 5.06/5.33 | ( Xa2 = Ma2 ) ) )
% 5.06/5.33 @ ( 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 @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.06/5.33 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_insert.pelims
% 5.06/5.33 thf(fact_4017_vebt__member_Opelims_I3_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.06/5.33 => ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.06/5.33 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.06/5.33 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.06/5.33 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.06/5.33 => ( ( Xa2 != Mi2 )
% 5.06/5.33 => ( ( Xa2 != Ma2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_member.pelims(3)
% 5.06/5.33 thf(fact_4018_vebt__member_Opelims_I1_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.06/5.33 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.06/5.33 = Y )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.06/5.33 => ( ~ Y
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.06/5.33 => ( ~ Y
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.06/5.33 => ( ~ Y
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( ( Xa2 != Mi2 )
% 5.06/5.33 => ( ( Xa2 != Ma2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_member.pelims(1)
% 5.06/5.33 thf(fact_4019_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.06/5.33 => ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.06/5.33 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.06/5.33 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ Xa2 ) )
% 5.06/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.naive_member.pelims(3)
% 5.06/5.33 thf(fact_4020_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.06/5.33 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.06/5.33 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ Xa2 ) )
% 5.06/5.33 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.naive_member.pelims(2)
% 5.06/5.33 thf(fact_4021_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.06/5.33 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.06/5.33 = Y )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.06/5.33 => ( ~ Y
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.06/5.33 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) )
% 5.06/5.33 => ( ( Y
% 5.06/5.33 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.naive_member.pelims(1)
% 5.06/5.33 thf(fact_4022_vebt__member_Opelims_I2_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [A3: $o,B2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa2 ) )
% 5.06/5.33 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.33 => A3 )
% 5.06/5.33 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.33 => ( ( ( Xa2 = one_one_nat )
% 5.06/5.33 => B2 )
% 5.06/5.33 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.06/5.33 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.06/5.33 => ~ ( ( Xa2 != Mi2 )
% 5.06/5.33 => ( ( Xa2 != Ma2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.06/5.33 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.06/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % vebt_member.pelims(2)
% 5.06/5.33 thf(fact_4023_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.06/5.33 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.33 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.33 => ( ! [Uu2: $o,Uv2: $o] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 5.06/5.33 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.06/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.06/5.33 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 5.06/5.33 => ( ( Xa2 = Mi2 )
% 5.06/5.33 | ( Xa2 = Ma2 ) ) ) )
% 5.06/5.33 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.06/5.33 => ( ( Xa2 = Mi2 )
% 5.06/5.33 | ( Xa2 = Ma2 )
% 5.06/5.33 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.06/5.33 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.06/5.33 ( ( X
% 5.06/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.06/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.06/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % VEBT_internal.membermima.pelims(3)
% 5.06/5.33 thf(fact_4024_max__enat__simps_I2_J,axiom,
% 5.06/5.33 ! [Q2: extended_enat] :
% 5.06/5.33 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.06/5.33 = Q2 ) ).
% 5.06/5.33
% 5.06/5.33 % max_enat_simps(2)
% 5.06/5.33 thf(fact_4025_max__enat__simps_I3_J,axiom,
% 5.06/5.33 ! [Q2: extended_enat] :
% 5.06/5.33 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.06/5.33 = Q2 ) ).
% 5.06/5.33
% 5.06/5.33 % max_enat_simps(3)
% 5.06/5.33 thf(fact_4026_set__bit__nonnegative__int__iff,axiom,
% 5.06/5.33 ! [N2: nat,K: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) )
% 5.06/5.33 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.06/5.33
% 5.06/5.33 % set_bit_nonnegative_int_iff
% 5.06/5.33 thf(fact_4027_unset__bit__nonnegative__int__iff,axiom,
% 5.06/5.33 ! [N2: nat,K: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) )
% 5.06/5.33 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.06/5.33
% 5.06/5.33 % unset_bit_nonnegative_int_iff
% 5.06/5.33 thf(fact_4028_set__bit__negative__int__iff,axiom,
% 5.06/5.33 ! [N2: nat,K: int] :
% 5.06/5.33 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) @ zero_zero_int )
% 5.06/5.33 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.06/5.33
% 5.06/5.33 % set_bit_negative_int_iff
% 5.06/5.33 thf(fact_4029_unset__bit__negative__int__iff,axiom,
% 5.06/5.33 ! [N2: nat,K: int] :
% 5.06/5.33 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ zero_zero_int )
% 5.06/5.33 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.06/5.33
% 5.06/5.33 % unset_bit_negative_int_iff
% 5.06/5.33 thf(fact_4030_zle__add1__eq__le,axiom,
% 5.06/5.33 ! [W: int,Z: int] :
% 5.06/5.33 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.06/5.33 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.06/5.33
% 5.06/5.33 % zle_add1_eq_le
% 5.06/5.33 thf(fact_4031_zle__diff1__eq,axiom,
% 5.06/5.33 ! [W: int,Z: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.06/5.33 = ( ord_less_int @ W @ Z ) ) ).
% 5.06/5.33
% 5.06/5.33 % zle_diff1_eq
% 5.06/5.33 thf(fact_4032_mod__pos__pos__trivial,axiom,
% 5.06/5.33 ! [K: int,L2: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.33 => ( ( ord_less_int @ K @ L2 )
% 5.06/5.33 => ( ( modulo_modulo_int @ K @ L2 )
% 5.06/5.33 = K ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % mod_pos_pos_trivial
% 5.06/5.33 thf(fact_4033_mod__neg__neg__trivial,axiom,
% 5.06/5.33 ! [K: int,L2: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.06/5.33 => ( ( ord_less_int @ L2 @ K )
% 5.06/5.33 => ( ( modulo_modulo_int @ K @ L2 )
% 5.06/5.33 = K ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % mod_neg_neg_trivial
% 5.06/5.33 thf(fact_4034_add1__zle__eq,axiom,
% 5.06/5.33 ! [W: int,Z: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.06/5.33 = ( ord_less_int @ W @ Z ) ) ).
% 5.06/5.33
% 5.06/5.33 % add1_zle_eq
% 5.06/5.33 thf(fact_4035_le__imp__0__less,axiom,
% 5.06/5.33 ! [Z: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.33 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % le_imp_0_less
% 5.06/5.33 thf(fact_4036_int__less__induct,axiom,
% 5.06/5.33 ! [I2: int,K: int,P: int > $o] :
% 5.06/5.33 ( ( ord_less_int @ I2 @ K )
% 5.06/5.33 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.06/5.33 => ( ! [I3: int] :
% 5.06/5.33 ( ( ord_less_int @ I3 @ K )
% 5.06/5.33 => ( ( P @ I3 )
% 5.06/5.33 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.06/5.33 => ( P @ I2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % int_less_induct
% 5.06/5.33 thf(fact_4037_zless__imp__add1__zle,axiom,
% 5.06/5.33 ! [W: int,Z: int] :
% 5.06/5.33 ( ( ord_less_int @ W @ Z )
% 5.06/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.06/5.33
% 5.06/5.33 % zless_imp_add1_zle
% 5.06/5.33 thf(fact_4038_int__one__le__iff__zero__less,axiom,
% 5.06/5.33 ! [Z: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.06/5.33 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.06/5.33
% 5.06/5.33 % int_one_le_iff_zero_less
% 5.06/5.33 thf(fact_4039_minus__int__code_I1_J,axiom,
% 5.06/5.33 ! [K: int] :
% 5.06/5.33 ( ( minus_minus_int @ K @ zero_zero_int )
% 5.06/5.33 = K ) ).
% 5.06/5.33
% 5.06/5.33 % minus_int_code(1)
% 5.06/5.33 thf(fact_4040_mod__pos__neg__trivial,axiom,
% 5.06/5.33 ! [K: int,L2: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.33 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.06/5.33 => ( ( modulo_modulo_int @ K @ L2 )
% 5.06/5.33 = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % mod_pos_neg_trivial
% 5.06/5.33 thf(fact_4041_unique__quotient__lemma__neg,axiom,
% 5.06/5.33 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.06/5.33 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.06/5.33 => ( ( ord_less_int @ B @ R2 )
% 5.06/5.33 => ( ( ord_less_int @ B @ R4 )
% 5.06/5.33 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % unique_quotient_lemma_neg
% 5.06/5.33 thf(fact_4042_Euclidean__Division_Opos__mod__sign,axiom,
% 5.06/5.33 ! [L2: int,K: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.06/5.33 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % Euclidean_Division.pos_mod_sign
% 5.06/5.33 thf(fact_4043_neg__mod__sign,axiom,
% 5.06/5.33 ! [L2: int,K: int] :
% 5.06/5.33 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.06/5.33 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 5.06/5.33
% 5.06/5.33 % neg_mod_sign
% 5.06/5.33 thf(fact_4044_unique__quotient__lemma,axiom,
% 5.06/5.33 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.06/5.33 => ( ( ord_less_int @ R4 @ B )
% 5.06/5.33 => ( ( ord_less_int @ R2 @ B )
% 5.06/5.33 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % unique_quotient_lemma
% 5.06/5.33 thf(fact_4045_zdiv__mono2__neg__lemma,axiom,
% 5.06/5.33 ! [B: int,Q2: int,R2: int,B6: int,Q5: int,R4: int] :
% 5.06/5.33 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ B6 @ Q5 ) @ R4 ) )
% 5.06/5.33 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.06/5.33 => ( ( ord_less_int @ R2 @ B )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 5.06/5.33 => ( ( ord_less_eq_int @ B6 @ B )
% 5.06/5.33 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zdiv_mono2_neg_lemma
% 5.06/5.33 thf(fact_4046_zmod__trivial__iff,axiom,
% 5.06/5.33 ! [I2: int,K: int] :
% 5.06/5.33 ( ( ( modulo_modulo_int @ I2 @ K )
% 5.06/5.33 = I2 )
% 5.06/5.33 = ( ( K = zero_zero_int )
% 5.06/5.33 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.06/5.33 & ( ord_less_int @ I2 @ K ) )
% 5.06/5.33 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.06/5.33 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zmod_trivial_iff
% 5.06/5.33 thf(fact_4047_zdiv__mono2__lemma,axiom,
% 5.06/5.33 ! [B: int,Q2: int,R2: int,B6: int,Q5: int,R4: int] :
% 5.06/5.33 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ B6 @ Q5 ) @ R4 ) )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q5 ) @ R4 ) )
% 5.06/5.33 => ( ( ord_less_int @ R4 @ B6 )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 5.06/5.33 => ( ( ord_less_eq_int @ B6 @ B )
% 5.06/5.33 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zdiv_mono2_lemma
% 5.06/5.33 thf(fact_4048_int__mod__pos__eq,axiom,
% 5.06/5.33 ! [A: int,B: int,Q2: int,R2: int] :
% 5.06/5.33 ( ( A
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.06/5.33 => ( ( ord_less_int @ R2 @ B )
% 5.06/5.33 => ( ( modulo_modulo_int @ A @ B )
% 5.06/5.33 = R2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % int_mod_pos_eq
% 5.06/5.33 thf(fact_4049_int__mod__neg__eq,axiom,
% 5.06/5.33 ! [A: int,B: int,Q2: int,R2: int] :
% 5.06/5.33 ( ( A
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.06/5.33 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.06/5.33 => ( ( ord_less_int @ B @ R2 )
% 5.06/5.33 => ( ( modulo_modulo_int @ A @ B )
% 5.06/5.33 = R2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % int_mod_neg_eq
% 5.06/5.33 thf(fact_4050_pos__mod__conj,axiom,
% 5.06/5.33 ! [B: int,A: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.06/5.33 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % pos_mod_conj
% 5.06/5.33 thf(fact_4051_neg__mod__conj,axiom,
% 5.06/5.33 ! [B: int,A: int] :
% 5.06/5.33 ( ( ord_less_int @ B @ zero_zero_int )
% 5.06/5.33 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.06/5.33 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % neg_mod_conj
% 5.06/5.33 thf(fact_4052_q__pos__lemma,axiom,
% 5.06/5.33 ! [B6: int,Q5: int,R4: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q5 ) @ R4 ) )
% 5.06/5.33 => ( ( ord_less_int @ R4 @ B6 )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 5.06/5.33 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % q_pos_lemma
% 5.06/5.33 thf(fact_4053_mod__pos__geq,axiom,
% 5.06/5.33 ! [L2: int,K: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.06/5.33 => ( ( ord_less_eq_int @ L2 @ K )
% 5.06/5.33 => ( ( modulo_modulo_int @ K @ L2 )
% 5.06/5.33 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % mod_pos_geq
% 5.06/5.33 thf(fact_4054_split__zmod,axiom,
% 5.06/5.33 ! [P: int > $o,N2: int,K: int] :
% 5.06/5.33 ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 5.06/5.33 = ( ( ( K = zero_zero_int )
% 5.06/5.33 => ( P @ N2 ) )
% 5.06/5.33 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.33 => ! [I5: int,J3: int] :
% 5.06/5.33 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.06/5.33 & ( ord_less_int @ J3 @ K )
% 5.06/5.33 & ( N2
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.06/5.33 => ( P @ J3 ) ) )
% 5.06/5.33 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.06/5.33 => ! [I5: int,J3: int] :
% 5.06/5.33 ( ( ( ord_less_int @ K @ J3 )
% 5.06/5.33 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.06/5.33 & ( N2
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.06/5.33 => ( P @ J3 ) ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % split_zmod
% 5.06/5.33 thf(fact_4055_zmult__zless__mono2,axiom,
% 5.06/5.33 ! [I2: int,J: int,K: int] :
% 5.06/5.33 ( ( ord_less_int @ I2 @ J )
% 5.06/5.33 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.33 => ( ord_less_int @ ( times_times_int @ K @ I2 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zmult_zless_mono2
% 5.06/5.33 thf(fact_4056_pos__zmult__eq__1__iff,axiom,
% 5.06/5.33 ! [M: int,N2: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ M )
% 5.06/5.33 => ( ( ( times_times_int @ M @ N2 )
% 5.06/5.33 = one_one_int )
% 5.06/5.33 = ( ( M = one_one_int )
% 5.06/5.33 & ( N2 = one_one_int ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % pos_zmult_eq_1_iff
% 5.06/5.33 thf(fact_4057_odd__less__0__iff,axiom,
% 5.06/5.33 ! [Z: int] :
% 5.06/5.33 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.06/5.33 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.06/5.33
% 5.06/5.33 % odd_less_0_iff
% 5.06/5.33 thf(fact_4058_zless__add1__eq,axiom,
% 5.06/5.33 ! [W: int,Z: int] :
% 5.06/5.33 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.06/5.33 = ( ( ord_less_int @ W @ Z )
% 5.06/5.33 | ( W = Z ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zless_add1_eq
% 5.06/5.33 thf(fact_4059_int__gr__induct,axiom,
% 5.06/5.33 ! [K: int,I2: int,P: int > $o] :
% 5.06/5.33 ( ( ord_less_int @ K @ I2 )
% 5.06/5.33 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.06/5.33 => ( ! [I3: int] :
% 5.06/5.33 ( ( ord_less_int @ K @ I3 )
% 5.06/5.33 => ( ( P @ I3 )
% 5.06/5.33 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.06/5.33 => ( P @ I2 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % int_gr_induct
% 5.06/5.33 thf(fact_4060_Euclidean__Division_Opos__mod__bound,axiom,
% 5.06/5.33 ! [L2: int,K: int] :
% 5.06/5.33 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.06/5.33 => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 5.06/5.33
% 5.06/5.33 % Euclidean_Division.pos_mod_bound
% 5.06/5.33 thf(fact_4061_neg__mod__bound,axiom,
% 5.06/5.33 ! [L2: int,K: int] :
% 5.06/5.33 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.06/5.33 => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % neg_mod_bound
% 5.06/5.33 thf(fact_4062_less__eq__int__code_I1_J,axiom,
% 5.06/5.33 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.06/5.33
% 5.06/5.33 % less_eq_int_code(1)
% 5.06/5.33 thf(fact_4063_zmod__le__nonneg__dividend,axiom,
% 5.06/5.33 ! [M: int,K: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.06/5.33 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.06/5.33
% 5.06/5.33 % zmod_le_nonneg_dividend
% 5.06/5.33 thf(fact_4064_plus__int__code_I2_J,axiom,
% 5.06/5.33 ! [L2: int] :
% 5.06/5.33 ( ( plus_plus_int @ zero_zero_int @ L2 )
% 5.06/5.33 = L2 ) ).
% 5.06/5.33
% 5.06/5.33 % plus_int_code(2)
% 5.06/5.33 thf(fact_4065_plus__int__code_I1_J,axiom,
% 5.06/5.33 ! [K: int] :
% 5.06/5.33 ( ( plus_plus_int @ K @ zero_zero_int )
% 5.06/5.33 = K ) ).
% 5.06/5.33
% 5.06/5.33 % plus_int_code(1)
% 5.06/5.33 thf(fact_4066_odd__nonzero,axiom,
% 5.06/5.33 ! [Z: int] :
% 5.06/5.33 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 5.06/5.33 != zero_zero_int ) ).
% 5.06/5.33
% 5.06/5.33 % odd_nonzero
% 5.06/5.33 thf(fact_4067_zmod__eq__0__iff,axiom,
% 5.06/5.33 ! [M: int,D: int] :
% 5.06/5.33 ( ( ( modulo_modulo_int @ M @ D )
% 5.06/5.33 = zero_zero_int )
% 5.06/5.33 = ( ? [Q4: int] :
% 5.06/5.33 ( M
% 5.06/5.33 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zmod_eq_0_iff
% 5.06/5.33 thf(fact_4068_zmod__eq__0D,axiom,
% 5.06/5.33 ! [M: int,D: int] :
% 5.06/5.33 ( ( ( modulo_modulo_int @ M @ D )
% 5.06/5.33 = zero_zero_int )
% 5.06/5.33 => ? [Q3: int] :
% 5.06/5.33 ( M
% 5.06/5.33 = ( times_times_int @ D @ Q3 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % zmod_eq_0D
% 5.06/5.33 thf(fact_4069_times__int__code_I1_J,axiom,
% 5.06/5.33 ! [K: int] :
% 5.06/5.33 ( ( times_times_int @ K @ zero_zero_int )
% 5.06/5.33 = zero_zero_int ) ).
% 5.06/5.33
% 5.06/5.33 % times_int_code(1)
% 5.06/5.33 thf(fact_4070_times__int__code_I2_J,axiom,
% 5.06/5.33 ! [L2: int] :
% 5.06/5.33 ( ( times_times_int @ zero_zero_int @ L2 )
% 5.06/5.33 = zero_zero_int ) ).
% 5.06/5.33
% 5.06/5.33 % times_int_code(2)
% 5.06/5.33 thf(fact_4071_imult__is__0,axiom,
% 5.06/5.33 ! [M: extended_enat,N2: extended_enat] :
% 5.06/5.33 ( ( ( times_7803423173614009249d_enat @ M @ N2 )
% 5.06/5.33 = zero_z5237406670263579293d_enat )
% 5.06/5.33 = ( ( M = zero_z5237406670263579293d_enat )
% 5.06/5.33 | ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % imult_is_0
% 5.06/5.33 thf(fact_4072_int__distrib_I1_J,axiom,
% 5.06/5.33 ! [Z1: int,Z22: int,W: int] :
% 5.06/5.33 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % int_distrib(1)
% 5.06/5.33 thf(fact_4073_int__distrib_I2_J,axiom,
% 5.06/5.33 ! [W: int,Z1: int,Z22: int] :
% 5.06/5.33 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.06/5.33 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.06/5.33
% 5.06/5.33 % int_distrib(2)
% 5.06/5.33 thf(fact_4074_set__bit__greater__eq,axiom,
% 5.06/5.33 ! [K: int,N2: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N2 @ K ) ) ).
% 5.06/5.33
% 5.06/5.33 % set_bit_greater_eq
% 5.06/5.33 thf(fact_4075_unset__bit__less__eq,axiom,
% 5.06/5.33 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ K ) ).
% 5.06/5.33
% 5.06/5.33 % unset_bit_less_eq
% 5.06/5.33 thf(fact_4076_verit__la__generic,axiom,
% 5.06/5.33 ! [A: int,X: int] :
% 5.06/5.33 ( ( ord_less_eq_int @ A @ X )
% 5.06/5.34 | ( A = X )
% 5.06/5.34 | ( ord_less_eq_int @ X @ A ) ) ).
% 5.06/5.34
% 5.06/5.34 % verit_la_generic
% 5.06/5.34 thf(fact_4077_int__distrib_I4_J,axiom,
% 5.06/5.34 ! [W: int,Z1: int,Z22: int] :
% 5.06/5.34 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.06/5.34 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % int_distrib(4)
% 5.06/5.34 thf(fact_4078_int__distrib_I3_J,axiom,
% 5.06/5.34 ! [Z1: int,Z22: int,W: int] :
% 5.06/5.34 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.06/5.34 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % int_distrib(3)
% 5.06/5.34 thf(fact_4079_int__le__induct,axiom,
% 5.06/5.34 ! [I2: int,K: int,P: int > $o] :
% 5.06/5.34 ( ( ord_less_eq_int @ I2 @ K )
% 5.06/5.34 => ( ( P @ K )
% 5.06/5.34 => ( ! [I3: int] :
% 5.06/5.34 ( ( ord_less_eq_int @ I3 @ K )
% 5.06/5.34 => ( ( P @ I3 )
% 5.06/5.34 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.06/5.34 => ( P @ I2 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % int_le_induct
% 5.06/5.34 thf(fact_4080_int__ge__induct,axiom,
% 5.06/5.34 ! [K: int,I2: int,P: int > $o] :
% 5.06/5.34 ( ( ord_less_eq_int @ K @ I2 )
% 5.06/5.34 => ( ( P @ K )
% 5.06/5.34 => ( ! [I3: int] :
% 5.06/5.34 ( ( ord_less_eq_int @ K @ I3 )
% 5.06/5.34 => ( ( P @ I3 )
% 5.06/5.34 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.06/5.34 => ( P @ I2 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % int_ge_induct
% 5.06/5.34 thf(fact_4081_int__induct,axiom,
% 5.06/5.34 ! [P: int > $o,K: int,I2: int] :
% 5.06/5.34 ( ( P @ K )
% 5.06/5.34 => ( ! [I3: int] :
% 5.06/5.34 ( ( ord_less_eq_int @ K @ I3 )
% 5.06/5.34 => ( ( P @ I3 )
% 5.06/5.34 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.06/5.34 => ( ! [I3: int] :
% 5.06/5.34 ( ( ord_less_eq_int @ I3 @ K )
% 5.06/5.34 => ( ( P @ I3 )
% 5.06/5.34 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.06/5.34 => ( P @ I2 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % int_induct
% 5.06/5.34 thf(fact_4082_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.06/5.34 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.34 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.06/5.34 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.34 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.06/5.34 ( ( X
% 5.06/5.34 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.06/5.34 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 5.06/5.34 => ~ ( ( Xa2 = Mi2 )
% 5.06/5.34 | ( Xa2 = Ma2 ) ) ) )
% 5.06/5.34 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.34 ( ( X
% 5.06/5.34 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.06/5.34 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.06/5.34 => ~ ( ( Xa2 = Mi2 )
% 5.06/5.34 | ( Xa2 = Ma2 )
% 5.06/5.34 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.34 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.34 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.06/5.34 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.06/5.34 ( ( X
% 5.06/5.34 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.06/5.34 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.06/5.34 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.34 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.34 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % VEBT_internal.membermima.pelims(2)
% 5.06/5.34 thf(fact_4083_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.06/5.34 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.06/5.34 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.06/5.34 = Y )
% 5.06/5.34 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.34 => ( ! [Uu2: $o,Uv2: $o] :
% 5.06/5.34 ( ( X
% 5.06/5.34 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.34 => ( ~ Y
% 5.06/5.34 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.06/5.34 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.06/5.34 ( ( X
% 5.06/5.34 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.06/5.34 => ( ~ Y
% 5.06/5.34 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.06/5.34 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.06/5.34 ( ( X
% 5.06/5.34 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.06/5.34 => ( ( Y
% 5.06/5.34 = ( ( Xa2 = Mi2 )
% 5.06/5.34 | ( Xa2 = Ma2 ) ) )
% 5.06/5.34 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 5.06/5.34 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.34 ( ( X
% 5.06/5.34 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.06/5.34 => ( ( Y
% 5.06/5.34 = ( ( Xa2 = Mi2 )
% 5.06/5.34 | ( Xa2 = Ma2 )
% 5.06/5.34 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.34 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.34 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.06/5.34 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 5.06/5.34 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.06/5.34 ( ( X
% 5.06/5.34 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.06/5.34 => ( ( Y
% 5.06/5.34 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.06/5.34 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( 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 ) ) ) ) ) )
% 5.06/5.34 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.06/5.34 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % VEBT_internal.membermima.pelims(1)
% 5.06/5.34 thf(fact_4084_atLeastatMost__empty,axiom,
% 5.06/5.34 ! [B: rat,A: rat] :
% 5.06/5.34 ( ( ord_less_rat @ B @ A )
% 5.06/5.34 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.06/5.34 = bot_bot_set_rat ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty
% 5.06/5.34 thf(fact_4085_atLeastatMost__empty,axiom,
% 5.06/5.34 ! [B: num,A: num] :
% 5.06/5.34 ( ( ord_less_num @ B @ A )
% 5.06/5.34 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.06/5.34 = bot_bot_set_num ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty
% 5.06/5.34 thf(fact_4086_atLeastatMost__empty,axiom,
% 5.06/5.34 ! [B: nat,A: nat] :
% 5.06/5.34 ( ( ord_less_nat @ B @ A )
% 5.06/5.34 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.06/5.34 = bot_bot_set_nat ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty
% 5.06/5.34 thf(fact_4087_atLeastatMost__empty,axiom,
% 5.06/5.34 ! [B: int,A: int] :
% 5.06/5.34 ( ( ord_less_int @ B @ A )
% 5.06/5.34 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.06/5.34 = bot_bot_set_int ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty
% 5.06/5.34 thf(fact_4088_atLeastatMost__empty,axiom,
% 5.06/5.34 ! [B: real,A: real] :
% 5.06/5.34 ( ( ord_less_real @ B @ A )
% 5.06/5.34 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.06/5.34 = bot_bot_set_real ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty
% 5.06/5.34 thf(fact_4089_atLeastatMost__subset__iff,axiom,
% 5.06/5.34 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 5.06/5.34 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_set_int @ C @ A )
% 5.06/5.34 & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_subset_iff
% 5.06/5.34 thf(fact_4090_atLeastatMost__subset__iff,axiom,
% 5.06/5.34 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.34 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_rat @ C @ A )
% 5.06/5.34 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_subset_iff
% 5.06/5.34 thf(fact_4091_atLeastatMost__subset__iff,axiom,
% 5.06/5.34 ! [A: num,B: num,C: num,D: num] :
% 5.06/5.34 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_num @ C @ A )
% 5.06/5.34 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_subset_iff
% 5.06/5.34 thf(fact_4092_atLeastatMost__subset__iff,axiom,
% 5.06/5.34 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.34 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_nat @ C @ A )
% 5.06/5.34 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_subset_iff
% 5.06/5.34 thf(fact_4093_atLeastatMost__subset__iff,axiom,
% 5.06/5.34 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.34 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_int @ C @ A )
% 5.06/5.34 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_subset_iff
% 5.06/5.34 thf(fact_4094_atLeastatMost__subset__iff,axiom,
% 5.06/5.34 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.34 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_real @ C @ A )
% 5.06/5.34 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_subset_iff
% 5.06/5.34 thf(fact_4095_atLeastatMost__empty__iff,axiom,
% 5.06/5.34 ! [A: set_int,B: set_int] :
% 5.06/5.34 ( ( ( set_or370866239135849197et_int @ A @ B )
% 5.06/5.34 = bot_bot_set_set_int )
% 5.06/5.34 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff
% 5.06/5.34 thf(fact_4096_atLeastatMost__empty__iff,axiom,
% 5.06/5.34 ! [A: rat,B: rat] :
% 5.06/5.34 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.06/5.34 = bot_bot_set_rat )
% 5.06/5.34 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff
% 5.06/5.34 thf(fact_4097_atLeastatMost__empty__iff,axiom,
% 5.06/5.34 ! [A: num,B: num] :
% 5.06/5.34 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.06/5.34 = bot_bot_set_num )
% 5.06/5.34 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff
% 5.06/5.34 thf(fact_4098_atLeastatMost__empty__iff,axiom,
% 5.06/5.34 ! [A: nat,B: nat] :
% 5.06/5.34 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.06/5.34 = bot_bot_set_nat )
% 5.06/5.34 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff
% 5.06/5.34 thf(fact_4099_atLeastatMost__empty__iff,axiom,
% 5.06/5.34 ! [A: int,B: int] :
% 5.06/5.34 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.06/5.34 = bot_bot_set_int )
% 5.06/5.34 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff
% 5.06/5.34 thf(fact_4100_atLeastatMost__empty__iff,axiom,
% 5.06/5.34 ! [A: real,B: real] :
% 5.06/5.34 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.06/5.34 = bot_bot_set_real )
% 5.06/5.34 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff
% 5.06/5.34 thf(fact_4101_atLeastatMost__empty__iff2,axiom,
% 5.06/5.34 ! [A: set_int,B: set_int] :
% 5.06/5.34 ( ( bot_bot_set_set_int
% 5.06/5.34 = ( set_or370866239135849197et_int @ A @ B ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff2
% 5.06/5.34 thf(fact_4102_atLeastatMost__empty__iff2,axiom,
% 5.06/5.34 ! [A: rat,B: rat] :
% 5.06/5.34 ( ( bot_bot_set_rat
% 5.06/5.34 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff2
% 5.06/5.34 thf(fact_4103_atLeastatMost__empty__iff2,axiom,
% 5.06/5.34 ! [A: num,B: num] :
% 5.06/5.34 ( ( bot_bot_set_num
% 5.06/5.34 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff2
% 5.06/5.34 thf(fact_4104_atLeastatMost__empty__iff2,axiom,
% 5.06/5.34 ! [A: nat,B: nat] :
% 5.06/5.34 ( ( bot_bot_set_nat
% 5.06/5.34 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff2
% 5.06/5.34 thf(fact_4105_atLeastatMost__empty__iff2,axiom,
% 5.06/5.34 ! [A: int,B: int] :
% 5.06/5.34 ( ( bot_bot_set_int
% 5.06/5.34 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff2
% 5.06/5.34 thf(fact_4106_atLeastatMost__empty__iff2,axiom,
% 5.06/5.34 ! [A: real,B: real] :
% 5.06/5.34 ( ( bot_bot_set_real
% 5.06/5.34 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.06/5.34 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_empty_iff2
% 5.06/5.34 thf(fact_4107_decr__mult__lemma,axiom,
% 5.06/5.34 ! [D: int,P: int > $o,K: int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D )
% 5.06/5.34 => ( ! [X3: int] :
% 5.06/5.34 ( ( P @ X3 )
% 5.06/5.34 => ( P @ ( minus_minus_int @ X3 @ D ) ) )
% 5.06/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ( P @ X5 )
% 5.06/5.34 => ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % decr_mult_lemma
% 5.06/5.34 thf(fact_4108_incr__mult__lemma,axiom,
% 5.06/5.34 ! [D: int,P: int > $o,K: int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D )
% 5.06/5.34 => ( ! [X3: int] :
% 5.06/5.34 ( ( P @ X3 )
% 5.06/5.34 => ( P @ ( plus_plus_int @ X3 @ D ) ) )
% 5.06/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ( P @ X5 )
% 5.06/5.34 => ( P @ ( plus_plus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % incr_mult_lemma
% 5.06/5.34 thf(fact_4109_Icc__eq__Icc,axiom,
% 5.06/5.34 ! [L2: set_int,H2: set_int,L3: set_int,H3: set_int] :
% 5.06/5.34 ( ( ( set_or370866239135849197et_int @ L2 @ H2 )
% 5.06/5.34 = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 5.06/5.34 = ( ( ( L2 = L3 )
% 5.06/5.34 & ( H2 = H3 ) )
% 5.06/5.34 | ( ~ ( ord_less_eq_set_int @ L2 @ H2 )
% 5.06/5.34 & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Icc_eq_Icc
% 5.06/5.34 thf(fact_4110_Icc__eq__Icc,axiom,
% 5.06/5.34 ! [L2: rat,H2: rat,L3: rat,H3: rat] :
% 5.06/5.34 ( ( ( set_or633870826150836451st_rat @ L2 @ H2 )
% 5.06/5.34 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.06/5.34 = ( ( ( L2 = L3 )
% 5.06/5.34 & ( H2 = H3 ) )
% 5.06/5.34 | ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.06/5.34 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Icc_eq_Icc
% 5.06/5.34 thf(fact_4111_Icc__eq__Icc,axiom,
% 5.06/5.34 ! [L2: num,H2: num,L3: num,H3: num] :
% 5.06/5.34 ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 5.06/5.34 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.06/5.34 = ( ( ( L2 = L3 )
% 5.06/5.34 & ( H2 = H3 ) )
% 5.06/5.34 | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.06/5.34 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Icc_eq_Icc
% 5.06/5.34 thf(fact_4112_Icc__eq__Icc,axiom,
% 5.06/5.34 ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 5.06/5.34 ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 5.06/5.34 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.06/5.34 = ( ( ( L2 = L3 )
% 5.06/5.34 & ( H2 = H3 ) )
% 5.06/5.34 | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.06/5.34 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Icc_eq_Icc
% 5.06/5.34 thf(fact_4113_Icc__eq__Icc,axiom,
% 5.06/5.34 ! [L2: int,H2: int,L3: int,H3: int] :
% 5.06/5.34 ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 5.06/5.34 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.06/5.34 = ( ( ( L2 = L3 )
% 5.06/5.34 & ( H2 = H3 ) )
% 5.06/5.34 | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.06/5.34 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Icc_eq_Icc
% 5.06/5.34 thf(fact_4114_Icc__eq__Icc,axiom,
% 5.06/5.34 ! [L2: real,H2: real,L3: real,H3: real] :
% 5.06/5.34 ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 5.06/5.34 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.06/5.34 = ( ( ( L2 = L3 )
% 5.06/5.34 & ( H2 = H3 ) )
% 5.06/5.34 | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.06/5.34 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Icc_eq_Icc
% 5.06/5.34 thf(fact_4115_atLeastAtMost__iff,axiom,
% 5.06/5.34 ! [I2: set_nat,L2: set_nat,U: set_nat] :
% 5.06/5.34 ( ( member_set_nat @ I2 @ ( set_or4548717258645045905et_nat @ L2 @ U ) )
% 5.06/5.34 = ( ( ord_less_eq_set_nat @ L2 @ I2 )
% 5.06/5.34 & ( ord_less_eq_set_nat @ I2 @ U ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastAtMost_iff
% 5.06/5.34 thf(fact_4116_atLeastAtMost__iff,axiom,
% 5.06/5.34 ! [I2: set_int,L2: set_int,U: set_int] :
% 5.06/5.34 ( ( member_set_int @ I2 @ ( set_or370866239135849197et_int @ L2 @ U ) )
% 5.06/5.34 = ( ( ord_less_eq_set_int @ L2 @ I2 )
% 5.06/5.34 & ( ord_less_eq_set_int @ I2 @ U ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastAtMost_iff
% 5.06/5.34 thf(fact_4117_atLeastAtMost__iff,axiom,
% 5.06/5.34 ! [I2: rat,L2: rat,U: rat] :
% 5.06/5.34 ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L2 @ U ) )
% 5.06/5.34 = ( ( ord_less_eq_rat @ L2 @ I2 )
% 5.06/5.34 & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastAtMost_iff
% 5.06/5.34 thf(fact_4118_atLeastAtMost__iff,axiom,
% 5.06/5.34 ! [I2: num,L2: num,U: num] :
% 5.06/5.34 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 5.06/5.34 = ( ( ord_less_eq_num @ L2 @ I2 )
% 5.06/5.34 & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastAtMost_iff
% 5.06/5.34 thf(fact_4119_atLeastAtMost__iff,axiom,
% 5.06/5.34 ! [I2: nat,L2: nat,U: nat] :
% 5.06/5.34 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.06/5.34 = ( ( ord_less_eq_nat @ L2 @ I2 )
% 5.06/5.34 & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastAtMost_iff
% 5.06/5.34 thf(fact_4120_atLeastAtMost__iff,axiom,
% 5.06/5.34 ! [I2: int,L2: int,U: int] :
% 5.06/5.34 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.06/5.34 = ( ( ord_less_eq_int @ L2 @ I2 )
% 5.06/5.34 & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastAtMost_iff
% 5.06/5.34 thf(fact_4121_atLeastAtMost__iff,axiom,
% 5.06/5.34 ! [I2: real,L2: real,U: real] :
% 5.06/5.34 ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 5.06/5.34 = ( ( ord_less_eq_real @ L2 @ I2 )
% 5.06/5.34 & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastAtMost_iff
% 5.06/5.34 thf(fact_4122_aset_I2_J,axiom,
% 5.06/5.34 ! [D3: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.06/5.34 ( ! [X3: int] :
% 5.06/5.34 ( ! [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb2: int] :
% 5.06/5.34 ( ( member_int @ Xb2 @ A2 )
% 5.06/5.34 => ( X3
% 5.06/5.34 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: int] :
% 5.06/5.34 ( ! [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb2: int] :
% 5.06/5.34 ( ( member_int @ Xb2 @ A2 )
% 5.06/5.34 => ( X3
% 5.06/5.34 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 => ( Q @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ A2 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 => ( ( P @ ( plus_plus_int @ X5 @ D3 ) )
% 5.06/5.34 | ( Q @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % aset(2)
% 5.06/5.34 thf(fact_4123_aset_I1_J,axiom,
% 5.06/5.34 ! [D3: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.06/5.34 ( ! [X3: int] :
% 5.06/5.34 ( ! [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb2: int] :
% 5.06/5.34 ( ( member_int @ Xb2 @ A2 )
% 5.06/5.34 => ( X3
% 5.06/5.34 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: int] :
% 5.06/5.34 ( ! [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb2: int] :
% 5.06/5.34 ( ( member_int @ Xb2 @ A2 )
% 5.06/5.34 => ( X3
% 5.06/5.34 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 => ( Q @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ A2 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 => ( ( P @ ( plus_plus_int @ X5 @ D3 ) )
% 5.06/5.34 & ( Q @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % aset(1)
% 5.06/5.34 thf(fact_4124_bset_I2_J,axiom,
% 5.06/5.34 ! [D3: int,B3: set_int,P: int > $o,Q: int > $o] :
% 5.06/5.34 ( ! [X3: int] :
% 5.06/5.34 ( ! [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb2: int] :
% 5.06/5.34 ( ( member_int @ Xb2 @ B3 )
% 5.06/5.34 => ( X3
% 5.06/5.34 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: int] :
% 5.06/5.34 ( ! [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb2: int] :
% 5.06/5.34 ( ( member_int @ Xb2 @ B3 )
% 5.06/5.34 => ( X3
% 5.06/5.34 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 => ( Q @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ B3 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 => ( ( P @ ( minus_minus_int @ X5 @ D3 ) )
% 5.06/5.34 | ( Q @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % bset(2)
% 5.06/5.34 thf(fact_4125_bset_I1_J,axiom,
% 5.06/5.34 ! [D3: int,B3: set_int,P: int > $o,Q: int > $o] :
% 5.06/5.34 ( ! [X3: int] :
% 5.06/5.34 ( ! [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb2: int] :
% 5.06/5.34 ( ( member_int @ Xb2 @ B3 )
% 5.06/5.34 => ( X3
% 5.06/5.34 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: int] :
% 5.06/5.34 ( ! [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb2: int] :
% 5.06/5.34 ( ( member_int @ Xb2 @ B3 )
% 5.06/5.34 => ( X3
% 5.06/5.34 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 => ( Q @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ B3 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 => ( ( P @ ( minus_minus_int @ X5 @ D3 ) )
% 5.06/5.34 & ( Q @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % bset(1)
% 5.06/5.34 thf(fact_4126_pinf_I1_J,axiom,
% 5.06/5.34 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.06/5.34 ( ? [Z5: real] :
% 5.06/5.34 ! [X3: real] :
% 5.06/5.34 ( ( ord_less_real @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: real] :
% 5.06/5.34 ! [X3: real] :
% 5.06/5.34 ( ( ord_less_real @ Z5 @ X3 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ Z4 @ X5 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(1)
% 5.06/5.34 thf(fact_4127_pinf_I1_J,axiom,
% 5.06/5.34 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.06/5.34 ( ? [Z5: rat] :
% 5.06/5.34 ! [X3: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: rat] :
% 5.06/5.34 ! [X3: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z5 @ X3 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z4 @ X5 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(1)
% 5.06/5.34 thf(fact_4128_pinf_I1_J,axiom,
% 5.06/5.34 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.06/5.34 ( ? [Z5: num] :
% 5.06/5.34 ! [X3: num] :
% 5.06/5.34 ( ( ord_less_num @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: num] :
% 5.06/5.34 ! [X3: num] :
% 5.06/5.34 ( ( ord_less_num @ Z5 @ X3 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ Z4 @ X5 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(1)
% 5.06/5.34 thf(fact_4129_pinf_I1_J,axiom,
% 5.06/5.34 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.06/5.34 ( ? [Z5: nat] :
% 5.06/5.34 ! [X3: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: nat] :
% 5.06/5.34 ! [X3: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z5 @ X3 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z4 @ X5 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(1)
% 5.06/5.34 thf(fact_4130_pinf_I1_J,axiom,
% 5.06/5.34 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.06/5.34 ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ Z5 @ X3 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ Z4 @ X5 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(1)
% 5.06/5.34 thf(fact_4131_pinf_I2_J,axiom,
% 5.06/5.34 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.06/5.34 ( ? [Z5: real] :
% 5.06/5.34 ! [X3: real] :
% 5.06/5.34 ( ( ord_less_real @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: real] :
% 5.06/5.34 ! [X3: real] :
% 5.06/5.34 ( ( ord_less_real @ Z5 @ X3 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ Z4 @ X5 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(2)
% 5.06/5.34 thf(fact_4132_pinf_I2_J,axiom,
% 5.06/5.34 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.06/5.34 ( ? [Z5: rat] :
% 5.06/5.34 ! [X3: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: rat] :
% 5.06/5.34 ! [X3: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z5 @ X3 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z4 @ X5 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(2)
% 5.06/5.34 thf(fact_4133_pinf_I2_J,axiom,
% 5.06/5.34 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.06/5.34 ( ? [Z5: num] :
% 5.06/5.34 ! [X3: num] :
% 5.06/5.34 ( ( ord_less_num @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: num] :
% 5.06/5.34 ! [X3: num] :
% 5.06/5.34 ( ( ord_less_num @ Z5 @ X3 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ Z4 @ X5 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(2)
% 5.06/5.34 thf(fact_4134_pinf_I2_J,axiom,
% 5.06/5.34 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.06/5.34 ( ? [Z5: nat] :
% 5.06/5.34 ! [X3: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: nat] :
% 5.06/5.34 ! [X3: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z5 @ X3 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z4 @ X5 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(2)
% 5.06/5.34 thf(fact_4135_pinf_I2_J,axiom,
% 5.06/5.34 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.06/5.34 ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ Z5 @ X3 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ Z4 @ X5 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(2)
% 5.06/5.34 thf(fact_4136_pinf_I3_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ Z4 @ X5 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(3)
% 5.06/5.34 thf(fact_4137_pinf_I3_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z4 @ X5 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(3)
% 5.06/5.34 thf(fact_4138_pinf_I3_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ Z4 @ X5 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(3)
% 5.06/5.34 thf(fact_4139_pinf_I3_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z4 @ X5 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(3)
% 5.06/5.34 thf(fact_4140_pinf_I3_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ Z4 @ X5 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(3)
% 5.06/5.34 thf(fact_4141_pinf_I4_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ Z4 @ X5 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(4)
% 5.06/5.34 thf(fact_4142_pinf_I4_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z4 @ X5 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(4)
% 5.06/5.34 thf(fact_4143_pinf_I4_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ Z4 @ X5 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(4)
% 5.06/5.34 thf(fact_4144_pinf_I4_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z4 @ X5 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(4)
% 5.06/5.34 thf(fact_4145_pinf_I4_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ Z4 @ X5 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(4)
% 5.06/5.34 thf(fact_4146_pinf_I5_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ Z4 @ X5 )
% 5.06/5.34 => ~ ( ord_less_real @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(5)
% 5.06/5.34 thf(fact_4147_pinf_I5_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z4 @ X5 )
% 5.06/5.34 => ~ ( ord_less_rat @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(5)
% 5.06/5.34 thf(fact_4148_pinf_I5_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ Z4 @ X5 )
% 5.06/5.34 => ~ ( ord_less_num @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(5)
% 5.06/5.34 thf(fact_4149_pinf_I5_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z4 @ X5 )
% 5.06/5.34 => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(5)
% 5.06/5.34 thf(fact_4150_pinf_I5_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ Z4 @ X5 )
% 5.06/5.34 => ~ ( ord_less_int @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(5)
% 5.06/5.34 thf(fact_4151_pinf_I7_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ Z4 @ X5 )
% 5.06/5.34 => ( ord_less_real @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(7)
% 5.06/5.34 thf(fact_4152_pinf_I7_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z4 @ X5 )
% 5.06/5.34 => ( ord_less_rat @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(7)
% 5.06/5.34 thf(fact_4153_pinf_I7_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ Z4 @ X5 )
% 5.06/5.34 => ( ord_less_num @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(7)
% 5.06/5.34 thf(fact_4154_pinf_I7_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z4 @ X5 )
% 5.06/5.34 => ( ord_less_nat @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(7)
% 5.06/5.34 thf(fact_4155_pinf_I7_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ Z4 @ X5 )
% 5.06/5.34 => ( ord_less_int @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(7)
% 5.06/5.34 thf(fact_4156_minf_I1_J,axiom,
% 5.06/5.34 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.06/5.34 ( ? [Z5: real] :
% 5.06/5.34 ! [X3: real] :
% 5.06/5.34 ( ( ord_less_real @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: real] :
% 5.06/5.34 ! [X3: real] :
% 5.06/5.34 ( ( ord_less_real @ X3 @ Z5 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ X5 @ Z4 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(1)
% 5.06/5.34 thf(fact_4157_minf_I1_J,axiom,
% 5.06/5.34 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.06/5.34 ( ? [Z5: rat] :
% 5.06/5.34 ! [X3: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: rat] :
% 5.06/5.34 ! [X3: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X3 @ Z5 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X5 @ Z4 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(1)
% 5.06/5.34 thf(fact_4158_minf_I1_J,axiom,
% 5.06/5.34 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.06/5.34 ( ? [Z5: num] :
% 5.06/5.34 ! [X3: num] :
% 5.06/5.34 ( ( ord_less_num @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: num] :
% 5.06/5.34 ! [X3: num] :
% 5.06/5.34 ( ( ord_less_num @ X3 @ Z5 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ X5 @ Z4 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(1)
% 5.06/5.34 thf(fact_4159_minf_I1_J,axiom,
% 5.06/5.34 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.06/5.34 ( ? [Z5: nat] :
% 5.06/5.34 ! [X3: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: nat] :
% 5.06/5.34 ! [X3: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X3 @ Z5 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X5 @ Z4 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(1)
% 5.06/5.34 thf(fact_4160_minf_I1_J,axiom,
% 5.06/5.34 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.06/5.34 ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ X3 @ Z5 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ X5 @ Z4 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 & ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(1)
% 5.06/5.34 thf(fact_4161_minf_I2_J,axiom,
% 5.06/5.34 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.06/5.34 ( ? [Z5: real] :
% 5.06/5.34 ! [X3: real] :
% 5.06/5.34 ( ( ord_less_real @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: real] :
% 5.06/5.34 ! [X3: real] :
% 5.06/5.34 ( ( ord_less_real @ X3 @ Z5 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ X5 @ Z4 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(2)
% 5.06/5.34 thf(fact_4162_minf_I2_J,axiom,
% 5.06/5.34 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.06/5.34 ( ? [Z5: rat] :
% 5.06/5.34 ! [X3: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: rat] :
% 5.06/5.34 ! [X3: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X3 @ Z5 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X5 @ Z4 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(2)
% 5.06/5.34 thf(fact_4163_minf_I2_J,axiom,
% 5.06/5.34 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.06/5.34 ( ? [Z5: num] :
% 5.06/5.34 ! [X3: num] :
% 5.06/5.34 ( ( ord_less_num @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: num] :
% 5.06/5.34 ! [X3: num] :
% 5.06/5.34 ( ( ord_less_num @ X3 @ Z5 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ X5 @ Z4 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(2)
% 5.06/5.34 thf(fact_4164_minf_I2_J,axiom,
% 5.06/5.34 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.06/5.34 ( ? [Z5: nat] :
% 5.06/5.34 ! [X3: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: nat] :
% 5.06/5.34 ! [X3: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X3 @ Z5 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X5 @ Z4 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(2)
% 5.06/5.34 thf(fact_4165_minf_I2_J,axiom,
% 5.06/5.34 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.06/5.34 ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ X3 @ Z5 )
% 5.06/5.34 => ( ( Q @ X3 )
% 5.06/5.34 = ( Q6 @ X3 ) ) )
% 5.06/5.34 => ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ X5 @ Z4 )
% 5.06/5.34 => ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P6 @ X5 )
% 5.06/5.34 | ( Q6 @ X5 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(2)
% 5.06/5.34 thf(fact_4166_minf_I3_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ X5 @ Z4 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(3)
% 5.06/5.34 thf(fact_4167_minf_I3_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X5 @ Z4 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(3)
% 5.06/5.34 thf(fact_4168_minf_I3_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ X5 @ Z4 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(3)
% 5.06/5.34 thf(fact_4169_minf_I3_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X5 @ Z4 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(3)
% 5.06/5.34 thf(fact_4170_minf_I3_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ X5 @ Z4 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(3)
% 5.06/5.34 thf(fact_4171_minf_I4_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ X5 @ Z4 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(4)
% 5.06/5.34 thf(fact_4172_minf_I4_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X5 @ Z4 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(4)
% 5.06/5.34 thf(fact_4173_minf_I4_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ X5 @ Z4 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(4)
% 5.06/5.34 thf(fact_4174_minf_I4_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X5 @ Z4 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(4)
% 5.06/5.34 thf(fact_4175_minf_I4_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ X5 @ Z4 )
% 5.06/5.34 => ( X5 != T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(4)
% 5.06/5.34 thf(fact_4176_minf_I5_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ X5 @ Z4 )
% 5.06/5.34 => ( ord_less_real @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(5)
% 5.06/5.34 thf(fact_4177_minf_I5_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X5 @ Z4 )
% 5.06/5.34 => ( ord_less_rat @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(5)
% 5.06/5.34 thf(fact_4178_minf_I5_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ X5 @ Z4 )
% 5.06/5.34 => ( ord_less_num @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(5)
% 5.06/5.34 thf(fact_4179_minf_I5_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X5 @ Z4 )
% 5.06/5.34 => ( ord_less_nat @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(5)
% 5.06/5.34 thf(fact_4180_minf_I5_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ X5 @ Z4 )
% 5.06/5.34 => ( ord_less_int @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(5)
% 5.06/5.34 thf(fact_4181_minf_I7_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ X5 @ Z4 )
% 5.06/5.34 => ~ ( ord_less_real @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(7)
% 5.06/5.34 thf(fact_4182_minf_I7_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X5 @ Z4 )
% 5.06/5.34 => ~ ( ord_less_rat @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(7)
% 5.06/5.34 thf(fact_4183_minf_I7_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ X5 @ Z4 )
% 5.06/5.34 => ~ ( ord_less_num @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(7)
% 5.06/5.34 thf(fact_4184_minf_I7_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X5 @ Z4 )
% 5.06/5.34 => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(7)
% 5.06/5.34 thf(fact_4185_minf_I7_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ X5 @ Z4 )
% 5.06/5.34 => ~ ( ord_less_int @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(7)
% 5.06/5.34 thf(fact_4186_bounded__Max__nat,axiom,
% 5.06/5.34 ! [P: nat > $o,X: nat,M7: nat] :
% 5.06/5.34 ( ( P @ X )
% 5.06/5.34 => ( ! [X3: nat] :
% 5.06/5.34 ( ( P @ X3 )
% 5.06/5.34 => ( ord_less_eq_nat @ X3 @ M7 ) )
% 5.06/5.34 => ~ ! [M2: nat] :
% 5.06/5.34 ( ( P @ M2 )
% 5.06/5.34 => ~ ! [X5: nat] :
% 5.06/5.34 ( ( P @ X5 )
% 5.06/5.34 => ( ord_less_eq_nat @ X5 @ M2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % bounded_Max_nat
% 5.06/5.34 thf(fact_4187_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.06/5.34 ! [X: produc3368934014287244435at_num] :
% 5.06/5.34 ~ ! [F2: nat > num > num,A3: nat,B2: nat,Acc: num] :
% 5.06/5.34 ( X
% 5.06/5.34 != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A3 @ ( product_Pair_nat_num @ B2 @ Acc ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % fold_atLeastAtMost_nat.cases
% 5.06/5.34 thf(fact_4188_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.06/5.34 ! [X: produc4471711990508489141at_nat] :
% 5.06/5.34 ~ ! [F2: nat > nat > nat,A3: nat,B2: nat,Acc: nat] :
% 5.06/5.34 ( X
% 5.06/5.34 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A3 @ ( product_Pair_nat_nat @ B2 @ Acc ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % fold_atLeastAtMost_nat.cases
% 5.06/5.34 thf(fact_4189_periodic__finite__ex,axiom,
% 5.06/5.34 ! [D: int,P: int > $o] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D )
% 5.06/5.34 => ( ! [X3: int,K2: int] :
% 5.06/5.34 ( ( P @ X3 )
% 5.06/5.34 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.06/5.34 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.06/5.34 = ( ? [X2: int] :
% 5.06/5.34 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.06/5.34 & ( P @ X2 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % periodic_finite_ex
% 5.06/5.34 thf(fact_4190_bset_I3_J,axiom,
% 5.06/5.34 ! [D3: int,T: int,B3: set_int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ B3 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( X5 = T )
% 5.06/5.34 => ( ( minus_minus_int @ X5 @ D3 )
% 5.06/5.34 = T ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % bset(3)
% 5.06/5.34 thf(fact_4191_bset_I4_J,axiom,
% 5.06/5.34 ! [D3: int,T: int,B3: set_int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ( ( member_int @ T @ B3 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ B3 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( X5 != T )
% 5.06/5.34 => ( ( minus_minus_int @ X5 @ D3 )
% 5.06/5.34 != T ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % bset(4)
% 5.06/5.34 thf(fact_4192_bset_I5_J,axiom,
% 5.06/5.34 ! [D3: int,B3: set_int,T: int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ B3 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ord_less_int @ X5 @ T )
% 5.06/5.34 => ( ord_less_int @ ( minus_minus_int @ X5 @ D3 ) @ T ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % bset(5)
% 5.06/5.34 thf(fact_4193_bset_I7_J,axiom,
% 5.06/5.34 ! [D3: int,T: int,B3: set_int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ( ( member_int @ T @ B3 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ B3 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ord_less_int @ T @ X5 )
% 5.06/5.34 => ( ord_less_int @ T @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % bset(7)
% 5.06/5.34 thf(fact_4194_aset_I3_J,axiom,
% 5.06/5.34 ! [D3: int,T: int,A2: set_int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ A2 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( X5 = T )
% 5.06/5.34 => ( ( plus_plus_int @ X5 @ D3 )
% 5.06/5.34 = T ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % aset(3)
% 5.06/5.34 thf(fact_4195_aset_I4_J,axiom,
% 5.06/5.34 ! [D3: int,T: int,A2: set_int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ( ( member_int @ T @ A2 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ A2 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( X5 != T )
% 5.06/5.34 => ( ( plus_plus_int @ X5 @ D3 )
% 5.06/5.34 != T ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % aset(4)
% 5.06/5.34 thf(fact_4196_aset_I5_J,axiom,
% 5.06/5.34 ! [D3: int,T: int,A2: set_int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ( ( member_int @ T @ A2 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ A2 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ord_less_int @ X5 @ T )
% 5.06/5.34 => ( ord_less_int @ ( plus_plus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % aset(5)
% 5.06/5.34 thf(fact_4197_aset_I7_J,axiom,
% 5.06/5.34 ! [D3: int,A2: set_int,T: int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ A2 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ord_less_int @ T @ X5 )
% 5.06/5.34 => ( ord_less_int @ T @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % aset(7)
% 5.06/5.34 thf(fact_4198_bset_I6_J,axiom,
% 5.06/5.34 ! [D3: int,B3: set_int,T: int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ B3 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ord_less_eq_int @ X5 @ T )
% 5.06/5.34 => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D3 ) @ T ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % bset(6)
% 5.06/5.34 thf(fact_4199_bset_I8_J,axiom,
% 5.06/5.34 ! [D3: int,T: int,B3: set_int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ B3 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ord_less_eq_int @ T @ X5 )
% 5.06/5.34 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % bset(8)
% 5.06/5.34 thf(fact_4200_aset_I6_J,axiom,
% 5.06/5.34 ! [D3: int,T: int,A2: set_int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ A2 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ord_less_eq_int @ X5 @ T )
% 5.06/5.34 => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % aset(6)
% 5.06/5.34 thf(fact_4201_aset_I8_J,axiom,
% 5.06/5.34 ! [D3: int,A2: set_int,T: int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ! [X5: int] :
% 5.06/5.34 ( ! [Xa3: int] :
% 5.06/5.34 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb3: int] :
% 5.06/5.34 ( ( member_int @ Xb3 @ A2 )
% 5.06/5.34 => ( X5
% 5.06/5.34 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.34 => ( ( ord_less_eq_int @ T @ X5 )
% 5.06/5.34 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % aset(8)
% 5.06/5.34 thf(fact_4202_cppi,axiom,
% 5.06/5.34 ! [D3: int,P: int > $o,P6: int > $o,A2: set_int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ! [X3: int] :
% 5.06/5.34 ( ! [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb2: int] :
% 5.06/5.34 ( ( member_int @ Xb2 @ A2 )
% 5.06/5.34 => ( X3
% 5.06/5.34 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: int,K2: int] :
% 5.06/5.34 ( ( P6 @ X3 )
% 5.06/5.34 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.06/5.34 = ( ? [X2: int] :
% 5.06/5.34 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 & ( P6 @ X2 ) )
% 5.06/5.34 | ? [X2: int] :
% 5.06/5.34 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 & ? [Y2: int] :
% 5.06/5.34 ( ( member_int @ Y2 @ A2 )
% 5.06/5.34 & ( P @ ( minus_minus_int @ Y2 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % cppi
% 5.06/5.34 thf(fact_4203_cpmi,axiom,
% 5.06/5.34 ! [D3: int,P: int > $o,P6: int > $o,B3: set_int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.06/5.34 => ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ! [X3: int] :
% 5.06/5.34 ( ! [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 => ! [Xb2: int] :
% 5.06/5.34 ( ( member_int @ Xb2 @ B3 )
% 5.06/5.34 => ( X3
% 5.06/5.34 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: int,K2: int] :
% 5.06/5.34 ( ( P6 @ X3 )
% 5.06/5.34 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.06/5.34 = ( ? [X2: int] :
% 5.06/5.34 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 & ( P6 @ X2 ) )
% 5.06/5.34 | ? [X2: int] :
% 5.06/5.34 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.34 & ? [Y2: int] :
% 5.06/5.34 ( ( member_int @ Y2 @ B3 )
% 5.06/5.34 & ( P @ ( plus_plus_int @ Y2 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % cpmi
% 5.06/5.34 thf(fact_4204_pinf_I6_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ Z4 @ X5 )
% 5.06/5.34 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(6)
% 5.06/5.34 thf(fact_4205_pinf_I6_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z4 @ X5 )
% 5.06/5.34 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(6)
% 5.06/5.34 thf(fact_4206_pinf_I6_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ Z4 @ X5 )
% 5.06/5.34 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(6)
% 5.06/5.34 thf(fact_4207_pinf_I6_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z4 @ X5 )
% 5.06/5.34 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(6)
% 5.06/5.34 thf(fact_4208_pinf_I6_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ Z4 @ X5 )
% 5.06/5.34 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(6)
% 5.06/5.34 thf(fact_4209_pinf_I8_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ Z4 @ X5 )
% 5.06/5.34 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(8)
% 5.06/5.34 thf(fact_4210_pinf_I8_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ Z4 @ X5 )
% 5.06/5.34 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(8)
% 5.06/5.34 thf(fact_4211_pinf_I8_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ Z4 @ X5 )
% 5.06/5.34 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(8)
% 5.06/5.34 thf(fact_4212_pinf_I8_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z4 @ X5 )
% 5.06/5.34 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(8)
% 5.06/5.34 thf(fact_4213_pinf_I8_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ Z4 @ X5 )
% 5.06/5.34 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % pinf(8)
% 5.06/5.34 thf(fact_4214_minf_I6_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ X5 @ Z4 )
% 5.06/5.34 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(6)
% 5.06/5.34 thf(fact_4215_minf_I6_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X5 @ Z4 )
% 5.06/5.34 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(6)
% 5.06/5.34 thf(fact_4216_minf_I6_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ X5 @ Z4 )
% 5.06/5.34 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(6)
% 5.06/5.34 thf(fact_4217_minf_I6_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X5 @ Z4 )
% 5.06/5.34 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(6)
% 5.06/5.34 thf(fact_4218_minf_I6_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ X5 @ Z4 )
% 5.06/5.34 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(6)
% 5.06/5.34 thf(fact_4219_minf_I8_J,axiom,
% 5.06/5.34 ! [T: real] :
% 5.06/5.34 ? [Z4: real] :
% 5.06/5.34 ! [X5: real] :
% 5.06/5.34 ( ( ord_less_real @ X5 @ Z4 )
% 5.06/5.34 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(8)
% 5.06/5.34 thf(fact_4220_minf_I8_J,axiom,
% 5.06/5.34 ! [T: rat] :
% 5.06/5.34 ? [Z4: rat] :
% 5.06/5.34 ! [X5: rat] :
% 5.06/5.34 ( ( ord_less_rat @ X5 @ Z4 )
% 5.06/5.34 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(8)
% 5.06/5.34 thf(fact_4221_minf_I8_J,axiom,
% 5.06/5.34 ! [T: num] :
% 5.06/5.34 ? [Z4: num] :
% 5.06/5.34 ! [X5: num] :
% 5.06/5.34 ( ( ord_less_num @ X5 @ Z4 )
% 5.06/5.34 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(8)
% 5.06/5.34 thf(fact_4222_minf_I8_J,axiom,
% 5.06/5.34 ! [T: nat] :
% 5.06/5.34 ? [Z4: nat] :
% 5.06/5.34 ! [X5: nat] :
% 5.06/5.34 ( ( ord_less_nat @ X5 @ Z4 )
% 5.06/5.34 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(8)
% 5.06/5.34 thf(fact_4223_minf_I8_J,axiom,
% 5.06/5.34 ! [T: int] :
% 5.06/5.34 ? [Z4: int] :
% 5.06/5.34 ! [X5: int] :
% 5.06/5.34 ( ( ord_less_int @ X5 @ Z4 )
% 5.06/5.34 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % minf(8)
% 5.06/5.34 thf(fact_4224_inf__period_I2_J,axiom,
% 5.06/5.34 ! [P: real > $o,D3: real,Q: real > $o] :
% 5.06/5.34 ( ! [X3: real,K2: real] :
% 5.06/5.34 ( ( P @ X3 )
% 5.06/5.34 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: real,K2: real] :
% 5.06/5.34 ( ( Q @ X3 )
% 5.06/5.34 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ! [X5: real,K4: real] :
% 5.06/5.34 ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) )
% 5.06/5.34 | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % inf_period(2)
% 5.06/5.34 thf(fact_4225_inf__period_I2_J,axiom,
% 5.06/5.34 ! [P: rat > $o,D3: rat,Q: rat > $o] :
% 5.06/5.34 ( ! [X3: rat,K2: rat] :
% 5.06/5.34 ( ( P @ X3 )
% 5.06/5.34 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: rat,K2: rat] :
% 5.06/5.34 ( ( Q @ X3 )
% 5.06/5.34 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ! [X5: rat,K4: rat] :
% 5.06/5.34 ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) )
% 5.06/5.34 | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % inf_period(2)
% 5.06/5.34 thf(fact_4226_inf__period_I2_J,axiom,
% 5.06/5.34 ! [P: int > $o,D3: int,Q: int > $o] :
% 5.06/5.34 ( ! [X3: int,K2: int] :
% 5.06/5.34 ( ( P @ X3 )
% 5.06/5.34 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: int,K2: int] :
% 5.06/5.34 ( ( Q @ X3 )
% 5.06/5.34 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ! [X5: int,K4: int] :
% 5.06/5.34 ( ( ( P @ X5 )
% 5.06/5.34 | ( Q @ X5 ) )
% 5.06/5.34 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) )
% 5.06/5.34 | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % inf_period(2)
% 5.06/5.34 thf(fact_4227_inf__period_I1_J,axiom,
% 5.06/5.34 ! [P: real > $o,D3: real,Q: real > $o] :
% 5.06/5.34 ( ! [X3: real,K2: real] :
% 5.06/5.34 ( ( P @ X3 )
% 5.06/5.34 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: real,K2: real] :
% 5.06/5.34 ( ( Q @ X3 )
% 5.06/5.34 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ! [X5: real,K4: real] :
% 5.06/5.34 ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) )
% 5.06/5.34 & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % inf_period(1)
% 5.06/5.34 thf(fact_4228_inf__period_I1_J,axiom,
% 5.06/5.34 ! [P: rat > $o,D3: rat,Q: rat > $o] :
% 5.06/5.34 ( ! [X3: rat,K2: rat] :
% 5.06/5.34 ( ( P @ X3 )
% 5.06/5.34 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: rat,K2: rat] :
% 5.06/5.34 ( ( Q @ X3 )
% 5.06/5.34 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ! [X5: rat,K4: rat] :
% 5.06/5.34 ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) )
% 5.06/5.34 & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % inf_period(1)
% 5.06/5.34 thf(fact_4229_inf__period_I1_J,axiom,
% 5.06/5.34 ! [P: int > $o,D3: int,Q: int > $o] :
% 5.06/5.34 ( ! [X3: int,K2: int] :
% 5.06/5.34 ( ( P @ X3 )
% 5.06/5.34 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ( ! [X3: int,K2: int] :
% 5.06/5.34 ( ( Q @ X3 )
% 5.06/5.34 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.06/5.34 => ! [X5: int,K4: int] :
% 5.06/5.34 ( ( ( P @ X5 )
% 5.06/5.34 & ( Q @ X5 ) )
% 5.06/5.34 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) )
% 5.06/5.34 & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % inf_period(1)
% 5.06/5.34 thf(fact_4230_conj__le__cong,axiom,
% 5.06/5.34 ! [X: int,X7: int,P: $o,P6: $o] :
% 5.06/5.34 ( ( X = X7 )
% 5.06/5.34 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.06/5.34 => ( P = P6 ) )
% 5.06/5.34 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.34 & P )
% 5.06/5.34 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.06/5.34 & P6 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % conj_le_cong
% 5.06/5.34 thf(fact_4231_imp__le__cong,axiom,
% 5.06/5.34 ! [X: int,X7: int,P: $o,P6: $o] :
% 5.06/5.34 ( ( X = X7 )
% 5.06/5.34 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.06/5.34 => ( P = P6 ) )
% 5.06/5.34 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.34 => P )
% 5.06/5.34 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.06/5.34 => P6 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % imp_le_cong
% 5.06/5.34 thf(fact_4232_atLeastatMost__psubset__iff,axiom,
% 5.06/5.34 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 5.06/5.34 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.06/5.34 = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_set_int @ C @ A )
% 5.06/5.34 & ( ord_less_eq_set_int @ B @ D )
% 5.06/5.34 & ( ( ord_less_set_int @ C @ A )
% 5.06/5.34 | ( ord_less_set_int @ B @ D ) ) ) )
% 5.06/5.34 & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_psubset_iff
% 5.06/5.34 thf(fact_4233_atLeastatMost__psubset__iff,axiom,
% 5.06/5.34 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.34 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.06/5.34 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_rat @ C @ A )
% 5.06/5.34 & ( ord_less_eq_rat @ B @ D )
% 5.06/5.34 & ( ( ord_less_rat @ C @ A )
% 5.06/5.34 | ( ord_less_rat @ B @ D ) ) ) )
% 5.06/5.34 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_psubset_iff
% 5.06/5.34 thf(fact_4234_atLeastatMost__psubset__iff,axiom,
% 5.06/5.34 ! [A: num,B: num,C: num,D: num] :
% 5.06/5.34 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.06/5.34 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_num @ C @ A )
% 5.06/5.34 & ( ord_less_eq_num @ B @ D )
% 5.06/5.34 & ( ( ord_less_num @ C @ A )
% 5.06/5.34 | ( ord_less_num @ B @ D ) ) ) )
% 5.06/5.34 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_psubset_iff
% 5.06/5.34 thf(fact_4235_atLeastatMost__psubset__iff,axiom,
% 5.06/5.34 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.34 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.06/5.34 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_nat @ C @ A )
% 5.06/5.34 & ( ord_less_eq_nat @ B @ D )
% 5.06/5.34 & ( ( ord_less_nat @ C @ A )
% 5.06/5.34 | ( ord_less_nat @ B @ D ) ) ) )
% 5.06/5.34 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_psubset_iff
% 5.06/5.34 thf(fact_4236_atLeastatMost__psubset__iff,axiom,
% 5.06/5.34 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.34 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.06/5.34 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_int @ C @ A )
% 5.06/5.34 & ( ord_less_eq_int @ B @ D )
% 5.06/5.34 & ( ( ord_less_int @ C @ A )
% 5.06/5.34 | ( ord_less_int @ B @ D ) ) ) )
% 5.06/5.34 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_psubset_iff
% 5.06/5.34 thf(fact_4237_atLeastatMost__psubset__iff,axiom,
% 5.06/5.34 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.34 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.06/5.34 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.06/5.34 | ( ( ord_less_eq_real @ C @ A )
% 5.06/5.34 & ( ord_less_eq_real @ B @ D )
% 5.06/5.34 & ( ( ord_less_real @ C @ A )
% 5.06/5.34 | ( ord_less_real @ B @ D ) ) ) )
% 5.06/5.34 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % atLeastatMost_psubset_iff
% 5.06/5.34 thf(fact_4238_plusinfinity,axiom,
% 5.06/5.34 ! [D: int,P6: int > $o,P: int > $o] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D )
% 5.06/5.34 => ( ! [X3: int,K2: int] :
% 5.06/5.34 ( ( P6 @ X3 )
% 5.06/5.34 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.06/5.34 => ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ Z5 @ X3 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P6 @ X3 ) ) )
% 5.06/5.34 => ( ? [X_12: int] : ( P6 @ X_12 )
% 5.06/5.34 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % plusinfinity
% 5.06/5.34 thf(fact_4239_minusinfinity,axiom,
% 5.06/5.34 ! [D: int,P1: int > $o,P: int > $o] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ D )
% 5.06/5.34 => ( ! [X3: int,K2: int] :
% 5.06/5.34 ( ( P1 @ X3 )
% 5.06/5.34 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.06/5.34 => ( ? [Z5: int] :
% 5.06/5.34 ! [X3: int] :
% 5.06/5.34 ( ( ord_less_int @ X3 @ Z5 )
% 5.06/5.34 => ( ( P @ X3 )
% 5.06/5.34 = ( P1 @ X3 ) ) )
% 5.06/5.34 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.06/5.34 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % minusinfinity
% 5.06/5.34 thf(fact_4240_flip__bit__Suc,axiom,
% 5.06/5.34 ! [N2: nat,A: code_integer] :
% 5.06/5.34 ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 5.06/5.34 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % flip_bit_Suc
% 5.06/5.34 thf(fact_4241_flip__bit__Suc,axiom,
% 5.06/5.34 ! [N2: nat,A: int] :
% 5.06/5.34 ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 5.06/5.34 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % flip_bit_Suc
% 5.06/5.34 thf(fact_4242_flip__bit__Suc,axiom,
% 5.06/5.34 ! [N2: nat,A: nat] :
% 5.06/5.34 ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 5.06/5.34 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % flip_bit_Suc
% 5.06/5.34 thf(fact_4243_Bolzano,axiom,
% 5.06/5.34 ! [A: real,B: real,P: real > real > $o] :
% 5.06/5.34 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.34 => ( ! [A3: real,B2: real,C3: real] :
% 5.06/5.34 ( ( P @ A3 @ B2 )
% 5.06/5.34 => ( ( P @ B2 @ C3 )
% 5.06/5.34 => ( ( ord_less_eq_real @ A3 @ B2 )
% 5.06/5.34 => ( ( ord_less_eq_real @ B2 @ C3 )
% 5.06/5.34 => ( P @ A3 @ C3 ) ) ) ) )
% 5.06/5.34 => ( ! [X3: real] :
% 5.06/5.34 ( ( ord_less_eq_real @ A @ X3 )
% 5.06/5.34 => ( ( ord_less_eq_real @ X3 @ B )
% 5.06/5.34 => ? [D5: real] :
% 5.06/5.34 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.06/5.34 & ! [A3: real,B2: real] :
% 5.06/5.34 ( ( ( ord_less_eq_real @ A3 @ X3 )
% 5.06/5.34 & ( ord_less_eq_real @ X3 @ B2 )
% 5.06/5.34 & ( ord_less_real @ ( minus_minus_real @ B2 @ A3 ) @ D5 ) )
% 5.06/5.34 => ( P @ A3 @ B2 ) ) ) ) )
% 5.06/5.34 => ( P @ A @ B ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Bolzano
% 5.06/5.34 thf(fact_4244_mult__le__cancel__iff2,axiom,
% 5.06/5.34 ! [Z: real,X: real,Y: real] :
% 5.06/5.34 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.06/5.34 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 5.06/5.34 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % mult_le_cancel_iff2
% 5.06/5.34 thf(fact_4245_mult__le__cancel__iff2,axiom,
% 5.06/5.34 ! [Z: rat,X: rat,Y: rat] :
% 5.06/5.34 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.06/5.34 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 5.06/5.34 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % mult_le_cancel_iff2
% 5.06/5.34 thf(fact_4246_mult__le__cancel__iff2,axiom,
% 5.06/5.34 ! [Z: int,X: int,Y: int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.06/5.34 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 5.06/5.34 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % mult_le_cancel_iff2
% 5.06/5.34 thf(fact_4247_mult__le__cancel__iff1,axiom,
% 5.06/5.34 ! [Z: real,X: real,Y: real] :
% 5.06/5.34 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.06/5.34 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.06/5.34 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % mult_le_cancel_iff1
% 5.06/5.34 thf(fact_4248_mult__le__cancel__iff1,axiom,
% 5.06/5.34 ! [Z: rat,X: rat,Y: rat] :
% 5.06/5.34 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.06/5.34 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.06/5.34 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % mult_le_cancel_iff1
% 5.06/5.34 thf(fact_4249_mult__le__cancel__iff1,axiom,
% 5.06/5.34 ! [Z: int,X: int,Y: int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.06/5.34 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.06/5.34 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % mult_le_cancel_iff1
% 5.06/5.34 thf(fact_4250_divides__aux__eq,axiom,
% 5.06/5.34 ! [Q2: nat,R2: nat] :
% 5.06/5.34 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.06/5.34 = ( R2 = zero_zero_nat ) ) ).
% 5.06/5.34
% 5.06/5.34 % divides_aux_eq
% 5.06/5.34 thf(fact_4251_divides__aux__eq,axiom,
% 5.06/5.34 ! [Q2: int,R2: int] :
% 5.06/5.34 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.06/5.34 = ( R2 = zero_zero_int ) ) ).
% 5.06/5.34
% 5.06/5.34 % divides_aux_eq
% 5.06/5.34 thf(fact_4252_flip__bit__nonnegative__int__iff,axiom,
% 5.06/5.34 ! [N2: nat,K: int] :
% 5.06/5.34 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) )
% 5.06/5.34 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.06/5.34
% 5.06/5.34 % flip_bit_nonnegative_int_iff
% 5.06/5.34 thf(fact_4253_flip__bit__negative__int__iff,axiom,
% 5.06/5.34 ! [N2: nat,K: int] :
% 5.06/5.34 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) @ zero_zero_int )
% 5.06/5.34 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.06/5.34
% 5.06/5.34 % flip_bit_negative_int_iff
% 5.06/5.34 thf(fact_4254_mult__less__iff1,axiom,
% 5.06/5.34 ! [Z: real,X: real,Y: real] :
% 5.06/5.34 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.06/5.34 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.06/5.34 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % mult_less_iff1
% 5.06/5.34 thf(fact_4255_mult__less__iff1,axiom,
% 5.06/5.34 ! [Z: rat,X: rat,Y: rat] :
% 5.06/5.34 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.06/5.34 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.06/5.34 = ( ord_less_rat @ X @ Y ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % mult_less_iff1
% 5.06/5.34 thf(fact_4256_mult__less__iff1,axiom,
% 5.06/5.34 ! [Z: int,X: int,Y: int] :
% 5.06/5.34 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.06/5.34 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.06/5.34 = ( ord_less_int @ X @ Y ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % mult_less_iff1
% 5.06/5.34 thf(fact_4257_neg__eucl__rel__int__mult__2,axiom,
% 5.06/5.34 ! [B: int,A: int,Q2: int,R2: int] :
% 5.06/5.34 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.06/5.34 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.06/5.34 => ( 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 ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % neg_eucl_rel_int_mult_2
% 5.06/5.34 thf(fact_4258_product__nth,axiom,
% 5.06/5.34 ! [N2: nat,Xs2: list_num,Ys: list_num] :
% 5.06/5.34 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 5.06/5.34 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys ) @ N2 )
% 5.06/5.34 = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % product_nth
% 5.06/5.34 thf(fact_4259_product__nth,axiom,
% 5.06/5.34 ! [N2: nat,Xs2: list_nat,Ys: list_num] :
% 5.06/5.34 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 5.06/5.34 => ( ( nth_Pr8326237132889035090at_num @ ( product_nat_num @ Xs2 @ Ys ) @ N2 )
% 5.06/5.34 = ( product_Pair_nat_num @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % product_nth
% 5.06/5.34 thf(fact_4260_product__nth,axiom,
% 5.06/5.34 ! [N2: nat,Xs2: list_nat,Ys: list_nat] :
% 5.06/5.34 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.06/5.34 => ( ( nth_Pr7617993195940197384at_nat @ ( product_nat_nat @ Xs2 @ Ys ) @ N2 )
% 5.06/5.34 = ( product_Pair_nat_nat @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % product_nth
% 5.06/5.34 thf(fact_4261_product__nth,axiom,
% 5.06/5.34 ! [N2: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.06/5.34 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.06/5.34 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) @ N2 )
% 5.06/5.34 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % product_nth
% 5.06/5.34 thf(fact_4262_product__nth,axiom,
% 5.06/5.34 ! [N2: nat,Xs2: list_nat,Ys: list_o] :
% 5.06/5.34 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.06/5.34 => ( ( nth_Pr112076138515278198_nat_o @ ( product_nat_o @ Xs2 @ Ys ) @ N2 )
% 5.06/5.34 = ( product_Pair_nat_o @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % product_nth
% 5.06/5.34 thf(fact_4263_product__nth,axiom,
% 5.06/5.34 ! [N2: nat,Xs2: list_Code_integer,Ys: list_o] :
% 5.06/5.34 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.06/5.34 => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs2 @ Ys ) @ N2 )
% 5.06/5.34 = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % product_nth
% 5.06/5.34 thf(fact_4264_product__nth,axiom,
% 5.06/5.34 ! [N2: nat,Xs2: list_nat,Ys: list_int] :
% 5.06/5.34 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.06/5.34 => ( ( nth_Pr3440142176431000676at_int @ ( product_nat_int @ Xs2 @ Ys ) @ N2 )
% 5.06/5.34 = ( product_Pair_nat_int @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % product_nth
% 5.06/5.34 thf(fact_4265_product__nth,axiom,
% 5.06/5.34 ! [N2: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.06/5.34 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.06/5.34 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N2 )
% 5.06/5.34 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % product_nth
% 5.06/5.34 thf(fact_4266_product__nth,axiom,
% 5.06/5.34 ! [N2: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.06/5.34 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.06/5.34 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N2 )
% 5.06/5.34 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % product_nth
% 5.06/5.34 thf(fact_4267_product__nth,axiom,
% 5.06/5.34 ! [N2: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.06/5.34 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.06/5.34 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N2 )
% 5.06/5.34 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % product_nth
% 5.06/5.34 thf(fact_4268_obtain__set__pred,axiom,
% 5.06/5.34 ! [Z: nat,X: nat,A2: set_nat] :
% 5.06/5.34 ( ( ord_less_nat @ Z @ X )
% 5.06/5.34 => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 5.06/5.34 => ( ( finite_finite_nat @ A2 )
% 5.06/5.34 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_1 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % obtain_set_pred
% 5.06/5.34 thf(fact_4269_obtain__set__succ,axiom,
% 5.06/5.34 ! [X: nat,Z: nat,A2: set_nat,B3: set_nat] :
% 5.06/5.34 ( ( ord_less_nat @ X @ Z )
% 5.06/5.34 => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 5.06/5.34 => ( ( finite_finite_nat @ B3 )
% 5.06/5.34 => ( ( A2 = B3 )
% 5.06/5.34 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A2 @ X @ X_1 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % obtain_set_succ
% 5.06/5.34 thf(fact_4270_set__vebt__finite,axiom,
% 5.06/5.34 ! [T: vEBT_VEBT,N2: nat] :
% 5.06/5.34 ( ( vEBT_invar_vebt @ T @ N2 )
% 5.06/5.34 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % set_vebt_finite
% 5.06/5.34 thf(fact_4271_succ__none__empty,axiom,
% 5.06/5.34 ! [Xs2: set_nat,A: nat] :
% 5.06/5.34 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_1 )
% 5.06/5.34 => ( ( finite_finite_nat @ Xs2 )
% 5.06/5.34 => ~ ? [X5: nat] :
% 5.06/5.34 ( ( member_nat @ X5 @ Xs2 )
% 5.06/5.34 & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % succ_none_empty
% 5.06/5.34 thf(fact_4272_pred__none__empty,axiom,
% 5.06/5.34 ! [Xs2: set_nat,A: nat] :
% 5.06/5.34 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_1 )
% 5.06/5.34 => ( ( finite_finite_nat @ Xs2 )
% 5.06/5.34 => ~ ? [X5: nat] :
% 5.06/5.34 ( ( member_nat @ X5 @ Xs2 )
% 5.06/5.34 & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pred_none_empty
% 5.06/5.34 thf(fact_4273_prod_Oinject,axiom,
% 5.06/5.34 ! [X1: code_integer,X22: $o,Y1: code_integer,Y22: $o] :
% 5.06/5.34 ( ( ( produc6677183202524767010eger_o @ X1 @ X22 )
% 5.06/5.34 = ( produc6677183202524767010eger_o @ Y1 @ Y22 ) )
% 5.06/5.34 = ( ( X1 = Y1 )
% 5.06/5.34 & ( X22 = Y22 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % prod.inject
% 5.06/5.34 thf(fact_4274_prod_Oinject,axiom,
% 5.06/5.34 ! [X1: num,X22: num,Y1: num,Y22: num] :
% 5.06/5.34 ( ( ( product_Pair_num_num @ X1 @ X22 )
% 5.06/5.34 = ( product_Pair_num_num @ Y1 @ Y22 ) )
% 5.06/5.34 = ( ( X1 = Y1 )
% 5.06/5.34 & ( X22 = Y22 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % prod.inject
% 5.06/5.34 thf(fact_4275_prod_Oinject,axiom,
% 5.06/5.34 ! [X1: nat,X22: num,Y1: nat,Y22: num] :
% 5.06/5.34 ( ( ( product_Pair_nat_num @ X1 @ X22 )
% 5.06/5.34 = ( product_Pair_nat_num @ Y1 @ Y22 ) )
% 5.06/5.34 = ( ( X1 = Y1 )
% 5.06/5.34 & ( X22 = Y22 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % prod.inject
% 5.06/5.34 thf(fact_4276_prod_Oinject,axiom,
% 5.06/5.34 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 5.06/5.34 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 5.06/5.34 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 5.06/5.34 = ( ( X1 = Y1 )
% 5.06/5.34 & ( X22 = Y22 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % prod.inject
% 5.06/5.34 thf(fact_4277_prod_Oinject,axiom,
% 5.06/5.34 ! [X1: int,X22: int,Y1: int,Y22: int] :
% 5.06/5.34 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 5.06/5.34 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 5.06/5.34 = ( ( X1 = Y1 )
% 5.06/5.34 & ( X22 = Y22 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % prod.inject
% 5.06/5.34 thf(fact_4278_old_Oprod_Oinject,axiom,
% 5.06/5.34 ! [A: code_integer,B: $o,A6: code_integer,B6: $o] :
% 5.06/5.34 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 5.06/5.34 = ( produc6677183202524767010eger_o @ A6 @ B6 ) )
% 5.06/5.34 = ( ( A = A6 )
% 5.06/5.34 & ( B = B6 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % old.prod.inject
% 5.06/5.34 thf(fact_4279_old_Oprod_Oinject,axiom,
% 5.06/5.34 ! [A: num,B: num,A6: num,B6: num] :
% 5.06/5.34 ( ( ( product_Pair_num_num @ A @ B )
% 5.06/5.34 = ( product_Pair_num_num @ A6 @ B6 ) )
% 5.06/5.34 = ( ( A = A6 )
% 5.06/5.34 & ( B = B6 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % old.prod.inject
% 5.06/5.34 thf(fact_4280_old_Oprod_Oinject,axiom,
% 5.06/5.34 ! [A: nat,B: num,A6: nat,B6: num] :
% 5.06/5.34 ( ( ( product_Pair_nat_num @ A @ B )
% 5.06/5.34 = ( product_Pair_nat_num @ A6 @ B6 ) )
% 5.06/5.34 = ( ( A = A6 )
% 5.06/5.34 & ( B = B6 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % old.prod.inject
% 5.06/5.34 thf(fact_4281_old_Oprod_Oinject,axiom,
% 5.06/5.34 ! [A: nat,B: nat,A6: nat,B6: nat] :
% 5.06/5.34 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.06/5.34 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 5.06/5.34 = ( ( A = A6 )
% 5.06/5.34 & ( B = B6 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % old.prod.inject
% 5.06/5.34 thf(fact_4282_old_Oprod_Oinject,axiom,
% 5.06/5.34 ! [A: int,B: int,A6: int,B6: int] :
% 5.06/5.34 ( ( ( product_Pair_int_int @ A @ B )
% 5.06/5.34 = ( product_Pair_int_int @ A6 @ B6 ) )
% 5.06/5.34 = ( ( A = A6 )
% 5.06/5.34 & ( B = B6 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % old.prod.inject
% 5.06/5.34 thf(fact_4283_List_Ofinite__set,axiom,
% 5.06/5.34 ! [Xs2: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % List.finite_set
% 5.06/5.34 thf(fact_4284_List_Ofinite__set,axiom,
% 5.06/5.34 ! [Xs2: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % List.finite_set
% 5.06/5.34 thf(fact_4285_List_Ofinite__set,axiom,
% 5.06/5.34 ! [Xs2: list_int] : ( finite_finite_int @ ( set_int2 @ Xs2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % List.finite_set
% 5.06/5.34 thf(fact_4286_List_Ofinite__set,axiom,
% 5.06/5.34 ! [Xs2: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % List.finite_set
% 5.06/5.34 thf(fact_4287_infinite__Icc__iff,axiom,
% 5.06/5.34 ! [A: rat,B: rat] :
% 5.06/5.34 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 5.06/5.34 = ( ord_less_rat @ A @ B ) ) ).
% 5.06/5.34
% 5.06/5.34 % infinite_Icc_iff
% 5.06/5.34 thf(fact_4288_infinite__Icc__iff,axiom,
% 5.06/5.34 ! [A: real,B: real] :
% 5.06/5.34 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 5.06/5.34 = ( ord_less_real @ A @ B ) ) ).
% 5.06/5.34
% 5.06/5.34 % infinite_Icc_iff
% 5.06/5.34 thf(fact_4289_length__product,axiom,
% 5.06/5.34 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.06/5.34 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 5.06/5.34 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % length_product
% 5.06/5.34 thf(fact_4290_length__product,axiom,
% 5.06/5.34 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.06/5.34 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 5.06/5.34 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % length_product
% 5.06/5.34 thf(fact_4291_length__product,axiom,
% 5.06/5.34 ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.06/5.34 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 5.06/5.34 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % length_product
% 5.06/5.34 thf(fact_4292_length__product,axiom,
% 5.06/5.34 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.06/5.34 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 5.06/5.34 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % length_product
% 5.06/5.34 thf(fact_4293_length__product,axiom,
% 5.06/5.34 ! [Xs2: list_o,Ys: list_o] :
% 5.06/5.34 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 5.06/5.34 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % length_product
% 5.06/5.34 thf(fact_4294_length__product,axiom,
% 5.06/5.34 ! [Xs2: list_o,Ys: list_int] :
% 5.06/5.34 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 5.06/5.34 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % length_product
% 5.06/5.34 thf(fact_4295_length__product,axiom,
% 5.06/5.34 ! [Xs2: list_int,Ys: list_VEBT_VEBT] :
% 5.06/5.34 ( ( size_s6639371672096860321T_VEBT @ ( produc662631939642741121T_VEBT @ Xs2 @ Ys ) )
% 5.06/5.34 = ( times_times_nat @ ( size_size_list_int @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % length_product
% 5.06/5.34 thf(fact_4296_length__product,axiom,
% 5.06/5.34 ! [Xs2: list_int,Ys: list_o] :
% 5.06/5.34 ( ( size_s4246224855604898693_int_o @ ( product_int_o @ Xs2 @ Ys ) )
% 5.06/5.34 = ( times_times_nat @ ( size_size_list_int @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % length_product
% 5.06/5.34 thf(fact_4297_length__product,axiom,
% 5.06/5.34 ! [Xs2: list_int,Ys: list_int] :
% 5.06/5.34 ( ( size_s5157815400016825771nt_int @ ( product_int_int @ Xs2 @ Ys ) )
% 5.06/5.34 = ( times_times_nat @ ( size_size_list_int @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % length_product
% 5.06/5.34 thf(fact_4298_finite__nat__set__iff__bounded,axiom,
% 5.06/5.34 ( finite_finite_nat
% 5.06/5.34 = ( ^ [N6: set_nat] :
% 5.06/5.34 ? [M6: nat] :
% 5.06/5.34 ! [X2: nat] :
% 5.06/5.34 ( ( member_nat @ X2 @ N6 )
% 5.06/5.34 => ( ord_less_nat @ X2 @ M6 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_nat_set_iff_bounded
% 5.06/5.34 thf(fact_4299_bounded__nat__set__is__finite,axiom,
% 5.06/5.34 ! [N4: set_nat,N2: nat] :
% 5.06/5.34 ( ! [X3: nat] :
% 5.06/5.34 ( ( member_nat @ X3 @ N4 )
% 5.06/5.34 => ( ord_less_nat @ X3 @ N2 ) )
% 5.06/5.34 => ( finite_finite_nat @ N4 ) ) ).
% 5.06/5.34
% 5.06/5.34 % bounded_nat_set_is_finite
% 5.06/5.34 thf(fact_4300_finite__nat__set__iff__bounded__le,axiom,
% 5.06/5.34 ( finite_finite_nat
% 5.06/5.34 = ( ^ [N6: set_nat] :
% 5.06/5.34 ? [M6: nat] :
% 5.06/5.34 ! [X2: nat] :
% 5.06/5.34 ( ( member_nat @ X2 @ N6 )
% 5.06/5.34 => ( ord_less_eq_nat @ X2 @ M6 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_nat_set_iff_bounded_le
% 5.06/5.34 thf(fact_4301_finite__list,axiom,
% 5.06/5.34 ! [A2: set_VEBT_VEBT] :
% 5.06/5.34 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.06/5.34 => ? [Xs3: list_VEBT_VEBT] :
% 5.06/5.34 ( ( set_VEBT_VEBT2 @ Xs3 )
% 5.06/5.34 = A2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_list
% 5.06/5.34 thf(fact_4302_finite__list,axiom,
% 5.06/5.34 ! [A2: set_nat] :
% 5.06/5.34 ( ( finite_finite_nat @ A2 )
% 5.06/5.34 => ? [Xs3: list_nat] :
% 5.06/5.34 ( ( set_nat2 @ Xs3 )
% 5.06/5.34 = A2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_list
% 5.06/5.34 thf(fact_4303_finite__list,axiom,
% 5.06/5.34 ! [A2: set_int] :
% 5.06/5.34 ( ( finite_finite_int @ A2 )
% 5.06/5.34 => ? [Xs3: list_int] :
% 5.06/5.34 ( ( set_int2 @ Xs3 )
% 5.06/5.34 = A2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_list
% 5.06/5.34 thf(fact_4304_finite__list,axiom,
% 5.06/5.34 ! [A2: set_complex] :
% 5.06/5.34 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.34 => ? [Xs3: list_complex] :
% 5.06/5.34 ( ( set_complex2 @ Xs3 )
% 5.06/5.34 = A2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_list
% 5.06/5.34 thf(fact_4305_finite__M__bounded__by__nat,axiom,
% 5.06/5.34 ! [P: nat > $o,I2: nat] :
% 5.06/5.34 ( finite_finite_nat
% 5.06/5.34 @ ( collect_nat
% 5.06/5.34 @ ^ [K3: nat] :
% 5.06/5.34 ( ( P @ K3 )
% 5.06/5.34 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_M_bounded_by_nat
% 5.06/5.34 thf(fact_4306_finite__less__ub,axiom,
% 5.06/5.34 ! [F: nat > nat,U: nat] :
% 5.06/5.34 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.06/5.34 => ( finite_finite_nat
% 5.06/5.34 @ ( collect_nat
% 5.06/5.34 @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_less_ub
% 5.06/5.34 thf(fact_4307_finite__lists__length__eq,axiom,
% 5.06/5.34 ! [A2: set_nat,N2: nat] :
% 5.06/5.34 ( ( finite_finite_nat @ A2 )
% 5.06/5.34 => ( finite8100373058378681591st_nat
% 5.06/5.34 @ ( collect_list_nat
% 5.06/5.34 @ ^ [Xs: list_nat] :
% 5.06/5.34 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.06/5.34 & ( ( size_size_list_nat @ Xs )
% 5.06/5.34 = N2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_lists_length_eq
% 5.06/5.34 thf(fact_4308_finite__lists__length__eq,axiom,
% 5.06/5.34 ! [A2: set_complex,N2: nat] :
% 5.06/5.34 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.34 => ( finite8712137658972009173omplex
% 5.06/5.34 @ ( collect_list_complex
% 5.06/5.34 @ ^ [Xs: list_complex] :
% 5.06/5.34 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.06/5.34 & ( ( size_s3451745648224563538omplex @ Xs )
% 5.06/5.34 = N2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_lists_length_eq
% 5.06/5.34 thf(fact_4309_finite__lists__length__eq,axiom,
% 5.06/5.34 ! [A2: set_VEBT_VEBT,N2: nat] :
% 5.06/5.34 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.06/5.34 => ( finite3004134309566078307T_VEBT
% 5.06/5.34 @ ( collec5608196760682091941T_VEBT
% 5.06/5.34 @ ^ [Xs: list_VEBT_VEBT] :
% 5.06/5.34 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.06/5.34 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.06/5.34 = N2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_lists_length_eq
% 5.06/5.34 thf(fact_4310_finite__lists__length__eq,axiom,
% 5.06/5.34 ! [A2: set_o,N2: nat] :
% 5.06/5.34 ( ( finite_finite_o @ A2 )
% 5.06/5.34 => ( finite_finite_list_o
% 5.06/5.34 @ ( collect_list_o
% 5.06/5.34 @ ^ [Xs: list_o] :
% 5.06/5.34 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.06/5.34 & ( ( size_size_list_o @ Xs )
% 5.06/5.34 = N2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_lists_length_eq
% 5.06/5.34 thf(fact_4311_finite__lists__length__eq,axiom,
% 5.06/5.34 ! [A2: set_int,N2: nat] :
% 5.06/5.34 ( ( finite_finite_int @ A2 )
% 5.06/5.34 => ( finite3922522038869484883st_int
% 5.06/5.34 @ ( collect_list_int
% 5.06/5.34 @ ^ [Xs: list_int] :
% 5.06/5.34 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.06/5.34 & ( ( size_size_list_int @ Xs )
% 5.06/5.34 = N2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_lists_length_eq
% 5.06/5.34 thf(fact_4312_infinite__Icc,axiom,
% 5.06/5.34 ! [A: rat,B: rat] :
% 5.06/5.34 ( ( ord_less_rat @ A @ B )
% 5.06/5.34 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % infinite_Icc
% 5.06/5.34 thf(fact_4313_infinite__Icc,axiom,
% 5.06/5.34 ! [A: real,B: real] :
% 5.06/5.34 ( ( ord_less_real @ A @ B )
% 5.06/5.34 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % infinite_Icc
% 5.06/5.34 thf(fact_4314_finite__lists__length__le,axiom,
% 5.06/5.34 ! [A2: set_nat,N2: nat] :
% 5.06/5.34 ( ( finite_finite_nat @ A2 )
% 5.06/5.34 => ( finite8100373058378681591st_nat
% 5.06/5.34 @ ( collect_list_nat
% 5.06/5.34 @ ^ [Xs: list_nat] :
% 5.06/5.34 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.06/5.34 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_lists_length_le
% 5.06/5.34 thf(fact_4315_finite__lists__length__le,axiom,
% 5.06/5.34 ! [A2: set_complex,N2: nat] :
% 5.06/5.34 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.34 => ( finite8712137658972009173omplex
% 5.06/5.34 @ ( collect_list_complex
% 5.06/5.34 @ ^ [Xs: list_complex] :
% 5.06/5.34 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.06/5.34 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_lists_length_le
% 5.06/5.34 thf(fact_4316_finite__lists__length__le,axiom,
% 5.06/5.34 ! [A2: set_VEBT_VEBT,N2: nat] :
% 5.06/5.34 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.06/5.34 => ( finite3004134309566078307T_VEBT
% 5.06/5.34 @ ( collec5608196760682091941T_VEBT
% 5.06/5.34 @ ^ [Xs: list_VEBT_VEBT] :
% 5.06/5.34 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.06/5.34 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_lists_length_le
% 5.06/5.34 thf(fact_4317_finite__lists__length__le,axiom,
% 5.06/5.34 ! [A2: set_o,N2: nat] :
% 5.06/5.34 ( ( finite_finite_o @ A2 )
% 5.06/5.34 => ( finite_finite_list_o
% 5.06/5.34 @ ( collect_list_o
% 5.06/5.34 @ ^ [Xs: list_o] :
% 5.06/5.34 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 5.06/5.34 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_lists_length_le
% 5.06/5.34 thf(fact_4318_finite__lists__length__le,axiom,
% 5.06/5.34 ! [A2: set_int,N2: nat] :
% 5.06/5.34 ( ( finite_finite_int @ A2 )
% 5.06/5.34 => ( finite3922522038869484883st_int
% 5.06/5.34 @ ( collect_list_int
% 5.06/5.34 @ ^ [Xs: list_int] :
% 5.06/5.34 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.06/5.34 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_lists_length_le
% 5.06/5.34 thf(fact_4319_eucl__rel__int__dividesI,axiom,
% 5.06/5.34 ! [L2: int,K: int,Q2: int] :
% 5.06/5.34 ( ( L2 != zero_zero_int )
% 5.06/5.34 => ( ( K
% 5.06/5.34 = ( times_times_int @ Q2 @ L2 ) )
% 5.06/5.34 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % eucl_rel_int_dividesI
% 5.06/5.34 thf(fact_4320_old_Oprod_Oexhaust,axiom,
% 5.06/5.34 ! [Y: produc6271795597528267376eger_o] :
% 5.06/5.34 ~ ! [A3: code_integer,B2: $o] :
% 5.06/5.34 ( Y
% 5.06/5.34 != ( produc6677183202524767010eger_o @ A3 @ B2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % old.prod.exhaust
% 5.06/5.34 thf(fact_4321_old_Oprod_Oexhaust,axiom,
% 5.06/5.34 ! [Y: product_prod_num_num] :
% 5.06/5.34 ~ ! [A3: num,B2: num] :
% 5.06/5.34 ( Y
% 5.06/5.34 != ( product_Pair_num_num @ A3 @ B2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % old.prod.exhaust
% 5.06/5.34 thf(fact_4322_old_Oprod_Oexhaust,axiom,
% 5.06/5.34 ! [Y: product_prod_nat_num] :
% 5.06/5.34 ~ ! [A3: nat,B2: num] :
% 5.06/5.34 ( Y
% 5.06/5.34 != ( product_Pair_nat_num @ A3 @ B2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % old.prod.exhaust
% 5.06/5.34 thf(fact_4323_old_Oprod_Oexhaust,axiom,
% 5.06/5.34 ! [Y: product_prod_nat_nat] :
% 5.06/5.34 ~ ! [A3: nat,B2: nat] :
% 5.06/5.34 ( Y
% 5.06/5.34 != ( product_Pair_nat_nat @ A3 @ B2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % old.prod.exhaust
% 5.06/5.34 thf(fact_4324_old_Oprod_Oexhaust,axiom,
% 5.06/5.34 ! [Y: product_prod_int_int] :
% 5.06/5.34 ~ ! [A3: int,B2: int] :
% 5.06/5.34 ( Y
% 5.06/5.34 != ( product_Pair_int_int @ A3 @ B2 ) ) ).
% 5.06/5.34
% 5.06/5.34 % old.prod.exhaust
% 5.06/5.34 thf(fact_4325_surj__pair,axiom,
% 5.06/5.34 ! [P4: produc6271795597528267376eger_o] :
% 5.06/5.34 ? [X3: code_integer,Y5: $o] :
% 5.06/5.34 ( P4
% 5.06/5.34 = ( produc6677183202524767010eger_o @ X3 @ Y5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % surj_pair
% 5.06/5.34 thf(fact_4326_surj__pair,axiom,
% 5.06/5.34 ! [P4: product_prod_num_num] :
% 5.06/5.34 ? [X3: num,Y5: num] :
% 5.06/5.34 ( P4
% 5.06/5.34 = ( product_Pair_num_num @ X3 @ Y5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % surj_pair
% 5.06/5.34 thf(fact_4327_surj__pair,axiom,
% 5.06/5.34 ! [P4: product_prod_nat_num] :
% 5.06/5.34 ? [X3: nat,Y5: num] :
% 5.06/5.34 ( P4
% 5.06/5.34 = ( product_Pair_nat_num @ X3 @ Y5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % surj_pair
% 5.06/5.34 thf(fact_4328_surj__pair,axiom,
% 5.06/5.34 ! [P4: product_prod_nat_nat] :
% 5.06/5.34 ? [X3: nat,Y5: nat] :
% 5.06/5.34 ( P4
% 5.06/5.34 = ( product_Pair_nat_nat @ X3 @ Y5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % surj_pair
% 5.06/5.34 thf(fact_4329_surj__pair,axiom,
% 5.06/5.34 ! [P4: product_prod_int_int] :
% 5.06/5.34 ? [X3: int,Y5: int] :
% 5.06/5.34 ( P4
% 5.06/5.34 = ( product_Pair_int_int @ X3 @ Y5 ) ) ).
% 5.06/5.34
% 5.06/5.34 % surj_pair
% 5.06/5.34 thf(fact_4330_prod__cases,axiom,
% 5.06/5.34 ! [P: produc6271795597528267376eger_o > $o,P4: produc6271795597528267376eger_o] :
% 5.06/5.34 ( ! [A3: code_integer,B2: $o] : ( P @ ( produc6677183202524767010eger_o @ A3 @ B2 ) )
% 5.06/5.34 => ( P @ P4 ) ) ).
% 5.06/5.34
% 5.06/5.34 % prod_cases
% 5.06/5.34 thf(fact_4331_prod__cases,axiom,
% 5.06/5.34 ! [P: product_prod_num_num > $o,P4: product_prod_num_num] :
% 5.06/5.34 ( ! [A3: num,B2: num] : ( P @ ( product_Pair_num_num @ A3 @ B2 ) )
% 5.06/5.34 => ( P @ P4 ) ) ).
% 5.06/5.34
% 5.06/5.34 % prod_cases
% 5.06/5.34 thf(fact_4332_prod__cases,axiom,
% 5.06/5.34 ! [P: product_prod_nat_num > $o,P4: product_prod_nat_num] :
% 5.06/5.34 ( ! [A3: nat,B2: num] : ( P @ ( product_Pair_nat_num @ A3 @ B2 ) )
% 5.06/5.34 => ( P @ P4 ) ) ).
% 5.06/5.34
% 5.06/5.34 % prod_cases
% 5.06/5.34 thf(fact_4333_prod__cases,axiom,
% 5.06/5.34 ! [P: product_prod_nat_nat > $o,P4: product_prod_nat_nat] :
% 5.06/5.34 ( ! [A3: nat,B2: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B2 ) )
% 5.06/5.34 => ( P @ P4 ) ) ).
% 5.06/5.34
% 5.06/5.34 % prod_cases
% 5.06/5.34 thf(fact_4334_prod__cases,axiom,
% 5.06/5.34 ! [P: product_prod_int_int > $o,P4: product_prod_int_int] :
% 5.06/5.34 ( ! [A3: int,B2: int] : ( P @ ( product_Pair_int_int @ A3 @ B2 ) )
% 5.06/5.34 => ( P @ P4 ) ) ).
% 5.06/5.34
% 5.06/5.34 % prod_cases
% 5.06/5.34 thf(fact_4335_Pair__inject,axiom,
% 5.06/5.34 ! [A: code_integer,B: $o,A6: code_integer,B6: $o] :
% 5.06/5.34 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 5.06/5.34 = ( produc6677183202524767010eger_o @ A6 @ B6 ) )
% 5.06/5.34 => ~ ( ( A = A6 )
% 5.06/5.34 => ( B = ~ B6 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Pair_inject
% 5.06/5.34 thf(fact_4336_Pair__inject,axiom,
% 5.06/5.34 ! [A: num,B: num,A6: num,B6: num] :
% 5.06/5.34 ( ( ( product_Pair_num_num @ A @ B )
% 5.06/5.34 = ( product_Pair_num_num @ A6 @ B6 ) )
% 5.06/5.34 => ~ ( ( A = A6 )
% 5.06/5.34 => ( B != B6 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Pair_inject
% 5.06/5.34 thf(fact_4337_Pair__inject,axiom,
% 5.06/5.34 ! [A: nat,B: num,A6: nat,B6: num] :
% 5.06/5.34 ( ( ( product_Pair_nat_num @ A @ B )
% 5.06/5.34 = ( product_Pair_nat_num @ A6 @ B6 ) )
% 5.06/5.34 => ~ ( ( A = A6 )
% 5.06/5.34 => ( B != B6 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Pair_inject
% 5.06/5.34 thf(fact_4338_Pair__inject,axiom,
% 5.06/5.34 ! [A: nat,B: nat,A6: nat,B6: nat] :
% 5.06/5.34 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.06/5.34 = ( product_Pair_nat_nat @ A6 @ B6 ) )
% 5.06/5.34 => ~ ( ( A = A6 )
% 5.06/5.34 => ( B != B6 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Pair_inject
% 5.06/5.34 thf(fact_4339_Pair__inject,axiom,
% 5.06/5.34 ! [A: int,B: int,A6: int,B6: int] :
% 5.06/5.34 ( ( ( product_Pair_int_int @ A @ B )
% 5.06/5.34 = ( product_Pair_int_int @ A6 @ B6 ) )
% 5.06/5.34 => ~ ( ( A = A6 )
% 5.06/5.34 => ( B != B6 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % Pair_inject
% 5.06/5.34 thf(fact_4340_subset__eq__atLeast0__atMost__finite,axiom,
% 5.06/5.34 ! [N4: set_nat,N2: nat] :
% 5.06/5.34 ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.34 => ( finite_finite_nat @ N4 ) ) ).
% 5.06/5.34
% 5.06/5.34 % subset_eq_atLeast0_atMost_finite
% 5.06/5.34 thf(fact_4341_eucl__rel__int__iff,axiom,
% 5.06/5.34 ! [K: int,L2: int,Q2: int,R2: int] :
% 5.06/5.34 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.06/5.34 = ( ( K
% 5.06/5.34 = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R2 ) )
% 5.06/5.34 & ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.06/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.06/5.34 & ( ord_less_int @ R2 @ L2 ) ) )
% 5.06/5.34 & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 5.06/5.34 => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.06/5.34 => ( ( ord_less_int @ L2 @ R2 )
% 5.06/5.34 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 5.06/5.34 & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 5.06/5.34 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % eucl_rel_int_iff
% 5.06/5.34 thf(fact_4342_pos__eucl__rel__int__mult__2,axiom,
% 5.06/5.34 ! [B: int,A: int,Q2: int,R2: int] :
% 5.06/5.34 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.34 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.06/5.34 => ( 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 ) ) @ R2 ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pos_eucl_rel_int_mult_2
% 5.06/5.34 thf(fact_4343_finite__Collect__le__nat,axiom,
% 5.06/5.34 ! [K: nat] :
% 5.06/5.34 ( finite_finite_nat
% 5.06/5.34 @ ( collect_nat
% 5.06/5.34 @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_le_nat
% 5.06/5.34 thf(fact_4344_finite__Collect__less__nat,axiom,
% 5.06/5.34 ! [K: nat] :
% 5.06/5.34 ( finite_finite_nat
% 5.06/5.34 @ ( collect_nat
% 5.06/5.34 @ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_less_nat
% 5.06/5.34 thf(fact_4345_finite__Collect__subsets,axiom,
% 5.06/5.34 ! [A2: set_nat] :
% 5.06/5.34 ( ( finite_finite_nat @ A2 )
% 5.06/5.34 => ( finite1152437895449049373et_nat
% 5.06/5.34 @ ( collect_set_nat
% 5.06/5.34 @ ^ [B5: set_nat] : ( ord_less_eq_set_nat @ B5 @ A2 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_subsets
% 5.06/5.34 thf(fact_4346_finite__Collect__subsets,axiom,
% 5.06/5.34 ! [A2: set_complex] :
% 5.06/5.34 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.34 => ( finite6551019134538273531omplex
% 5.06/5.34 @ ( collect_set_complex
% 5.06/5.34 @ ^ [B5: set_complex] : ( ord_le211207098394363844omplex @ B5 @ A2 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_subsets
% 5.06/5.34 thf(fact_4347_finite__Collect__subsets,axiom,
% 5.06/5.34 ! [A2: set_int] :
% 5.06/5.34 ( ( finite_finite_int @ A2 )
% 5.06/5.34 => ( finite6197958912794628473et_int
% 5.06/5.34 @ ( collect_set_int
% 5.06/5.34 @ ^ [B5: set_int] : ( ord_less_eq_set_int @ B5 @ A2 ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_subsets
% 5.06/5.34 thf(fact_4348_finite__roots__unity,axiom,
% 5.06/5.34 ! [N2: nat] :
% 5.06/5.34 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.34 => ( finite_finite_real
% 5.06/5.34 @ ( collect_real
% 5.06/5.34 @ ^ [Z2: real] :
% 5.06/5.34 ( ( power_power_real @ Z2 @ N2 )
% 5.06/5.34 = one_one_real ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_roots_unity
% 5.06/5.34 thf(fact_4349_finite__roots__unity,axiom,
% 5.06/5.34 ! [N2: nat] :
% 5.06/5.34 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.34 => ( finite3207457112153483333omplex
% 5.06/5.34 @ ( collect_complex
% 5.06/5.34 @ ^ [Z2: complex] :
% 5.06/5.34 ( ( power_power_complex @ Z2 @ N2 )
% 5.06/5.34 = one_one_complex ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_roots_unity
% 5.06/5.34 thf(fact_4350_finite__Diff2,axiom,
% 5.06/5.34 ! [B3: set_int,A2: set_int] :
% 5.06/5.34 ( ( finite_finite_int @ B3 )
% 5.06/5.34 => ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.06/5.34 = ( finite_finite_int @ A2 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Diff2
% 5.06/5.34 thf(fact_4351_finite__Diff2,axiom,
% 5.06/5.34 ! [B3: set_complex,A2: set_complex] :
% 5.06/5.34 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.34 => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.06/5.34 = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Diff2
% 5.06/5.34 thf(fact_4352_finite__Diff2,axiom,
% 5.06/5.34 ! [B3: set_nat,A2: set_nat] :
% 5.06/5.34 ( ( finite_finite_nat @ B3 )
% 5.06/5.34 => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.06/5.34 = ( finite_finite_nat @ A2 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Diff2
% 5.06/5.34 thf(fact_4353_finite__Diff,axiom,
% 5.06/5.34 ! [A2: set_int,B3: set_int] :
% 5.06/5.34 ( ( finite_finite_int @ A2 )
% 5.06/5.34 => ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Diff
% 5.06/5.34 thf(fact_4354_finite__Diff,axiom,
% 5.06/5.34 ! [A2: set_complex,B3: set_complex] :
% 5.06/5.34 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.34 => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Diff
% 5.06/5.34 thf(fact_4355_finite__Diff,axiom,
% 5.06/5.34 ! [A2: set_nat,B3: set_nat] :
% 5.06/5.34 ( ( finite_finite_nat @ A2 )
% 5.06/5.34 => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Diff
% 5.06/5.34 thf(fact_4356_finite__Collect__disjI,axiom,
% 5.06/5.34 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.06/5.34 ( ( finite2998713641127702882nt_int
% 5.06/5.34 @ ( collec213857154873943460nt_int
% 5.06/5.34 @ ^ [X2: product_prod_int_int] :
% 5.06/5.34 ( ( P @ X2 )
% 5.06/5.34 | ( Q @ X2 ) ) ) )
% 5.06/5.34 = ( ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.06/5.34 & ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ Q ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_disjI
% 5.06/5.34 thf(fact_4357_finite__Collect__disjI,axiom,
% 5.06/5.34 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.06/5.34 ( ( finite1152437895449049373et_nat
% 5.06/5.34 @ ( collect_set_nat
% 5.06/5.34 @ ^ [X2: set_nat] :
% 5.06/5.34 ( ( P @ X2 )
% 5.06/5.34 | ( Q @ X2 ) ) ) )
% 5.06/5.34 = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.06/5.34 & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_disjI
% 5.06/5.34 thf(fact_4358_finite__Collect__disjI,axiom,
% 5.06/5.34 ! [P: nat > $o,Q: nat > $o] :
% 5.06/5.34 ( ( finite_finite_nat
% 5.06/5.34 @ ( collect_nat
% 5.06/5.34 @ ^ [X2: nat] :
% 5.06/5.34 ( ( P @ X2 )
% 5.06/5.34 | ( Q @ X2 ) ) ) )
% 5.06/5.34 = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.34 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_disjI
% 5.06/5.34 thf(fact_4359_finite__Collect__disjI,axiom,
% 5.06/5.34 ! [P: int > $o,Q: int > $o] :
% 5.06/5.34 ( ( finite_finite_int
% 5.06/5.34 @ ( collect_int
% 5.06/5.34 @ ^ [X2: int] :
% 5.06/5.34 ( ( P @ X2 )
% 5.06/5.34 | ( Q @ X2 ) ) ) )
% 5.06/5.34 = ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.06/5.34 & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_disjI
% 5.06/5.34 thf(fact_4360_finite__Collect__disjI,axiom,
% 5.06/5.34 ! [P: complex > $o,Q: complex > $o] :
% 5.06/5.34 ( ( finite3207457112153483333omplex
% 5.06/5.34 @ ( collect_complex
% 5.06/5.34 @ ^ [X2: complex] :
% 5.06/5.34 ( ( P @ X2 )
% 5.06/5.34 | ( Q @ X2 ) ) ) )
% 5.06/5.34 = ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.06/5.34 & ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_disjI
% 5.06/5.34 thf(fact_4361_finite__Collect__conjI,axiom,
% 5.06/5.34 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.06/5.34 ( ( ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.06/5.34 | ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ Q ) ) )
% 5.06/5.34 => ( finite2998713641127702882nt_int
% 5.06/5.34 @ ( collec213857154873943460nt_int
% 5.06/5.34 @ ^ [X2: product_prod_int_int] :
% 5.06/5.34 ( ( P @ X2 )
% 5.06/5.34 & ( Q @ X2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_conjI
% 5.06/5.34 thf(fact_4362_finite__Collect__conjI,axiom,
% 5.06/5.34 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.06/5.34 ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.06/5.34 | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) )
% 5.06/5.34 => ( finite1152437895449049373et_nat
% 5.06/5.34 @ ( collect_set_nat
% 5.06/5.34 @ ^ [X2: set_nat] :
% 5.06/5.34 ( ( P @ X2 )
% 5.06/5.34 & ( Q @ X2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_conjI
% 5.06/5.34 thf(fact_4363_finite__Collect__conjI,axiom,
% 5.06/5.34 ! [P: nat > $o,Q: nat > $o] :
% 5.06/5.34 ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.34 | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 5.06/5.34 => ( finite_finite_nat
% 5.06/5.34 @ ( collect_nat
% 5.06/5.34 @ ^ [X2: nat] :
% 5.06/5.34 ( ( P @ X2 )
% 5.06/5.34 & ( Q @ X2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_conjI
% 5.06/5.34 thf(fact_4364_finite__Collect__conjI,axiom,
% 5.06/5.34 ! [P: int > $o,Q: int > $o] :
% 5.06/5.34 ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.06/5.34 | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 5.06/5.34 => ( finite_finite_int
% 5.06/5.34 @ ( collect_int
% 5.06/5.34 @ ^ [X2: int] :
% 5.06/5.34 ( ( P @ X2 )
% 5.06/5.34 & ( Q @ X2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_conjI
% 5.06/5.34 thf(fact_4365_finite__Collect__conjI,axiom,
% 5.06/5.34 ! [P: complex > $o,Q: complex > $o] :
% 5.06/5.34 ( ( ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.06/5.34 | ( finite3207457112153483333omplex @ ( collect_complex @ Q ) ) )
% 5.06/5.34 => ( finite3207457112153483333omplex
% 5.06/5.34 @ ( collect_complex
% 5.06/5.34 @ ^ [X2: complex] :
% 5.06/5.34 ( ( P @ X2 )
% 5.06/5.34 & ( Q @ X2 ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_Collect_conjI
% 5.06/5.34 thf(fact_4366_finite__interval__int1,axiom,
% 5.06/5.34 ! [A: int,B: int] :
% 5.06/5.34 ( finite_finite_int
% 5.06/5.34 @ ( collect_int
% 5.06/5.34 @ ^ [I5: int] :
% 5.06/5.34 ( ( ord_less_eq_int @ A @ I5 )
% 5.06/5.34 & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_interval_int1
% 5.06/5.34 thf(fact_4367_finite__interval__int4,axiom,
% 5.06/5.34 ! [A: int,B: int] :
% 5.06/5.34 ( finite_finite_int
% 5.06/5.34 @ ( collect_int
% 5.06/5.34 @ ^ [I5: int] :
% 5.06/5.34 ( ( ord_less_int @ A @ I5 )
% 5.06/5.34 & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_interval_int4
% 5.06/5.34 thf(fact_4368_finite__interval__int2,axiom,
% 5.06/5.34 ! [A: int,B: int] :
% 5.06/5.34 ( finite_finite_int
% 5.06/5.34 @ ( collect_int
% 5.06/5.34 @ ^ [I5: int] :
% 5.06/5.34 ( ( ord_less_eq_int @ A @ I5 )
% 5.06/5.34 & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_interval_int2
% 5.06/5.34 thf(fact_4369_finite__interval__int3,axiom,
% 5.06/5.34 ! [A: int,B: int] :
% 5.06/5.34 ( finite_finite_int
% 5.06/5.34 @ ( collect_int
% 5.06/5.34 @ ^ [I5: int] :
% 5.06/5.34 ( ( ord_less_int @ A @ I5 )
% 5.06/5.34 & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_interval_int3
% 5.06/5.34 thf(fact_4370_finite__maxlen,axiom,
% 5.06/5.34 ! [M7: set_list_VEBT_VEBT] :
% 5.06/5.34 ( ( finite3004134309566078307T_VEBT @ M7 )
% 5.06/5.34 => ? [N3: nat] :
% 5.06/5.34 ! [X5: list_VEBT_VEBT] :
% 5.06/5.34 ( ( member2936631157270082147T_VEBT @ X5 @ M7 )
% 5.06/5.34 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N3 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_maxlen
% 5.06/5.34 thf(fact_4371_finite__maxlen,axiom,
% 5.06/5.34 ! [M7: set_list_o] :
% 5.06/5.34 ( ( finite_finite_list_o @ M7 )
% 5.06/5.34 => ? [N3: nat] :
% 5.06/5.34 ! [X5: list_o] :
% 5.06/5.34 ( ( member_list_o @ X5 @ M7 )
% 5.06/5.34 => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N3 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_maxlen
% 5.06/5.34 thf(fact_4372_finite__maxlen,axiom,
% 5.06/5.34 ! [M7: set_list_int] :
% 5.06/5.34 ( ( finite3922522038869484883st_int @ M7 )
% 5.06/5.34 => ? [N3: nat] :
% 5.06/5.34 ! [X5: list_int] :
% 5.06/5.34 ( ( member_list_int @ X5 @ M7 )
% 5.06/5.34 => ( ord_less_nat @ ( size_size_list_int @ X5 ) @ N3 ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % finite_maxlen
% 5.06/5.34 thf(fact_4373_not__finite__existsD,axiom,
% 5.06/5.34 ! [P: product_prod_int_int > $o] :
% 5.06/5.34 ( ~ ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.06/5.34 => ? [X_1: product_prod_int_int] : ( P @ X_1 ) ) ).
% 5.06/5.34
% 5.06/5.34 % not_finite_existsD
% 5.06/5.34 thf(fact_4374_not__finite__existsD,axiom,
% 5.06/5.34 ! [P: set_nat > $o] :
% 5.06/5.34 ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.06/5.34 => ? [X_1: set_nat] : ( P @ X_1 ) ) ).
% 5.06/5.34
% 5.06/5.34 % not_finite_existsD
% 5.06/5.34 thf(fact_4375_not__finite__existsD,axiom,
% 5.06/5.34 ! [P: nat > $o] :
% 5.06/5.34 ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.34 => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 5.06/5.34
% 5.06/5.34 % not_finite_existsD
% 5.06/5.34 thf(fact_4376_not__finite__existsD,axiom,
% 5.06/5.34 ! [P: int > $o] :
% 5.06/5.34 ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 5.06/5.34 => ? [X_1: int] : ( P @ X_1 ) ) ).
% 5.06/5.34
% 5.06/5.34 % not_finite_existsD
% 5.06/5.34 thf(fact_4377_not__finite__existsD,axiom,
% 5.06/5.34 ! [P: complex > $o] :
% 5.06/5.34 ( ~ ( finite3207457112153483333omplex @ ( collect_complex @ P ) )
% 5.06/5.34 => ? [X_1: complex] : ( P @ X_1 ) ) ).
% 5.06/5.34
% 5.06/5.34 % not_finite_existsD
% 5.06/5.34 thf(fact_4378_pigeonhole__infinite__rel,axiom,
% 5.06/5.34 ! [A2: set_real,B3: set_nat,R: real > nat > $o] :
% 5.06/5.34 ( ~ ( finite_finite_real @ A2 )
% 5.06/5.34 => ( ( finite_finite_nat @ B3 )
% 5.06/5.34 => ( ! [X3: real] :
% 5.06/5.34 ( ( member_real @ X3 @ A2 )
% 5.06/5.34 => ? [Xa: nat] :
% 5.06/5.34 ( ( member_nat @ Xa @ B3 )
% 5.06/5.34 & ( R @ X3 @ Xa ) ) )
% 5.06/5.34 => ? [X3: nat] :
% 5.06/5.34 ( ( member_nat @ X3 @ B3 )
% 5.06/5.34 & ~ ( finite_finite_real
% 5.06/5.34 @ ( collect_real
% 5.06/5.34 @ ^ [A4: real] :
% 5.06/5.34 ( ( member_real @ A4 @ A2 )
% 5.06/5.34 & ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pigeonhole_infinite_rel
% 5.06/5.34 thf(fact_4379_pigeonhole__infinite__rel,axiom,
% 5.06/5.34 ! [A2: set_real,B3: set_int,R: real > int > $o] :
% 5.06/5.34 ( ~ ( finite_finite_real @ A2 )
% 5.06/5.34 => ( ( finite_finite_int @ B3 )
% 5.06/5.34 => ( ! [X3: real] :
% 5.06/5.34 ( ( member_real @ X3 @ A2 )
% 5.06/5.34 => ? [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ B3 )
% 5.06/5.34 & ( R @ X3 @ Xa ) ) )
% 5.06/5.34 => ? [X3: int] :
% 5.06/5.34 ( ( member_int @ X3 @ B3 )
% 5.06/5.34 & ~ ( finite_finite_real
% 5.06/5.34 @ ( collect_real
% 5.06/5.34 @ ^ [A4: real] :
% 5.06/5.34 ( ( member_real @ A4 @ A2 )
% 5.06/5.34 & ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pigeonhole_infinite_rel
% 5.06/5.34 thf(fact_4380_pigeonhole__infinite__rel,axiom,
% 5.06/5.34 ! [A2: set_real,B3: set_complex,R: real > complex > $o] :
% 5.06/5.34 ( ~ ( finite_finite_real @ A2 )
% 5.06/5.34 => ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.34 => ( ! [X3: real] :
% 5.06/5.34 ( ( member_real @ X3 @ A2 )
% 5.06/5.34 => ? [Xa: complex] :
% 5.06/5.34 ( ( member_complex @ Xa @ B3 )
% 5.06/5.34 & ( R @ X3 @ Xa ) ) )
% 5.06/5.34 => ? [X3: complex] :
% 5.06/5.34 ( ( member_complex @ X3 @ B3 )
% 5.06/5.34 & ~ ( finite_finite_real
% 5.06/5.34 @ ( collect_real
% 5.06/5.34 @ ^ [A4: real] :
% 5.06/5.34 ( ( member_real @ A4 @ A2 )
% 5.06/5.34 & ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pigeonhole_infinite_rel
% 5.06/5.34 thf(fact_4381_pigeonhole__infinite__rel,axiom,
% 5.06/5.34 ! [A2: set_nat,B3: set_nat,R: nat > nat > $o] :
% 5.06/5.34 ( ~ ( finite_finite_nat @ A2 )
% 5.06/5.34 => ( ( finite_finite_nat @ B3 )
% 5.06/5.34 => ( ! [X3: nat] :
% 5.06/5.34 ( ( member_nat @ X3 @ A2 )
% 5.06/5.34 => ? [Xa: nat] :
% 5.06/5.34 ( ( member_nat @ Xa @ B3 )
% 5.06/5.34 & ( R @ X3 @ Xa ) ) )
% 5.06/5.34 => ? [X3: nat] :
% 5.06/5.34 ( ( member_nat @ X3 @ B3 )
% 5.06/5.34 & ~ ( finite_finite_nat
% 5.06/5.34 @ ( collect_nat
% 5.06/5.34 @ ^ [A4: nat] :
% 5.06/5.34 ( ( member_nat @ A4 @ A2 )
% 5.06/5.34 & ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.34
% 5.06/5.34 % pigeonhole_infinite_rel
% 5.06/5.34 thf(fact_4382_pigeonhole__infinite__rel,axiom,
% 5.06/5.34 ! [A2: set_nat,B3: set_int,R: nat > int > $o] :
% 5.06/5.34 ( ~ ( finite_finite_nat @ A2 )
% 5.06/5.34 => ( ( finite_finite_int @ B3 )
% 5.06/5.34 => ( ! [X3: nat] :
% 5.06/5.34 ( ( member_nat @ X3 @ A2 )
% 5.06/5.34 => ? [Xa: int] :
% 5.06/5.34 ( ( member_int @ Xa @ B3 )
% 5.06/5.34 & ( R @ X3 @ Xa ) ) )
% 5.06/5.34 => ? [X3: int] :
% 5.06/5.35 ( ( member_int @ X3 @ B3 )
% 5.06/5.35 & ~ ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [A4: nat] :
% 5.06/5.35 ( ( member_nat @ A4 @ A2 )
% 5.06/5.35 & ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % pigeonhole_infinite_rel
% 5.06/5.35 thf(fact_4383_pigeonhole__infinite__rel,axiom,
% 5.06/5.35 ! [A2: set_nat,B3: set_complex,R: nat > complex > $o] :
% 5.06/5.35 ( ~ ( finite_finite_nat @ A2 )
% 5.06/5.35 => ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.35 => ( ! [X3: nat] :
% 5.06/5.35 ( ( member_nat @ X3 @ A2 )
% 5.06/5.35 => ? [Xa: complex] :
% 5.06/5.35 ( ( member_complex @ Xa @ B3 )
% 5.06/5.35 & ( R @ X3 @ Xa ) ) )
% 5.06/5.35 => ? [X3: complex] :
% 5.06/5.35 ( ( member_complex @ X3 @ B3 )
% 5.06/5.35 & ~ ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [A4: nat] :
% 5.06/5.35 ( ( member_nat @ A4 @ A2 )
% 5.06/5.35 & ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % pigeonhole_infinite_rel
% 5.06/5.35 thf(fact_4384_pigeonhole__infinite__rel,axiom,
% 5.06/5.35 ! [A2: set_int,B3: set_nat,R: int > nat > $o] :
% 5.06/5.35 ( ~ ( finite_finite_int @ A2 )
% 5.06/5.35 => ( ( finite_finite_nat @ B3 )
% 5.06/5.35 => ( ! [X3: int] :
% 5.06/5.35 ( ( member_int @ X3 @ A2 )
% 5.06/5.35 => ? [Xa: nat] :
% 5.06/5.35 ( ( member_nat @ Xa @ B3 )
% 5.06/5.35 & ( R @ X3 @ Xa ) ) )
% 5.06/5.35 => ? [X3: nat] :
% 5.06/5.35 ( ( member_nat @ X3 @ B3 )
% 5.06/5.35 & ~ ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [A4: int] :
% 5.06/5.35 ( ( member_int @ A4 @ A2 )
% 5.06/5.35 & ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % pigeonhole_infinite_rel
% 5.06/5.35 thf(fact_4385_pigeonhole__infinite__rel,axiom,
% 5.06/5.35 ! [A2: set_int,B3: set_int,R: int > int > $o] :
% 5.06/5.35 ( ~ ( finite_finite_int @ A2 )
% 5.06/5.35 => ( ( finite_finite_int @ B3 )
% 5.06/5.35 => ( ! [X3: int] :
% 5.06/5.35 ( ( member_int @ X3 @ A2 )
% 5.06/5.35 => ? [Xa: int] :
% 5.06/5.35 ( ( member_int @ Xa @ B3 )
% 5.06/5.35 & ( R @ X3 @ Xa ) ) )
% 5.06/5.35 => ? [X3: int] :
% 5.06/5.35 ( ( member_int @ X3 @ B3 )
% 5.06/5.35 & ~ ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [A4: int] :
% 5.06/5.35 ( ( member_int @ A4 @ A2 )
% 5.06/5.35 & ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % pigeonhole_infinite_rel
% 5.06/5.35 thf(fact_4386_pigeonhole__infinite__rel,axiom,
% 5.06/5.35 ! [A2: set_int,B3: set_complex,R: int > complex > $o] :
% 5.06/5.35 ( ~ ( finite_finite_int @ A2 )
% 5.06/5.35 => ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.35 => ( ! [X3: int] :
% 5.06/5.35 ( ( member_int @ X3 @ A2 )
% 5.06/5.35 => ? [Xa: complex] :
% 5.06/5.35 ( ( member_complex @ Xa @ B3 )
% 5.06/5.35 & ( R @ X3 @ Xa ) ) )
% 5.06/5.35 => ? [X3: complex] :
% 5.06/5.35 ( ( member_complex @ X3 @ B3 )
% 5.06/5.35 & ~ ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [A4: int] :
% 5.06/5.35 ( ( member_int @ A4 @ A2 )
% 5.06/5.35 & ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % pigeonhole_infinite_rel
% 5.06/5.35 thf(fact_4387_pigeonhole__infinite__rel,axiom,
% 5.06/5.35 ! [A2: set_complex,B3: set_nat,R: complex > nat > $o] :
% 5.06/5.35 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.06/5.35 => ( ( finite_finite_nat @ B3 )
% 5.06/5.35 => ( ! [X3: complex] :
% 5.06/5.35 ( ( member_complex @ X3 @ A2 )
% 5.06/5.35 => ? [Xa: nat] :
% 5.06/5.35 ( ( member_nat @ Xa @ B3 )
% 5.06/5.35 & ( R @ X3 @ Xa ) ) )
% 5.06/5.35 => ? [X3: nat] :
% 5.06/5.35 ( ( member_nat @ X3 @ B3 )
% 5.06/5.35 & ~ ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [A4: complex] :
% 5.06/5.35 ( ( member_complex @ A4 @ A2 )
% 5.06/5.35 & ( R @ A4 @ X3 ) ) ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % pigeonhole_infinite_rel
% 5.06/5.35 thf(fact_4388_finite__has__minimal2,axiom,
% 5.06/5.35 ! [A2: set_real,A: real] :
% 5.06/5.35 ( ( finite_finite_real @ A2 )
% 5.06/5.35 => ( ( member_real @ A @ A2 )
% 5.06/5.35 => ? [X3: real] :
% 5.06/5.35 ( ( member_real @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_real @ X3 @ A )
% 5.06/5.35 & ! [Xa: real] :
% 5.06/5.35 ( ( member_real @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal2
% 5.06/5.35 thf(fact_4389_finite__has__minimal2,axiom,
% 5.06/5.35 ! [A2: set_set_nat,A: set_nat] :
% 5.06/5.35 ( ( finite1152437895449049373et_nat @ A2 )
% 5.06/5.35 => ( ( member_set_nat @ A @ A2 )
% 5.06/5.35 => ? [X3: set_nat] :
% 5.06/5.35 ( ( member_set_nat @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_set_nat @ X3 @ A )
% 5.06/5.35 & ! [Xa: set_nat] :
% 5.06/5.35 ( ( member_set_nat @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal2
% 5.06/5.35 thf(fact_4390_finite__has__minimal2,axiom,
% 5.06/5.35 ! [A2: set_set_int,A: set_int] :
% 5.06/5.35 ( ( finite6197958912794628473et_int @ A2 )
% 5.06/5.35 => ( ( member_set_int @ A @ A2 )
% 5.06/5.35 => ? [X3: set_int] :
% 5.06/5.35 ( ( member_set_int @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_set_int @ X3 @ A )
% 5.06/5.35 & ! [Xa: set_int] :
% 5.06/5.35 ( ( member_set_int @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_set_int @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal2
% 5.06/5.35 thf(fact_4391_finite__has__minimal2,axiom,
% 5.06/5.35 ! [A2: set_rat,A: rat] :
% 5.06/5.35 ( ( finite_finite_rat @ A2 )
% 5.06/5.35 => ( ( member_rat @ A @ A2 )
% 5.06/5.35 => ? [X3: rat] :
% 5.06/5.35 ( ( member_rat @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_rat @ X3 @ A )
% 5.06/5.35 & ! [Xa: rat] :
% 5.06/5.35 ( ( member_rat @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal2
% 5.06/5.35 thf(fact_4392_finite__has__minimal2,axiom,
% 5.06/5.35 ! [A2: set_num,A: num] :
% 5.06/5.35 ( ( finite_finite_num @ A2 )
% 5.06/5.35 => ( ( member_num @ A @ A2 )
% 5.06/5.35 => ? [X3: num] :
% 5.06/5.35 ( ( member_num @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_num @ X3 @ A )
% 5.06/5.35 & ! [Xa: num] :
% 5.06/5.35 ( ( member_num @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal2
% 5.06/5.35 thf(fact_4393_finite__has__minimal2,axiom,
% 5.06/5.35 ! [A2: set_nat,A: nat] :
% 5.06/5.35 ( ( finite_finite_nat @ A2 )
% 5.06/5.35 => ( ( member_nat @ A @ A2 )
% 5.06/5.35 => ? [X3: nat] :
% 5.06/5.35 ( ( member_nat @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_nat @ X3 @ A )
% 5.06/5.35 & ! [Xa: nat] :
% 5.06/5.35 ( ( member_nat @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal2
% 5.06/5.35 thf(fact_4394_finite__has__minimal2,axiom,
% 5.06/5.35 ! [A2: set_int,A: int] :
% 5.06/5.35 ( ( finite_finite_int @ A2 )
% 5.06/5.35 => ( ( member_int @ A @ A2 )
% 5.06/5.35 => ? [X3: int] :
% 5.06/5.35 ( ( member_int @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_int @ X3 @ A )
% 5.06/5.35 & ! [Xa: int] :
% 5.06/5.35 ( ( member_int @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal2
% 5.06/5.35 thf(fact_4395_finite__has__maximal2,axiom,
% 5.06/5.35 ! [A2: set_real,A: real] :
% 5.06/5.35 ( ( finite_finite_real @ A2 )
% 5.06/5.35 => ( ( member_real @ A @ A2 )
% 5.06/5.35 => ? [X3: real] :
% 5.06/5.35 ( ( member_real @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_real @ A @ X3 )
% 5.06/5.35 & ! [Xa: real] :
% 5.06/5.35 ( ( member_real @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal2
% 5.06/5.35 thf(fact_4396_finite__has__maximal2,axiom,
% 5.06/5.35 ! [A2: set_set_nat,A: set_nat] :
% 5.06/5.35 ( ( finite1152437895449049373et_nat @ A2 )
% 5.06/5.35 => ( ( member_set_nat @ A @ A2 )
% 5.06/5.35 => ? [X3: set_nat] :
% 5.06/5.35 ( ( member_set_nat @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_set_nat @ A @ X3 )
% 5.06/5.35 & ! [Xa: set_nat] :
% 5.06/5.35 ( ( member_set_nat @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal2
% 5.06/5.35 thf(fact_4397_finite__has__maximal2,axiom,
% 5.06/5.35 ! [A2: set_set_int,A: set_int] :
% 5.06/5.35 ( ( finite6197958912794628473et_int @ A2 )
% 5.06/5.35 => ( ( member_set_int @ A @ A2 )
% 5.06/5.35 => ? [X3: set_int] :
% 5.06/5.35 ( ( member_set_int @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_set_int @ A @ X3 )
% 5.06/5.35 & ! [Xa: set_int] :
% 5.06/5.35 ( ( member_set_int @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_set_int @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal2
% 5.06/5.35 thf(fact_4398_finite__has__maximal2,axiom,
% 5.06/5.35 ! [A2: set_rat,A: rat] :
% 5.06/5.35 ( ( finite_finite_rat @ A2 )
% 5.06/5.35 => ( ( member_rat @ A @ A2 )
% 5.06/5.35 => ? [X3: rat] :
% 5.06/5.35 ( ( member_rat @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_rat @ A @ X3 )
% 5.06/5.35 & ! [Xa: rat] :
% 5.06/5.35 ( ( member_rat @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal2
% 5.06/5.35 thf(fact_4399_finite__has__maximal2,axiom,
% 5.06/5.35 ! [A2: set_num,A: num] :
% 5.06/5.35 ( ( finite_finite_num @ A2 )
% 5.06/5.35 => ( ( member_num @ A @ A2 )
% 5.06/5.35 => ? [X3: num] :
% 5.06/5.35 ( ( member_num @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_num @ A @ X3 )
% 5.06/5.35 & ! [Xa: num] :
% 5.06/5.35 ( ( member_num @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal2
% 5.06/5.35 thf(fact_4400_finite__has__maximal2,axiom,
% 5.06/5.35 ! [A2: set_nat,A: nat] :
% 5.06/5.35 ( ( finite_finite_nat @ A2 )
% 5.06/5.35 => ( ( member_nat @ A @ A2 )
% 5.06/5.35 => ? [X3: nat] :
% 5.06/5.35 ( ( member_nat @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_nat @ A @ X3 )
% 5.06/5.35 & ! [Xa: nat] :
% 5.06/5.35 ( ( member_nat @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal2
% 5.06/5.35 thf(fact_4401_finite__has__maximal2,axiom,
% 5.06/5.35 ! [A2: set_int,A: int] :
% 5.06/5.35 ( ( finite_finite_int @ A2 )
% 5.06/5.35 => ( ( member_int @ A @ A2 )
% 5.06/5.35 => ? [X3: int] :
% 5.06/5.35 ( ( member_int @ X3 @ A2 )
% 5.06/5.35 & ( ord_less_eq_int @ A @ X3 )
% 5.06/5.35 & ! [Xa: int] :
% 5.06/5.35 ( ( member_int @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal2
% 5.06/5.35 thf(fact_4402_finite__subset,axiom,
% 5.06/5.35 ! [A2: set_nat,B3: set_nat] :
% 5.06/5.35 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.06/5.35 => ( ( finite_finite_nat @ B3 )
% 5.06/5.35 => ( finite_finite_nat @ A2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_subset
% 5.06/5.35 thf(fact_4403_finite__subset,axiom,
% 5.06/5.35 ! [A2: set_complex,B3: set_complex] :
% 5.06/5.35 ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.06/5.35 => ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.35 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_subset
% 5.06/5.35 thf(fact_4404_finite__subset,axiom,
% 5.06/5.35 ! [A2: set_int,B3: set_int] :
% 5.06/5.35 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.06/5.35 => ( ( finite_finite_int @ B3 )
% 5.06/5.35 => ( finite_finite_int @ A2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_subset
% 5.06/5.35 thf(fact_4405_infinite__super,axiom,
% 5.06/5.35 ! [S3: set_nat,T3: set_nat] :
% 5.06/5.35 ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.06/5.35 => ( ~ ( finite_finite_nat @ S3 )
% 5.06/5.35 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % infinite_super
% 5.06/5.35 thf(fact_4406_infinite__super,axiom,
% 5.06/5.35 ! [S3: set_complex,T3: set_complex] :
% 5.06/5.35 ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.35 => ( ~ ( finite3207457112153483333omplex @ S3 )
% 5.06/5.35 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % infinite_super
% 5.06/5.35 thf(fact_4407_infinite__super,axiom,
% 5.06/5.35 ! [S3: set_int,T3: set_int] :
% 5.06/5.35 ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.06/5.35 => ( ~ ( finite_finite_int @ S3 )
% 5.06/5.35 => ~ ( finite_finite_int @ T3 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % infinite_super
% 5.06/5.35 thf(fact_4408_rev__finite__subset,axiom,
% 5.06/5.35 ! [B3: set_nat,A2: set_nat] :
% 5.06/5.35 ( ( finite_finite_nat @ B3 )
% 5.06/5.35 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.06/5.35 => ( finite_finite_nat @ A2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % rev_finite_subset
% 5.06/5.35 thf(fact_4409_rev__finite__subset,axiom,
% 5.06/5.35 ! [B3: set_complex,A2: set_complex] :
% 5.06/5.35 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.35 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.06/5.35 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % rev_finite_subset
% 5.06/5.35 thf(fact_4410_rev__finite__subset,axiom,
% 5.06/5.35 ! [B3: set_int,A2: set_int] :
% 5.06/5.35 ( ( finite_finite_int @ B3 )
% 5.06/5.35 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.06/5.35 => ( finite_finite_int @ A2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % rev_finite_subset
% 5.06/5.35 thf(fact_4411_Diff__infinite__finite,axiom,
% 5.06/5.35 ! [T3: set_int,S3: set_int] :
% 5.06/5.35 ( ( finite_finite_int @ T3 )
% 5.06/5.35 => ( ~ ( finite_finite_int @ S3 )
% 5.06/5.35 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S3 @ T3 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % Diff_infinite_finite
% 5.06/5.35 thf(fact_4412_Diff__infinite__finite,axiom,
% 5.06/5.35 ! [T3: set_complex,S3: set_complex] :
% 5.06/5.35 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.35 => ( ~ ( finite3207457112153483333omplex @ S3 )
% 5.06/5.35 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S3 @ T3 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % Diff_infinite_finite
% 5.06/5.35 thf(fact_4413_Diff__infinite__finite,axiom,
% 5.06/5.35 ! [T3: set_nat,S3: set_nat] :
% 5.06/5.35 ( ( finite_finite_nat @ T3 )
% 5.06/5.35 => ( ~ ( finite_finite_nat @ S3 )
% 5.06/5.35 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S3 @ T3 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % Diff_infinite_finite
% 5.06/5.35 thf(fact_4414_finite__has__maximal,axiom,
% 5.06/5.35 ! [A2: set_real] :
% 5.06/5.35 ( ( finite_finite_real @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_real )
% 5.06/5.35 => ? [X3: real] :
% 5.06/5.35 ( ( member_real @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: real] :
% 5.06/5.35 ( ( member_real @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_real @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal
% 5.06/5.35 thf(fact_4415_finite__has__maximal,axiom,
% 5.06/5.35 ! [A2: set_set_int] :
% 5.06/5.35 ( ( finite6197958912794628473et_int @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_set_int )
% 5.06/5.35 => ? [X3: set_int] :
% 5.06/5.35 ( ( member_set_int @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: set_int] :
% 5.06/5.35 ( ( member_set_int @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_set_int @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal
% 5.06/5.35 thf(fact_4416_finite__has__maximal,axiom,
% 5.06/5.35 ! [A2: set_rat] :
% 5.06/5.35 ( ( finite_finite_rat @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_rat )
% 5.06/5.35 => ? [X3: rat] :
% 5.06/5.35 ( ( member_rat @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: rat] :
% 5.06/5.35 ( ( member_rat @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal
% 5.06/5.35 thf(fact_4417_finite__has__maximal,axiom,
% 5.06/5.35 ! [A2: set_num] :
% 5.06/5.35 ( ( finite_finite_num @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_num )
% 5.06/5.35 => ? [X3: num] :
% 5.06/5.35 ( ( member_num @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: num] :
% 5.06/5.35 ( ( member_num @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_num @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal
% 5.06/5.35 thf(fact_4418_finite__has__maximal,axiom,
% 5.06/5.35 ! [A2: set_nat] :
% 5.06/5.35 ( ( finite_finite_nat @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_nat )
% 5.06/5.35 => ? [X3: nat] :
% 5.06/5.35 ( ( member_nat @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: nat] :
% 5.06/5.35 ( ( member_nat @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal
% 5.06/5.35 thf(fact_4419_finite__has__maximal,axiom,
% 5.06/5.35 ! [A2: set_int] :
% 5.06/5.35 ( ( finite_finite_int @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_int )
% 5.06/5.35 => ? [X3: int] :
% 5.06/5.35 ( ( member_int @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: int] :
% 5.06/5.35 ( ( member_int @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_int @ X3 @ Xa )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_maximal
% 5.06/5.35 thf(fact_4420_finite__has__minimal,axiom,
% 5.06/5.35 ! [A2: set_real] :
% 5.06/5.35 ( ( finite_finite_real @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_real )
% 5.06/5.35 => ? [X3: real] :
% 5.06/5.35 ( ( member_real @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: real] :
% 5.06/5.35 ( ( member_real @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_real @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal
% 5.06/5.35 thf(fact_4421_finite__has__minimal,axiom,
% 5.06/5.35 ! [A2: set_set_int] :
% 5.06/5.35 ( ( finite6197958912794628473et_int @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_set_int )
% 5.06/5.35 => ? [X3: set_int] :
% 5.06/5.35 ( ( member_set_int @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: set_int] :
% 5.06/5.35 ( ( member_set_int @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_set_int @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal
% 5.06/5.35 thf(fact_4422_finite__has__minimal,axiom,
% 5.06/5.35 ! [A2: set_rat] :
% 5.06/5.35 ( ( finite_finite_rat @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_rat )
% 5.06/5.35 => ? [X3: rat] :
% 5.06/5.35 ( ( member_rat @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: rat] :
% 5.06/5.35 ( ( member_rat @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal
% 5.06/5.35 thf(fact_4423_finite__has__minimal,axiom,
% 5.06/5.35 ! [A2: set_num] :
% 5.06/5.35 ( ( finite_finite_num @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_num )
% 5.06/5.35 => ? [X3: num] :
% 5.06/5.35 ( ( member_num @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: num] :
% 5.06/5.35 ( ( member_num @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_num @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal
% 5.06/5.35 thf(fact_4424_finite__has__minimal,axiom,
% 5.06/5.35 ! [A2: set_nat] :
% 5.06/5.35 ( ( finite_finite_nat @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_nat )
% 5.06/5.35 => ? [X3: nat] :
% 5.06/5.35 ( ( member_nat @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: nat] :
% 5.06/5.35 ( ( member_nat @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal
% 5.06/5.35 thf(fact_4425_finite__has__minimal,axiom,
% 5.06/5.35 ! [A2: set_int] :
% 5.06/5.35 ( ( finite_finite_int @ A2 )
% 5.06/5.35 => ( ( A2 != bot_bot_set_int )
% 5.06/5.35 => ? [X3: int] :
% 5.06/5.35 ( ( member_int @ X3 @ A2 )
% 5.06/5.35 & ! [Xa: int] :
% 5.06/5.35 ( ( member_int @ Xa @ A2 )
% 5.06/5.35 => ( ( ord_less_eq_int @ Xa @ X3 )
% 5.06/5.35 => ( X3 = Xa ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_has_minimal
% 5.06/5.35 thf(fact_4426_arcosh__1,axiom,
% 5.06/5.35 ( ( arcosh_real @ one_one_real )
% 5.06/5.35 = zero_zero_real ) ).
% 5.06/5.35
% 5.06/5.35 % arcosh_1
% 5.06/5.35 thf(fact_4427_finite__nth__roots,axiom,
% 5.06/5.35 ! [N2: nat,C: complex] :
% 5.06/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.35 => ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [Z2: complex] :
% 5.06/5.35 ( ( power_power_complex @ Z2 @ N2 )
% 5.06/5.35 = C ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_nth_roots
% 5.06/5.35 thf(fact_4428_prod_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_real,X: real > complex,Y: real > complex] :
% 5.06/5.35 ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != one_one_complex ) ) ) )
% 5.06/5.35 => ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != one_one_complex ) ) ) )
% 5.06/5.35 => ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != one_one_complex ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % prod.finite_Collect_op
% 5.06/5.35 thf(fact_4429_prod_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 5.06/5.35 ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != one_one_complex ) ) ) )
% 5.06/5.35 => ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != one_one_complex ) ) ) )
% 5.06/5.35 => ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != one_one_complex ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % prod.finite_Collect_op
% 5.06/5.35 thf(fact_4430_prod_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_int,X: int > complex,Y: int > complex] :
% 5.06/5.35 ( ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != one_one_complex ) ) ) )
% 5.06/5.35 => ( ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != one_one_complex ) ) ) )
% 5.06/5.35 => ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != one_one_complex ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % prod.finite_Collect_op
% 5.06/5.35 thf(fact_4431_prod_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 5.06/5.35 ( ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != one_one_complex ) ) ) )
% 5.06/5.35 => ( ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != one_one_complex ) ) ) )
% 5.06/5.35 => ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != one_one_complex ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % prod.finite_Collect_op
% 5.06/5.35 thf(fact_4432_prod_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_real,X: real > real,Y: real > real] :
% 5.06/5.35 ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != one_one_real ) ) ) )
% 5.06/5.35 => ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != one_one_real ) ) ) )
% 5.06/5.35 => ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != one_one_real ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % prod.finite_Collect_op
% 5.06/5.35 thf(fact_4433_prod_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_nat,X: nat > real,Y: nat > real] :
% 5.06/5.35 ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != one_one_real ) ) ) )
% 5.06/5.35 => ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != one_one_real ) ) ) )
% 5.06/5.35 => ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != one_one_real ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % prod.finite_Collect_op
% 5.06/5.35 thf(fact_4434_prod_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_int,X: int > real,Y: int > real] :
% 5.06/5.35 ( ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != one_one_real ) ) ) )
% 5.06/5.35 => ( ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != one_one_real ) ) ) )
% 5.06/5.35 => ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != one_one_real ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % prod.finite_Collect_op
% 5.06/5.35 thf(fact_4435_prod_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_complex,X: complex > real,Y: complex > real] :
% 5.06/5.35 ( ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != one_one_real ) ) ) )
% 5.06/5.35 => ( ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != one_one_real ) ) ) )
% 5.06/5.35 => ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != one_one_real ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % prod.finite_Collect_op
% 5.06/5.35 thf(fact_4436_prod_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_real,X: real > rat,Y: real > rat] :
% 5.06/5.35 ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != one_one_rat ) ) ) )
% 5.06/5.35 => ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != one_one_rat ) ) ) )
% 5.06/5.35 => ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( times_times_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != one_one_rat ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % prod.finite_Collect_op
% 5.06/5.35 thf(fact_4437_prod_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_nat,X: nat > rat,Y: nat > rat] :
% 5.06/5.35 ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != one_one_rat ) ) ) )
% 5.06/5.35 => ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != one_one_rat ) ) ) )
% 5.06/5.35 => ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( times_times_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != one_one_rat ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % prod.finite_Collect_op
% 5.06/5.35 thf(fact_4438_sum_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_real,X: real > complex,Y: real > complex] :
% 5.06/5.35 ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != zero_zero_complex ) ) ) )
% 5.06/5.35 => ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != zero_zero_complex ) ) ) )
% 5.06/5.35 => ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != zero_zero_complex ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % sum.finite_Collect_op
% 5.06/5.35 thf(fact_4439_sum_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 5.06/5.35 ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != zero_zero_complex ) ) ) )
% 5.06/5.35 => ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != zero_zero_complex ) ) ) )
% 5.06/5.35 => ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != zero_zero_complex ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % sum.finite_Collect_op
% 5.06/5.35 thf(fact_4440_sum_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_int,X: int > complex,Y: int > complex] :
% 5.06/5.35 ( ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != zero_zero_complex ) ) ) )
% 5.06/5.35 => ( ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != zero_zero_complex ) ) ) )
% 5.06/5.35 => ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != zero_zero_complex ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % sum.finite_Collect_op
% 5.06/5.35 thf(fact_4441_sum_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 5.06/5.35 ( ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != zero_zero_complex ) ) ) )
% 5.06/5.35 => ( ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != zero_zero_complex ) ) ) )
% 5.06/5.35 => ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != zero_zero_complex ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % sum.finite_Collect_op
% 5.06/5.35 thf(fact_4442_sum_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_real,X: real > real,Y: real > real] :
% 5.06/5.35 ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != zero_zero_real ) ) ) )
% 5.06/5.35 => ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != zero_zero_real ) ) ) )
% 5.06/5.35 => ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % sum.finite_Collect_op
% 5.06/5.35 thf(fact_4443_sum_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_nat,X: nat > real,Y: nat > real] :
% 5.06/5.35 ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != zero_zero_real ) ) ) )
% 5.06/5.35 => ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != zero_zero_real ) ) ) )
% 5.06/5.35 => ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % sum.finite_Collect_op
% 5.06/5.35 thf(fact_4444_sum_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_int,X: int > real,Y: int > real] :
% 5.06/5.35 ( ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != zero_zero_real ) ) ) )
% 5.06/5.35 => ( ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != zero_zero_real ) ) ) )
% 5.06/5.35 => ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [I5: int] :
% 5.06/5.35 ( ( member_int @ I5 @ I6 )
% 5.06/5.35 & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % sum.finite_Collect_op
% 5.06/5.35 thf(fact_4445_sum_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_complex,X: complex > real,Y: complex > real] :
% 5.06/5.35 ( ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != zero_zero_real ) ) ) )
% 5.06/5.35 => ( ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != zero_zero_real ) ) ) )
% 5.06/5.35 => ( finite3207457112153483333omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [I5: complex] :
% 5.06/5.35 ( ( member_complex @ I5 @ I6 )
% 5.06/5.35 & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % sum.finite_Collect_op
% 5.06/5.35 thf(fact_4446_sum_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_real,X: real > rat,Y: real > rat] :
% 5.06/5.35 ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != zero_zero_rat ) ) ) )
% 5.06/5.35 => ( ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != zero_zero_rat ) ) ) )
% 5.06/5.35 => ( finite_finite_real
% 5.06/5.35 @ ( collect_real
% 5.06/5.35 @ ^ [I5: real] :
% 5.06/5.35 ( ( member_real @ I5 @ I6 )
% 5.06/5.35 & ( ( plus_plus_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % sum.finite_Collect_op
% 5.06/5.35 thf(fact_4447_sum_Ofinite__Collect__op,axiom,
% 5.06/5.35 ! [I6: set_nat,X: nat > rat,Y: nat > rat] :
% 5.06/5.35 ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( X @ I5 )
% 5.06/5.35 != zero_zero_rat ) ) ) )
% 5.06/5.35 => ( ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( Y @ I5 )
% 5.06/5.35 != zero_zero_rat ) ) ) )
% 5.06/5.35 => ( finite_finite_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [I5: nat] :
% 5.06/5.35 ( ( member_nat @ I5 @ I6 )
% 5.06/5.35 & ( ( plus_plus_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.06/5.35 != zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % sum.finite_Collect_op
% 5.06/5.35 thf(fact_4448_gcd__nat__induct,axiom,
% 5.06/5.35 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 5.06/5.35 ( ! [M2: nat] : ( P @ M2 @ zero_zero_nat )
% 5.06/5.35 => ( ! [M2: nat,N3: nat] :
% 5.06/5.35 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.06/5.35 => ( ( P @ N3 @ ( modulo_modulo_nat @ M2 @ N3 ) )
% 5.06/5.35 => ( P @ M2 @ N3 ) ) )
% 5.06/5.35 => ( P @ M @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % gcd_nat_induct
% 5.06/5.35 thf(fact_4449_concat__bit__Suc,axiom,
% 5.06/5.35 ! [N2: nat,K: int,L2: int] :
% 5.06/5.35 ( ( bit_concat_bit @ ( suc @ N2 ) @ K @ L2 )
% 5.06/5.35 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N2 @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L2 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % concat_bit_Suc
% 5.06/5.35 thf(fact_4450_dbl__simps_I3_J,axiom,
% 5.06/5.35 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.06/5.35 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(3)
% 5.06/5.35 thf(fact_4451_dbl__simps_I3_J,axiom,
% 5.06/5.35 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.06/5.35 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(3)
% 5.06/5.35 thf(fact_4452_dbl__simps_I3_J,axiom,
% 5.06/5.35 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.06/5.35 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(3)
% 5.06/5.35 thf(fact_4453_dbl__simps_I3_J,axiom,
% 5.06/5.35 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.06/5.35 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(3)
% 5.06/5.35 thf(fact_4454_even__succ__mod__exp,axiom,
% 5.06/5.35 ! [A: nat,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.35 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.35 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_mod_exp
% 5.06/5.35 thf(fact_4455_even__succ__mod__exp,axiom,
% 5.06/5.35 ! [A: int,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.35 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.35 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_mod_exp
% 5.06/5.35 thf(fact_4456_even__succ__mod__exp,axiom,
% 5.06/5.35 ! [A: code_integer,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.35 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.35 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_mod_exp
% 5.06/5.35 thf(fact_4457_even__succ__div__exp,axiom,
% 5.06/5.35 ! [A: code_integer,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.35 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.35 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_div_exp
% 5.06/5.35 thf(fact_4458_even__succ__div__exp,axiom,
% 5.06/5.35 ! [A: nat,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.35 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.35 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_div_exp
% 5.06/5.35 thf(fact_4459_even__succ__div__exp,axiom,
% 5.06/5.35 ! [A: int,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.35 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.35 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_div_exp
% 5.06/5.35 thf(fact_4460_nat__dvd__1__iff__1,axiom,
% 5.06/5.35 ! [M: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.06/5.35 = ( M = one_one_nat ) ) ).
% 5.06/5.35
% 5.06/5.35 % nat_dvd_1_iff_1
% 5.06/5.35 thf(fact_4461_dvd__0__left__iff,axiom,
% 5.06/5.35 ! [A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.06/5.35 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left_iff
% 5.06/5.35 thf(fact_4462_dvd__0__left__iff,axiom,
% 5.06/5.35 ! [A: complex] :
% 5.06/5.35 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.06/5.35 = ( A = zero_zero_complex ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left_iff
% 5.06/5.35 thf(fact_4463_dvd__0__left__iff,axiom,
% 5.06/5.35 ! [A: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.06/5.35 = ( A = zero_zero_real ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left_iff
% 5.06/5.35 thf(fact_4464_dvd__0__left__iff,axiom,
% 5.06/5.35 ! [A: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.06/5.35 = ( A = zero_zero_rat ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left_iff
% 5.06/5.35 thf(fact_4465_dvd__0__left__iff,axiom,
% 5.06/5.35 ! [A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.06/5.35 = ( A = zero_zero_nat ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left_iff
% 5.06/5.35 thf(fact_4466_dvd__0__left__iff,axiom,
% 5.06/5.35 ! [A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.06/5.35 = ( A = zero_zero_int ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left_iff
% 5.06/5.35 thf(fact_4467_dvd__0__right,axiom,
% 5.06/5.35 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_right
% 5.06/5.35 thf(fact_4468_dvd__0__right,axiom,
% 5.06/5.35 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_right
% 5.06/5.35 thf(fact_4469_dvd__0__right,axiom,
% 5.06/5.35 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_right
% 5.06/5.35 thf(fact_4470_dvd__0__right,axiom,
% 5.06/5.35 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_right
% 5.06/5.35 thf(fact_4471_dvd__0__right,axiom,
% 5.06/5.35 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_right
% 5.06/5.35 thf(fact_4472_dvd__0__right,axiom,
% 5.06/5.35 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_right
% 5.06/5.35 thf(fact_4473_dvd__1__iff__1,axiom,
% 5.06/5.35 ! [M: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.06/5.35 = ( M
% 5.06/5.35 = ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_1_iff_1
% 5.06/5.35 thf(fact_4474_dvd__1__left,axiom,
% 5.06/5.35 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_1_left
% 5.06/5.35 thf(fact_4475_dvd__add__triv__right__iff,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_triv_right_iff
% 5.06/5.35 thf(fact_4476_dvd__add__triv__right__iff,axiom,
% 5.06/5.35 ! [A: real,B: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.06/5.35 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_triv_right_iff
% 5.06/5.35 thf(fact_4477_dvd__add__triv__right__iff,axiom,
% 5.06/5.35 ! [A: rat,B: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.06/5.35 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_triv_right_iff
% 5.06/5.35 thf(fact_4478_dvd__add__triv__right__iff,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.06/5.35 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_triv_right_iff
% 5.06/5.35 thf(fact_4479_dvd__add__triv__right__iff,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.06/5.35 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_triv_right_iff
% 5.06/5.35 thf(fact_4480_dvd__add__triv__left__iff,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_triv_left_iff
% 5.06/5.35 thf(fact_4481_dvd__add__triv__left__iff,axiom,
% 5.06/5.35 ! [A: real,B: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.06/5.35 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_triv_left_iff
% 5.06/5.35 thf(fact_4482_dvd__add__triv__left__iff,axiom,
% 5.06/5.35 ! [A: rat,B: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.06/5.35 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_triv_left_iff
% 5.06/5.35 thf(fact_4483_dvd__add__triv__left__iff,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.06/5.35 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_triv_left_iff
% 5.06/5.35 thf(fact_4484_dvd__add__triv__left__iff,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.06/5.35 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_triv_left_iff
% 5.06/5.35 thf(fact_4485_div__dvd__div,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_dvd_div
% 5.06/5.35 thf(fact_4486_div__dvd__div,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_nat @ A @ C )
% 5.06/5.35 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.06/5.35 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_dvd_div
% 5.06/5.35 thf(fact_4487_div__dvd__div,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_int @ A @ C )
% 5.06/5.35 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.06/5.35 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_dvd_div
% 5.06/5.35 thf(fact_4488_nat__mult__dvd__cancel__disj,axiom,
% 5.06/5.35 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.06/5.35 = ( ( K = zero_zero_nat )
% 5.06/5.35 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % nat_mult_dvd_cancel_disj
% 5.06/5.35 thf(fact_4489_concat__bit__0,axiom,
% 5.06/5.35 ! [K: int,L2: int] :
% 5.06/5.35 ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 5.06/5.35 = L2 ) ).
% 5.06/5.35
% 5.06/5.35 % concat_bit_0
% 5.06/5.35 thf(fact_4490_dbl__simps_I2_J,axiom,
% 5.06/5.35 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.06/5.35 = zero_zero_complex ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(2)
% 5.06/5.35 thf(fact_4491_dbl__simps_I2_J,axiom,
% 5.06/5.35 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.06/5.35 = zero_zero_real ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(2)
% 5.06/5.35 thf(fact_4492_dbl__simps_I2_J,axiom,
% 5.06/5.35 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.06/5.35 = zero_zero_rat ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(2)
% 5.06/5.35 thf(fact_4493_dbl__simps_I2_J,axiom,
% 5.06/5.35 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.06/5.35 = zero_zero_int ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(2)
% 5.06/5.35 thf(fact_4494_dvd__mult__cancel__left,axiom,
% 5.06/5.35 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.06/5.35 = ( ( C = zero_z3403309356797280102nteger )
% 5.06/5.35 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_cancel_left
% 5.06/5.35 thf(fact_4495_dvd__mult__cancel__left,axiom,
% 5.06/5.35 ! [C: complex,A: complex,B: complex] :
% 5.06/5.35 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.06/5.35 = ( ( C = zero_zero_complex )
% 5.06/5.35 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_cancel_left
% 5.06/5.35 thf(fact_4496_dvd__mult__cancel__left,axiom,
% 5.06/5.35 ! [C: real,A: real,B: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.06/5.35 = ( ( C = zero_zero_real )
% 5.06/5.35 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_cancel_left
% 5.06/5.35 thf(fact_4497_dvd__mult__cancel__left,axiom,
% 5.06/5.35 ! [C: rat,A: rat,B: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.06/5.35 = ( ( C = zero_zero_rat )
% 5.06/5.35 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_cancel_left
% 5.06/5.35 thf(fact_4498_dvd__mult__cancel__left,axiom,
% 5.06/5.35 ! [C: int,A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.35 = ( ( C = zero_zero_int )
% 5.06/5.35 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_cancel_left
% 5.06/5.35 thf(fact_4499_dvd__mult__cancel__right,axiom,
% 5.06/5.35 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.06/5.35 = ( ( C = zero_z3403309356797280102nteger )
% 5.06/5.35 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_cancel_right
% 5.06/5.35 thf(fact_4500_dvd__mult__cancel__right,axiom,
% 5.06/5.35 ! [A: complex,C: complex,B: complex] :
% 5.06/5.35 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.06/5.35 = ( ( C = zero_zero_complex )
% 5.06/5.35 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_cancel_right
% 5.06/5.35 thf(fact_4501_dvd__mult__cancel__right,axiom,
% 5.06/5.35 ! [A: real,C: real,B: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.06/5.35 = ( ( C = zero_zero_real )
% 5.06/5.35 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_cancel_right
% 5.06/5.35 thf(fact_4502_dvd__mult__cancel__right,axiom,
% 5.06/5.35 ! [A: rat,C: rat,B: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.06/5.35 = ( ( C = zero_zero_rat )
% 5.06/5.35 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_cancel_right
% 5.06/5.35 thf(fact_4503_dvd__mult__cancel__right,axiom,
% 5.06/5.35 ! [A: int,C: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.06/5.35 = ( ( C = zero_zero_int )
% 5.06/5.35 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_cancel_right
% 5.06/5.35 thf(fact_4504_dvd__times__left__cancel__iff,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.35 ( ( A != zero_z3403309356797280102nteger )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_times_left_cancel_iff
% 5.06/5.35 thf(fact_4505_dvd__times__left__cancel__iff,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( A != zero_zero_nat )
% 5.06/5.35 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.06/5.35 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_times_left_cancel_iff
% 5.06/5.35 thf(fact_4506_dvd__times__left__cancel__iff,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( A != zero_zero_int )
% 5.06/5.35 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.06/5.35 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_times_left_cancel_iff
% 5.06/5.35 thf(fact_4507_dvd__times__right__cancel__iff,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.35 ( ( A != zero_z3403309356797280102nteger )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_times_right_cancel_iff
% 5.06/5.35 thf(fact_4508_dvd__times__right__cancel__iff,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( A != zero_zero_nat )
% 5.06/5.35 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.06/5.35 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_times_right_cancel_iff
% 5.06/5.35 thf(fact_4509_dvd__times__right__cancel__iff,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( A != zero_zero_int )
% 5.06/5.35 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.06/5.35 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_times_right_cancel_iff
% 5.06/5.35 thf(fact_4510_dvd__add__times__triv__right__iff,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_times_triv_right_iff
% 5.06/5.35 thf(fact_4511_dvd__add__times__triv__right__iff,axiom,
% 5.06/5.35 ! [A: real,B: real,C: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.06/5.35 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_times_triv_right_iff
% 5.06/5.35 thf(fact_4512_dvd__add__times__triv__right__iff,axiom,
% 5.06/5.35 ! [A: rat,B: rat,C: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.06/5.35 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_times_triv_right_iff
% 5.06/5.35 thf(fact_4513_dvd__add__times__triv__right__iff,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.06/5.35 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_times_triv_right_iff
% 5.06/5.35 thf(fact_4514_dvd__add__times__triv__right__iff,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.06/5.35 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_times_triv_right_iff
% 5.06/5.35 thf(fact_4515_dvd__add__times__triv__left__iff,axiom,
% 5.06/5.35 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_times_triv_left_iff
% 5.06/5.35 thf(fact_4516_dvd__add__times__triv__left__iff,axiom,
% 5.06/5.35 ! [A: real,C: real,B: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.06/5.35 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_times_triv_left_iff
% 5.06/5.35 thf(fact_4517_dvd__add__times__triv__left__iff,axiom,
% 5.06/5.35 ! [A: rat,C: rat,B: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.06/5.35 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_times_triv_left_iff
% 5.06/5.35 thf(fact_4518_dvd__add__times__triv__left__iff,axiom,
% 5.06/5.35 ! [A: nat,C: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.06/5.35 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_times_triv_left_iff
% 5.06/5.35 thf(fact_4519_dvd__add__times__triv__left__iff,axiom,
% 5.06/5.35 ! [A: int,C: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.06/5.35 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_times_triv_left_iff
% 5.06/5.35 thf(fact_4520_unit__prod,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_prod
% 5.06/5.35 thf(fact_4521_unit__prod,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.35 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.35 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_prod
% 5.06/5.35 thf(fact_4522_unit__prod,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.35 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.35 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_prod
% 5.06/5.35 thf(fact_4523_dvd__mult__div__cancel,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.06/5.35 = B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_div_cancel
% 5.06/5.35 thf(fact_4524_dvd__mult__div__cancel,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.06/5.35 = B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_div_cancel
% 5.06/5.35 thf(fact_4525_dvd__mult__div__cancel,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.06/5.35 = B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_div_cancel
% 5.06/5.35 thf(fact_4526_dvd__div__mult__self,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.06/5.35 = B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_mult_self
% 5.06/5.35 thf(fact_4527_dvd__div__mult__self,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.06/5.35 = B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_mult_self
% 5.06/5.35 thf(fact_4528_dvd__div__mult__self,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.06/5.35 = B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_mult_self
% 5.06/5.35 thf(fact_4529_div__add,axiom,
% 5.06/5.35 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.35 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.06/5.35 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_add
% 5.06/5.35 thf(fact_4530_div__add,axiom,
% 5.06/5.35 ! [C: nat,A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.35 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.06/5.35 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_add
% 5.06/5.35 thf(fact_4531_div__add,axiom,
% 5.06/5.35 ! [C: int,A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_int @ C @ B )
% 5.06/5.35 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.06/5.35 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_add
% 5.06/5.35 thf(fact_4532_unit__div,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div
% 5.06/5.35 thf(fact_4533_unit__div,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.35 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.35 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div
% 5.06/5.35 thf(fact_4534_unit__div,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.35 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.35 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div
% 5.06/5.35 thf(fact_4535_unit__div__1__unit,axiom,
% 5.06/5.35 ! [A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div_1_unit
% 5.06/5.35 thf(fact_4536_unit__div__1__unit,axiom,
% 5.06/5.35 ! [A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.35 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div_1_unit
% 5.06/5.35 thf(fact_4537_unit__div__1__unit,axiom,
% 5.06/5.35 ! [A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.35 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div_1_unit
% 5.06/5.35 thf(fact_4538_unit__div__1__div__1,axiom,
% 5.06/5.35 ! [A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.35 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.06/5.35 = A ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div_1_div_1
% 5.06/5.35 thf(fact_4539_unit__div__1__div__1,axiom,
% 5.06/5.35 ! [A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.35 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.06/5.35 = A ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div_1_div_1
% 5.06/5.35 thf(fact_4540_unit__div__1__div__1,axiom,
% 5.06/5.35 ! [A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.35 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.06/5.35 = A ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div_1_div_1
% 5.06/5.35 thf(fact_4541_div__diff,axiom,
% 5.06/5.35 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.35 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.06/5.35 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_diff
% 5.06/5.35 thf(fact_4542_div__diff,axiom,
% 5.06/5.35 ! [C: int,A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_int @ C @ B )
% 5.06/5.35 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.06/5.35 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_diff
% 5.06/5.35 thf(fact_4543_dvd__imp__mod__0,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 => ( ( modulo_modulo_nat @ B @ A )
% 5.06/5.35 = zero_zero_nat ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_imp_mod_0
% 5.06/5.35 thf(fact_4544_dvd__imp__mod__0,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 => ( ( modulo_modulo_int @ B @ A )
% 5.06/5.35 = zero_zero_int ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_imp_mod_0
% 5.06/5.35 thf(fact_4545_dvd__imp__mod__0,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 => ( ( modulo364778990260209775nteger @ B @ A )
% 5.06/5.35 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_imp_mod_0
% 5.06/5.35 thf(fact_4546_concat__bit__nonnegative__iff,axiom,
% 5.06/5.35 ! [N2: nat,K: int,L2: int] :
% 5.06/5.35 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N2 @ K @ L2 ) )
% 5.06/5.35 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 5.06/5.35
% 5.06/5.35 % concat_bit_nonnegative_iff
% 5.06/5.35 thf(fact_4547_concat__bit__negative__iff,axiom,
% 5.06/5.35 ! [N2: nat,K: int,L2: int] :
% 5.06/5.35 ( ( ord_less_int @ ( bit_concat_bit @ N2 @ K @ L2 ) @ zero_zero_int )
% 5.06/5.35 = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 5.06/5.35
% 5.06/5.35 % concat_bit_negative_iff
% 5.06/5.35 thf(fact_4548_dbl__simps_I5_J,axiom,
% 5.06/5.35 ! [K: num] :
% 5.06/5.35 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.06/5.35 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(5)
% 5.06/5.35 thf(fact_4549_dbl__simps_I5_J,axiom,
% 5.06/5.35 ! [K: num] :
% 5.06/5.35 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.06/5.35 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(5)
% 5.06/5.35 thf(fact_4550_dbl__simps_I5_J,axiom,
% 5.06/5.35 ! [K: num] :
% 5.06/5.35 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.06/5.35 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(5)
% 5.06/5.35 thf(fact_4551_dbl__simps_I5_J,axiom,
% 5.06/5.35 ! [K: num] :
% 5.06/5.35 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.06/5.35 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dbl_simps(5)
% 5.06/5.35 thf(fact_4552_even__Suc__Suc__iff,axiom,
% 5.06/5.35 ! [N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N2 ) ) )
% 5.06/5.35 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_Suc_Suc_iff
% 5.06/5.35 thf(fact_4553_even__Suc,axiom,
% 5.06/5.35 ! [N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) )
% 5.06/5.35 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_Suc
% 5.06/5.35 thf(fact_4554_unit__div__mult__self,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.35 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.06/5.35 = B ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div_mult_self
% 5.06/5.35 thf(fact_4555_unit__div__mult__self,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.35 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.06/5.35 = B ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div_mult_self
% 5.06/5.35 thf(fact_4556_unit__div__mult__self,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.35 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.06/5.35 = B ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_div_mult_self
% 5.06/5.35 thf(fact_4557_unit__mult__div__div,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.35 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.06/5.35 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_mult_div_div
% 5.06/5.35 thf(fact_4558_unit__mult__div__div,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.35 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.06/5.35 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_mult_div_div
% 5.06/5.35 thf(fact_4559_unit__mult__div__div,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.35 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.06/5.35 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_mult_div_div
% 5.06/5.35 thf(fact_4560_pow__divides__pow__iff,axiom,
% 5.06/5.35 ! [N2: nat,A: nat,B: nat] :
% 5.06/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.35 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.06/5.35 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % pow_divides_pow_iff
% 5.06/5.35 thf(fact_4561_pow__divides__pow__iff,axiom,
% 5.06/5.35 ! [N2: nat,A: int,B: int] :
% 5.06/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.35 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.06/5.35 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % pow_divides_pow_iff
% 5.06/5.35 thf(fact_4562_even__mult__iff,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.06/5.35 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_mult_iff
% 5.06/5.35 thf(fact_4563_even__mult__iff,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.06/5.35 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_mult_iff
% 5.06/5.35 thf(fact_4564_even__mult__iff,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.06/5.35 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_mult_iff
% 5.06/5.35 thf(fact_4565_even__add,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.06/5.35 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_add
% 5.06/5.35 thf(fact_4566_even__add,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.06/5.35 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_add
% 5.06/5.35 thf(fact_4567_even__add,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.06/5.35 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_add
% 5.06/5.35 thf(fact_4568_odd__add,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.06/5.35 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.06/5.35 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_add
% 5.06/5.35 thf(fact_4569_odd__add,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.06/5.35 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.06/5.35 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_add
% 5.06/5.35 thf(fact_4570_odd__add,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.06/5.35 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.06/5.35 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_add
% 5.06/5.35 thf(fact_4571_even__mod__2__iff,axiom,
% 5.06/5.35 ! [A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.35 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_mod_2_iff
% 5.06/5.35 thf(fact_4572_even__mod__2__iff,axiom,
% 5.06/5.35 ! [A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.06/5.35 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_mod_2_iff
% 5.06/5.35 thf(fact_4573_even__mod__2__iff,axiom,
% 5.06/5.35 ! [A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_mod_2_iff
% 5.06/5.35 thf(fact_4574_even__Suc__div__two,axiom,
% 5.06/5.35 ! [N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.35 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_Suc_div_two
% 5.06/5.35 thf(fact_4575_odd__Suc__div__two,axiom,
% 5.06/5.35 ! [N2: nat] :
% 5.06/5.35 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.35 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_Suc_div_two
% 5.06/5.35 thf(fact_4576_zero__le__power__eq__numeral,axiom,
% 5.06/5.35 ! [A: real,W: num] :
% 5.06/5.35 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.06/5.35 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % zero_le_power_eq_numeral
% 5.06/5.35 thf(fact_4577_zero__le__power__eq__numeral,axiom,
% 5.06/5.35 ! [A: rat,W: num] :
% 5.06/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.06/5.35 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % zero_le_power_eq_numeral
% 5.06/5.35 thf(fact_4578_zero__le__power__eq__numeral,axiom,
% 5.06/5.35 ! [A: int,W: num] :
% 5.06/5.35 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.06/5.35 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % zero_le_power_eq_numeral
% 5.06/5.35 thf(fact_4579_power__less__zero__eq__numeral,axiom,
% 5.06/5.35 ! [A: real,W: num] :
% 5.06/5.35 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.06/5.35 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % power_less_zero_eq_numeral
% 5.06/5.35 thf(fact_4580_power__less__zero__eq__numeral,axiom,
% 5.06/5.35 ! [A: rat,W: num] :
% 5.06/5.35 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.06/5.35 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % power_less_zero_eq_numeral
% 5.06/5.35 thf(fact_4581_power__less__zero__eq__numeral,axiom,
% 5.06/5.35 ! [A: int,W: num] :
% 5.06/5.35 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.06/5.35 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % power_less_zero_eq_numeral
% 5.06/5.35 thf(fact_4582_power__less__zero__eq,axiom,
% 5.06/5.35 ! [A: real,N2: nat] :
% 5.06/5.35 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 5.06/5.35 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.35 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % power_less_zero_eq
% 5.06/5.35 thf(fact_4583_power__less__zero__eq,axiom,
% 5.06/5.35 ! [A: rat,N2: nat] :
% 5.06/5.35 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 5.06/5.35 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.35 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % power_less_zero_eq
% 5.06/5.35 thf(fact_4584_power__less__zero__eq,axiom,
% 5.06/5.35 ! [A: int,N2: nat] :
% 5.06/5.35 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.06/5.35 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.35 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % power_less_zero_eq
% 5.06/5.35 thf(fact_4585_even__plus__one__iff,axiom,
% 5.06/5.35 ! [A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.06/5.35 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_plus_one_iff
% 5.06/5.35 thf(fact_4586_even__plus__one__iff,axiom,
% 5.06/5.35 ! [A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.06/5.35 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_plus_one_iff
% 5.06/5.35 thf(fact_4587_even__plus__one__iff,axiom,
% 5.06/5.35 ! [A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.06/5.35 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_plus_one_iff
% 5.06/5.35 thf(fact_4588_even__diff,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_diff
% 5.06/5.35 thf(fact_4589_even__diff,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.06/5.35 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_diff
% 5.06/5.35 thf(fact_4590_odd__Suc__minus__one,axiom,
% 5.06/5.35 ! [N2: nat] :
% 5.06/5.35 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.35 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.06/5.35 = N2 ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_Suc_minus_one
% 5.06/5.35 thf(fact_4591_even__diff__nat,axiom,
% 5.06/5.35 ! [M: nat,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.35 = ( ( ord_less_nat @ M @ N2 )
% 5.06/5.35 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_diff_nat
% 5.06/5.35 thf(fact_4592_zero__less__power__eq__numeral,axiom,
% 5.06/5.35 ! [A: real,W: num] :
% 5.06/5.35 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.06/5.35 = ( ( ( numeral_numeral_nat @ W )
% 5.06/5.35 = zero_zero_nat )
% 5.06/5.35 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( A != zero_zero_real ) )
% 5.06/5.35 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % zero_less_power_eq_numeral
% 5.06/5.35 thf(fact_4593_zero__less__power__eq__numeral,axiom,
% 5.06/5.35 ! [A: rat,W: num] :
% 5.06/5.35 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.06/5.35 = ( ( ( numeral_numeral_nat @ W )
% 5.06/5.35 = zero_zero_nat )
% 5.06/5.35 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( A != zero_zero_rat ) )
% 5.06/5.35 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % zero_less_power_eq_numeral
% 5.06/5.35 thf(fact_4594_zero__less__power__eq__numeral,axiom,
% 5.06/5.35 ! [A: int,W: num] :
% 5.06/5.35 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.06/5.35 = ( ( ( numeral_numeral_nat @ W )
% 5.06/5.35 = zero_zero_nat )
% 5.06/5.35 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( A != zero_zero_int ) )
% 5.06/5.35 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % zero_less_power_eq_numeral
% 5.06/5.35 thf(fact_4595_even__succ__div__two,axiom,
% 5.06/5.35 ! [A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_div_two
% 5.06/5.35 thf(fact_4596_even__succ__div__two,axiom,
% 5.06/5.35 ! [A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_div_two
% 5.06/5.35 thf(fact_4597_even__succ__div__two,axiom,
% 5.06/5.35 ! [A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_div_two
% 5.06/5.35 thf(fact_4598_odd__succ__div__two,axiom,
% 5.06/5.35 ! [A: code_integer] :
% 5.06/5.35 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_succ_div_two
% 5.06/5.35 thf(fact_4599_odd__succ__div__two,axiom,
% 5.06/5.35 ! [A: nat] :
% 5.06/5.35 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_succ_div_two
% 5.06/5.35 thf(fact_4600_odd__succ__div__two,axiom,
% 5.06/5.35 ! [A: int] :
% 5.06/5.35 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_succ_div_two
% 5.06/5.35 thf(fact_4601_even__succ__div__2,axiom,
% 5.06/5.35 ! [A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_div_2
% 5.06/5.35 thf(fact_4602_even__succ__div__2,axiom,
% 5.06/5.35 ! [A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_div_2
% 5.06/5.35 thf(fact_4603_even__succ__div__2,axiom,
% 5.06/5.35 ! [A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.35 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_succ_div_2
% 5.06/5.35 thf(fact_4604_even__power,axiom,
% 5.06/5.35 ! [A: code_integer,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.06/5.35 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_power
% 5.06/5.35 thf(fact_4605_even__power,axiom,
% 5.06/5.35 ! [A: nat,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 5.06/5.35 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_power
% 5.06/5.35 thf(fact_4606_even__power,axiom,
% 5.06/5.35 ! [A: int,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 5.06/5.35 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % even_power
% 5.06/5.35 thf(fact_4607_odd__two__times__div__two__nat,axiom,
% 5.06/5.35 ! [N2: nat] :
% 5.06/5.35 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.35 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.35 = ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_two_times_div_two_nat
% 5.06/5.35 thf(fact_4608_odd__two__times__div__two__succ,axiom,
% 5.06/5.35 ! [A: code_integer] :
% 5.06/5.35 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.06/5.35 = A ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_two_times_div_two_succ
% 5.06/5.35 thf(fact_4609_odd__two__times__div__two__succ,axiom,
% 5.06/5.35 ! [A: nat] :
% 5.06/5.35 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.06/5.35 = A ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_two_times_div_two_succ
% 5.06/5.35 thf(fact_4610_odd__two__times__div__two__succ,axiom,
% 5.06/5.35 ! [A: int] :
% 5.06/5.35 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.35 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.06/5.35 = A ) ) ).
% 5.06/5.35
% 5.06/5.35 % odd_two_times_div_two_succ
% 5.06/5.35 thf(fact_4611_power__le__zero__eq__numeral,axiom,
% 5.06/5.35 ! [A: real,W: num] :
% 5.06/5.35 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.06/5.35 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.06/5.35 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % power_le_zero_eq_numeral
% 5.06/5.35 thf(fact_4612_power__le__zero__eq__numeral,axiom,
% 5.06/5.35 ! [A: rat,W: num] :
% 5.06/5.35 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.06/5.35 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.06/5.35 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % power_le_zero_eq_numeral
% 5.06/5.35 thf(fact_4613_power__le__zero__eq__numeral,axiom,
% 5.06/5.35 ! [A: int,W: num] :
% 5.06/5.35 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.06/5.35 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.06/5.35 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.35 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % power_le_zero_eq_numeral
% 5.06/5.35 thf(fact_4614_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.06/5.35 ! [N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 5.06/5.35 = ( N2 = zero_zero_nat ) ) ).
% 5.06/5.35
% 5.06/5.35 % semiring_parity_class.even_mask_iff
% 5.06/5.35 thf(fact_4615_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.06/5.35 ! [N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 5.06/5.35 = ( N2 = zero_zero_nat ) ) ).
% 5.06/5.35
% 5.06/5.35 % semiring_parity_class.even_mask_iff
% 5.06/5.35 thf(fact_4616_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.06/5.35 ! [N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 5.06/5.35 = ( N2 = zero_zero_nat ) ) ).
% 5.06/5.35
% 5.06/5.35 % semiring_parity_class.even_mask_iff
% 5.06/5.35 thf(fact_4617_dvd__trans,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_nat @ B @ C )
% 5.06/5.35 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_trans
% 5.06/5.35 thf(fact_4618_dvd__trans,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_int @ B @ C )
% 5.06/5.35 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_trans
% 5.06/5.35 thf(fact_4619_dvd__trans,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ B @ C )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_trans
% 5.06/5.35 thf(fact_4620_dvd__refl,axiom,
% 5.06/5.35 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_refl
% 5.06/5.35 thf(fact_4621_dvd__refl,axiom,
% 5.06/5.35 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_refl
% 5.06/5.35 thf(fact_4622_dvd__refl,axiom,
% 5.06/5.35 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_refl
% 5.06/5.35 thf(fact_4623_division__decomp,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.06/5.35 => ? [B7: nat,C5: nat] :
% 5.06/5.35 ( ( A
% 5.06/5.35 = ( times_times_nat @ B7 @ C5 ) )
% 5.06/5.35 & ( dvd_dvd_nat @ B7 @ B )
% 5.06/5.35 & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % division_decomp
% 5.06/5.35 thf(fact_4624_division__decomp,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.06/5.35 => ? [B7: int,C5: int] :
% 5.06/5.35 ( ( A
% 5.06/5.35 = ( times_times_int @ B7 @ C5 ) )
% 5.06/5.35 & ( dvd_dvd_int @ B7 @ B )
% 5.06/5.35 & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % division_decomp
% 5.06/5.35 thf(fact_4625_dvd__productE,axiom,
% 5.06/5.35 ! [P4: nat,A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ P4 @ ( times_times_nat @ A @ B ) )
% 5.06/5.35 => ~ ! [X3: nat,Y5: nat] :
% 5.06/5.35 ( ( P4
% 5.06/5.35 = ( times_times_nat @ X3 @ Y5 ) )
% 5.06/5.35 => ( ( dvd_dvd_nat @ X3 @ A )
% 5.06/5.35 => ~ ( dvd_dvd_nat @ Y5 @ B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_productE
% 5.06/5.35 thf(fact_4626_dvd__productE,axiom,
% 5.06/5.35 ! [P4: int,A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ P4 @ ( times_times_int @ A @ B ) )
% 5.06/5.35 => ~ ! [X3: int,Y5: int] :
% 5.06/5.35 ( ( P4
% 5.06/5.35 = ( times_times_int @ X3 @ Y5 ) )
% 5.06/5.35 => ( ( dvd_dvd_int @ X3 @ A )
% 5.06/5.35 => ~ ( dvd_dvd_int @ Y5 @ B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_productE
% 5.06/5.35 thf(fact_4627_dvd__0__left,axiom,
% 5.06/5.35 ! [A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.06/5.35 => ( A = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left
% 5.06/5.35 thf(fact_4628_dvd__0__left,axiom,
% 5.06/5.35 ! [A: complex] :
% 5.06/5.35 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.06/5.35 => ( A = zero_zero_complex ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left
% 5.06/5.35 thf(fact_4629_dvd__0__left,axiom,
% 5.06/5.35 ! [A: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.06/5.35 => ( A = zero_zero_real ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left
% 5.06/5.35 thf(fact_4630_dvd__0__left,axiom,
% 5.06/5.35 ! [A: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.06/5.35 => ( A = zero_zero_rat ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left
% 5.06/5.35 thf(fact_4631_dvd__0__left,axiom,
% 5.06/5.35 ! [A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.06/5.35 => ( A = zero_zero_nat ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left
% 5.06/5.35 thf(fact_4632_dvd__0__left,axiom,
% 5.06/5.35 ! [A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.06/5.35 => ( A = zero_zero_int ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_0_left
% 5.06/5.35 thf(fact_4633_dvd__triv__right,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_triv_right
% 5.06/5.35 thf(fact_4634_dvd__triv__right,axiom,
% 5.06/5.35 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_triv_right
% 5.06/5.35 thf(fact_4635_dvd__triv__right,axiom,
% 5.06/5.35 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_triv_right
% 5.06/5.35 thf(fact_4636_dvd__triv__right,axiom,
% 5.06/5.35 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_triv_right
% 5.06/5.35 thf(fact_4637_dvd__triv__right,axiom,
% 5.06/5.35 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_triv_right
% 5.06/5.35 thf(fact_4638_dvd__mult__right,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_right
% 5.06/5.35 thf(fact_4639_dvd__mult__right,axiom,
% 5.06/5.35 ! [A: real,B: real,C: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.06/5.35 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_right
% 5.06/5.35 thf(fact_4640_dvd__mult__right,axiom,
% 5.06/5.35 ! [A: rat,B: rat,C: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.06/5.35 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_right
% 5.06/5.35 thf(fact_4641_dvd__mult__right,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.06/5.35 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_right
% 5.06/5.35 thf(fact_4642_dvd__mult__right,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.06/5.35 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_right
% 5.06/5.35 thf(fact_4643_mult__dvd__mono,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % mult_dvd_mono
% 5.06/5.35 thf(fact_4644_mult__dvd__mono,axiom,
% 5.06/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_real @ C @ D )
% 5.06/5.35 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % mult_dvd_mono
% 5.06/5.35 thf(fact_4645_mult__dvd__mono,axiom,
% 5.06/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_rat @ C @ D )
% 5.06/5.35 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % mult_dvd_mono
% 5.06/5.35 thf(fact_4646_mult__dvd__mono,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_nat @ C @ D )
% 5.06/5.35 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % mult_dvd_mono
% 5.06/5.35 thf(fact_4647_mult__dvd__mono,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_int @ C @ D )
% 5.06/5.35 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % mult_dvd_mono
% 5.06/5.35 thf(fact_4648_dvd__triv__left,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_triv_left
% 5.06/5.35 thf(fact_4649_dvd__triv__left,axiom,
% 5.06/5.35 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_triv_left
% 5.06/5.35 thf(fact_4650_dvd__triv__left,axiom,
% 5.06/5.35 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_triv_left
% 5.06/5.35 thf(fact_4651_dvd__triv__left,axiom,
% 5.06/5.35 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_triv_left
% 5.06/5.35 thf(fact_4652_dvd__triv__left,axiom,
% 5.06/5.35 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_triv_left
% 5.06/5.35 thf(fact_4653_dvd__mult__left,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_left
% 5.06/5.35 thf(fact_4654_dvd__mult__left,axiom,
% 5.06/5.35 ! [A: real,B: real,C: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.06/5.35 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_left
% 5.06/5.35 thf(fact_4655_dvd__mult__left,axiom,
% 5.06/5.35 ! [A: rat,B: rat,C: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.06/5.35 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_left
% 5.06/5.35 thf(fact_4656_dvd__mult__left,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.06/5.35 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_left
% 5.06/5.35 thf(fact_4657_dvd__mult__left,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.06/5.35 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult_left
% 5.06/5.35 thf(fact_4658_dvd__mult2,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult2
% 5.06/5.35 thf(fact_4659_dvd__mult2,axiom,
% 5.06/5.35 ! [A: real,B: real,C: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ A @ B )
% 5.06/5.35 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult2
% 5.06/5.35 thf(fact_4660_dvd__mult2,axiom,
% 5.06/5.35 ! [A: rat,B: rat,C: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ A @ B )
% 5.06/5.35 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult2
% 5.06/5.35 thf(fact_4661_dvd__mult2,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult2
% 5.06/5.35 thf(fact_4662_dvd__mult2,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult2
% 5.06/5.35 thf(fact_4663_dvd__mult,axiom,
% 5.06/5.35 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult
% 5.06/5.35 thf(fact_4664_dvd__mult,axiom,
% 5.06/5.35 ! [A: real,C: real,B: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ A @ C )
% 5.06/5.35 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult
% 5.06/5.35 thf(fact_4665_dvd__mult,axiom,
% 5.06/5.35 ! [A: rat,C: rat,B: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ A @ C )
% 5.06/5.35 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult
% 5.06/5.35 thf(fact_4666_dvd__mult,axiom,
% 5.06/5.35 ! [A: nat,C: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ C )
% 5.06/5.35 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult
% 5.06/5.35 thf(fact_4667_dvd__mult,axiom,
% 5.06/5.35 ! [A: int,C: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ C )
% 5.06/5.35 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mult
% 5.06/5.35 thf(fact_4668_dvd__def,axiom,
% 5.06/5.35 ( dvd_dvd_Code_integer
% 5.06/5.35 = ( ^ [B4: code_integer,A4: code_integer] :
% 5.06/5.35 ? [K3: code_integer] :
% 5.06/5.35 ( A4
% 5.06/5.35 = ( times_3573771949741848930nteger @ B4 @ K3 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_def
% 5.06/5.35 thf(fact_4669_dvd__def,axiom,
% 5.06/5.35 ( dvd_dvd_real
% 5.06/5.35 = ( ^ [B4: real,A4: real] :
% 5.06/5.35 ? [K3: real] :
% 5.06/5.35 ( A4
% 5.06/5.35 = ( times_times_real @ B4 @ K3 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_def
% 5.06/5.35 thf(fact_4670_dvd__def,axiom,
% 5.06/5.35 ( dvd_dvd_rat
% 5.06/5.35 = ( ^ [B4: rat,A4: rat] :
% 5.06/5.35 ? [K3: rat] :
% 5.06/5.35 ( A4
% 5.06/5.35 = ( times_times_rat @ B4 @ K3 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_def
% 5.06/5.35 thf(fact_4671_dvd__def,axiom,
% 5.06/5.35 ( dvd_dvd_nat
% 5.06/5.35 = ( ^ [B4: nat,A4: nat] :
% 5.06/5.35 ? [K3: nat] :
% 5.06/5.35 ( A4
% 5.06/5.35 = ( times_times_nat @ B4 @ K3 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_def
% 5.06/5.35 thf(fact_4672_dvd__def,axiom,
% 5.06/5.35 ( dvd_dvd_int
% 5.06/5.35 = ( ^ [B4: int,A4: int] :
% 5.06/5.35 ? [K3: int] :
% 5.06/5.35 ( A4
% 5.06/5.35 = ( times_times_int @ B4 @ K3 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_def
% 5.06/5.35 thf(fact_4673_dvdI,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.06/5.35 ( ( A
% 5.06/5.35 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvdI
% 5.06/5.35 thf(fact_4674_dvdI,axiom,
% 5.06/5.35 ! [A: real,B: real,K: real] :
% 5.06/5.35 ( ( A
% 5.06/5.35 = ( times_times_real @ B @ K ) )
% 5.06/5.35 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvdI
% 5.06/5.35 thf(fact_4675_dvdI,axiom,
% 5.06/5.35 ! [A: rat,B: rat,K: rat] :
% 5.06/5.35 ( ( A
% 5.06/5.35 = ( times_times_rat @ B @ K ) )
% 5.06/5.35 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvdI
% 5.06/5.35 thf(fact_4676_dvdI,axiom,
% 5.06/5.35 ! [A: nat,B: nat,K: nat] :
% 5.06/5.35 ( ( A
% 5.06/5.35 = ( times_times_nat @ B @ K ) )
% 5.06/5.35 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvdI
% 5.06/5.35 thf(fact_4677_dvdI,axiom,
% 5.06/5.35 ! [A: int,B: int,K: int] :
% 5.06/5.35 ( ( A
% 5.06/5.35 = ( times_times_int @ B @ K ) )
% 5.06/5.35 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvdI
% 5.06/5.35 thf(fact_4678_dvdE,axiom,
% 5.06/5.35 ! [B: code_integer,A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.06/5.35 => ~ ! [K2: code_integer] :
% 5.06/5.35 ( A
% 5.06/5.35 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvdE
% 5.06/5.35 thf(fact_4679_dvdE,axiom,
% 5.06/5.35 ! [B: real,A: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ B @ A )
% 5.06/5.35 => ~ ! [K2: real] :
% 5.06/5.35 ( A
% 5.06/5.35 != ( times_times_real @ B @ K2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvdE
% 5.06/5.35 thf(fact_4680_dvdE,axiom,
% 5.06/5.35 ! [B: rat,A: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ B @ A )
% 5.06/5.35 => ~ ! [K2: rat] :
% 5.06/5.35 ( A
% 5.06/5.35 != ( times_times_rat @ B @ K2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvdE
% 5.06/5.35 thf(fact_4681_dvdE,axiom,
% 5.06/5.35 ! [B: nat,A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ B @ A )
% 5.06/5.35 => ~ ! [K2: nat] :
% 5.06/5.35 ( A
% 5.06/5.35 != ( times_times_nat @ B @ K2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvdE
% 5.06/5.35 thf(fact_4682_dvdE,axiom,
% 5.06/5.35 ! [B: int,A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ B @ A )
% 5.06/5.35 => ~ ! [K2: int] :
% 5.06/5.35 ( A
% 5.06/5.35 != ( times_times_int @ B @ K2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvdE
% 5.06/5.35 thf(fact_4683_dvd__add__right__iff,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_right_iff
% 5.06/5.35 thf(fact_4684_dvd__add__right__iff,axiom,
% 5.06/5.35 ! [A: real,B: real,C: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.06/5.35 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_right_iff
% 5.06/5.35 thf(fact_4685_dvd__add__right__iff,axiom,
% 5.06/5.35 ! [A: rat,B: rat,C: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.06/5.35 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_right_iff
% 5.06/5.35 thf(fact_4686_dvd__add__right__iff,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.06/5.35 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_right_iff
% 5.06/5.35 thf(fact_4687_dvd__add__right__iff,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.06/5.35 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_right_iff
% 5.06/5.35 thf(fact_4688_dvd__add__left__iff,axiom,
% 5.06/5.35 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_left_iff
% 5.06/5.35 thf(fact_4689_dvd__add__left__iff,axiom,
% 5.06/5.35 ! [A: real,C: real,B: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ A @ C )
% 5.06/5.35 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.06/5.35 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_left_iff
% 5.06/5.35 thf(fact_4690_dvd__add__left__iff,axiom,
% 5.06/5.35 ! [A: rat,C: rat,B: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ A @ C )
% 5.06/5.35 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.06/5.35 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_left_iff
% 5.06/5.35 thf(fact_4691_dvd__add__left__iff,axiom,
% 5.06/5.35 ! [A: nat,C: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ C )
% 5.06/5.35 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.06/5.35 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_left_iff
% 5.06/5.35 thf(fact_4692_dvd__add__left__iff,axiom,
% 5.06/5.35 ! [A: int,C: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ C )
% 5.06/5.35 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.06/5.35 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add_left_iff
% 5.06/5.35 thf(fact_4693_dvd__add,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add
% 5.06/5.35 thf(fact_4694_dvd__add,axiom,
% 5.06/5.35 ! [A: real,B: real,C: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_real @ A @ C )
% 5.06/5.35 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add
% 5.06/5.35 thf(fact_4695_dvd__add,axiom,
% 5.06/5.35 ! [A: rat,B: rat,C: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_rat @ A @ C )
% 5.06/5.35 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add
% 5.06/5.35 thf(fact_4696_dvd__add,axiom,
% 5.06/5.35 ! [A: nat,B: nat,C: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_nat @ A @ C )
% 5.06/5.35 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add
% 5.06/5.35 thf(fact_4697_dvd__add,axiom,
% 5.06/5.35 ! [A: int,B: int,C: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_int @ A @ C )
% 5.06/5.35 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_add
% 5.06/5.35 thf(fact_4698_one__dvd,axiom,
% 5.06/5.35 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.06/5.35
% 5.06/5.35 % one_dvd
% 5.06/5.35 thf(fact_4699_one__dvd,axiom,
% 5.06/5.35 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.06/5.35
% 5.06/5.35 % one_dvd
% 5.06/5.35 thf(fact_4700_one__dvd,axiom,
% 5.06/5.35 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.06/5.35
% 5.06/5.35 % one_dvd
% 5.06/5.35 thf(fact_4701_one__dvd,axiom,
% 5.06/5.35 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.06/5.35
% 5.06/5.35 % one_dvd
% 5.06/5.35 thf(fact_4702_one__dvd,axiom,
% 5.06/5.35 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.06/5.35
% 5.06/5.35 % one_dvd
% 5.06/5.35 thf(fact_4703_one__dvd,axiom,
% 5.06/5.35 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.06/5.35
% 5.06/5.35 % one_dvd
% 5.06/5.35 thf(fact_4704_unit__imp__dvd,axiom,
% 5.06/5.35 ! [B: code_integer,A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_imp_dvd
% 5.06/5.35 thf(fact_4705_unit__imp__dvd,axiom,
% 5.06/5.35 ! [B: nat,A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.35 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_imp_dvd
% 5.06/5.35 thf(fact_4706_unit__imp__dvd,axiom,
% 5.06/5.35 ! [B: int,A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.35 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.06/5.35
% 5.06/5.35 % unit_imp_dvd
% 5.06/5.35 thf(fact_4707_dvd__unit__imp__unit,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_unit_imp_unit
% 5.06/5.35 thf(fact_4708_dvd__unit__imp__unit,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.35 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_unit_imp_unit
% 5.06/5.35 thf(fact_4709_dvd__unit__imp__unit,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.35 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_unit_imp_unit
% 5.06/5.35 thf(fact_4710_dvd__diff,axiom,
% 5.06/5.35 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ X @ Z )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ X @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_diff
% 5.06/5.35 thf(fact_4711_dvd__diff,axiom,
% 5.06/5.35 ! [X: real,Y: real,Z: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ X @ Y )
% 5.06/5.35 => ( ( dvd_dvd_real @ X @ Z )
% 5.06/5.35 => ( dvd_dvd_real @ X @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_diff
% 5.06/5.35 thf(fact_4712_dvd__diff,axiom,
% 5.06/5.35 ! [X: rat,Y: rat,Z: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ X @ Y )
% 5.06/5.35 => ( ( dvd_dvd_rat @ X @ Z )
% 5.06/5.35 => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_diff
% 5.06/5.35 thf(fact_4713_dvd__diff,axiom,
% 5.06/5.35 ! [X: int,Y: int,Z: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ X @ Y )
% 5.06/5.35 => ( ( dvd_dvd_int @ X @ Z )
% 5.06/5.35 => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_diff
% 5.06/5.35 thf(fact_4714_dvd__diff__commute,axiom,
% 5.06/5.35 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_diff_commute
% 5.06/5.35 thf(fact_4715_dvd__diff__commute,axiom,
% 5.06/5.35 ! [A: int,C: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.06/5.35 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_diff_commute
% 5.06/5.35 thf(fact_4716_div__div__div__same,axiom,
% 5.06/5.35 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.06/5.35 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.06/5.35 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_div_div_same
% 5.06/5.35 thf(fact_4717_div__div__div__same,axiom,
% 5.06/5.35 ! [D: nat,B: nat,A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ D @ B )
% 5.06/5.35 => ( ( dvd_dvd_nat @ B @ A )
% 5.06/5.35 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.06/5.35 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_div_div_same
% 5.06/5.35 thf(fact_4718_div__div__div__same,axiom,
% 5.06/5.35 ! [D: int,B: int,A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ D @ B )
% 5.06/5.35 => ( ( dvd_dvd_int @ B @ A )
% 5.06/5.35 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.06/5.35 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % div_div_div_same
% 5.06/5.35 thf(fact_4719_dvd__div__eq__cancel,axiom,
% 5.06/5.35 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.35 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.06/5.35 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.35 => ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_cancel
% 5.06/5.35 thf(fact_4720_dvd__div__eq__cancel,axiom,
% 5.06/5.35 ! [A: complex,C: complex,B: complex] :
% 5.06/5.35 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.06/5.35 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.06/5.35 => ( ( dvd_dvd_complex @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_complex @ C @ B )
% 5.06/5.35 => ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_cancel
% 5.06/5.35 thf(fact_4721_dvd__div__eq__cancel,axiom,
% 5.06/5.35 ! [A: real,C: real,B: real] :
% 5.06/5.35 ( ( ( divide_divide_real @ A @ C )
% 5.06/5.35 = ( divide_divide_real @ B @ C ) )
% 5.06/5.35 => ( ( dvd_dvd_real @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_real @ C @ B )
% 5.06/5.35 => ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_cancel
% 5.06/5.35 thf(fact_4722_dvd__div__eq__cancel,axiom,
% 5.06/5.35 ! [A: rat,C: rat,B: rat] :
% 5.06/5.35 ( ( ( divide_divide_rat @ A @ C )
% 5.06/5.35 = ( divide_divide_rat @ B @ C ) )
% 5.06/5.35 => ( ( dvd_dvd_rat @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_rat @ C @ B )
% 5.06/5.35 => ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_cancel
% 5.06/5.35 thf(fact_4723_dvd__div__eq__cancel,axiom,
% 5.06/5.35 ! [A: nat,C: nat,B: nat] :
% 5.06/5.35 ( ( ( divide_divide_nat @ A @ C )
% 5.06/5.35 = ( divide_divide_nat @ B @ C ) )
% 5.06/5.35 => ( ( dvd_dvd_nat @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.35 => ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_cancel
% 5.06/5.35 thf(fact_4724_dvd__div__eq__cancel,axiom,
% 5.06/5.35 ! [A: int,C: int,B: int] :
% 5.06/5.35 ( ( ( divide_divide_int @ A @ C )
% 5.06/5.35 = ( divide_divide_int @ B @ C ) )
% 5.06/5.35 => ( ( dvd_dvd_int @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_int @ C @ B )
% 5.06/5.35 => ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_cancel
% 5.06/5.35 thf(fact_4725_dvd__div__eq__iff,axiom,
% 5.06/5.35 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.35 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.06/5.35 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.06/5.35 = ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_iff
% 5.06/5.35 thf(fact_4726_dvd__div__eq__iff,axiom,
% 5.06/5.35 ! [C: complex,A: complex,B: complex] :
% 5.06/5.35 ( ( dvd_dvd_complex @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_complex @ C @ B )
% 5.06/5.35 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.06/5.35 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.06/5.35 = ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_iff
% 5.06/5.35 thf(fact_4727_dvd__div__eq__iff,axiom,
% 5.06/5.35 ! [C: real,A: real,B: real] :
% 5.06/5.35 ( ( dvd_dvd_real @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_real @ C @ B )
% 5.06/5.35 => ( ( ( divide_divide_real @ A @ C )
% 5.06/5.35 = ( divide_divide_real @ B @ C ) )
% 5.06/5.35 = ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_iff
% 5.06/5.35 thf(fact_4728_dvd__div__eq__iff,axiom,
% 5.06/5.35 ! [C: rat,A: rat,B: rat] :
% 5.06/5.35 ( ( dvd_dvd_rat @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_rat @ C @ B )
% 5.06/5.35 => ( ( ( divide_divide_rat @ A @ C )
% 5.06/5.35 = ( divide_divide_rat @ B @ C ) )
% 5.06/5.35 = ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_iff
% 5.06/5.35 thf(fact_4729_dvd__div__eq__iff,axiom,
% 5.06/5.35 ! [C: nat,A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.35 => ( ( ( divide_divide_nat @ A @ C )
% 5.06/5.35 = ( divide_divide_nat @ B @ C ) )
% 5.06/5.35 = ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_iff
% 5.06/5.35 thf(fact_4730_dvd__div__eq__iff,axiom,
% 5.06/5.35 ! [C: int,A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ C @ A )
% 5.06/5.35 => ( ( dvd_dvd_int @ C @ B )
% 5.06/5.35 => ( ( ( divide_divide_int @ A @ C )
% 5.06/5.35 = ( divide_divide_int @ B @ C ) )
% 5.06/5.35 = ( A = B ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_div_eq_iff
% 5.06/5.35 thf(fact_4731_dvd__power__same,axiom,
% 5.06/5.35 ! [X: code_integer,Y: code_integer,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_power_same
% 5.06/5.35 thf(fact_4732_dvd__power__same,axiom,
% 5.06/5.35 ! [X: nat,Y: nat,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ X @ Y )
% 5.06/5.35 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_power_same
% 5.06/5.35 thf(fact_4733_dvd__power__same,axiom,
% 5.06/5.35 ! [X: real,Y: real,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_real @ X @ Y )
% 5.06/5.35 => ( dvd_dvd_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_power_same
% 5.06/5.35 thf(fact_4734_dvd__power__same,axiom,
% 5.06/5.35 ! [X: int,Y: int,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_int @ X @ Y )
% 5.06/5.35 => ( dvd_dvd_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_power_same
% 5.06/5.35 thf(fact_4735_dvd__power__same,axiom,
% 5.06/5.35 ! [X: complex,Y: complex,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_complex @ X @ Y )
% 5.06/5.35 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_power_same
% 5.06/5.35 thf(fact_4736_mod__mod__cancel,axiom,
% 5.06/5.35 ! [C: nat,B: nat,A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.35 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.06/5.35 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % mod_mod_cancel
% 5.06/5.35 thf(fact_4737_mod__mod__cancel,axiom,
% 5.06/5.35 ! [C: int,B: int,A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ C @ B )
% 5.06/5.35 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.06/5.35 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % mod_mod_cancel
% 5.06/5.35 thf(fact_4738_mod__mod__cancel,axiom,
% 5.06/5.35 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.35 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.06/5.35 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % mod_mod_cancel
% 5.06/5.35 thf(fact_4739_dvd__mod,axiom,
% 5.06/5.35 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ K @ M )
% 5.06/5.35 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.06/5.35 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mod
% 5.06/5.35 thf(fact_4740_dvd__mod,axiom,
% 5.06/5.35 ! [K: int,M: int,N2: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ K @ M )
% 5.06/5.35 => ( ( dvd_dvd_int @ K @ N2 )
% 5.06/5.35 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N2 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mod
% 5.06/5.35 thf(fact_4741_dvd__mod,axiom,
% 5.06/5.35 ! [K: code_integer,M: code_integer,N2: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ K @ N2 )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N2 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mod
% 5.06/5.35 thf(fact_4742_dvd__mod__imp__dvd,axiom,
% 5.06/5.35 ! [C: nat,A: nat,B: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.06/5.35 => ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.35 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mod_imp_dvd
% 5.06/5.35 thf(fact_4743_dvd__mod__imp__dvd,axiom,
% 5.06/5.35 ! [C: int,A: int,B: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.06/5.35 => ( ( dvd_dvd_int @ C @ B )
% 5.06/5.35 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mod_imp_dvd
% 5.06/5.35 thf(fact_4744_dvd__mod__imp__dvd,axiom,
% 5.06/5.35 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.35 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mod_imp_dvd
% 5.06/5.35 thf(fact_4745_dvd__mod__iff,axiom,
% 5.06/5.35 ! [C: nat,B: nat,A: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.35 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.06/5.35 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mod_iff
% 5.06/5.35 thf(fact_4746_dvd__mod__iff,axiom,
% 5.06/5.35 ! [C: int,B: int,A: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ C @ B )
% 5.06/5.35 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.06/5.35 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mod_iff
% 5.06/5.35 thf(fact_4747_dvd__mod__iff,axiom,
% 5.06/5.35 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.35 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_mod_iff
% 5.06/5.35 thf(fact_4748_dvd__diff__nat,axiom,
% 5.06/5.35 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ K @ M )
% 5.06/5.35 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.06/5.35 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_diff_nat
% 5.06/5.35 thf(fact_4749_zdvd__zdiffD,axiom,
% 5.06/5.35 ! [K: int,M: int,N2: int] :
% 5.06/5.35 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N2 ) )
% 5.06/5.35 => ( ( dvd_dvd_int @ K @ N2 )
% 5.06/5.35 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % zdvd_zdiffD
% 5.06/5.35 thf(fact_4750_dvd__pos__nat,axiom,
% 5.06/5.35 ! [N2: nat,M: nat] :
% 5.06/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.35 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.06/5.35 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % dvd_pos_nat
% 5.06/5.35 thf(fact_4751_bezout__lemma__nat,axiom,
% 5.06/5.35 ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ D @ A )
% 5.06/5.35 => ( ( dvd_dvd_nat @ D @ B )
% 5.06/5.35 => ( ( ( ( times_times_nat @ A @ X )
% 5.06/5.35 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 5.06/5.35 | ( ( times_times_nat @ B @ X )
% 5.06/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 5.06/5.35 => ? [X3: nat,Y5: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ D @ A )
% 5.06/5.35 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.06/5.35 & ( ( ( times_times_nat @ A @ X3 )
% 5.06/5.35 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y5 ) @ D ) )
% 5.06/5.35 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 5.06/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D ) ) ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % bezout_lemma_nat
% 5.06/5.35 thf(fact_4752_bezout__add__nat,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ? [D4: nat,X3: nat,Y5: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ D4 @ A )
% 5.06/5.35 & ( dvd_dvd_nat @ D4 @ B )
% 5.06/5.35 & ( ( ( times_times_nat @ A @ X3 )
% 5.06/5.35 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D4 ) )
% 5.06/5.35 | ( ( times_times_nat @ B @ X3 )
% 5.06/5.35 = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D4 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % bezout_add_nat
% 5.06/5.35 thf(fact_4753_bezout1__nat,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ? [D4: nat,X3: nat,Y5: nat] :
% 5.06/5.35 ( ( dvd_dvd_nat @ D4 @ A )
% 5.06/5.35 & ( dvd_dvd_nat @ D4 @ B )
% 5.06/5.35 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y5 ) )
% 5.06/5.35 = D4 )
% 5.06/5.35 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y5 ) )
% 5.06/5.35 = D4 ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % bezout1_nat
% 5.06/5.35 thf(fact_4754_subset__divisors__dvd,axiom,
% 5.06/5.35 ! [A: complex,B: complex] :
% 5.06/5.35 ( ( ord_le211207098394363844omplex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ A ) )
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ B ) ) )
% 5.06/5.35 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % subset_divisors_dvd
% 5.06/5.35 thf(fact_4755_subset__divisors__dvd,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( ord_less_eq_set_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A ) )
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B ) ) )
% 5.06/5.35 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % subset_divisors_dvd
% 5.06/5.35 thf(fact_4756_subset__divisors__dvd,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( ord_le7084787975880047091nteger
% 5.06/5.35 @ ( collect_Code_integer
% 5.06/5.35 @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ A ) )
% 5.06/5.35 @ ( collect_Code_integer
% 5.06/5.35 @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ B ) ) )
% 5.06/5.35 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % subset_divisors_dvd
% 5.06/5.35 thf(fact_4757_subset__divisors__dvd,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( ord_less_eq_set_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A ) )
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B ) ) )
% 5.06/5.35 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.06/5.35
% 5.06/5.35 % subset_divisors_dvd
% 5.06/5.35 thf(fact_4758_concat__bit__assoc,axiom,
% 5.06/5.35 ! [N2: nat,K: int,M: nat,L2: int,R2: int] :
% 5.06/5.35 ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M @ L2 @ R2 ) )
% 5.06/5.35 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L2 ) @ R2 ) ) ).
% 5.06/5.35
% 5.06/5.35 % concat_bit_assoc
% 5.06/5.35 thf(fact_4759_strict__subset__divisors__dvd,axiom,
% 5.06/5.35 ! [A: complex,B: complex] :
% 5.06/5.35 ( ( ord_less_set_complex
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ A ) )
% 5.06/5.35 @ ( collect_complex
% 5.06/5.35 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ B ) ) )
% 5.06/5.35 = ( ( dvd_dvd_complex @ A @ B )
% 5.06/5.35 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % strict_subset_divisors_dvd
% 5.06/5.35 thf(fact_4760_strict__subset__divisors__dvd,axiom,
% 5.06/5.35 ! [A: nat,B: nat] :
% 5.06/5.35 ( ( ord_less_set_nat
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A ) )
% 5.06/5.35 @ ( collect_nat
% 5.06/5.35 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B ) ) )
% 5.06/5.35 = ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.35 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % strict_subset_divisors_dvd
% 5.06/5.35 thf(fact_4761_strict__subset__divisors__dvd,axiom,
% 5.06/5.35 ! [A: int,B: int] :
% 5.06/5.35 ( ( ord_less_set_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A ) )
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B ) ) )
% 5.06/5.35 = ( ( dvd_dvd_int @ A @ B )
% 5.06/5.35 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % strict_subset_divisors_dvd
% 5.06/5.35 thf(fact_4762_strict__subset__divisors__dvd,axiom,
% 5.06/5.35 ! [A: code_integer,B: code_integer] :
% 5.06/5.35 ( ( ord_le1307284697595431911nteger
% 5.06/5.35 @ ( collect_Code_integer
% 5.06/5.35 @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ A ) )
% 5.06/5.35 @ ( collect_Code_integer
% 5.06/5.35 @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ B ) ) )
% 5.06/5.35 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.35 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % strict_subset_divisors_dvd
% 5.06/5.35 thf(fact_4763_finite__divisors__int,axiom,
% 5.06/5.35 ! [I2: int] :
% 5.06/5.35 ( ( I2 != zero_zero_int )
% 5.06/5.35 => ( finite_finite_int
% 5.06/5.35 @ ( collect_int
% 5.06/5.35 @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ I2 ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % finite_divisors_int
% 5.06/5.35 thf(fact_4764_not__is__unit__0,axiom,
% 5.06/5.35 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.06/5.35
% 5.06/5.35 % not_is_unit_0
% 5.06/5.35 thf(fact_4765_not__is__unit__0,axiom,
% 5.06/5.35 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.06/5.35
% 5.06/5.35 % not_is_unit_0
% 5.06/5.35 thf(fact_4766_not__is__unit__0,axiom,
% 5.06/5.35 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.06/5.35
% 5.06/5.35 % not_is_unit_0
% 5.06/5.35 thf(fact_4767_minf_I10_J,axiom,
% 5.06/5.35 ! [D: code_integer,S2: code_integer] :
% 5.06/5.35 ? [Z4: code_integer] :
% 5.06/5.35 ! [X5: code_integer] :
% 5.06/5.35 ( ( ord_le6747313008572928689nteger @ X5 @ Z4 )
% 5.06/5.35 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) )
% 5.06/5.35 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % minf(10)
% 5.06/5.35 thf(fact_4768_minf_I10_J,axiom,
% 5.06/5.35 ! [D: real,S2: real] :
% 5.06/5.35 ? [Z4: real] :
% 5.06/5.35 ! [X5: real] :
% 5.06/5.35 ( ( ord_less_real @ X5 @ Z4 )
% 5.06/5.35 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) )
% 5.06/5.35 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % minf(10)
% 5.06/5.35 thf(fact_4769_minf_I10_J,axiom,
% 5.06/5.35 ! [D: rat,S2: rat] :
% 5.06/5.35 ? [Z4: rat] :
% 5.06/5.35 ! [X5: rat] :
% 5.06/5.35 ( ( ord_less_rat @ X5 @ Z4 )
% 5.06/5.35 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) )
% 5.06/5.35 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % minf(10)
% 5.06/5.35 thf(fact_4770_minf_I10_J,axiom,
% 5.06/5.35 ! [D: nat,S2: nat] :
% 5.06/5.35 ? [Z4: nat] :
% 5.06/5.35 ! [X5: nat] :
% 5.06/5.35 ( ( ord_less_nat @ X5 @ Z4 )
% 5.06/5.35 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) )
% 5.06/5.35 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % minf(10)
% 5.06/5.35 thf(fact_4771_minf_I10_J,axiom,
% 5.06/5.35 ! [D: int,S2: int] :
% 5.06/5.35 ? [Z4: int] :
% 5.06/5.35 ! [X5: int] :
% 5.06/5.35 ( ( ord_less_int @ X5 @ Z4 )
% 5.06/5.35 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) )
% 5.06/5.35 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ) ).
% 5.06/5.35
% 5.06/5.35 % minf(10)
% 5.06/5.35 thf(fact_4772_minf_I9_J,axiom,
% 5.06/5.35 ! [D: code_integer,S2: code_integer] :
% 5.06/5.35 ? [Z4: code_integer] :
% 5.06/5.35 ! [X5: code_integer] :
% 5.06/5.35 ( ( ord_le6747313008572928689nteger @ X5 @ Z4 )
% 5.06/5.35 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % minf(9)
% 5.06/5.36 thf(fact_4773_minf_I9_J,axiom,
% 5.06/5.36 ! [D: real,S2: real] :
% 5.06/5.36 ? [Z4: real] :
% 5.06/5.36 ! [X5: real] :
% 5.06/5.36 ( ( ord_less_real @ X5 @ Z4 )
% 5.06/5.36 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) )
% 5.06/5.36 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % minf(9)
% 5.06/5.36 thf(fact_4774_minf_I9_J,axiom,
% 5.06/5.36 ! [D: rat,S2: rat] :
% 5.06/5.36 ? [Z4: rat] :
% 5.06/5.36 ! [X5: rat] :
% 5.06/5.36 ( ( ord_less_rat @ X5 @ Z4 )
% 5.06/5.36 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) )
% 5.06/5.36 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % minf(9)
% 5.06/5.36 thf(fact_4775_minf_I9_J,axiom,
% 5.06/5.36 ! [D: nat,S2: nat] :
% 5.06/5.36 ? [Z4: nat] :
% 5.06/5.36 ! [X5: nat] :
% 5.06/5.36 ( ( ord_less_nat @ X5 @ Z4 )
% 5.06/5.36 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) )
% 5.06/5.36 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % minf(9)
% 5.06/5.36 thf(fact_4776_minf_I9_J,axiom,
% 5.06/5.36 ! [D: int,S2: int] :
% 5.06/5.36 ? [Z4: int] :
% 5.06/5.36 ! [X5: int] :
% 5.06/5.36 ( ( ord_less_int @ X5 @ Z4 )
% 5.06/5.36 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) )
% 5.06/5.36 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % minf(9)
% 5.06/5.36 thf(fact_4777_pinf_I10_J,axiom,
% 5.06/5.36 ! [D: code_integer,S2: code_integer] :
% 5.06/5.36 ? [Z4: code_integer] :
% 5.06/5.36 ! [X5: code_integer] :
% 5.06/5.36 ( ( ord_le6747313008572928689nteger @ Z4 @ X5 )
% 5.06/5.36 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % pinf(10)
% 5.06/5.36 thf(fact_4778_pinf_I10_J,axiom,
% 5.06/5.36 ! [D: real,S2: real] :
% 5.06/5.36 ? [Z4: real] :
% 5.06/5.36 ! [X5: real] :
% 5.06/5.36 ( ( ord_less_real @ Z4 @ X5 )
% 5.06/5.36 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % pinf(10)
% 5.06/5.36 thf(fact_4779_pinf_I10_J,axiom,
% 5.06/5.36 ! [D: rat,S2: rat] :
% 5.06/5.36 ? [Z4: rat] :
% 5.06/5.36 ! [X5: rat] :
% 5.06/5.36 ( ( ord_less_rat @ Z4 @ X5 )
% 5.06/5.36 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % pinf(10)
% 5.06/5.36 thf(fact_4780_pinf_I10_J,axiom,
% 5.06/5.36 ! [D: nat,S2: nat] :
% 5.06/5.36 ? [Z4: nat] :
% 5.06/5.36 ! [X5: nat] :
% 5.06/5.36 ( ( ord_less_nat @ Z4 @ X5 )
% 5.06/5.36 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % pinf(10)
% 5.06/5.36 thf(fact_4781_pinf_I10_J,axiom,
% 5.06/5.36 ! [D: int,S2: int] :
% 5.06/5.36 ? [Z4: int] :
% 5.06/5.36 ! [X5: int] :
% 5.06/5.36 ( ( ord_less_int @ Z4 @ X5 )
% 5.06/5.36 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % pinf(10)
% 5.06/5.36 thf(fact_4782_pinf_I9_J,axiom,
% 5.06/5.36 ! [D: code_integer,S2: code_integer] :
% 5.06/5.36 ? [Z4: code_integer] :
% 5.06/5.36 ! [X5: code_integer] :
% 5.06/5.36 ( ( ord_le6747313008572928689nteger @ Z4 @ X5 )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % pinf(9)
% 5.06/5.36 thf(fact_4783_pinf_I9_J,axiom,
% 5.06/5.36 ! [D: real,S2: real] :
% 5.06/5.36 ? [Z4: real] :
% 5.06/5.36 ! [X5: real] :
% 5.06/5.36 ( ( ord_less_real @ Z4 @ X5 )
% 5.06/5.36 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) )
% 5.06/5.36 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % pinf(9)
% 5.06/5.36 thf(fact_4784_pinf_I9_J,axiom,
% 5.06/5.36 ! [D: rat,S2: rat] :
% 5.06/5.36 ? [Z4: rat] :
% 5.06/5.36 ! [X5: rat] :
% 5.06/5.36 ( ( ord_less_rat @ Z4 @ X5 )
% 5.06/5.36 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) )
% 5.06/5.36 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % pinf(9)
% 5.06/5.36 thf(fact_4785_pinf_I9_J,axiom,
% 5.06/5.36 ! [D: nat,S2: nat] :
% 5.06/5.36 ? [Z4: nat] :
% 5.06/5.36 ! [X5: nat] :
% 5.06/5.36 ( ( ord_less_nat @ Z4 @ X5 )
% 5.06/5.36 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) )
% 5.06/5.36 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % pinf(9)
% 5.06/5.36 thf(fact_4786_pinf_I9_J,axiom,
% 5.06/5.36 ! [D: int,S2: int] :
% 5.06/5.36 ? [Z4: int] :
% 5.06/5.36 ! [X5: int] :
% 5.06/5.36 ( ( ord_less_int @ Z4 @ X5 )
% 5.06/5.36 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) )
% 5.06/5.36 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % pinf(9)
% 5.06/5.36 thf(fact_4787_dvd__div__eq__0__iff,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.06/5.36 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.06/5.36 = zero_z3403309356797280102nteger )
% 5.06/5.36 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_eq_0_iff
% 5.06/5.36 thf(fact_4788_dvd__div__eq__0__iff,axiom,
% 5.06/5.36 ! [B: complex,A: complex] :
% 5.06/5.36 ( ( dvd_dvd_complex @ B @ A )
% 5.06/5.36 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.06/5.36 = zero_zero_complex )
% 5.06/5.36 = ( A = zero_zero_complex ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_eq_0_iff
% 5.06/5.36 thf(fact_4789_dvd__div__eq__0__iff,axiom,
% 5.06/5.36 ! [B: real,A: real] :
% 5.06/5.36 ( ( dvd_dvd_real @ B @ A )
% 5.06/5.36 => ( ( ( divide_divide_real @ A @ B )
% 5.06/5.36 = zero_zero_real )
% 5.06/5.36 = ( A = zero_zero_real ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_eq_0_iff
% 5.06/5.36 thf(fact_4790_dvd__div__eq__0__iff,axiom,
% 5.06/5.36 ! [B: rat,A: rat] :
% 5.06/5.36 ( ( dvd_dvd_rat @ B @ A )
% 5.06/5.36 => ( ( ( divide_divide_rat @ A @ B )
% 5.06/5.36 = zero_zero_rat )
% 5.06/5.36 = ( A = zero_zero_rat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_eq_0_iff
% 5.06/5.36 thf(fact_4791_dvd__div__eq__0__iff,axiom,
% 5.06/5.36 ! [B: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ A )
% 5.06/5.36 => ( ( ( divide_divide_nat @ A @ B )
% 5.06/5.36 = zero_zero_nat )
% 5.06/5.36 = ( A = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_eq_0_iff
% 5.06/5.36 thf(fact_4792_dvd__div__eq__0__iff,axiom,
% 5.06/5.36 ! [B: int,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ A )
% 5.06/5.36 => ( ( ( divide_divide_int @ A @ B )
% 5.06/5.36 = zero_zero_int )
% 5.06/5.36 = ( A = zero_zero_int ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_eq_0_iff
% 5.06/5.36 thf(fact_4793_unit__mult__right__cancel,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.36 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.06/5.36 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.06/5.36 = ( B = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_mult_right_cancel
% 5.06/5.36 thf(fact_4794_unit__mult__right__cancel,axiom,
% 5.06/5.36 ! [A: nat,B: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.36 => ( ( ( times_times_nat @ B @ A )
% 5.06/5.36 = ( times_times_nat @ C @ A ) )
% 5.06/5.36 = ( B = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_mult_right_cancel
% 5.06/5.36 thf(fact_4795_unit__mult__right__cancel,axiom,
% 5.06/5.36 ! [A: int,B: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.36 => ( ( ( times_times_int @ B @ A )
% 5.06/5.36 = ( times_times_int @ C @ A ) )
% 5.06/5.36 = ( B = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_mult_right_cancel
% 5.06/5.36 thf(fact_4796_unit__mult__left__cancel,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.36 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.06/5.36 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.06/5.36 = ( B = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_mult_left_cancel
% 5.06/5.36 thf(fact_4797_unit__mult__left__cancel,axiom,
% 5.06/5.36 ! [A: nat,B: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.36 => ( ( ( times_times_nat @ A @ B )
% 5.06/5.36 = ( times_times_nat @ A @ C ) )
% 5.06/5.36 = ( B = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_mult_left_cancel
% 5.06/5.36 thf(fact_4798_unit__mult__left__cancel,axiom,
% 5.06/5.36 ! [A: int,B: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.36 => ( ( ( times_times_int @ A @ B )
% 5.06/5.36 = ( times_times_int @ A @ C ) )
% 5.06/5.36 = ( B = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_mult_left_cancel
% 5.06/5.36 thf(fact_4799_mult__unit__dvd__iff_H,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_unit_dvd_iff'
% 5.06/5.36 thf(fact_4800_mult__unit__dvd__iff_H,axiom,
% 5.06/5.36 ! [A: nat,B: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_unit_dvd_iff'
% 5.06/5.36 thf(fact_4801_mult__unit__dvd__iff_H,axiom,
% 5.06/5.36 ! [A: int,B: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_unit_dvd_iff'
% 5.06/5.36 thf(fact_4802_dvd__mult__unit__iff_H,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_unit_iff'
% 5.06/5.36 thf(fact_4803_dvd__mult__unit__iff_H,axiom,
% 5.06/5.36 ! [B: nat,A: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.06/5.36 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_unit_iff'
% 5.06/5.36 thf(fact_4804_dvd__mult__unit__iff_H,axiom,
% 5.06/5.36 ! [B: int,A: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.06/5.36 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_unit_iff'
% 5.06/5.36 thf(fact_4805_mult__unit__dvd__iff,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_unit_dvd_iff
% 5.06/5.36 thf(fact_4806_mult__unit__dvd__iff,axiom,
% 5.06/5.36 ! [B: nat,A: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_unit_dvd_iff
% 5.06/5.36 thf(fact_4807_mult__unit__dvd__iff,axiom,
% 5.06/5.36 ! [B: int,A: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_unit_dvd_iff
% 5.06/5.36 thf(fact_4808_dvd__mult__unit__iff,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_unit_iff
% 5.06/5.36 thf(fact_4809_dvd__mult__unit__iff,axiom,
% 5.06/5.36 ! [B: nat,A: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.06/5.36 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_unit_iff
% 5.06/5.36 thf(fact_4810_dvd__mult__unit__iff,axiom,
% 5.06/5.36 ! [B: int,A: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.06/5.36 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_unit_iff
% 5.06/5.36 thf(fact_4811_is__unit__mult__iff,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.06/5.36 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.36 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_mult_iff
% 5.06/5.36 thf(fact_4812_is__unit__mult__iff,axiom,
% 5.06/5.36 ! [A: nat,B: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.06/5.36 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.36 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_mult_iff
% 5.06/5.36 thf(fact_4813_is__unit__mult__iff,axiom,
% 5.06/5.36 ! [A: int,B: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.06/5.36 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.36 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_mult_iff
% 5.06/5.36 thf(fact_4814_div__mult__div__if__dvd,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.06/5.36 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.06/5.36 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_mult_div_if_dvd
% 5.06/5.36 thf(fact_4815_div__mult__div__if__dvd,axiom,
% 5.06/5.36 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ A )
% 5.06/5.36 => ( ( dvd_dvd_nat @ D @ C )
% 5.06/5.36 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.06/5.36 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_mult_div_if_dvd
% 5.06/5.36 thf(fact_4816_div__mult__div__if__dvd,axiom,
% 5.06/5.36 ! [B: int,A: int,D: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ A )
% 5.06/5.36 => ( ( dvd_dvd_int @ D @ C )
% 5.06/5.36 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.06/5.36 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_mult_div_if_dvd
% 5.06/5.36 thf(fact_4817_dvd__mult__imp__div,axiom,
% 5.06/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.06/5.36 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_imp_div
% 5.06/5.36 thf(fact_4818_dvd__mult__imp__div,axiom,
% 5.06/5.36 ! [A: nat,C: nat,B: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.06/5.36 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_imp_div
% 5.06/5.36 thf(fact_4819_dvd__mult__imp__div,axiom,
% 5.06/5.36 ! [A: int,C: int,B: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.06/5.36 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_imp_div
% 5.06/5.36 thf(fact_4820_dvd__div__mult2__eq,axiom,
% 5.06/5.36 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.06/5.36 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.06/5.36 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_mult2_eq
% 5.06/5.36 thf(fact_4821_dvd__div__mult2__eq,axiom,
% 5.06/5.36 ! [B: nat,C: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.06/5.36 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.06/5.36 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_mult2_eq
% 5.06/5.36 thf(fact_4822_dvd__div__mult2__eq,axiom,
% 5.06/5.36 ! [B: int,C: int,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.06/5.36 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.06/5.36 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_mult2_eq
% 5.06/5.36 thf(fact_4823_div__div__eq__right,axiom,
% 5.06/5.36 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.06/5.36 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.06/5.36 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_div_eq_right
% 5.06/5.36 thf(fact_4824_div__div__eq__right,axiom,
% 5.06/5.36 ! [C: nat,B: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.36 => ( ( dvd_dvd_nat @ B @ A )
% 5.06/5.36 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.06/5.36 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_div_eq_right
% 5.06/5.36 thf(fact_4825_div__div__eq__right,axiom,
% 5.06/5.36 ! [C: int,B: int,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ C @ B )
% 5.06/5.36 => ( ( dvd_dvd_int @ B @ A )
% 5.06/5.36 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.06/5.36 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_div_eq_right
% 5.06/5.36 thf(fact_4826_div__mult__swap,axiom,
% 5.06/5.36 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.36 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.06/5.36 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_mult_swap
% 5.06/5.36 thf(fact_4827_div__mult__swap,axiom,
% 5.06/5.36 ! [C: nat,B: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.36 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.06/5.36 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_mult_swap
% 5.06/5.36 thf(fact_4828_div__mult__swap,axiom,
% 5.06/5.36 ! [C: int,B: int,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ C @ B )
% 5.06/5.36 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.06/5.36 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_mult_swap
% 5.06/5.36 thf(fact_4829_dvd__div__mult,axiom,
% 5.06/5.36 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.36 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.06/5.36 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_mult
% 5.06/5.36 thf(fact_4830_dvd__div__mult,axiom,
% 5.06/5.36 ! [C: nat,B: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.36 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.06/5.36 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_mult
% 5.06/5.36 thf(fact_4831_dvd__div__mult,axiom,
% 5.06/5.36 ! [C: int,B: int,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ C @ B )
% 5.06/5.36 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.06/5.36 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_mult
% 5.06/5.36 thf(fact_4832_div__plus__div__distrib__dvd__right,axiom,
% 5.06/5.36 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.36 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.06/5.36 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_plus_div_distrib_dvd_right
% 5.06/5.36 thf(fact_4833_div__plus__div__distrib__dvd__right,axiom,
% 5.06/5.36 ! [C: nat,B: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.36 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.06/5.36 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_plus_div_distrib_dvd_right
% 5.06/5.36 thf(fact_4834_div__plus__div__distrib__dvd__right,axiom,
% 5.06/5.36 ! [C: int,B: int,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ C @ B )
% 5.06/5.36 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.06/5.36 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_plus_div_distrib_dvd_right
% 5.06/5.36 thf(fact_4835_div__plus__div__distrib__dvd__left,axiom,
% 5.06/5.36 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.06/5.36 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.06/5.36 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_plus_div_distrib_dvd_left
% 5.06/5.36 thf(fact_4836_div__plus__div__distrib__dvd__left,axiom,
% 5.06/5.36 ! [C: nat,A: nat,B: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ C @ A )
% 5.06/5.36 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.06/5.36 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_plus_div_distrib_dvd_left
% 5.06/5.36 thf(fact_4837_div__plus__div__distrib__dvd__left,axiom,
% 5.06/5.36 ! [C: int,A: int,B: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ C @ A )
% 5.06/5.36 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.06/5.36 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_plus_div_distrib_dvd_left
% 5.06/5.36 thf(fact_4838_unit__div__cancel,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.36 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.06/5.36 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.06/5.36 = ( B = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_cancel
% 5.06/5.36 thf(fact_4839_unit__div__cancel,axiom,
% 5.06/5.36 ! [A: nat,B: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.36 => ( ( ( divide_divide_nat @ B @ A )
% 5.06/5.36 = ( divide_divide_nat @ C @ A ) )
% 5.06/5.36 = ( B = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_cancel
% 5.06/5.36 thf(fact_4840_unit__div__cancel,axiom,
% 5.06/5.36 ! [A: int,B: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.36 => ( ( ( divide_divide_int @ B @ A )
% 5.06/5.36 = ( divide_divide_int @ C @ A ) )
% 5.06/5.36 = ( B = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_cancel
% 5.06/5.36 thf(fact_4841_div__unit__dvd__iff,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_unit_dvd_iff
% 5.06/5.36 thf(fact_4842_div__unit__dvd__iff,axiom,
% 5.06/5.36 ! [B: nat,A: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_unit_dvd_iff
% 5.06/5.36 thf(fact_4843_div__unit__dvd__iff,axiom,
% 5.06/5.36 ! [B: int,A: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_unit_dvd_iff
% 5.06/5.36 thf(fact_4844_dvd__div__unit__iff,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_unit_iff
% 5.06/5.36 thf(fact_4845_dvd__div__unit__iff,axiom,
% 5.06/5.36 ! [B: nat,A: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.06/5.36 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_unit_iff
% 5.06/5.36 thf(fact_4846_dvd__div__unit__iff,axiom,
% 5.06/5.36 ! [B: int,A: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.06/5.36 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_unit_iff
% 5.06/5.36 thf(fact_4847_div__power,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.06/5.36 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N2 )
% 5.06/5.36 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_power
% 5.06/5.36 thf(fact_4848_div__power,axiom,
% 5.06/5.36 ! [B: nat,A: nat,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ A )
% 5.06/5.36 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N2 )
% 5.06/5.36 = ( divide_divide_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_power
% 5.06/5.36 thf(fact_4849_div__power,axiom,
% 5.06/5.36 ! [B: int,A: int,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ A )
% 5.06/5.36 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N2 )
% 5.06/5.36 = ( divide_divide_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_power
% 5.06/5.36 thf(fact_4850_mod__eq__0__iff__dvd,axiom,
% 5.06/5.36 ! [A: nat,B: nat] :
% 5.06/5.36 ( ( ( modulo_modulo_nat @ A @ B )
% 5.06/5.36 = zero_zero_nat )
% 5.06/5.36 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_eq_0_iff_dvd
% 5.06/5.36 thf(fact_4851_mod__eq__0__iff__dvd,axiom,
% 5.06/5.36 ! [A: int,B: int] :
% 5.06/5.36 ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.36 = zero_zero_int )
% 5.06/5.36 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_eq_0_iff_dvd
% 5.06/5.36 thf(fact_4852_mod__eq__0__iff__dvd,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer] :
% 5.06/5.36 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.06/5.36 = zero_z3403309356797280102nteger )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_eq_0_iff_dvd
% 5.06/5.36 thf(fact_4853_dvd__eq__mod__eq__0,axiom,
% 5.06/5.36 ( dvd_dvd_nat
% 5.06/5.36 = ( ^ [A4: nat,B4: nat] :
% 5.06/5.36 ( ( modulo_modulo_nat @ B4 @ A4 )
% 5.06/5.36 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_eq_mod_eq_0
% 5.06/5.36 thf(fact_4854_dvd__eq__mod__eq__0,axiom,
% 5.06/5.36 ( dvd_dvd_int
% 5.06/5.36 = ( ^ [A4: int,B4: int] :
% 5.06/5.36 ( ( modulo_modulo_int @ B4 @ A4 )
% 5.06/5.36 = zero_zero_int ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_eq_mod_eq_0
% 5.06/5.36 thf(fact_4855_dvd__eq__mod__eq__0,axiom,
% 5.06/5.36 ( dvd_dvd_Code_integer
% 5.06/5.36 = ( ^ [A4: code_integer,B4: code_integer] :
% 5.06/5.36 ( ( modulo364778990260209775nteger @ B4 @ A4 )
% 5.06/5.36 = zero_z3403309356797280102nteger ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_eq_mod_eq_0
% 5.06/5.36 thf(fact_4856_mod__0__imp__dvd,axiom,
% 5.06/5.36 ! [A: nat,B: nat] :
% 5.06/5.36 ( ( ( modulo_modulo_nat @ A @ B )
% 5.06/5.36 = zero_zero_nat )
% 5.06/5.36 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_0_imp_dvd
% 5.06/5.36 thf(fact_4857_mod__0__imp__dvd,axiom,
% 5.06/5.36 ! [A: int,B: int] :
% 5.06/5.36 ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.36 = zero_zero_int )
% 5.06/5.36 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_0_imp_dvd
% 5.06/5.36 thf(fact_4858_mod__0__imp__dvd,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer] :
% 5.06/5.36 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.06/5.36 = zero_z3403309356797280102nteger )
% 5.06/5.36 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_0_imp_dvd
% 5.06/5.36 thf(fact_4859_dvd__power__le,axiom,
% 5.06/5.36 ! [X: code_integer,Y: code_integer,N2: nat,M: nat] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.06/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.36 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power_le
% 5.06/5.36 thf(fact_4860_dvd__power__le,axiom,
% 5.06/5.36 ! [X: nat,Y: nat,N2: nat,M: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ X @ Y )
% 5.06/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.36 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power_le
% 5.06/5.36 thf(fact_4861_dvd__power__le,axiom,
% 5.06/5.36 ! [X: real,Y: real,N2: nat,M: nat] :
% 5.06/5.36 ( ( dvd_dvd_real @ X @ Y )
% 5.06/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.36 => ( dvd_dvd_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power_le
% 5.06/5.36 thf(fact_4862_dvd__power__le,axiom,
% 5.06/5.36 ! [X: int,Y: int,N2: nat,M: nat] :
% 5.06/5.36 ( ( dvd_dvd_int @ X @ Y )
% 5.06/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.36 => ( dvd_dvd_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power_le
% 5.06/5.36 thf(fact_4863_dvd__power__le,axiom,
% 5.06/5.36 ! [X: complex,Y: complex,N2: nat,M: nat] :
% 5.06/5.36 ( ( dvd_dvd_complex @ X @ Y )
% 5.06/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.36 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power_le
% 5.06/5.36 thf(fact_4864_power__le__dvd,axiom,
% 5.06/5.36 ! [A: code_integer,N2: nat,B: code_integer,M: nat] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ B )
% 5.06/5.36 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_le_dvd
% 5.06/5.36 thf(fact_4865_power__le__dvd,axiom,
% 5.06/5.36 ! [A: nat,N2: nat,B: nat,M: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 5.06/5.36 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_le_dvd
% 5.06/5.36 thf(fact_4866_power__le__dvd,axiom,
% 5.06/5.36 ! [A: real,N2: nat,B: real,M: nat] :
% 5.06/5.36 ( ( dvd_dvd_real @ ( power_power_real @ A @ N2 ) @ B )
% 5.06/5.36 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_le_dvd
% 5.06/5.36 thf(fact_4867_power__le__dvd,axiom,
% 5.06/5.36 ! [A: int,N2: nat,B: int,M: nat] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 5.06/5.36 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_le_dvd
% 5.06/5.36 thf(fact_4868_power__le__dvd,axiom,
% 5.06/5.36 ! [A: complex,N2: nat,B: complex,M: nat] :
% 5.06/5.36 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N2 ) @ B )
% 5.06/5.36 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_le_dvd
% 5.06/5.36 thf(fact_4869_le__imp__power__dvd,axiom,
% 5.06/5.36 ! [M: nat,N2: nat,A: code_integer] :
% 5.06/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % le_imp_power_dvd
% 5.06/5.36 thf(fact_4870_le__imp__power__dvd,axiom,
% 5.06/5.36 ! [M: nat,N2: nat,A: nat] :
% 5.06/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % le_imp_power_dvd
% 5.06/5.36 thf(fact_4871_le__imp__power__dvd,axiom,
% 5.06/5.36 ! [M: nat,N2: nat,A: real] :
% 5.06/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % le_imp_power_dvd
% 5.06/5.36 thf(fact_4872_le__imp__power__dvd,axiom,
% 5.06/5.36 ! [M: nat,N2: nat,A: int] :
% 5.06/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % le_imp_power_dvd
% 5.06/5.36 thf(fact_4873_le__imp__power__dvd,axiom,
% 5.06/5.36 ! [M: nat,N2: nat,A: complex] :
% 5.06/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % le_imp_power_dvd
% 5.06/5.36 thf(fact_4874_dvd__minus__mod,axiom,
% 5.06/5.36 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_minus_mod
% 5.06/5.36 thf(fact_4875_dvd__minus__mod,axiom,
% 5.06/5.36 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_minus_mod
% 5.06/5.36 thf(fact_4876_dvd__minus__mod,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_minus_mod
% 5.06/5.36 thf(fact_4877_mod__eq__dvd__iff,axiom,
% 5.06/5.36 ! [A: int,C: int,B: int] :
% 5.06/5.36 ( ( ( modulo_modulo_int @ A @ C )
% 5.06/5.36 = ( modulo_modulo_int @ B @ C ) )
% 5.06/5.36 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_eq_dvd_iff
% 5.06/5.36 thf(fact_4878_mod__eq__dvd__iff,axiom,
% 5.06/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.06/5.36 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.06/5.36 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_eq_dvd_iff
% 5.06/5.36 thf(fact_4879_nat__dvd__not__less,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.36 => ( ( ord_less_nat @ M @ N2 )
% 5.06/5.36 => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % nat_dvd_not_less
% 5.06/5.36 thf(fact_4880_bezout__add__strong__nat,axiom,
% 5.06/5.36 ! [A: nat,B: nat] :
% 5.06/5.36 ( ( A != zero_zero_nat )
% 5.06/5.36 => ? [D4: nat,X3: nat,Y5: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ D4 @ A )
% 5.06/5.36 & ( dvd_dvd_nat @ D4 @ B )
% 5.06/5.36 & ( ( times_times_nat @ A @ X3 )
% 5.06/5.36 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D4 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bezout_add_strong_nat
% 5.06/5.36 thf(fact_4881_dvd__minus__self,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 5.06/5.36 = ( ( ord_less_nat @ N2 @ M )
% 5.06/5.36 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_minus_self
% 5.06/5.36 thf(fact_4882_zdvd__antisym__nonneg,axiom,
% 5.06/5.36 ! [M: int,N2: int] :
% 5.06/5.36 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.06/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.06/5.36 => ( ( dvd_dvd_int @ M @ N2 )
% 5.06/5.36 => ( ( dvd_dvd_int @ N2 @ M )
% 5.06/5.36 => ( M = N2 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zdvd_antisym_nonneg
% 5.06/5.36 thf(fact_4883_dvd__diffD,axiom,
% 5.06/5.36 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.36 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.06/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.36 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_diffD
% 5.06/5.36 thf(fact_4884_dvd__diffD1,axiom,
% 5.06/5.36 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.36 => ( ( dvd_dvd_nat @ K @ M )
% 5.06/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.36 => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_diffD1
% 5.06/5.36 thf(fact_4885_less__eq__dvd__minus,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.06/5.36 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % less_eq_dvd_minus
% 5.06/5.36 thf(fact_4886_zdvd__mult__cancel,axiom,
% 5.06/5.36 ! [K: int,M: int,N2: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N2 ) )
% 5.06/5.36 => ( ( K != zero_zero_int )
% 5.06/5.36 => ( dvd_dvd_int @ M @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zdvd_mult_cancel
% 5.06/5.36 thf(fact_4887_zdvd__mono,axiom,
% 5.06/5.36 ! [K: int,M: int,T: int] :
% 5.06/5.36 ( ( K != zero_zero_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ M @ T )
% 5.06/5.36 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zdvd_mono
% 5.06/5.36 thf(fact_4888_dbl__def,axiom,
% 5.06/5.36 ( neg_numeral_dbl_real
% 5.06/5.36 = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dbl_def
% 5.06/5.36 thf(fact_4889_dbl__def,axiom,
% 5.06/5.36 ( neg_numeral_dbl_rat
% 5.06/5.36 = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dbl_def
% 5.06/5.36 thf(fact_4890_dbl__def,axiom,
% 5.06/5.36 ( neg_numeral_dbl_int
% 5.06/5.36 = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dbl_def
% 5.06/5.36 thf(fact_4891_zdvd__reduce,axiom,
% 5.06/5.36 ! [K: int,N2: int,M: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N2 @ ( times_times_int @ K @ M ) ) )
% 5.06/5.36 = ( dvd_dvd_int @ K @ N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % zdvd_reduce
% 5.06/5.36 thf(fact_4892_zdvd__period,axiom,
% 5.06/5.36 ! [A: int,D: int,X: int,T: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ A @ D )
% 5.06/5.36 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 5.06/5.36 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zdvd_period
% 5.06/5.36 thf(fact_4893_finite__divisors__nat,axiom,
% 5.06/5.36 ! [M: nat] :
% 5.06/5.36 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.36 => ( finite_finite_nat
% 5.06/5.36 @ ( collect_nat
% 5.06/5.36 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % finite_divisors_nat
% 5.06/5.36 thf(fact_4894_div2__even__ext__nat,axiom,
% 5.06/5.36 ! [X: nat,Y: nat] :
% 5.06/5.36 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.36 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 5.06/5.36 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 5.06/5.36 => ( X = Y ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div2_even_ext_nat
% 5.06/5.36 thf(fact_4895_unity__coeff__ex,axiom,
% 5.06/5.36 ! [P: code_integer > $o,L2: code_integer] :
% 5.06/5.36 ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X2 ) ) )
% 5.06/5.36 = ( ? [X2: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 5.06/5.36 & ( P @ X2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unity_coeff_ex
% 5.06/5.36 thf(fact_4896_unity__coeff__ex,axiom,
% 5.06/5.36 ! [P: complex > $o,L2: complex] :
% 5.06/5.36 ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L2 @ X2 ) ) )
% 5.06/5.36 = ( ? [X2: complex] :
% 5.06/5.36 ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 5.06/5.36 & ( P @ X2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unity_coeff_ex
% 5.06/5.36 thf(fact_4897_unity__coeff__ex,axiom,
% 5.06/5.36 ! [P: real > $o,L2: real] :
% 5.06/5.36 ( ( ? [X2: real] : ( P @ ( times_times_real @ L2 @ X2 ) ) )
% 5.06/5.36 = ( ? [X2: real] :
% 5.06/5.36 ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 5.06/5.36 & ( P @ X2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unity_coeff_ex
% 5.06/5.36 thf(fact_4898_unity__coeff__ex,axiom,
% 5.06/5.36 ! [P: rat > $o,L2: rat] :
% 5.06/5.36 ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L2 @ X2 ) ) )
% 5.06/5.36 = ( ? [X2: rat] :
% 5.06/5.36 ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 5.06/5.36 & ( P @ X2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unity_coeff_ex
% 5.06/5.36 thf(fact_4899_unity__coeff__ex,axiom,
% 5.06/5.36 ! [P: nat > $o,L2: nat] :
% 5.06/5.36 ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L2 @ X2 ) ) )
% 5.06/5.36 = ( ? [X2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 5.06/5.36 & ( P @ X2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unity_coeff_ex
% 5.06/5.36 thf(fact_4900_unity__coeff__ex,axiom,
% 5.06/5.36 ! [P: int > $o,L2: int] :
% 5.06/5.36 ( ( ? [X2: int] : ( P @ ( times_times_int @ L2 @ X2 ) ) )
% 5.06/5.36 = ( ? [X2: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 5.06/5.36 & ( P @ X2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unity_coeff_ex
% 5.06/5.36 thf(fact_4901_unit__dvdE,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.36 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.06/5.36 => ! [C3: code_integer] :
% 5.06/5.36 ( B
% 5.06/5.36 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_dvdE
% 5.06/5.36 thf(fact_4902_unit__dvdE,axiom,
% 5.06/5.36 ! [A: nat,B: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.36 => ~ ( ( A != zero_zero_nat )
% 5.06/5.36 => ! [C3: nat] :
% 5.06/5.36 ( B
% 5.06/5.36 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_dvdE
% 5.06/5.36 thf(fact_4903_unit__dvdE,axiom,
% 5.06/5.36 ! [A: int,B: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.36 => ~ ( ( A != zero_zero_int )
% 5.06/5.36 => ! [C3: int] :
% 5.06/5.36 ( B
% 5.06/5.36 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_dvdE
% 5.06/5.36 thf(fact_4904_dvd__div__div__eq__mult,axiom,
% 5.06/5.36 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.06/5.36 ( ( A != zero_z3403309356797280102nteger )
% 5.06/5.36 => ( ( C != zero_z3403309356797280102nteger )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.06/5.36 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.06/5.36 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.06/5.36 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.06/5.36 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_div_eq_mult
% 5.06/5.36 thf(fact_4905_dvd__div__div__eq__mult,axiom,
% 5.06/5.36 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.06/5.36 ( ( A != zero_zero_nat )
% 5.06/5.36 => ( ( C != zero_zero_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.36 => ( ( dvd_dvd_nat @ C @ D )
% 5.06/5.36 => ( ( ( divide_divide_nat @ B @ A )
% 5.06/5.36 = ( divide_divide_nat @ D @ C ) )
% 5.06/5.36 = ( ( times_times_nat @ B @ C )
% 5.06/5.36 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_div_eq_mult
% 5.06/5.36 thf(fact_4906_dvd__div__div__eq__mult,axiom,
% 5.06/5.36 ! [A: int,C: int,B: int,D: int] :
% 5.06/5.36 ( ( A != zero_zero_int )
% 5.06/5.36 => ( ( C != zero_zero_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ A @ B )
% 5.06/5.36 => ( ( dvd_dvd_int @ C @ D )
% 5.06/5.36 => ( ( ( divide_divide_int @ B @ A )
% 5.06/5.36 = ( divide_divide_int @ D @ C ) )
% 5.06/5.36 = ( ( times_times_int @ B @ C )
% 5.06/5.36 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_div_eq_mult
% 5.06/5.36 thf(fact_4907_dvd__div__iff__mult,axiom,
% 5.06/5.36 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( C != zero_z3403309356797280102nteger )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_iff_mult
% 5.06/5.36 thf(fact_4908_dvd__div__iff__mult,axiom,
% 5.06/5.36 ! [C: nat,B: nat,A: nat] :
% 5.06/5.36 ( ( C != zero_zero_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ C @ B )
% 5.06/5.36 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.06/5.36 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_iff_mult
% 5.06/5.36 thf(fact_4909_dvd__div__iff__mult,axiom,
% 5.06/5.36 ! [C: int,B: int,A: int] :
% 5.06/5.36 ( ( C != zero_zero_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ C @ B )
% 5.06/5.36 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.06/5.36 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_iff_mult
% 5.06/5.36 thf(fact_4910_div__dvd__iff__mult,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.06/5.36 ( ( B != zero_z3403309356797280102nteger )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_dvd_iff_mult
% 5.06/5.36 thf(fact_4911_div__dvd__iff__mult,axiom,
% 5.06/5.36 ! [B: nat,A: nat,C: nat] :
% 5.06/5.36 ( ( B != zero_zero_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ B @ A )
% 5.06/5.36 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_dvd_iff_mult
% 5.06/5.36 thf(fact_4912_div__dvd__iff__mult,axiom,
% 5.06/5.36 ! [B: int,A: int,C: int] :
% 5.06/5.36 ( ( B != zero_zero_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ B @ A )
% 5.06/5.36 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.06/5.36 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_dvd_iff_mult
% 5.06/5.36 thf(fact_4913_dvd__div__eq__mult,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.06/5.36 ( ( A != zero_z3403309356797280102nteger )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.06/5.36 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.06/5.36 = C )
% 5.06/5.36 = ( B
% 5.06/5.36 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_eq_mult
% 5.06/5.36 thf(fact_4914_dvd__div__eq__mult,axiom,
% 5.06/5.36 ! [A: nat,B: nat,C: nat] :
% 5.06/5.36 ( ( A != zero_zero_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ A @ B )
% 5.06/5.36 => ( ( ( divide_divide_nat @ B @ A )
% 5.06/5.36 = C )
% 5.06/5.36 = ( B
% 5.06/5.36 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_eq_mult
% 5.06/5.36 thf(fact_4915_dvd__div__eq__mult,axiom,
% 5.06/5.36 ! [A: int,B: int,C: int] :
% 5.06/5.36 ( ( A != zero_zero_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ A @ B )
% 5.06/5.36 => ( ( ( divide_divide_int @ B @ A )
% 5.06/5.36 = C )
% 5.06/5.36 = ( B
% 5.06/5.36 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_div_eq_mult
% 5.06/5.36 thf(fact_4916_even__numeral,axiom,
% 5.06/5.36 ! [N2: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_numeral
% 5.06/5.36 thf(fact_4917_even__numeral,axiom,
% 5.06/5.36 ! [N2: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_numeral
% 5.06/5.36 thf(fact_4918_even__numeral,axiom,
% 5.06/5.36 ! [N2: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_numeral
% 5.06/5.36 thf(fact_4919_unit__div__eq__0__iff,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.06/5.36 = zero_z3403309356797280102nteger )
% 5.06/5.36 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_eq_0_iff
% 5.06/5.36 thf(fact_4920_unit__div__eq__0__iff,axiom,
% 5.06/5.36 ! [B: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( ( divide_divide_nat @ A @ B )
% 5.06/5.36 = zero_zero_nat )
% 5.06/5.36 = ( A = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_eq_0_iff
% 5.06/5.36 thf(fact_4921_unit__div__eq__0__iff,axiom,
% 5.06/5.36 ! [B: int,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( ( divide_divide_int @ A @ B )
% 5.06/5.36 = zero_zero_int )
% 5.06/5.36 = ( A = zero_zero_int ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_eq_0_iff
% 5.06/5.36 thf(fact_4922_inf__period_I3_J,axiom,
% 5.06/5.36 ! [D: code_integer,D3: code_integer,T: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ D @ D3 )
% 5.06/5.36 => ! [X5: code_integer,K4: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % inf_period(3)
% 5.06/5.36 thf(fact_4923_inf__period_I3_J,axiom,
% 5.06/5.36 ! [D: real,D3: real,T: real] :
% 5.06/5.36 ( ( dvd_dvd_real @ D @ D3 )
% 5.06/5.36 => ! [X5: real,K4: real] :
% 5.06/5.36 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) )
% 5.06/5.36 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % inf_period(3)
% 5.06/5.36 thf(fact_4924_inf__period_I3_J,axiom,
% 5.06/5.36 ! [D: rat,D3: rat,T: rat] :
% 5.06/5.36 ( ( dvd_dvd_rat @ D @ D3 )
% 5.06/5.36 => ! [X5: rat,K4: rat] :
% 5.06/5.36 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) )
% 5.06/5.36 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % inf_period(3)
% 5.06/5.36 thf(fact_4925_inf__period_I3_J,axiom,
% 5.06/5.36 ! [D: int,D3: int,T: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ D @ D3 )
% 5.06/5.36 => ! [X5: int,K4: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.06/5.36 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % inf_period(3)
% 5.06/5.36 thf(fact_4926_inf__period_I4_J,axiom,
% 5.06/5.36 ! [D: code_integer,D3: code_integer,T: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ D @ D3 )
% 5.06/5.36 => ! [X5: code_integer,K4: code_integer] :
% 5.06/5.36 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % inf_period(4)
% 5.06/5.36 thf(fact_4927_inf__period_I4_J,axiom,
% 5.06/5.36 ! [D: real,D3: real,T: real] :
% 5.06/5.36 ( ( dvd_dvd_real @ D @ D3 )
% 5.06/5.36 => ! [X5: real,K4: real] :
% 5.06/5.36 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % inf_period(4)
% 5.06/5.36 thf(fact_4928_inf__period_I4_J,axiom,
% 5.06/5.36 ! [D: rat,D3: rat,T: rat] :
% 5.06/5.36 ( ( dvd_dvd_rat @ D @ D3 )
% 5.06/5.36 => ! [X5: rat,K4: rat] :
% 5.06/5.36 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % inf_period(4)
% 5.06/5.36 thf(fact_4929_inf__period_I4_J,axiom,
% 5.06/5.36 ! [D: int,D3: int,T: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ D @ D3 )
% 5.06/5.36 => ! [X5: int,K4: int] :
% 5.06/5.36 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % inf_period(4)
% 5.06/5.36 thf(fact_4930_is__unit__div__mult2__eq,axiom,
% 5.06/5.36 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.06/5.36 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.06/5.36 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_div_mult2_eq
% 5.06/5.36 thf(fact_4931_is__unit__div__mult2__eq,axiom,
% 5.06/5.36 ! [B: nat,C: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.06/5.36 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.06/5.36 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_div_mult2_eq
% 5.06/5.36 thf(fact_4932_is__unit__div__mult2__eq,axiom,
% 5.06/5.36 ! [B: int,C: int,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.06/5.36 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.06/5.36 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_div_mult2_eq
% 5.06/5.36 thf(fact_4933_unit__div__mult__swap,axiom,
% 5.06/5.36 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.06/5.36 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.06/5.36 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_mult_swap
% 5.06/5.36 thf(fact_4934_unit__div__mult__swap,axiom,
% 5.06/5.36 ! [C: nat,A: nat,B: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.06/5.36 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.06/5.36 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_mult_swap
% 5.06/5.36 thf(fact_4935_unit__div__mult__swap,axiom,
% 5.06/5.36 ! [C: int,A: int,B: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.06/5.36 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.06/5.36 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_mult_swap
% 5.06/5.36 thf(fact_4936_unit__div__commute,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.06/5.36 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_commute
% 5.06/5.36 thf(fact_4937_unit__div__commute,axiom,
% 5.06/5.36 ! [B: nat,A: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.06/5.36 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_commute
% 5.06/5.36 thf(fact_4938_unit__div__commute,axiom,
% 5.06/5.36 ! [B: int,A: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.06/5.36 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_div_commute
% 5.06/5.36 thf(fact_4939_div__mult__unit2,axiom,
% 5.06/5.36 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.06/5.36 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.06/5.36 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_mult_unit2
% 5.06/5.36 thf(fact_4940_div__mult__unit2,axiom,
% 5.06/5.36 ! [C: nat,B: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ B @ A )
% 5.06/5.36 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.06/5.36 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_mult_unit2
% 5.06/5.36 thf(fact_4941_div__mult__unit2,axiom,
% 5.06/5.36 ! [C: int,B: int,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ B @ A )
% 5.06/5.36 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.06/5.36 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % div_mult_unit2
% 5.06/5.36 thf(fact_4942_unit__eq__div2,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( A
% 5.06/5.36 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.06/5.36 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.06/5.36 = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_eq_div2
% 5.06/5.36 thf(fact_4943_unit__eq__div2,axiom,
% 5.06/5.36 ! [B: nat,A: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( A
% 5.06/5.36 = ( divide_divide_nat @ C @ B ) )
% 5.06/5.36 = ( ( times_times_nat @ A @ B )
% 5.06/5.36 = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_eq_div2
% 5.06/5.36 thf(fact_4944_unit__eq__div2,axiom,
% 5.06/5.36 ! [B: int,A: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( A
% 5.06/5.36 = ( divide_divide_int @ C @ B ) )
% 5.06/5.36 = ( ( times_times_int @ A @ B )
% 5.06/5.36 = C ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_eq_div2
% 5.06/5.36 thf(fact_4945_unit__eq__div1,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.06/5.36 = C )
% 5.06/5.36 = ( A
% 5.06/5.36 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_eq_div1
% 5.06/5.36 thf(fact_4946_unit__eq__div1,axiom,
% 5.06/5.36 ! [B: nat,A: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( ( divide_divide_nat @ A @ B )
% 5.06/5.36 = C )
% 5.06/5.36 = ( A
% 5.06/5.36 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_eq_div1
% 5.06/5.36 thf(fact_4947_unit__eq__div1,axiom,
% 5.06/5.36 ! [B: int,A: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( ( divide_divide_int @ A @ B )
% 5.06/5.36 = C )
% 5.06/5.36 = ( A
% 5.06/5.36 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_eq_div1
% 5.06/5.36 thf(fact_4948_is__unit__power__iff,axiom,
% 5.06/5.36 ! [A: code_integer,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer )
% 5.06/5.36 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.36 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_power_iff
% 5.06/5.36 thf(fact_4949_is__unit__power__iff,axiom,
% 5.06/5.36 ! [A: nat,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 5.06/5.36 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.36 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_power_iff
% 5.06/5.36 thf(fact_4950_is__unit__power__iff,axiom,
% 5.06/5.36 ! [A: int,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 5.06/5.36 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.36 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_power_iff
% 5.06/5.36 thf(fact_4951_unit__imp__mod__eq__0,axiom,
% 5.06/5.36 ! [B: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( modulo_modulo_nat @ A @ B )
% 5.06/5.36 = zero_zero_nat ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_imp_mod_eq_0
% 5.06/5.36 thf(fact_4952_unit__imp__mod__eq__0,axiom,
% 5.06/5.36 ! [B: int,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( modulo_modulo_int @ A @ B )
% 5.06/5.36 = zero_zero_int ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_imp_mod_eq_0
% 5.06/5.36 thf(fact_4953_unit__imp__mod__eq__0,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.06/5.36 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.36
% 5.06/5.36 % unit_imp_mod_eq_0
% 5.06/5.36 thf(fact_4954_dvd__imp__le,axiom,
% 5.06/5.36 ! [K: nat,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ K @ N2 )
% 5.06/5.36 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.36 => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_imp_le
% 5.06/5.36 thf(fact_4955_dvd__mult__cancel,axiom,
% 5.06/5.36 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.06/5.36 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.36 => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_cancel
% 5.06/5.36 thf(fact_4956_nat__mult__dvd__cancel1,axiom,
% 5.06/5.36 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.36 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.36 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.06/5.36 = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % nat_mult_dvd_cancel1
% 5.06/5.36 thf(fact_4957_zdvd__imp__le,axiom,
% 5.06/5.36 ! [Z: int,N2: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ Z @ N2 )
% 5.06/5.36 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.06/5.36 => ( ord_less_eq_int @ Z @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zdvd_imp_le
% 5.06/5.36 thf(fact_4958_mod__greater__zero__iff__not__dvd,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_greater_zero_iff_not_dvd
% 5.06/5.36 thf(fact_4959_mod__eq__dvd__iff__nat,axiom,
% 5.06/5.36 ! [N2: nat,M: nat,Q2: nat] :
% 5.06/5.36 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.36 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.06/5.36 = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 5.06/5.36 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_eq_dvd_iff_nat
% 5.06/5.36 thf(fact_4960_prod__decode__aux_Ocases,axiom,
% 5.06/5.36 ! [X: product_prod_nat_nat] :
% 5.06/5.36 ~ ! [K2: nat,M2: nat] :
% 5.06/5.36 ( X
% 5.06/5.36 != ( product_Pair_nat_nat @ K2 @ M2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % prod_decode_aux.cases
% 5.06/5.36 thf(fact_4961_even__zero,axiom,
% 5.06/5.36 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.06/5.36
% 5.06/5.36 % even_zero
% 5.06/5.36 thf(fact_4962_even__zero,axiom,
% 5.06/5.36 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.06/5.36
% 5.06/5.36 % even_zero
% 5.06/5.36 thf(fact_4963_even__zero,axiom,
% 5.06/5.36 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.06/5.36
% 5.06/5.36 % even_zero
% 5.06/5.36 thf(fact_4964_evenE,axiom,
% 5.06/5.36 ! [A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ~ ! [B2: code_integer] :
% 5.06/5.36 ( A
% 5.06/5.36 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % evenE
% 5.06/5.36 thf(fact_4965_evenE,axiom,
% 5.06/5.36 ! [A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ~ ! [B2: nat] :
% 5.06/5.36 ( A
% 5.06/5.36 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % evenE
% 5.06/5.36 thf(fact_4966_evenE,axiom,
% 5.06/5.36 ! [A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ~ ! [B2: int] :
% 5.06/5.36 ( A
% 5.06/5.36 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % evenE
% 5.06/5.36 thf(fact_4967_is__unit__div__mult__cancel__right,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer] :
% 5.06/5.36 ( ( A != zero_z3403309356797280102nteger )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.06/5.36 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_div_mult_cancel_right
% 5.06/5.36 thf(fact_4968_is__unit__div__mult__cancel__right,axiom,
% 5.06/5.36 ! [A: nat,B: nat] :
% 5.06/5.36 ( ( A != zero_zero_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.06/5.36 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_div_mult_cancel_right
% 5.06/5.36 thf(fact_4969_is__unit__div__mult__cancel__right,axiom,
% 5.06/5.36 ! [A: int,B: int] :
% 5.06/5.36 ( ( A != zero_zero_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.06/5.36 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_div_mult_cancel_right
% 5.06/5.36 thf(fact_4970_is__unit__div__mult__cancel__left,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer] :
% 5.06/5.36 ( ( A != zero_z3403309356797280102nteger )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.06/5.36 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.06/5.36 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_div_mult_cancel_left
% 5.06/5.36 thf(fact_4971_is__unit__div__mult__cancel__left,axiom,
% 5.06/5.36 ! [A: nat,B: nat] :
% 5.06/5.36 ( ( A != zero_zero_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.06/5.36 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.06/5.36 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_div_mult_cancel_left
% 5.06/5.36 thf(fact_4972_is__unit__div__mult__cancel__left,axiom,
% 5.06/5.36 ! [A: int,B: int] :
% 5.06/5.36 ( ( A != zero_zero_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.06/5.36 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.06/5.36 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unit_div_mult_cancel_left
% 5.06/5.36 thf(fact_4973_is__unitE,axiom,
% 5.06/5.36 ! [A: code_integer,C: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.06/5.36 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.06/5.36 => ! [B2: code_integer] :
% 5.06/5.36 ( ( B2 != zero_z3403309356797280102nteger )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.06/5.36 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.06/5.36 = B2 )
% 5.06/5.36 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B2 )
% 5.06/5.36 = A )
% 5.06/5.36 => ( ( ( times_3573771949741848930nteger @ A @ B2 )
% 5.06/5.36 = one_one_Code_integer )
% 5.06/5.36 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.06/5.36 != ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unitE
% 5.06/5.36 thf(fact_4974_is__unitE,axiom,
% 5.06/5.36 ! [A: nat,C: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.06/5.36 => ~ ( ( A != zero_zero_nat )
% 5.06/5.36 => ! [B2: nat] :
% 5.06/5.36 ( ( B2 != zero_zero_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.06/5.36 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.06/5.36 = B2 )
% 5.06/5.36 => ( ( ( divide_divide_nat @ one_one_nat @ B2 )
% 5.06/5.36 = A )
% 5.06/5.36 => ( ( ( times_times_nat @ A @ B2 )
% 5.06/5.36 = one_one_nat )
% 5.06/5.36 => ( ( divide_divide_nat @ C @ A )
% 5.06/5.36 != ( times_times_nat @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unitE
% 5.06/5.36 thf(fact_4975_is__unitE,axiom,
% 5.06/5.36 ! [A: int,C: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.06/5.36 => ~ ( ( A != zero_zero_int )
% 5.06/5.36 => ! [B2: int] :
% 5.06/5.36 ( ( B2 != zero_zero_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.06/5.36 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.06/5.36 = B2 )
% 5.06/5.36 => ( ( ( divide_divide_int @ one_one_int @ B2 )
% 5.06/5.36 = A )
% 5.06/5.36 => ( ( ( times_times_int @ A @ B2 )
% 5.06/5.36 = one_one_int )
% 5.06/5.36 => ( ( divide_divide_int @ C @ A )
% 5.06/5.36 != ( times_times_int @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % is_unitE
% 5.06/5.36 thf(fact_4976_odd__even__add,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer] :
% 5.06/5.36 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.06/5.36 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % odd_even_add
% 5.06/5.36 thf(fact_4977_odd__even__add,axiom,
% 5.06/5.36 ! [A: nat,B: nat] :
% 5.06/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.06/5.36 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % odd_even_add
% 5.06/5.36 thf(fact_4978_odd__even__add,axiom,
% 5.06/5.36 ! [A: int,B: int] :
% 5.06/5.36 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.06/5.36 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % odd_even_add
% 5.06/5.36 thf(fact_4979_odd__one,axiom,
% 5.06/5.36 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.06/5.36
% 5.06/5.36 % odd_one
% 5.06/5.36 thf(fact_4980_odd__one,axiom,
% 5.06/5.36 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.06/5.36
% 5.06/5.36 % odd_one
% 5.06/5.36 thf(fact_4981_odd__one,axiom,
% 5.06/5.36 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.06/5.36
% 5.06/5.36 % odd_one
% 5.06/5.36 thf(fact_4982_bit__eq__rec,axiom,
% 5.06/5.36 ( ( ^ [Y4: code_integer,Z3: code_integer] : ( Y4 = Z3 ) )
% 5.06/5.36 = ( ^ [A4: code_integer,B4: code_integer] :
% 5.06/5.36 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) )
% 5.06/5.36 & ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.36 = ( divide6298287555418463151nteger @ B4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bit_eq_rec
% 5.06/5.36 thf(fact_4983_bit__eq__rec,axiom,
% 5.06/5.36 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 5.06/5.36 = ( ^ [A4: nat,B4: nat] :
% 5.06/5.36 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 )
% 5.06/5.36 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) )
% 5.06/5.36 & ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 = ( divide_divide_nat @ B4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bit_eq_rec
% 5.06/5.36 thf(fact_4984_bit__eq__rec,axiom,
% 5.06/5.36 ( ( ^ [Y4: int,Z3: int] : ( Y4 = Z3 ) )
% 5.06/5.36 = ( ^ [A4: int,B4: int] :
% 5.06/5.36 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 )
% 5.06/5.36 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) )
% 5.06/5.36 & ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.36 = ( divide_divide_int @ B4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bit_eq_rec
% 5.06/5.36 thf(fact_4985_dvd__power__iff,axiom,
% 5.06/5.36 ! [X: code_integer,M: nat,N2: nat] :
% 5.06/5.36 ( ( X != zero_z3403309356797280102nteger )
% 5.06/5.36 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 5.06/5.36 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 5.06/5.36 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power_iff
% 5.06/5.36 thf(fact_4986_dvd__power__iff,axiom,
% 5.06/5.36 ! [X: nat,M: nat,N2: nat] :
% 5.06/5.36 ( ( X != zero_zero_nat )
% 5.06/5.36 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N2 ) )
% 5.06/5.36 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 5.06/5.36 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power_iff
% 5.06/5.36 thf(fact_4987_dvd__power__iff,axiom,
% 5.06/5.36 ! [X: int,M: nat,N2: nat] :
% 5.06/5.36 ( ( X != zero_zero_int )
% 5.06/5.36 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N2 ) )
% 5.06/5.36 = ( ( dvd_dvd_int @ X @ one_one_int )
% 5.06/5.36 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power_iff
% 5.06/5.36 thf(fact_4988_dvd__power,axiom,
% 5.06/5.36 ! [N2: nat,X: code_integer] :
% 5.06/5.36 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.36 | ( X = one_one_Code_integer ) )
% 5.06/5.36 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power
% 5.06/5.36 thf(fact_4989_dvd__power,axiom,
% 5.06/5.36 ! [N2: nat,X: rat] :
% 5.06/5.36 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.36 | ( X = one_one_rat ) )
% 5.06/5.36 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power
% 5.06/5.36 thf(fact_4990_dvd__power,axiom,
% 5.06/5.36 ! [N2: nat,X: nat] :
% 5.06/5.36 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.36 | ( X = one_one_nat ) )
% 5.06/5.36 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power
% 5.06/5.36 thf(fact_4991_dvd__power,axiom,
% 5.06/5.36 ! [N2: nat,X: real] :
% 5.06/5.36 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.36 | ( X = one_one_real ) )
% 5.06/5.36 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power
% 5.06/5.36 thf(fact_4992_dvd__power,axiom,
% 5.06/5.36 ! [N2: nat,X: int] :
% 5.06/5.36 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.36 | ( X = one_one_int ) )
% 5.06/5.36 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power
% 5.06/5.36 thf(fact_4993_dvd__power,axiom,
% 5.06/5.36 ! [N2: nat,X: complex] :
% 5.06/5.36 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.36 | ( X = one_one_complex ) )
% 5.06/5.36 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power
% 5.06/5.36 thf(fact_4994_even__even__mod__4__iff,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_even_mod_4_iff
% 5.06/5.36 thf(fact_4995_dvd__mult__cancel1,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.36 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 5.06/5.36 = ( N2 = one_one_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_cancel1
% 5.06/5.36 thf(fact_4996_dvd__mult__cancel2,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.36 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 5.06/5.36 = ( N2 = one_one_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_mult_cancel2
% 5.06/5.36 thf(fact_4997_dvd__minus__add,axiom,
% 5.06/5.36 ! [Q2: nat,N2: nat,R2: nat,M: nat] :
% 5.06/5.36 ( ( ord_less_eq_nat @ Q2 @ N2 )
% 5.06/5.36 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R2 @ M ) )
% 5.06/5.36 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q2 ) )
% 5.06/5.36 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_minus_add
% 5.06/5.36 thf(fact_4998_power__dvd__imp__le,axiom,
% 5.06/5.36 ! [I2: nat,M: nat,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 5.06/5.36 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 5.06/5.36 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_dvd_imp_le
% 5.06/5.36 thf(fact_4999_mod__nat__eqI,axiom,
% 5.06/5.36 ! [R2: nat,N2: nat,M: nat] :
% 5.06/5.36 ( ( ord_less_nat @ R2 @ N2 )
% 5.06/5.36 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.06/5.36 => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R2 ) )
% 5.06/5.36 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.06/5.36 = R2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_nat_eqI
% 5.06/5.36 thf(fact_5000_mod__int__pos__iff,axiom,
% 5.06/5.36 ! [K: int,L2: int] :
% 5.06/5.36 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.06/5.36 = ( ( dvd_dvd_int @ L2 @ K )
% 5.06/5.36 | ( ( L2 = zero_zero_int )
% 5.06/5.36 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.06/5.36 | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod_int_pos_iff
% 5.06/5.36 thf(fact_5001_bset_I9_J,axiom,
% 5.06/5.36 ! [D: int,D3: int,B3: set_int,T: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ D @ D3 )
% 5.06/5.36 => ! [X5: int] :
% 5.06/5.36 ( ! [Xa3: int] :
% 5.06/5.36 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.36 => ! [Xb3: int] :
% 5.06/5.36 ( ( member_int @ Xb3 @ B3 )
% 5.06/5.36 => ( X5
% 5.06/5.36 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.36 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.06/5.36 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bset(9)
% 5.06/5.36 thf(fact_5002_bset_I10_J,axiom,
% 5.06/5.36 ! [D: int,D3: int,B3: set_int,T: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ D @ D3 )
% 5.06/5.36 => ! [X5: int] :
% 5.06/5.36 ( ! [Xa3: int] :
% 5.06/5.36 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.36 => ! [Xb3: int] :
% 5.06/5.36 ( ( member_int @ Xb3 @ B3 )
% 5.06/5.36 => ( X5
% 5.06/5.36 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.36 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.06/5.36 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bset(10)
% 5.06/5.36 thf(fact_5003_aset_I9_J,axiom,
% 5.06/5.36 ! [D: int,D3: int,A2: set_int,T: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ D @ D3 )
% 5.06/5.36 => ! [X5: int] :
% 5.06/5.36 ( ! [Xa3: int] :
% 5.06/5.36 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.36 => ! [Xb3: int] :
% 5.06/5.36 ( ( member_int @ Xb3 @ A2 )
% 5.06/5.36 => ( X5
% 5.06/5.36 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.36 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.06/5.36 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % aset(9)
% 5.06/5.36 thf(fact_5004_aset_I10_J,axiom,
% 5.06/5.36 ! [D: int,D3: int,A2: set_int,T: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ D @ D3 )
% 5.06/5.36 => ! [X5: int] :
% 5.06/5.36 ( ! [Xa3: int] :
% 5.06/5.36 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.06/5.36 => ! [Xb3: int] :
% 5.06/5.36 ( ( member_int @ Xb3 @ A2 )
% 5.06/5.36 => ( X5
% 5.06/5.36 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.06/5.36 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.06/5.36 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % aset(10)
% 5.06/5.36 thf(fact_5005_even__two__times__div__two,axiom,
% 5.06/5.36 ! [A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.06/5.36 = A ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_two_times_div_two
% 5.06/5.36 thf(fact_5006_even__two__times__div__two,axiom,
% 5.06/5.36 ! [A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.36 = A ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_two_times_div_two
% 5.06/5.36 thf(fact_5007_even__two__times__div__two,axiom,
% 5.06/5.36 ! [A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.06/5.36 = A ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_two_times_div_two
% 5.06/5.36 thf(fact_5008_even__iff__mod__2__eq__zero,axiom,
% 5.06/5.36 ! [A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 = zero_zero_nat ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_iff_mod_2_eq_zero
% 5.06/5.36 thf(fact_5009_even__iff__mod__2__eq__zero,axiom,
% 5.06/5.36 ! [A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.36 = zero_zero_int ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_iff_mod_2_eq_zero
% 5.06/5.36 thf(fact_5010_even__iff__mod__2__eq__zero,axiom,
% 5.06/5.36 ! [A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.36 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_iff_mod_2_eq_zero
% 5.06/5.36 thf(fact_5011_odd__iff__mod__2__eq__one,axiom,
% 5.06/5.36 ! [A: nat] :
% 5.06/5.36 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.06/5.36 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 = one_one_nat ) ) ).
% 5.06/5.36
% 5.06/5.36 % odd_iff_mod_2_eq_one
% 5.06/5.36 thf(fact_5012_odd__iff__mod__2__eq__one,axiom,
% 5.06/5.36 ! [A: int] :
% 5.06/5.36 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.06/5.36 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.36 = one_one_int ) ) ).
% 5.06/5.36
% 5.06/5.36 % odd_iff_mod_2_eq_one
% 5.06/5.36 thf(fact_5013_odd__iff__mod__2__eq__one,axiom,
% 5.06/5.36 ! [A: code_integer] :
% 5.06/5.36 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.06/5.36 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.36 = one_one_Code_integer ) ) ).
% 5.06/5.36
% 5.06/5.36 % odd_iff_mod_2_eq_one
% 5.06/5.36 thf(fact_5014_power__mono__odd,axiom,
% 5.06/5.36 ! [N2: nat,A: real,B: real] :
% 5.06/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 => ( ( ord_less_eq_real @ A @ B )
% 5.06/5.36 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_mono_odd
% 5.06/5.36 thf(fact_5015_power__mono__odd,axiom,
% 5.06/5.36 ! [N2: nat,A: rat,B: rat] :
% 5.06/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 => ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.36 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_mono_odd
% 5.06/5.36 thf(fact_5016_power__mono__odd,axiom,
% 5.06/5.36 ! [N2: nat,A: int,B: int] :
% 5.06/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 => ( ( ord_less_eq_int @ A @ B )
% 5.06/5.36 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_mono_odd
% 5.06/5.36 thf(fact_5017_odd__pos,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % odd_pos
% 5.06/5.36 thf(fact_5018_dvd__power__iff__le,axiom,
% 5.06/5.36 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.36 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.06/5.36 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) )
% 5.06/5.36 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_power_iff_le
% 5.06/5.36 thf(fact_5019_even__unset__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.06/5.36 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 | ( M = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_unset_bit_iff
% 5.06/5.36 thf(fact_5020_even__unset__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.06/5.36 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 | ( M = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_unset_bit_iff
% 5.06/5.36 thf(fact_5021_even__unset__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.06/5.36 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 | ( M = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_unset_bit_iff
% 5.06/5.36 thf(fact_5022_even__set__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.06/5.36 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 & ( M != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_set_bit_iff
% 5.06/5.36 thf(fact_5023_even__set__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.06/5.36 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 & ( M != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_set_bit_iff
% 5.06/5.36 thf(fact_5024_even__set__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.06/5.36 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 & ( M != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_set_bit_iff
% 5.06/5.36 thf(fact_5025_even__flip__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.06/5.36 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 != ( M = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_flip_bit_iff
% 5.06/5.36 thf(fact_5026_even__flip__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.06/5.36 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 != ( M = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_flip_bit_iff
% 5.06/5.36 thf(fact_5027_even__flip__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.06/5.36 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 != ( M = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_flip_bit_iff
% 5.06/5.36 thf(fact_5028_even__diff__iff,axiom,
% 5.06/5.36 ! [K: int,L2: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 5.06/5.36 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_diff_iff
% 5.06/5.36 thf(fact_5029_oddE,axiom,
% 5.06/5.36 ! [A: code_integer] :
% 5.06/5.36 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ~ ! [B2: code_integer] :
% 5.06/5.36 ( A
% 5.06/5.36 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) @ one_one_Code_integer ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % oddE
% 5.06/5.36 thf(fact_5030_oddE,axiom,
% 5.06/5.36 ! [A: nat] :
% 5.06/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ~ ! [B2: nat] :
% 5.06/5.36 ( A
% 5.06/5.36 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) @ one_one_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % oddE
% 5.06/5.36 thf(fact_5031_oddE,axiom,
% 5.06/5.36 ! [A: int] :
% 5.06/5.36 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ~ ! [B2: int] :
% 5.06/5.36 ( A
% 5.06/5.36 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % oddE
% 5.06/5.36 thf(fact_5032_parity__cases,axiom,
% 5.06/5.36 ! [A: nat] :
% 5.06/5.36 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 != zero_zero_nat ) )
% 5.06/5.36 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 != one_one_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % parity_cases
% 5.06/5.36 thf(fact_5033_parity__cases,axiom,
% 5.06/5.36 ! [A: int] :
% 5.06/5.36 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.36 != zero_zero_int ) )
% 5.06/5.36 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.36 != one_one_int ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % parity_cases
% 5.06/5.36 thf(fact_5034_parity__cases,axiom,
% 5.06/5.36 ! [A: code_integer] :
% 5.06/5.36 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.36 != zero_z3403309356797280102nteger ) )
% 5.06/5.36 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.36 != one_one_Code_integer ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % parity_cases
% 5.06/5.36 thf(fact_5035_mod2__eq__if,axiom,
% 5.06/5.36 ! [A: nat] :
% 5.06/5.36 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 = zero_zero_nat ) )
% 5.06/5.36 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 = one_one_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod2_eq_if
% 5.06/5.36 thf(fact_5036_mod2__eq__if,axiom,
% 5.06/5.36 ! [A: int] :
% 5.06/5.36 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.36 = zero_zero_int ) )
% 5.06/5.36 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.36 = one_one_int ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod2_eq_if
% 5.06/5.36 thf(fact_5037_mod2__eq__if,axiom,
% 5.06/5.36 ! [A: code_integer] :
% 5.06/5.36 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.36 = zero_z3403309356797280102nteger ) )
% 5.06/5.36 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.06/5.36 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.36 = one_one_Code_integer ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mod2_eq_if
% 5.06/5.36 thf(fact_5038_zero__le__even__power,axiom,
% 5.06/5.36 ! [N2: nat,A: real] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_le_even_power
% 5.06/5.36 thf(fact_5039_zero__le__even__power,axiom,
% 5.06/5.36 ! [N2: nat,A: rat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_le_even_power
% 5.06/5.36 thf(fact_5040_zero__le__even__power,axiom,
% 5.06/5.36 ! [N2: nat,A: int] :
% 5.06/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_le_even_power
% 5.06/5.36 thf(fact_5041_zero__le__odd__power,axiom,
% 5.06/5.36 ! [N2: nat,A: real] :
% 5.06/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.06/5.36 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_le_odd_power
% 5.06/5.36 thf(fact_5042_zero__le__odd__power,axiom,
% 5.06/5.36 ! [N2: nat,A: rat] :
% 5.06/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.06/5.36 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_le_odd_power
% 5.06/5.36 thf(fact_5043_zero__le__odd__power,axiom,
% 5.06/5.36 ! [N2: nat,A: int] :
% 5.06/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.06/5.36 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_le_odd_power
% 5.06/5.36 thf(fact_5044_zero__le__power__eq,axiom,
% 5.06/5.36 ! [A: real,N2: nat] :
% 5.06/5.36 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.06/5.36 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_le_power_eq
% 5.06/5.36 thf(fact_5045_zero__le__power__eq,axiom,
% 5.06/5.36 ! [A: rat,N2: nat] :
% 5.06/5.36 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.06/5.36 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_le_power_eq
% 5.06/5.36 thf(fact_5046_zero__le__power__eq,axiom,
% 5.06/5.36 ! [A: int,N2: nat] :
% 5.06/5.36 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.06/5.36 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_le_power_eq
% 5.06/5.36 thf(fact_5047_list__decode_Ocases,axiom,
% 5.06/5.36 ! [X: nat] :
% 5.06/5.36 ( ( X != zero_zero_nat )
% 5.06/5.36 => ~ ! [N3: nat] :
% 5.06/5.36 ( X
% 5.06/5.36 != ( suc @ N3 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % list_decode.cases
% 5.06/5.36 thf(fact_5048_zero__less__power__eq,axiom,
% 5.06/5.36 ! [A: real,N2: nat] :
% 5.06/5.36 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.06/5.36 = ( ( N2 = zero_zero_nat )
% 5.06/5.36 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( A != zero_zero_real ) )
% 5.06/5.36 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_power_eq
% 5.06/5.36 thf(fact_5049_zero__less__power__eq,axiom,
% 5.06/5.36 ! [A: rat,N2: nat] :
% 5.06/5.36 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.06/5.36 = ( ( N2 = zero_zero_nat )
% 5.06/5.36 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( A != zero_zero_rat ) )
% 5.06/5.36 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_power_eq
% 5.06/5.36 thf(fact_5050_zero__less__power__eq,axiom,
% 5.06/5.36 ! [A: int,N2: nat] :
% 5.06/5.36 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.06/5.36 = ( ( N2 = zero_zero_nat )
% 5.06/5.36 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( A != zero_zero_int ) )
% 5.06/5.36 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_power_eq
% 5.06/5.36 thf(fact_5051_Euclid__induct,axiom,
% 5.06/5.36 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.06/5.36 ( ! [A3: nat,B2: nat] :
% 5.06/5.36 ( ( P @ A3 @ B2 )
% 5.06/5.36 = ( P @ B2 @ A3 ) )
% 5.06/5.36 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 5.06/5.36 => ( ! [A3: nat,B2: nat] :
% 5.06/5.36 ( ( P @ A3 @ B2 )
% 5.06/5.36 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B2 ) ) )
% 5.06/5.36 => ( P @ A @ B ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % Euclid_induct
% 5.06/5.36 thf(fact_5052_even__mask__div__iff_H,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( 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 ) ) @ N2 ) ) )
% 5.06/5.36 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_mask_div_iff'
% 5.06/5.36 thf(fact_5053_even__mask__div__iff_H,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( 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 ) ) @ N2 ) ) )
% 5.06/5.36 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_mask_div_iff'
% 5.06/5.36 thf(fact_5054_even__mask__div__iff_H,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( 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 ) ) @ N2 ) ) )
% 5.06/5.36 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_mask_div_iff'
% 5.06/5.36 thf(fact_5055_power__le__zero__eq,axiom,
% 5.06/5.36 ! [A: real,N2: nat] :
% 5.06/5.36 ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 5.06/5.36 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.36 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.06/5.36 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_le_zero_eq
% 5.06/5.36 thf(fact_5056_power__le__zero__eq,axiom,
% 5.06/5.36 ! [A: rat,N2: nat] :
% 5.06/5.36 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 5.06/5.36 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.36 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.06/5.36 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_le_zero_eq
% 5.06/5.36 thf(fact_5057_power__le__zero__eq,axiom,
% 5.06/5.36 ! [A: int,N2: nat] :
% 5.06/5.36 ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.06/5.36 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.36 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.06/5.36 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % power_le_zero_eq
% 5.06/5.36 thf(fact_5058_even__mod__4__div__2,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.06/5.36 = ( suc @ zero_zero_nat ) )
% 5.06/5.36 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_mod_4_div_2
% 5.06/5.36 thf(fact_5059_even__mask__div__iff,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( 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 ) ) @ N2 ) ) )
% 5.06/5.36 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 = zero_z3403309356797280102nteger )
% 5.06/5.36 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_mask_div_iff
% 5.06/5.36 thf(fact_5060_even__mask__div__iff,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( 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 ) ) @ N2 ) ) )
% 5.06/5.36 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 = zero_zero_nat )
% 5.06/5.36 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_mask_div_iff
% 5.06/5.36 thf(fact_5061_even__mask__div__iff,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( 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 ) ) @ N2 ) ) )
% 5.06/5.36 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 = zero_zero_int )
% 5.06/5.36 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_mask_div_iff
% 5.06/5.36 thf(fact_5062_even__mult__exp__div__exp__iff,axiom,
% 5.06/5.36 ! [A: code_integer,M: nat,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.36 = ( ( ord_less_nat @ N2 @ M )
% 5.06/5.36 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 = zero_z3403309356797280102nteger )
% 5.06/5.36 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_mult_exp_div_exp_iff
% 5.06/5.36 thf(fact_5063_even__mult__exp__div__exp__iff,axiom,
% 5.06/5.36 ! [A: nat,M: nat,N2: nat] :
% 5.06/5.36 ( ( 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 ) ) @ N2 ) ) )
% 5.06/5.36 = ( ( ord_less_nat @ N2 @ M )
% 5.06/5.36 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 = zero_zero_nat )
% 5.06/5.36 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_mult_exp_div_exp_iff
% 5.06/5.36 thf(fact_5064_even__mult__exp__div__exp__iff,axiom,
% 5.06/5.36 ! [A: int,M: nat,N2: nat] :
% 5.06/5.36 ( ( 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 ) ) @ N2 ) ) )
% 5.06/5.36 = ( ( ord_less_nat @ N2 @ M )
% 5.06/5.36 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.36 = zero_zero_int )
% 5.06/5.36 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.36 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_mult_exp_div_exp_iff
% 5.06/5.36 thf(fact_5065_infinite__growing,axiom,
% 5.06/5.36 ! [X8: set_real] :
% 5.06/5.36 ( ( X8 != bot_bot_set_real )
% 5.06/5.36 => ( ! [X3: real] :
% 5.06/5.36 ( ( member_real @ X3 @ X8 )
% 5.06/5.36 => ? [Xa: real] :
% 5.06/5.36 ( ( member_real @ Xa @ X8 )
% 5.06/5.36 & ( ord_less_real @ X3 @ Xa ) ) )
% 5.06/5.36 => ~ ( finite_finite_real @ X8 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % infinite_growing
% 5.06/5.36 thf(fact_5066_infinite__growing,axiom,
% 5.06/5.36 ! [X8: set_rat] :
% 5.06/5.36 ( ( X8 != bot_bot_set_rat )
% 5.06/5.36 => ( ! [X3: rat] :
% 5.06/5.36 ( ( member_rat @ X3 @ X8 )
% 5.06/5.36 => ? [Xa: rat] :
% 5.06/5.36 ( ( member_rat @ Xa @ X8 )
% 5.06/5.36 & ( ord_less_rat @ X3 @ Xa ) ) )
% 5.06/5.36 => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % infinite_growing
% 5.06/5.36 thf(fact_5067_infinite__growing,axiom,
% 5.06/5.36 ! [X8: set_num] :
% 5.06/5.36 ( ( X8 != bot_bot_set_num )
% 5.06/5.36 => ( ! [X3: num] :
% 5.06/5.36 ( ( member_num @ X3 @ X8 )
% 5.06/5.36 => ? [Xa: num] :
% 5.06/5.36 ( ( member_num @ Xa @ X8 )
% 5.06/5.36 & ( ord_less_num @ X3 @ Xa ) ) )
% 5.06/5.36 => ~ ( finite_finite_num @ X8 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % infinite_growing
% 5.06/5.36 thf(fact_5068_infinite__growing,axiom,
% 5.06/5.36 ! [X8: set_nat] :
% 5.06/5.36 ( ( X8 != bot_bot_set_nat )
% 5.06/5.36 => ( ! [X3: nat] :
% 5.06/5.36 ( ( member_nat @ X3 @ X8 )
% 5.06/5.36 => ? [Xa: nat] :
% 5.06/5.36 ( ( member_nat @ Xa @ X8 )
% 5.06/5.36 & ( ord_less_nat @ X3 @ Xa ) ) )
% 5.06/5.36 => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % infinite_growing
% 5.06/5.36 thf(fact_5069_infinite__growing,axiom,
% 5.06/5.36 ! [X8: set_int] :
% 5.06/5.36 ( ( X8 != bot_bot_set_int )
% 5.06/5.36 => ( ! [X3: int] :
% 5.06/5.36 ( ( member_int @ X3 @ X8 )
% 5.06/5.36 => ? [Xa: int] :
% 5.06/5.36 ( ( member_int @ Xa @ X8 )
% 5.06/5.36 & ( ord_less_int @ X3 @ Xa ) ) )
% 5.06/5.36 => ~ ( finite_finite_int @ X8 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % infinite_growing
% 5.06/5.36 thf(fact_5070_ex__min__if__finite,axiom,
% 5.06/5.36 ! [S3: set_real] :
% 5.06/5.36 ( ( finite_finite_real @ S3 )
% 5.06/5.36 => ( ( S3 != bot_bot_set_real )
% 5.06/5.36 => ? [X3: real] :
% 5.06/5.36 ( ( member_real @ X3 @ S3 )
% 5.06/5.36 & ~ ? [Xa: real] :
% 5.06/5.36 ( ( member_real @ Xa @ S3 )
% 5.06/5.36 & ( ord_less_real @ Xa @ X3 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % ex_min_if_finite
% 5.06/5.36 thf(fact_5071_ex__min__if__finite,axiom,
% 5.06/5.36 ! [S3: set_rat] :
% 5.06/5.36 ( ( finite_finite_rat @ S3 )
% 5.06/5.36 => ( ( S3 != bot_bot_set_rat )
% 5.06/5.36 => ? [X3: rat] :
% 5.06/5.36 ( ( member_rat @ X3 @ S3 )
% 5.06/5.36 & ~ ? [Xa: rat] :
% 5.06/5.36 ( ( member_rat @ Xa @ S3 )
% 5.06/5.36 & ( ord_less_rat @ Xa @ X3 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % ex_min_if_finite
% 5.06/5.36 thf(fact_5072_ex__min__if__finite,axiom,
% 5.06/5.36 ! [S3: set_num] :
% 5.06/5.36 ( ( finite_finite_num @ S3 )
% 5.06/5.36 => ( ( S3 != bot_bot_set_num )
% 5.06/5.36 => ? [X3: num] :
% 5.06/5.36 ( ( member_num @ X3 @ S3 )
% 5.06/5.36 & ~ ? [Xa: num] :
% 5.06/5.36 ( ( member_num @ Xa @ S3 )
% 5.06/5.36 & ( ord_less_num @ Xa @ X3 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % ex_min_if_finite
% 5.06/5.36 thf(fact_5073_ex__min__if__finite,axiom,
% 5.06/5.36 ! [S3: set_nat] :
% 5.06/5.36 ( ( finite_finite_nat @ S3 )
% 5.06/5.36 => ( ( S3 != bot_bot_set_nat )
% 5.06/5.36 => ? [X3: nat] :
% 5.06/5.36 ( ( member_nat @ X3 @ S3 )
% 5.06/5.36 & ~ ? [Xa: nat] :
% 5.06/5.36 ( ( member_nat @ Xa @ S3 )
% 5.06/5.36 & ( ord_less_nat @ Xa @ X3 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % ex_min_if_finite
% 5.06/5.36 thf(fact_5074_ex__min__if__finite,axiom,
% 5.06/5.36 ! [S3: set_int] :
% 5.06/5.36 ( ( finite_finite_int @ S3 )
% 5.06/5.36 => ( ( S3 != bot_bot_set_int )
% 5.06/5.36 => ? [X3: int] :
% 5.06/5.36 ( ( member_int @ X3 @ S3 )
% 5.06/5.36 & ~ ? [Xa: int] :
% 5.06/5.36 ( ( member_int @ Xa @ S3 )
% 5.06/5.36 & ( ord_less_int @ Xa @ X3 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % ex_min_if_finite
% 5.06/5.36 thf(fact_5075_triangle__def,axiom,
% 5.06/5.36 ( nat_triangle
% 5.06/5.36 = ( ^ [N: nat] : ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % triangle_def
% 5.06/5.36 thf(fact_5076_vebt__buildup_Oelims,axiom,
% 5.06/5.36 ! [X: nat,Y: vEBT_VEBT] :
% 5.06/5.36 ( ( ( vEBT_vebt_buildup @ X )
% 5.06/5.36 = Y )
% 5.06/5.36 => ( ( ( X = zero_zero_nat )
% 5.06/5.36 => ( Y
% 5.06/5.36 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.06/5.36 => ( ( ( X
% 5.06/5.36 = ( suc @ zero_zero_nat ) )
% 5.06/5.36 => ( Y
% 5.06/5.36 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.06/5.36 => ~ ! [Va2: nat] :
% 5.06/5.36 ( ( X
% 5.06/5.36 = ( suc @ ( suc @ Va2 ) ) )
% 5.06/5.36 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.06/5.36 => ( Y
% 5.06/5.36 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.06/5.36 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.06/5.36 => ( Y
% 5.06/5.36 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % vebt_buildup.elims
% 5.06/5.36 thf(fact_5077_flip__bit__0,axiom,
% 5.06/5.36 ! [A: code_integer] :
% 5.06/5.36 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.06/5.36 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % flip_bit_0
% 5.06/5.36 thf(fact_5078_flip__bit__0,axiom,
% 5.06/5.36 ! [A: int] :
% 5.06/5.36 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.06/5.36 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % flip_bit_0
% 5.06/5.36 thf(fact_5079_flip__bit__0,axiom,
% 5.06/5.36 ! [A: nat] :
% 5.06/5.36 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.06/5.36 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % flip_bit_0
% 5.06/5.36 thf(fact_5080_option_Osize__gen_I2_J,axiom,
% 5.06/5.36 ! [X: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 5.06/5.36 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.06/5.36 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % option.size_gen(2)
% 5.06/5.36 thf(fact_5081_option_Osize__gen_I2_J,axiom,
% 5.06/5.36 ! [X: nat > nat,X22: nat] :
% 5.06/5.36 ( ( size_option_nat @ X @ ( some_nat @ X22 ) )
% 5.06/5.36 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % option.size_gen(2)
% 5.06/5.36 thf(fact_5082_option_Osize__gen_I2_J,axiom,
% 5.06/5.36 ! [X: num > nat,X22: num] :
% 5.06/5.36 ( ( size_option_num @ X @ ( some_num @ X22 ) )
% 5.06/5.36 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % option.size_gen(2)
% 5.06/5.36 thf(fact_5083_signed__take__bit__Suc,axiom,
% 5.06/5.36 ! [N2: nat,A: code_integer] :
% 5.06/5.36 ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 5.06/5.36 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_Suc
% 5.06/5.36 thf(fact_5084_signed__take__bit__Suc,axiom,
% 5.06/5.36 ! [N2: nat,A: int] :
% 5.06/5.36 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 5.06/5.36 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_Suc
% 5.06/5.36 thf(fact_5085_set__decode__Suc,axiom,
% 5.06/5.36 ! [N2: nat,X: nat] :
% 5.06/5.36 ( ( member_nat @ ( suc @ N2 ) @ ( nat_set_decode @ X ) )
% 5.06/5.36 = ( member_nat @ N2 @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % set_decode_Suc
% 5.06/5.36 thf(fact_5086_diff__shunt__var,axiom,
% 5.06/5.36 ! [X: set_real,Y: set_real] :
% 5.06/5.36 ( ( ( minus_minus_set_real @ X @ Y )
% 5.06/5.36 = bot_bot_set_real )
% 5.06/5.36 = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 5.06/5.36
% 5.06/5.36 % diff_shunt_var
% 5.06/5.36 thf(fact_5087_diff__shunt__var,axiom,
% 5.06/5.36 ! [X: set_nat,Y: set_nat] :
% 5.06/5.36 ( ( ( minus_minus_set_nat @ X @ Y )
% 5.06/5.36 = bot_bot_set_nat )
% 5.06/5.36 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.06/5.36
% 5.06/5.36 % diff_shunt_var
% 5.06/5.36 thf(fact_5088_diff__shunt__var,axiom,
% 5.06/5.36 ! [X: set_int,Y: set_int] :
% 5.06/5.36 ( ( ( minus_minus_set_int @ X @ Y )
% 5.06/5.36 = bot_bot_set_int )
% 5.06/5.36 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.06/5.36
% 5.06/5.36 % diff_shunt_var
% 5.06/5.36 thf(fact_5089_intind,axiom,
% 5.06/5.36 ! [I2: nat,N2: nat,P: nat > $o,X: nat] :
% 5.06/5.36 ( ( ord_less_nat @ I2 @ N2 )
% 5.06/5.36 => ( ( P @ X )
% 5.06/5.36 => ( P @ ( nth_nat @ ( replicate_nat @ N2 @ X ) @ I2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % intind
% 5.06/5.36 thf(fact_5090_intind,axiom,
% 5.06/5.36 ! [I2: nat,N2: nat,P: int > $o,X: int] :
% 5.06/5.36 ( ( ord_less_nat @ I2 @ N2 )
% 5.06/5.36 => ( ( P @ X )
% 5.06/5.36 => ( P @ ( nth_int @ ( replicate_int @ N2 @ X ) @ I2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % intind
% 5.06/5.36 thf(fact_5091_intind,axiom,
% 5.06/5.36 ! [I2: nat,N2: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.06/5.36 ( ( ord_less_nat @ I2 @ N2 )
% 5.06/5.36 => ( ( P @ X )
% 5.06/5.36 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) @ I2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % intind
% 5.06/5.36 thf(fact_5092_of__bool__less__eq__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.06/5.36 = ( P
% 5.06/5.36 => Q ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_eq_iff
% 5.06/5.36 thf(fact_5093_of__bool__less__eq__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.06/5.36 = ( P
% 5.06/5.36 => Q ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_eq_iff
% 5.06/5.36 thf(fact_5094_of__bool__less__eq__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.06/5.36 = ( P
% 5.06/5.36 => Q ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_eq_iff
% 5.06/5.36 thf(fact_5095_of__bool__less__eq__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.06/5.36 = ( P
% 5.06/5.36 => Q ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_eq_iff
% 5.06/5.36 thf(fact_5096_of__bool__eq_I1_J,axiom,
% 5.06/5.36 ( ( zero_n1201886186963655149omplex @ $false )
% 5.06/5.36 = zero_zero_complex ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(1)
% 5.06/5.36 thf(fact_5097_of__bool__eq_I1_J,axiom,
% 5.06/5.36 ( ( zero_n3304061248610475627l_real @ $false )
% 5.06/5.36 = zero_zero_real ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(1)
% 5.06/5.36 thf(fact_5098_of__bool__eq_I1_J,axiom,
% 5.06/5.36 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.06/5.36 = zero_zero_rat ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(1)
% 5.06/5.36 thf(fact_5099_of__bool__eq_I1_J,axiom,
% 5.06/5.36 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.06/5.36 = zero_zero_nat ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(1)
% 5.06/5.36 thf(fact_5100_of__bool__eq_I1_J,axiom,
% 5.06/5.36 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.06/5.36 = zero_zero_int ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(1)
% 5.06/5.36 thf(fact_5101_of__bool__eq_I1_J,axiom,
% 5.06/5.36 ( ( zero_n356916108424825756nteger @ $false )
% 5.06/5.36 = zero_z3403309356797280102nteger ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(1)
% 5.06/5.36 thf(fact_5102_of__bool__eq__0__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.06/5.36 = zero_zero_complex )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_0_iff
% 5.06/5.36 thf(fact_5103_of__bool__eq__0__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.06/5.36 = zero_zero_real )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_0_iff
% 5.06/5.36 thf(fact_5104_of__bool__eq__0__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.06/5.36 = zero_zero_rat )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_0_iff
% 5.06/5.36 thf(fact_5105_of__bool__eq__0__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.06/5.36 = zero_zero_nat )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_0_iff
% 5.06/5.36 thf(fact_5106_of__bool__eq__0__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.06/5.36 = zero_zero_int )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_0_iff
% 5.06/5.36 thf(fact_5107_of__bool__eq__0__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n356916108424825756nteger @ P )
% 5.06/5.36 = zero_z3403309356797280102nteger )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_0_iff
% 5.06/5.36 thf(fact_5108_of__bool__less__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.06/5.36 = ( ~ P
% 5.06/5.36 & Q ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_iff
% 5.06/5.36 thf(fact_5109_of__bool__less__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.06/5.36 = ( ~ P
% 5.06/5.36 & Q ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_iff
% 5.06/5.36 thf(fact_5110_of__bool__less__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.06/5.36 = ( ~ P
% 5.06/5.36 & Q ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_iff
% 5.06/5.36 thf(fact_5111_of__bool__less__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.06/5.36 = ( ~ P
% 5.06/5.36 & Q ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_iff
% 5.06/5.36 thf(fact_5112_of__bool__less__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.06/5.36 = ( ~ P
% 5.06/5.36 & Q ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_iff
% 5.06/5.36 thf(fact_5113_of__bool__eq__1__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.06/5.36 = one_one_complex )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_1_iff
% 5.06/5.36 thf(fact_5114_of__bool__eq__1__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.06/5.36 = one_one_real )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_1_iff
% 5.06/5.36 thf(fact_5115_of__bool__eq__1__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.06/5.36 = one_one_rat )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_1_iff
% 5.06/5.36 thf(fact_5116_of__bool__eq__1__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.06/5.36 = one_one_nat )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_1_iff
% 5.06/5.36 thf(fact_5117_of__bool__eq__1__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.06/5.36 = one_one_int )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_1_iff
% 5.06/5.36 thf(fact_5118_of__bool__eq__1__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ( zero_n356916108424825756nteger @ P )
% 5.06/5.36 = one_one_Code_integer )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_1_iff
% 5.06/5.36 thf(fact_5119_of__bool__eq_I2_J,axiom,
% 5.06/5.36 ( ( zero_n1201886186963655149omplex @ $true )
% 5.06/5.36 = one_one_complex ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(2)
% 5.06/5.36 thf(fact_5120_of__bool__eq_I2_J,axiom,
% 5.06/5.36 ( ( zero_n3304061248610475627l_real @ $true )
% 5.06/5.36 = one_one_real ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(2)
% 5.06/5.36 thf(fact_5121_of__bool__eq_I2_J,axiom,
% 5.06/5.36 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.06/5.36 = one_one_rat ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(2)
% 5.06/5.36 thf(fact_5122_of__bool__eq_I2_J,axiom,
% 5.06/5.36 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.06/5.36 = one_one_nat ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(2)
% 5.06/5.36 thf(fact_5123_of__bool__eq_I2_J,axiom,
% 5.06/5.36 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.06/5.36 = one_one_int ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(2)
% 5.06/5.36 thf(fact_5124_of__bool__eq_I2_J,axiom,
% 5.06/5.36 ( ( zero_n356916108424825756nteger @ $true )
% 5.06/5.36 = one_one_Code_integer ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq(2)
% 5.06/5.36 thf(fact_5125_signed__take__bit__of__0,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( bit_ri631733984087533419it_int @ N2 @ zero_zero_int )
% 5.06/5.36 = zero_zero_int ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_of_0
% 5.06/5.36 thf(fact_5126_replicate__eq__replicate,axiom,
% 5.06/5.36 ! [M: nat,X: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 5.06/5.36 ( ( ( replicate_VEBT_VEBT @ M @ X )
% 5.06/5.36 = ( replicate_VEBT_VEBT @ N2 @ Y ) )
% 5.06/5.36 = ( ( M = N2 )
% 5.06/5.36 & ( ( M != zero_zero_nat )
% 5.06/5.36 => ( X = Y ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_eq_replicate
% 5.06/5.36 thf(fact_5127_length__replicate,axiom,
% 5.06/5.36 ! [N2: nat,X: vEBT_VEBT] :
% 5.06/5.36 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) )
% 5.06/5.36 = N2 ) ).
% 5.06/5.36
% 5.06/5.36 % length_replicate
% 5.06/5.36 thf(fact_5128_length__replicate,axiom,
% 5.06/5.36 ! [N2: nat,X: $o] :
% 5.06/5.36 ( ( size_size_list_o @ ( replicate_o @ N2 @ X ) )
% 5.06/5.36 = N2 ) ).
% 5.06/5.36
% 5.06/5.36 % length_replicate
% 5.06/5.36 thf(fact_5129_length__replicate,axiom,
% 5.06/5.36 ! [N2: nat,X: int] :
% 5.06/5.36 ( ( size_size_list_int @ ( replicate_int @ N2 @ X ) )
% 5.06/5.36 = N2 ) ).
% 5.06/5.36
% 5.06/5.36 % length_replicate
% 5.06/5.36 thf(fact_5130_of__bool__or__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( zero_n2687167440665602831ol_nat
% 5.06/5.36 @ ( P
% 5.06/5.36 | Q ) )
% 5.06/5.36 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_or_iff
% 5.06/5.36 thf(fact_5131_of__bool__or__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( zero_n2684676970156552555ol_int
% 5.06/5.36 @ ( P
% 5.06/5.36 | Q ) )
% 5.06/5.36 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_or_iff
% 5.06/5.36 thf(fact_5132_of__bool__or__iff,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( zero_n356916108424825756nteger
% 5.06/5.36 @ ( P
% 5.06/5.36 | Q ) )
% 5.06/5.36 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_or_iff
% 5.06/5.36 thf(fact_5133_zero__less__of__bool__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_of_bool_iff
% 5.06/5.36 thf(fact_5134_zero__less__of__bool__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_of_bool_iff
% 5.06/5.36 thf(fact_5135_zero__less__of__bool__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_of_bool_iff
% 5.06/5.36 thf(fact_5136_zero__less__of__bool__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_of_bool_iff
% 5.06/5.36 thf(fact_5137_zero__less__of__bool__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.06/5.36 = P ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_of_bool_iff
% 5.06/5.36 thf(fact_5138_of__bool__less__one__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_one_iff
% 5.06/5.36 thf(fact_5139_of__bool__less__one__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_one_iff
% 5.06/5.36 thf(fact_5140_of__bool__less__one__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_one_iff
% 5.06/5.36 thf(fact_5141_of__bool__less__one__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_one_iff
% 5.06/5.36 thf(fact_5142_of__bool__less__one__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.06/5.36 = ~ P ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_one_iff
% 5.06/5.36 thf(fact_5143_of__bool__not__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.06/5.36 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_not_iff
% 5.06/5.36 thf(fact_5144_of__bool__not__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.06/5.36 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_not_iff
% 5.06/5.36 thf(fact_5145_of__bool__not__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.06/5.36 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_not_iff
% 5.06/5.36 thf(fact_5146_of__bool__not__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.06/5.36 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_not_iff
% 5.06/5.36 thf(fact_5147_of__bool__not__iff,axiom,
% 5.06/5.36 ! [P: $o] :
% 5.06/5.36 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.06/5.36 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_not_iff
% 5.06/5.36 thf(fact_5148_Suc__0__mod__eq,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.36 = ( zero_n2687167440665602831ol_nat
% 5.06/5.36 @ ( N2
% 5.06/5.36 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % Suc_0_mod_eq
% 5.06/5.36 thf(fact_5149_signed__take__bit__Suc__1,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ one_one_int )
% 5.06/5.36 = one_one_int ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_Suc_1
% 5.06/5.36 thf(fact_5150_signed__take__bit__numeral__of__1,axiom,
% 5.06/5.36 ! [K: num] :
% 5.06/5.36 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.06/5.36 = one_one_int ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_numeral_of_1
% 5.06/5.36 thf(fact_5151_in__set__replicate,axiom,
% 5.06/5.36 ! [X: complex,N2: nat,Y: complex] :
% 5.06/5.36 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N2 @ Y ) ) )
% 5.06/5.36 = ( ( X = Y )
% 5.06/5.36 & ( N2 != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % in_set_replicate
% 5.06/5.36 thf(fact_5152_in__set__replicate,axiom,
% 5.06/5.36 ! [X: real,N2: nat,Y: real] :
% 5.06/5.36 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N2 @ Y ) ) )
% 5.06/5.36 = ( ( X = Y )
% 5.06/5.36 & ( N2 != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % in_set_replicate
% 5.06/5.36 thf(fact_5153_in__set__replicate,axiom,
% 5.06/5.36 ! [X: set_nat,N2: nat,Y: set_nat] :
% 5.06/5.36 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N2 @ Y ) ) )
% 5.06/5.36 = ( ( X = Y )
% 5.06/5.36 & ( N2 != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % in_set_replicate
% 5.06/5.36 thf(fact_5154_in__set__replicate,axiom,
% 5.06/5.36 ! [X: nat,N2: nat,Y: nat] :
% 5.06/5.36 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ Y ) ) )
% 5.06/5.36 = ( ( X = Y )
% 5.06/5.36 & ( N2 != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % in_set_replicate
% 5.06/5.36 thf(fact_5155_in__set__replicate,axiom,
% 5.06/5.36 ! [X: int,N2: nat,Y: int] :
% 5.06/5.36 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ Y ) ) )
% 5.06/5.36 = ( ( X = Y )
% 5.06/5.36 & ( N2 != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % in_set_replicate
% 5.06/5.36 thf(fact_5156_in__set__replicate,axiom,
% 5.06/5.36 ! [X: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 5.06/5.36 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ Y ) ) )
% 5.06/5.36 = ( ( X = Y )
% 5.06/5.36 & ( N2 != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % in_set_replicate
% 5.06/5.36 thf(fact_5157_Bex__set__replicate,axiom,
% 5.06/5.36 ! [N2: nat,A: int,P: int > $o] :
% 5.06/5.36 ( ( ? [X2: int] :
% 5.06/5.36 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 5.06/5.36 & ( P @ X2 ) ) )
% 5.06/5.36 = ( ( P @ A )
% 5.06/5.36 & ( N2 != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % Bex_set_replicate
% 5.06/5.36 thf(fact_5158_Bex__set__replicate,axiom,
% 5.06/5.36 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.06/5.36 ( ( ? [X2: vEBT_VEBT] :
% 5.06/5.36 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 5.06/5.36 & ( P @ X2 ) ) )
% 5.06/5.36 = ( ( P @ A )
% 5.06/5.36 & ( N2 != zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % Bex_set_replicate
% 5.06/5.36 thf(fact_5159_Ball__set__replicate,axiom,
% 5.06/5.36 ! [N2: nat,A: int,P: int > $o] :
% 5.06/5.36 ( ( ! [X2: int] :
% 5.06/5.36 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 5.06/5.36 => ( P @ X2 ) ) )
% 5.06/5.36 = ( ( P @ A )
% 5.06/5.36 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % Ball_set_replicate
% 5.06/5.36 thf(fact_5160_Ball__set__replicate,axiom,
% 5.06/5.36 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.06/5.36 ( ( ! [X2: vEBT_VEBT] :
% 5.06/5.36 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 5.06/5.36 => ( P @ X2 ) ) )
% 5.06/5.36 = ( ( P @ A )
% 5.06/5.36 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % Ball_set_replicate
% 5.06/5.36 thf(fact_5161_nth__replicate,axiom,
% 5.06/5.36 ! [I2: nat,N2: nat,X: nat] :
% 5.06/5.36 ( ( ord_less_nat @ I2 @ N2 )
% 5.06/5.36 => ( ( nth_nat @ ( replicate_nat @ N2 @ X ) @ I2 )
% 5.06/5.36 = X ) ) ).
% 5.06/5.36
% 5.06/5.36 % nth_replicate
% 5.06/5.36 thf(fact_5162_nth__replicate,axiom,
% 5.06/5.36 ! [I2: nat,N2: nat,X: int] :
% 5.06/5.36 ( ( ord_less_nat @ I2 @ N2 )
% 5.06/5.36 => ( ( nth_int @ ( replicate_int @ N2 @ X ) @ I2 )
% 5.06/5.36 = X ) ) ).
% 5.06/5.36
% 5.06/5.36 % nth_replicate
% 5.06/5.36 thf(fact_5163_nth__replicate,axiom,
% 5.06/5.36 ! [I2: nat,N2: nat,X: vEBT_VEBT] :
% 5.06/5.36 ( ( ord_less_nat @ I2 @ N2 )
% 5.06/5.36 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X ) @ I2 )
% 5.06/5.36 = X ) ) ).
% 5.06/5.36
% 5.06/5.36 % nth_replicate
% 5.06/5.36 thf(fact_5164_triangle__Suc,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( nat_triangle @ ( suc @ N2 ) )
% 5.06/5.36 = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % triangle_Suc
% 5.06/5.36 thf(fact_5165_signed__take__bit__Suc__bit0,axiom,
% 5.06/5.36 ! [N2: nat,K: num] :
% 5.06/5.36 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.06/5.36 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_Suc_bit0
% 5.06/5.36 thf(fact_5166_odd__of__bool__self,axiom,
% 5.06/5.36 ! [P4: $o] :
% 5.06/5.36 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P4 ) ) )
% 5.06/5.36 = P4 ) ).
% 5.06/5.36
% 5.06/5.36 % odd_of_bool_self
% 5.06/5.36 thf(fact_5167_odd__of__bool__self,axiom,
% 5.06/5.36 ! [P4: $o] :
% 5.06/5.36 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P4 ) ) )
% 5.06/5.36 = P4 ) ).
% 5.06/5.36
% 5.06/5.36 % odd_of_bool_self
% 5.06/5.36 thf(fact_5168_odd__of__bool__self,axiom,
% 5.06/5.36 ! [P4: $o] :
% 5.06/5.36 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P4 ) ) )
% 5.06/5.36 = P4 ) ).
% 5.06/5.36
% 5.06/5.36 % odd_of_bool_self
% 5.06/5.36 thf(fact_5169_of__bool__half__eq__0,axiom,
% 5.06/5.36 ! [B: $o] :
% 5.06/5.36 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 = zero_zero_nat ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_half_eq_0
% 5.06/5.36 thf(fact_5170_of__bool__half__eq__0,axiom,
% 5.06/5.36 ! [B: $o] :
% 5.06/5.36 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.36 = zero_zero_int ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_half_eq_0
% 5.06/5.36 thf(fact_5171_of__bool__half__eq__0,axiom,
% 5.06/5.36 ! [B: $o] :
% 5.06/5.36 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.36 = zero_z3403309356797280102nteger ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_half_eq_0
% 5.06/5.36 thf(fact_5172_set__decode__0,axiom,
% 5.06/5.36 ! [X: nat] :
% 5.06/5.36 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 5.06/5.36 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % set_decode_0
% 5.06/5.36 thf(fact_5173_one__div__2__pow__eq,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % one_div_2_pow_eq
% 5.06/5.36 thf(fact_5174_one__div__2__pow__eq,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % one_div_2_pow_eq
% 5.06/5.36 thf(fact_5175_one__div__2__pow__eq,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % one_div_2_pow_eq
% 5.06/5.36 thf(fact_5176_bits__1__div__exp,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bits_1_div_exp
% 5.06/5.36 thf(fact_5177_bits__1__div__exp,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bits_1_div_exp
% 5.06/5.36 thf(fact_5178_bits__1__div__exp,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bits_1_div_exp
% 5.06/5.36 thf(fact_5179_one__mod__2__pow__eq,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % one_mod_2_pow_eq
% 5.06/5.36 thf(fact_5180_one__mod__2__pow__eq,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % one_mod_2_pow_eq
% 5.06/5.36 thf(fact_5181_one__mod__2__pow__eq,axiom,
% 5.06/5.36 ! [N2: nat] :
% 5.06/5.36 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % one_mod_2_pow_eq
% 5.06/5.36 thf(fact_5182_dvd__antisym,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( dvd_dvd_nat @ M @ N2 )
% 5.06/5.36 => ( ( dvd_dvd_nat @ N2 @ M )
% 5.06/5.36 => ( M = N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % dvd_antisym
% 5.06/5.36 thf(fact_5183_of__bool__eq__iff,axiom,
% 5.06/5.36 ! [P4: $o,Q2: $o] :
% 5.06/5.36 ( ( ( zero_n2687167440665602831ol_nat @ P4 )
% 5.06/5.36 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 5.06/5.36 = ( P4 = Q2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_iff
% 5.06/5.36 thf(fact_5184_of__bool__eq__iff,axiom,
% 5.06/5.36 ! [P4: $o,Q2: $o] :
% 5.06/5.36 ( ( ( zero_n2684676970156552555ol_int @ P4 )
% 5.06/5.36 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 5.06/5.36 = ( P4 = Q2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_iff
% 5.06/5.36 thf(fact_5185_of__bool__eq__iff,axiom,
% 5.06/5.36 ! [P4: $o,Q2: $o] :
% 5.06/5.36 ( ( ( zero_n356916108424825756nteger @ P4 )
% 5.06/5.36 = ( zero_n356916108424825756nteger @ Q2 ) )
% 5.06/5.36 = ( P4 = Q2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_eq_iff
% 5.06/5.36 thf(fact_5186_of__bool__conj,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( zero_n3304061248610475627l_real
% 5.06/5.36 @ ( P
% 5.06/5.36 & Q ) )
% 5.06/5.36 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_conj
% 5.06/5.36 thf(fact_5187_of__bool__conj,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( zero_n2052037380579107095ol_rat
% 5.06/5.36 @ ( P
% 5.06/5.36 & Q ) )
% 5.06/5.36 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_conj
% 5.06/5.36 thf(fact_5188_of__bool__conj,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( zero_n2687167440665602831ol_nat
% 5.06/5.36 @ ( P
% 5.06/5.36 & Q ) )
% 5.06/5.36 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_conj
% 5.06/5.36 thf(fact_5189_of__bool__conj,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( zero_n2684676970156552555ol_int
% 5.06/5.36 @ ( P
% 5.06/5.36 & Q ) )
% 5.06/5.36 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_conj
% 5.06/5.36 thf(fact_5190_of__bool__conj,axiom,
% 5.06/5.36 ! [P: $o,Q: $o] :
% 5.06/5.36 ( ( zero_n356916108424825756nteger
% 5.06/5.36 @ ( P
% 5.06/5.36 & Q ) )
% 5.06/5.36 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_conj
% 5.06/5.36 thf(fact_5191_signed__take__bit__mult,axiom,
% 5.06/5.36 ! [N2: nat,K: int,L2: int] :
% 5.06/5.36 ( ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L2 ) ) )
% 5.06/5.36 = ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_mult
% 5.06/5.36 thf(fact_5192_signed__take__bit__add,axiom,
% 5.06/5.36 ! [N2: nat,K: int,L2: int] :
% 5.06/5.36 ( ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L2 ) ) )
% 5.06/5.36 = ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_add
% 5.06/5.36 thf(fact_5193_signed__take__bit__diff,axiom,
% 5.06/5.36 ! [N2: nat,K: int,L2: int] :
% 5.06/5.36 ( ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L2 ) ) )
% 5.06/5.36 = ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_diff
% 5.06/5.36 thf(fact_5194_zero__less__eq__of__bool,axiom,
% 5.06/5.36 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_eq_of_bool
% 5.06/5.36 thf(fact_5195_zero__less__eq__of__bool,axiom,
% 5.06/5.36 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_eq_of_bool
% 5.06/5.36 thf(fact_5196_zero__less__eq__of__bool,axiom,
% 5.06/5.36 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_eq_of_bool
% 5.06/5.36 thf(fact_5197_zero__less__eq__of__bool,axiom,
% 5.06/5.36 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_eq_of_bool
% 5.06/5.36 thf(fact_5198_zero__less__eq__of__bool,axiom,
% 5.06/5.36 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.06/5.36
% 5.06/5.36 % zero_less_eq_of_bool
% 5.06/5.36 thf(fact_5199_of__bool__less__eq__one,axiom,
% 5.06/5.36 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_eq_one
% 5.06/5.36 thf(fact_5200_of__bool__less__eq__one,axiom,
% 5.06/5.36 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_eq_one
% 5.06/5.36 thf(fact_5201_of__bool__less__eq__one,axiom,
% 5.06/5.36 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_eq_one
% 5.06/5.36 thf(fact_5202_of__bool__less__eq__one,axiom,
% 5.06/5.36 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_eq_one
% 5.06/5.36 thf(fact_5203_of__bool__less__eq__one,axiom,
% 5.06/5.36 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_less_eq_one
% 5.06/5.36 thf(fact_5204_of__bool__def,axiom,
% 5.06/5.36 ( zero_n1201886186963655149omplex
% 5.06/5.36 = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_def
% 5.06/5.36 thf(fact_5205_of__bool__def,axiom,
% 5.06/5.36 ( zero_n3304061248610475627l_real
% 5.06/5.36 = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_def
% 5.06/5.36 thf(fact_5206_of__bool__def,axiom,
% 5.06/5.36 ( zero_n2052037380579107095ol_rat
% 5.06/5.36 = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_def
% 5.06/5.36 thf(fact_5207_of__bool__def,axiom,
% 5.06/5.36 ( zero_n2687167440665602831ol_nat
% 5.06/5.36 = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_def
% 5.06/5.36 thf(fact_5208_of__bool__def,axiom,
% 5.06/5.36 ( zero_n2684676970156552555ol_int
% 5.06/5.36 = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_def
% 5.06/5.36 thf(fact_5209_of__bool__def,axiom,
% 5.06/5.36 ( zero_n356916108424825756nteger
% 5.06/5.36 = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_def
% 5.06/5.36 thf(fact_5210_split__of__bool,axiom,
% 5.06/5.36 ! [P: complex > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n1201886186963655149omplex @ P4 ) )
% 5.06/5.36 = ( ( P4
% 5.06/5.36 => ( P @ one_one_complex ) )
% 5.06/5.36 & ( ~ P4
% 5.06/5.36 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool
% 5.06/5.36 thf(fact_5211_split__of__bool,axiom,
% 5.06/5.36 ! [P: real > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n3304061248610475627l_real @ P4 ) )
% 5.06/5.36 = ( ( P4
% 5.06/5.36 => ( P @ one_one_real ) )
% 5.06/5.36 & ( ~ P4
% 5.06/5.36 => ( P @ zero_zero_real ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool
% 5.06/5.36 thf(fact_5212_split__of__bool,axiom,
% 5.06/5.36 ! [P: rat > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 5.06/5.36 = ( ( P4
% 5.06/5.36 => ( P @ one_one_rat ) )
% 5.06/5.36 & ( ~ P4
% 5.06/5.36 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool
% 5.06/5.36 thf(fact_5213_split__of__bool,axiom,
% 5.06/5.36 ! [P: nat > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 5.06/5.36 = ( ( P4
% 5.06/5.36 => ( P @ one_one_nat ) )
% 5.06/5.36 & ( ~ P4
% 5.06/5.36 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool
% 5.06/5.36 thf(fact_5214_split__of__bool,axiom,
% 5.06/5.36 ! [P: int > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 5.06/5.36 = ( ( P4
% 5.06/5.36 => ( P @ one_one_int ) )
% 5.06/5.36 & ( ~ P4
% 5.06/5.36 => ( P @ zero_zero_int ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool
% 5.06/5.36 thf(fact_5215_split__of__bool,axiom,
% 5.06/5.36 ! [P: code_integer > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 5.06/5.36 = ( ( P4
% 5.06/5.36 => ( P @ one_one_Code_integer ) )
% 5.06/5.36 & ( ~ P4
% 5.06/5.36 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool
% 5.06/5.36 thf(fact_5216_split__of__bool__asm,axiom,
% 5.06/5.36 ! [P: complex > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n1201886186963655149omplex @ P4 ) )
% 5.06/5.36 = ( ~ ( ( P4
% 5.06/5.36 & ~ ( P @ one_one_complex ) )
% 5.06/5.36 | ( ~ P4
% 5.06/5.36 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool_asm
% 5.06/5.36 thf(fact_5217_split__of__bool__asm,axiom,
% 5.06/5.36 ! [P: real > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n3304061248610475627l_real @ P4 ) )
% 5.06/5.36 = ( ~ ( ( P4
% 5.06/5.36 & ~ ( P @ one_one_real ) )
% 5.06/5.36 | ( ~ P4
% 5.06/5.36 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool_asm
% 5.06/5.36 thf(fact_5218_split__of__bool__asm,axiom,
% 5.06/5.36 ! [P: rat > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 5.06/5.36 = ( ~ ( ( P4
% 5.06/5.36 & ~ ( P @ one_one_rat ) )
% 5.06/5.36 | ( ~ P4
% 5.06/5.36 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool_asm
% 5.06/5.36 thf(fact_5219_split__of__bool__asm,axiom,
% 5.06/5.36 ! [P: nat > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 5.06/5.36 = ( ~ ( ( P4
% 5.06/5.36 & ~ ( P @ one_one_nat ) )
% 5.06/5.36 | ( ~ P4
% 5.06/5.36 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool_asm
% 5.06/5.36 thf(fact_5220_split__of__bool__asm,axiom,
% 5.06/5.36 ! [P: int > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 5.06/5.36 = ( ~ ( ( P4
% 5.06/5.36 & ~ ( P @ one_one_int ) )
% 5.06/5.36 | ( ~ P4
% 5.06/5.36 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool_asm
% 5.06/5.36 thf(fact_5221_split__of__bool__asm,axiom,
% 5.06/5.36 ! [P: code_integer > $o,P4: $o] :
% 5.06/5.36 ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 5.06/5.36 = ( ~ ( ( P4
% 5.06/5.36 & ~ ( P @ one_one_Code_integer ) )
% 5.06/5.36 | ( ~ P4
% 5.06/5.36 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % split_of_bool_asm
% 5.06/5.36 thf(fact_5222_replicate__eqI,axiom,
% 5.06/5.36 ! [Xs2: list_complex,N2: nat,X: complex] :
% 5.06/5.36 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.06/5.36 = N2 )
% 5.06/5.36 => ( ! [Y5: complex] :
% 5.06/5.36 ( ( member_complex @ Y5 @ ( set_complex2 @ Xs2 ) )
% 5.06/5.36 => ( Y5 = X ) )
% 5.06/5.36 => ( Xs2
% 5.06/5.36 = ( replicate_complex @ N2 @ X ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_eqI
% 5.06/5.36 thf(fact_5223_replicate__eqI,axiom,
% 5.06/5.36 ! [Xs2: list_real,N2: nat,X: real] :
% 5.06/5.36 ( ( ( size_size_list_real @ Xs2 )
% 5.06/5.36 = N2 )
% 5.06/5.36 => ( ! [Y5: real] :
% 5.06/5.36 ( ( member_real @ Y5 @ ( set_real2 @ Xs2 ) )
% 5.06/5.36 => ( Y5 = X ) )
% 5.06/5.36 => ( Xs2
% 5.06/5.36 = ( replicate_real @ N2 @ X ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_eqI
% 5.06/5.36 thf(fact_5224_replicate__eqI,axiom,
% 5.06/5.36 ! [Xs2: list_set_nat,N2: nat,X: set_nat] :
% 5.06/5.36 ( ( ( size_s3254054031482475050et_nat @ Xs2 )
% 5.06/5.36 = N2 )
% 5.06/5.36 => ( ! [Y5: set_nat] :
% 5.06/5.36 ( ( member_set_nat @ Y5 @ ( set_set_nat2 @ Xs2 ) )
% 5.06/5.36 => ( Y5 = X ) )
% 5.06/5.36 => ( Xs2
% 5.06/5.36 = ( replicate_set_nat @ N2 @ X ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_eqI
% 5.06/5.36 thf(fact_5225_replicate__eqI,axiom,
% 5.06/5.36 ! [Xs2: list_nat,N2: nat,X: nat] :
% 5.06/5.36 ( ( ( size_size_list_nat @ Xs2 )
% 5.06/5.36 = N2 )
% 5.06/5.36 => ( ! [Y5: nat] :
% 5.06/5.36 ( ( member_nat @ Y5 @ ( set_nat2 @ Xs2 ) )
% 5.06/5.36 => ( Y5 = X ) )
% 5.06/5.36 => ( Xs2
% 5.06/5.36 = ( replicate_nat @ N2 @ X ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_eqI
% 5.06/5.36 thf(fact_5226_replicate__eqI,axiom,
% 5.06/5.36 ! [Xs2: list_VEBT_VEBT,N2: nat,X: vEBT_VEBT] :
% 5.06/5.36 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.06/5.36 = N2 )
% 5.06/5.36 => ( ! [Y5: vEBT_VEBT] :
% 5.06/5.36 ( ( member_VEBT_VEBT @ Y5 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.06/5.36 => ( Y5 = X ) )
% 5.06/5.36 => ( Xs2
% 5.06/5.36 = ( replicate_VEBT_VEBT @ N2 @ X ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_eqI
% 5.06/5.36 thf(fact_5227_replicate__eqI,axiom,
% 5.06/5.36 ! [Xs2: list_o,N2: nat,X: $o] :
% 5.06/5.36 ( ( ( size_size_list_o @ Xs2 )
% 5.06/5.36 = N2 )
% 5.06/5.36 => ( ! [Y5: $o] :
% 5.06/5.36 ( ( member_o @ Y5 @ ( set_o2 @ Xs2 ) )
% 5.06/5.36 => ( Y5 = X ) )
% 5.06/5.36 => ( Xs2
% 5.06/5.36 = ( replicate_o @ N2 @ X ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_eqI
% 5.06/5.36 thf(fact_5228_replicate__eqI,axiom,
% 5.06/5.36 ! [Xs2: list_int,N2: nat,X: int] :
% 5.06/5.36 ( ( ( size_size_list_int @ Xs2 )
% 5.06/5.36 = N2 )
% 5.06/5.36 => ( ! [Y5: int] :
% 5.06/5.36 ( ( member_int @ Y5 @ ( set_int2 @ Xs2 ) )
% 5.06/5.36 => ( Y5 = X ) )
% 5.06/5.36 => ( Xs2
% 5.06/5.36 = ( replicate_int @ N2 @ X ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_eqI
% 5.06/5.36 thf(fact_5229_replicate__length__same,axiom,
% 5.06/5.36 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.06/5.36 ( ! [X3: vEBT_VEBT] :
% 5.06/5.36 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.06/5.36 => ( X3 = X ) )
% 5.06/5.36 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 5.06/5.36 = Xs2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_length_same
% 5.06/5.36 thf(fact_5230_replicate__length__same,axiom,
% 5.06/5.36 ! [Xs2: list_o,X: $o] :
% 5.06/5.36 ( ! [X3: $o] :
% 5.06/5.36 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 5.06/5.36 => ( X3 = X ) )
% 5.06/5.36 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 5.06/5.36 = Xs2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_length_same
% 5.06/5.36 thf(fact_5231_replicate__length__same,axiom,
% 5.06/5.36 ! [Xs2: list_int,X: int] :
% 5.06/5.36 ( ! [X3: int] :
% 5.06/5.36 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 5.06/5.36 => ( X3 = X ) )
% 5.06/5.36 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 5.06/5.36 = Xs2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % replicate_length_same
% 5.06/5.36 thf(fact_5232_subset__decode__imp__le,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 5.06/5.36 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % subset_decode_imp_le
% 5.06/5.36 thf(fact_5233_of__bool__odd__eq__mod__2,axiom,
% 5.06/5.36 ! [A: nat] :
% 5.06/5.36 ( ( zero_n2687167440665602831ol_nat
% 5.06/5.36 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.06/5.36 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_odd_eq_mod_2
% 5.06/5.36 thf(fact_5234_of__bool__odd__eq__mod__2,axiom,
% 5.06/5.36 ! [A: int] :
% 5.06/5.36 ( ( zero_n2684676970156552555ol_int
% 5.06/5.36 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.06/5.36 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_odd_eq_mod_2
% 5.06/5.36 thf(fact_5235_of__bool__odd__eq__mod__2,axiom,
% 5.06/5.36 ! [A: code_integer] :
% 5.06/5.36 ( ( zero_n356916108424825756nteger
% 5.06/5.36 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.06/5.36 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % of_bool_odd_eq_mod_2
% 5.06/5.36 thf(fact_5236_signed__take__bit__int__less__exp,axiom,
% 5.06/5.36 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_int_less_exp
% 5.06/5.36 thf(fact_5237_even__signed__take__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: code_integer] :
% 5.06/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.06/5.36 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_signed_take_bit_iff
% 5.06/5.36 thf(fact_5238_even__signed__take__bit__iff,axiom,
% 5.06/5.36 ! [M: nat,A: int] :
% 5.06/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.06/5.36 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.06/5.36
% 5.06/5.36 % even_signed_take_bit_iff
% 5.06/5.36 thf(fact_5239_bits__induct,axiom,
% 5.06/5.36 ! [P: nat > $o,A: nat] :
% 5.06/5.36 ( ! [A3: nat] :
% 5.06/5.36 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 = A3 )
% 5.06/5.36 => ( P @ A3 ) )
% 5.06/5.36 => ( ! [A3: nat,B2: $o] :
% 5.06/5.36 ( ( P @ A3 )
% 5.06/5.36 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.36 = A3 )
% 5.06/5.36 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.06/5.36 => ( P @ A ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bits_induct
% 5.06/5.36 thf(fact_5240_bits__induct,axiom,
% 5.06/5.36 ! [P: int > $o,A: int] :
% 5.06/5.36 ( ! [A3: int] :
% 5.06/5.36 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.36 = A3 )
% 5.06/5.36 => ( P @ A3 ) )
% 5.06/5.36 => ( ! [A3: int,B2: $o] :
% 5.06/5.36 ( ( P @ A3 )
% 5.06/5.36 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.36 = A3 )
% 5.06/5.36 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.06/5.36 => ( P @ A ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bits_induct
% 5.06/5.36 thf(fact_5241_bits__induct,axiom,
% 5.06/5.36 ! [P: code_integer > $o,A: code_integer] :
% 5.06/5.36 ( ! [A3: code_integer] :
% 5.06/5.36 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.36 = A3 )
% 5.06/5.36 => ( P @ A3 ) )
% 5.06/5.36 => ( ! [A3: code_integer,B2: $o] :
% 5.06/5.36 ( ( P @ A3 )
% 5.06/5.36 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.36 = A3 )
% 5.06/5.36 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.06/5.36 => ( P @ A ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % bits_induct
% 5.06/5.36 thf(fact_5242_signed__take__bit__int__less__self__iff,axiom,
% 5.06/5.36 ! [N2: nat,K: int] :
% 5.06/5.36 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.06/5.36 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_int_less_self_iff
% 5.06/5.36 thf(fact_5243_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.06/5.36 ! [K: int,N2: nat] :
% 5.06/5.36 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.06/5.36 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_int_greater_eq_self_iff
% 5.06/5.36 thf(fact_5244_exp__mod__exp,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % exp_mod_exp
% 5.06/5.36 thf(fact_5245_exp__mod__exp,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % exp_mod_exp
% 5.06/5.36 thf(fact_5246_exp__mod__exp,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % exp_mod_exp
% 5.06/5.36 thf(fact_5247_signed__take__bit__int__less__eq,axiom,
% 5.06/5.36 ! [N2: nat,K: int] :
% 5.06/5.36 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.06/5.36 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_int_less_eq
% 5.06/5.36 thf(fact_5248_option_Osize__gen_I1_J,axiom,
% 5.06/5.36 ! [X: nat > nat] :
% 5.06/5.36 ( ( size_option_nat @ X @ none_nat )
% 5.06/5.36 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.36
% 5.06/5.36 % option.size_gen(1)
% 5.06/5.36 thf(fact_5249_option_Osize__gen_I1_J,axiom,
% 5.06/5.36 ! [X: product_prod_nat_nat > nat] :
% 5.06/5.36 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 5.06/5.36 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.36
% 5.06/5.36 % option.size_gen(1)
% 5.06/5.36 thf(fact_5250_option_Osize__gen_I1_J,axiom,
% 5.06/5.36 ! [X: num > nat] :
% 5.06/5.36 ( ( size_option_num @ X @ none_num )
% 5.06/5.36 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.36
% 5.06/5.36 % option.size_gen(1)
% 5.06/5.36 thf(fact_5251_set__decode__def,axiom,
% 5.06/5.36 ( nat_set_decode
% 5.06/5.36 = ( ^ [X2: nat] :
% 5.06/5.36 ( collect_nat
% 5.06/5.36 @ ^ [N: nat] :
% 5.06/5.36 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % set_decode_def
% 5.06/5.36 thf(fact_5252_exp__div__exp__eq,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( times_times_nat
% 5.06/5.36 @ ( zero_n2687167440665602831ol_nat
% 5.06/5.36 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.06/5.36 != zero_zero_nat )
% 5.06/5.36 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.06/5.36 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % exp_div_exp_eq
% 5.06/5.36 thf(fact_5253_exp__div__exp__eq,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( times_times_int
% 5.06/5.36 @ ( zero_n2684676970156552555ol_int
% 5.06/5.36 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.06/5.36 != zero_zero_int )
% 5.06/5.36 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.06/5.36 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % exp_div_exp_eq
% 5.06/5.36 thf(fact_5254_exp__div__exp__eq,axiom,
% 5.06/5.36 ! [M: nat,N2: nat] :
% 5.06/5.36 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.36 = ( times_3573771949741848930nteger
% 5.06/5.36 @ ( zero_n356916108424825756nteger
% 5.06/5.36 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.06/5.36 != zero_z3403309356797280102nteger )
% 5.06/5.36 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.06/5.36 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % exp_div_exp_eq
% 5.06/5.36 thf(fact_5255_vebt__buildup_Osimps_I3_J,axiom,
% 5.06/5.36 ! [Va: nat] :
% 5.06/5.36 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.06/5.36 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.06/5.36 = ( 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 ) ) ) ) ) ) )
% 5.06/5.36 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.06/5.36 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.06/5.36 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % vebt_buildup.simps(3)
% 5.06/5.36 thf(fact_5256_Divides_Oadjust__div__eq,axiom,
% 5.06/5.36 ! [Q2: int,R2: int] :
% 5.06/5.36 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.06/5.36 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % Divides.adjust_div_eq
% 5.06/5.36 thf(fact_5257_signed__take__bit__rec,axiom,
% 5.06/5.36 ( bit_ri6519982836138164636nteger
% 5.06/5.36 = ( ^ [N: nat,A4: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_rec
% 5.06/5.36 thf(fact_5258_signed__take__bit__rec,axiom,
% 5.06/5.36 ( bit_ri631733984087533419it_int
% 5.06/5.36 = ( ^ [N: nat,A4: int] : ( if_int @ ( N = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % signed_take_bit_rec
% 5.06/5.36 thf(fact_5259_vebt__buildup_Opelims,axiom,
% 5.06/5.36 ! [X: nat,Y: vEBT_VEBT] :
% 5.06/5.36 ( ( ( vEBT_vebt_buildup @ X )
% 5.06/5.36 = Y )
% 5.06/5.36 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 5.06/5.36 => ( ( ( X = zero_zero_nat )
% 5.06/5.36 => ( ( Y
% 5.06/5.36 = ( vEBT_Leaf @ $false @ $false ) )
% 5.06/5.36 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.06/5.36 => ( ( ( X
% 5.06/5.36 = ( suc @ zero_zero_nat ) )
% 5.06/5.36 => ( ( Y
% 5.06/5.36 = ( vEBT_Leaf @ $false @ $false ) )
% 5.06/5.36 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.06/5.36 => ~ ! [Va2: nat] :
% 5.06/5.36 ( ( X
% 5.06/5.36 = ( suc @ ( suc @ Va2 ) ) )
% 5.06/5.36 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.06/5.36 => ( Y
% 5.06/5.36 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.06/5.36 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.06/5.36 => ( Y
% 5.06/5.36 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.06/5.36 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % vebt_buildup.pelims
% 5.06/5.36 thf(fact_5260_add__scale__eq__noteq,axiom,
% 5.06/5.36 ! [R2: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.06/5.36 ( ( R2 != zero_zero_complex )
% 5.06/5.36 => ( ( ( A = B )
% 5.06/5.36 & ( C != D ) )
% 5.06/5.36 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 5.06/5.36 != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % add_scale_eq_noteq
% 5.06/5.36 thf(fact_5261_add__scale__eq__noteq,axiom,
% 5.06/5.36 ! [R2: real,A: real,B: real,C: real,D: real] :
% 5.06/5.36 ( ( R2 != zero_zero_real )
% 5.06/5.36 => ( ( ( A = B )
% 5.06/5.36 & ( C != D ) )
% 5.06/5.36 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 5.06/5.36 != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % add_scale_eq_noteq
% 5.06/5.36 thf(fact_5262_add__scale__eq__noteq,axiom,
% 5.06/5.36 ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.36 ( ( R2 != zero_zero_rat )
% 5.06/5.36 => ( ( ( A = B )
% 5.06/5.36 & ( C != D ) )
% 5.06/5.36 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 5.06/5.36 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % add_scale_eq_noteq
% 5.06/5.36 thf(fact_5263_add__scale__eq__noteq,axiom,
% 5.06/5.36 ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.36 ( ( R2 != zero_zero_nat )
% 5.06/5.36 => ( ( ( A = B )
% 5.06/5.36 & ( C != D ) )
% 5.06/5.36 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 5.06/5.36 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % add_scale_eq_noteq
% 5.06/5.36 thf(fact_5264_add__scale__eq__noteq,axiom,
% 5.06/5.36 ! [R2: int,A: int,B: int,C: int,D: int] :
% 5.06/5.36 ( ( R2 != zero_zero_int )
% 5.06/5.36 => ( ( ( A = B )
% 5.06/5.36 & ( C != D ) )
% 5.06/5.36 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 5.06/5.36 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % add_scale_eq_noteq
% 5.06/5.36 thf(fact_5265_artanh__def,axiom,
% 5.06/5.36 ( artanh_real
% 5.06/5.36 = ( ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % artanh_def
% 5.06/5.36 thf(fact_5266_Sum__Icc__int,axiom,
% 5.06/5.36 ! [M: int,N2: int] :
% 5.06/5.36 ( ( ord_less_eq_int @ M @ N2 )
% 5.06/5.36 => ( ( groups4538972089207619220nt_int
% 5.06/5.36 @ ^ [X2: int] : X2
% 5.06/5.36 @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 5.06/5.36 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % Sum_Icc_int
% 5.06/5.36 thf(fact_5267_divmod__step__def,axiom,
% 5.06/5.36 ( unique5026877609467782581ep_nat
% 5.06/5.36 = ( ^ [L: num] :
% 5.06/5.36 ( produc2626176000494625587at_nat
% 5.06/5.36 @ ^ [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 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % divmod_step_def
% 5.06/5.36 thf(fact_5268_divmod__step__def,axiom,
% 5.06/5.36 ( unique5024387138958732305ep_int
% 5.06/5.36 = ( ^ [L: num] :
% 5.06/5.36 ( produc4245557441103728435nt_int
% 5.06/5.36 @ ^ [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 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % divmod_step_def
% 5.06/5.36 thf(fact_5269_divmod__step__def,axiom,
% 5.06/5.36 ( unique4921790084139445826nteger
% 5.06/5.36 = ( ^ [L: num] :
% 5.06/5.36 ( produc6916734918728496179nteger
% 5.06/5.36 @ ^ [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 ) ) ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % divmod_step_def
% 5.06/5.36 thf(fact_5270_Compl__anti__mono,axiom,
% 5.06/5.36 ! [A2: set_int,B3: set_int] :
% 5.06/5.36 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.06/5.36 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B3 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % Compl_anti_mono
% 5.06/5.36 thf(fact_5271_Compl__subset__Compl__iff,axiom,
% 5.06/5.36 ! [A2: set_int,B3: set_int] :
% 5.06/5.36 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B3 ) )
% 5.06/5.36 = ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % Compl_subset_Compl_iff
% 5.06/5.36 thf(fact_5272_neg__le__iff__le,axiom,
% 5.06/5.36 ! [B: real,A: real] :
% 5.06/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.06/5.36 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_le_iff_le
% 5.06/5.36 thf(fact_5273_neg__le__iff__le,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.06/5.36 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_le_iff_le
% 5.06/5.36 thf(fact_5274_neg__le__iff__le,axiom,
% 5.06/5.36 ! [B: rat,A: rat] :
% 5.06/5.36 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.06/5.36 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_le_iff_le
% 5.06/5.36 thf(fact_5275_neg__le__iff__le,axiom,
% 5.06/5.36 ! [B: int,A: int] :
% 5.06/5.36 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.06/5.36 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_le_iff_le
% 5.06/5.36 thf(fact_5276_compl__le__compl__iff,axiom,
% 5.06/5.36 ! [X: set_int,Y: set_int] :
% 5.06/5.36 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y ) )
% 5.06/5.36 = ( ord_less_eq_set_int @ Y @ X ) ) ).
% 5.06/5.36
% 5.06/5.36 % compl_le_compl_iff
% 5.06/5.36 thf(fact_5277_neg__less__iff__less,axiom,
% 5.06/5.36 ! [B: real,A: real] :
% 5.06/5.36 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.06/5.36 = ( ord_less_real @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_less_iff_less
% 5.06/5.36 thf(fact_5278_neg__less__iff__less,axiom,
% 5.06/5.36 ! [B: int,A: int] :
% 5.06/5.36 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.06/5.36 = ( ord_less_int @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_less_iff_less
% 5.06/5.36 thf(fact_5279_neg__less__iff__less,axiom,
% 5.06/5.36 ! [B: rat,A: rat] :
% 5.06/5.36 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.06/5.36 = ( ord_less_rat @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_less_iff_less
% 5.06/5.36 thf(fact_5280_neg__less__iff__less,axiom,
% 5.06/5.36 ! [B: code_integer,A: code_integer] :
% 5.06/5.36 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.06/5.36 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_less_iff_less
% 5.06/5.36 thf(fact_5281_neg__numeral__eq__iff,axiom,
% 5.06/5.36 ! [M: num,N2: num] :
% 5.06/5.36 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.06/5.36 = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.36 = ( M = N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_numeral_eq_iff
% 5.06/5.36 thf(fact_5282_neg__numeral__eq__iff,axiom,
% 5.06/5.36 ! [M: num,N2: num] :
% 5.06/5.36 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.06/5.36 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.36 = ( M = N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_numeral_eq_iff
% 5.06/5.36 thf(fact_5283_neg__numeral__eq__iff,axiom,
% 5.06/5.36 ! [M: num,N2: num] :
% 5.06/5.36 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.06/5.36 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.06/5.36 = ( M = N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_numeral_eq_iff
% 5.06/5.36 thf(fact_5284_neg__numeral__eq__iff,axiom,
% 5.06/5.36 ! [M: num,N2: num] :
% 5.06/5.36 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.06/5.36 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.06/5.36 = ( M = N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_numeral_eq_iff
% 5.06/5.36 thf(fact_5285_neg__numeral__eq__iff,axiom,
% 5.06/5.36 ! [M: num,N2: num] :
% 5.06/5.36 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.06/5.36 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.06/5.36 = ( M = N2 ) ) ).
% 5.06/5.36
% 5.06/5.36 % neg_numeral_eq_iff
% 5.06/5.36 thf(fact_5286_mult__minus__right,axiom,
% 5.06/5.36 ! [A: real,B: real] :
% 5.06/5.36 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.06/5.36 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_minus_right
% 5.06/5.36 thf(fact_5287_mult__minus__right,axiom,
% 5.06/5.36 ! [A: int,B: int] :
% 5.06/5.36 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.36 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_minus_right
% 5.06/5.36 thf(fact_5288_mult__minus__right,axiom,
% 5.06/5.36 ! [A: complex,B: complex] :
% 5.06/5.36 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.06/5.36 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_minus_right
% 5.06/5.36 thf(fact_5289_mult__minus__right,axiom,
% 5.06/5.36 ! [A: rat,B: rat] :
% 5.06/5.36 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.06/5.36 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_minus_right
% 5.06/5.36 thf(fact_5290_mult__minus__right,axiom,
% 5.06/5.36 ! [A: code_integer,B: code_integer] :
% 5.06/5.36 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.36 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.06/5.36
% 5.06/5.36 % mult_minus_right
% 5.06/5.36 thf(fact_5291_minus__mult__minus,axiom,
% 5.06/5.36 ! [A: real,B: real] :
% 5.06/5.36 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.06/5.36 = ( times_times_real @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % minus_mult_minus
% 5.06/5.36 thf(fact_5292_minus__mult__minus,axiom,
% 5.06/5.36 ! [A: int,B: int] :
% 5.06/5.36 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.06/5.36 = ( times_times_int @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % minus_mult_minus
% 5.06/5.36 thf(fact_5293_minus__mult__minus,axiom,
% 5.06/5.36 ! [A: complex,B: complex] :
% 5.06/5.36 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.06/5.36 = ( times_times_complex @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % minus_mult_minus
% 5.06/5.36 thf(fact_5294_minus__mult__minus,axiom,
% 5.06/5.36 ! [A: rat,B: rat] :
% 5.06/5.36 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.06/5.36 = ( times_times_rat @ A @ B ) ) ).
% 5.06/5.36
% 5.06/5.36 % minus_mult_minus
% 5.06/5.37 thf(fact_5295_minus__mult__minus,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.37 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_mult_minus
% 5.06/5.37 thf(fact_5296_mult__minus__left,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.06/5.37 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus_left
% 5.06/5.37 thf(fact_5297_mult__minus__left,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.37 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus_left
% 5.06/5.37 thf(fact_5298_mult__minus__left,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus_left
% 5.06/5.37 thf(fact_5299_mult__minus__left,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.06/5.37 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus_left
% 5.06/5.37 thf(fact_5300_mult__minus__left,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus_left
% 5.06/5.37 thf(fact_5301_minus__add__distrib,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.06/5.37 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_add_distrib
% 5.06/5.37 thf(fact_5302_minus__add__distrib,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.06/5.37 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_add_distrib
% 5.06/5.37 thf(fact_5303_minus__add__distrib,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.06/5.37 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_add_distrib
% 5.06/5.37 thf(fact_5304_minus__add__distrib,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.06/5.37 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_add_distrib
% 5.06/5.37 thf(fact_5305_minus__add__distrib,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.06/5.37 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_add_distrib
% 5.06/5.37 thf(fact_5306_minus__add__cancel,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.06/5.37 = B ) ).
% 5.06/5.37
% 5.06/5.37 % minus_add_cancel
% 5.06/5.37 thf(fact_5307_minus__add__cancel,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.06/5.37 = B ) ).
% 5.06/5.37
% 5.06/5.37 % minus_add_cancel
% 5.06/5.37 thf(fact_5308_minus__add__cancel,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.06/5.37 = B ) ).
% 5.06/5.37
% 5.06/5.37 % minus_add_cancel
% 5.06/5.37 thf(fact_5309_minus__add__cancel,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.06/5.37 = B ) ).
% 5.06/5.37
% 5.06/5.37 % minus_add_cancel
% 5.06/5.37 thf(fact_5310_minus__add__cancel,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.06/5.37 = B ) ).
% 5.06/5.37
% 5.06/5.37 % minus_add_cancel
% 5.06/5.37 thf(fact_5311_add__minus__cancel,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.06/5.37 = B ) ).
% 5.06/5.37
% 5.06/5.37 % add_minus_cancel
% 5.06/5.37 thf(fact_5312_add__minus__cancel,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.06/5.37 = B ) ).
% 5.06/5.37
% 5.06/5.37 % add_minus_cancel
% 5.06/5.37 thf(fact_5313_add__minus__cancel,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.06/5.37 = B ) ).
% 5.06/5.37
% 5.06/5.37 % add_minus_cancel
% 5.06/5.37 thf(fact_5314_add__minus__cancel,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.06/5.37 = B ) ).
% 5.06/5.37
% 5.06/5.37 % add_minus_cancel
% 5.06/5.37 thf(fact_5315_add__minus__cancel,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.06/5.37 = B ) ).
% 5.06/5.37
% 5.06/5.37 % add_minus_cancel
% 5.06/5.37 thf(fact_5316_minus__diff__eq,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.06/5.37 = ( minus_minus_real @ B @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_eq
% 5.06/5.37 thf(fact_5317_minus__diff__eq,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.06/5.37 = ( minus_minus_int @ B @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_eq
% 5.06/5.37 thf(fact_5318_minus__diff__eq,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.06/5.37 = ( minus_minus_complex @ B @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_eq
% 5.06/5.37 thf(fact_5319_minus__diff__eq,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.06/5.37 = ( minus_minus_rat @ B @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_eq
% 5.06/5.37 thf(fact_5320_minus__diff__eq,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.06/5.37 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_eq
% 5.06/5.37 thf(fact_5321_div__minus__minus,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.06/5.37 = ( divide_divide_int @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % div_minus_minus
% 5.06/5.37 thf(fact_5322_div__minus__minus,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.37 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % div_minus_minus
% 5.06/5.37 thf(fact_5323_minus__dvd__iff,axiom,
% 5.06/5.37 ! [X: real,Y: real] :
% 5.06/5.37 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 5.06/5.37 = ( dvd_dvd_real @ X @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_dvd_iff
% 5.06/5.37 thf(fact_5324_minus__dvd__iff,axiom,
% 5.06/5.37 ! [X: int,Y: int] :
% 5.06/5.37 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 5.06/5.37 = ( dvd_dvd_int @ X @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_dvd_iff
% 5.06/5.37 thf(fact_5325_minus__dvd__iff,axiom,
% 5.06/5.37 ! [X: complex,Y: complex] :
% 5.06/5.37 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y )
% 5.06/5.37 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_dvd_iff
% 5.06/5.37 thf(fact_5326_minus__dvd__iff,axiom,
% 5.06/5.37 ! [X: rat,Y: rat] :
% 5.06/5.37 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 5.06/5.37 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_dvd_iff
% 5.06/5.37 thf(fact_5327_minus__dvd__iff,axiom,
% 5.06/5.37 ! [X: code_integer,Y: code_integer] :
% 5.06/5.37 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 5.06/5.37 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_dvd_iff
% 5.06/5.37 thf(fact_5328_dvd__minus__iff,axiom,
% 5.06/5.37 ! [X: real,Y: real] :
% 5.06/5.37 ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 5.06/5.37 = ( dvd_dvd_real @ X @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % dvd_minus_iff
% 5.06/5.37 thf(fact_5329_dvd__minus__iff,axiom,
% 5.06/5.37 ! [X: int,Y: int] :
% 5.06/5.37 ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 5.06/5.37 = ( dvd_dvd_int @ X @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % dvd_minus_iff
% 5.06/5.37 thf(fact_5330_dvd__minus__iff,axiom,
% 5.06/5.37 ! [X: complex,Y: complex] :
% 5.06/5.37 ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y ) )
% 5.06/5.37 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % dvd_minus_iff
% 5.06/5.37 thf(fact_5331_dvd__minus__iff,axiom,
% 5.06/5.37 ! [X: rat,Y: rat] :
% 5.06/5.37 ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 5.06/5.37 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % dvd_minus_iff
% 5.06/5.37 thf(fact_5332_dvd__minus__iff,axiom,
% 5.06/5.37 ! [X: code_integer,Y: code_integer] :
% 5.06/5.37 ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 5.06/5.37 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % dvd_minus_iff
% 5.06/5.37 thf(fact_5333_mod__minus__minus,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mod_minus_minus
% 5.06/5.37 thf(fact_5334_mod__minus__minus,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mod_minus_minus
% 5.06/5.37 thf(fact_5335_real__add__minus__iff,axiom,
% 5.06/5.37 ! [X: real,A: real] :
% 5.06/5.37 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 5.06/5.37 = zero_zero_real )
% 5.06/5.37 = ( X = A ) ) ).
% 5.06/5.37
% 5.06/5.37 % real_add_minus_iff
% 5.06/5.37 thf(fact_5336_sum_Oneutral__const,axiom,
% 5.06/5.37 ! [A2: set_int] :
% 5.06/5.37 ( ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [Uu3: int] : zero_zero_int
% 5.06/5.37 @ A2 )
% 5.06/5.37 = zero_zero_int ) ).
% 5.06/5.37
% 5.06/5.37 % sum.neutral_const
% 5.06/5.37 thf(fact_5337_sum_Oneutral__const,axiom,
% 5.06/5.37 ! [A2: set_complex] :
% 5.06/5.37 ( ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [Uu3: complex] : zero_zero_complex
% 5.06/5.37 @ A2 )
% 5.06/5.37 = zero_zero_complex ) ).
% 5.06/5.37
% 5.06/5.37 % sum.neutral_const
% 5.06/5.37 thf(fact_5338_sum_Oneutral__const,axiom,
% 5.06/5.37 ! [A2: set_nat] :
% 5.06/5.37 ( ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [Uu3: nat] : zero_zero_nat
% 5.06/5.37 @ A2 )
% 5.06/5.37 = zero_zero_nat ) ).
% 5.06/5.37
% 5.06/5.37 % sum.neutral_const
% 5.06/5.37 thf(fact_5339_sum_Oneutral__const,axiom,
% 5.06/5.37 ! [A2: set_nat] :
% 5.06/5.37 ( ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [Uu3: nat] : zero_zero_real
% 5.06/5.37 @ A2 )
% 5.06/5.37 = zero_zero_real ) ).
% 5.06/5.37
% 5.06/5.37 % sum.neutral_const
% 5.06/5.37 thf(fact_5340_case__prod__conv,axiom,
% 5.06/5.37 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.06/5.37 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.06/5.37 = ( F @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % case_prod_conv
% 5.06/5.37 thf(fact_5341_case__prod__conv,axiom,
% 5.06/5.37 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.06/5.37 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.06/5.37 = ( F @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % case_prod_conv
% 5.06/5.37 thf(fact_5342_case__prod__conv,axiom,
% 5.06/5.37 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.06/5.37 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.06/5.37 = ( F @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % case_prod_conv
% 5.06/5.37 thf(fact_5343_case__prod__conv,axiom,
% 5.06/5.37 ! [F: int > int > $o,A: int,B: int] :
% 5.06/5.37 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.06/5.37 = ( F @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % case_prod_conv
% 5.06/5.37 thf(fact_5344_case__prod__conv,axiom,
% 5.06/5.37 ! [F: int > int > int,A: int,B: int] :
% 5.06/5.37 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.06/5.37 = ( F @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % case_prod_conv
% 5.06/5.37 thf(fact_5345_neg__less__eq__nonneg,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.06/5.37 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_eq_nonneg
% 5.06/5.37 thf(fact_5346_neg__less__eq__nonneg,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.06/5.37 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_eq_nonneg
% 5.06/5.37 thf(fact_5347_neg__less__eq__nonneg,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.06/5.37 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_eq_nonneg
% 5.06/5.37 thf(fact_5348_neg__less__eq__nonneg,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.06/5.37 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_eq_nonneg
% 5.06/5.37 thf(fact_5349_less__eq__neg__nonpos,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.06/5.37 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_eq_neg_nonpos
% 5.06/5.37 thf(fact_5350_less__eq__neg__nonpos,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.06/5.37 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_eq_neg_nonpos
% 5.06/5.37 thf(fact_5351_less__eq__neg__nonpos,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.06/5.37 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_eq_neg_nonpos
% 5.06/5.37 thf(fact_5352_less__eq__neg__nonpos,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.06/5.37 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_eq_neg_nonpos
% 5.06/5.37 thf(fact_5353_neg__le__0__iff__le,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.06/5.37 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_le_0_iff_le
% 5.06/5.37 thf(fact_5354_neg__le__0__iff__le,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.06/5.37 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_le_0_iff_le
% 5.06/5.37 thf(fact_5355_neg__le__0__iff__le,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.06/5.37 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_le_0_iff_le
% 5.06/5.37 thf(fact_5356_neg__le__0__iff__le,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.06/5.37 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_le_0_iff_le
% 5.06/5.37 thf(fact_5357_neg__0__le__iff__le,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.06/5.37 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_0_le_iff_le
% 5.06/5.37 thf(fact_5358_neg__0__le__iff__le,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.06/5.37 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_0_le_iff_le
% 5.06/5.37 thf(fact_5359_neg__0__le__iff__le,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.06/5.37 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_0_le_iff_le
% 5.06/5.37 thf(fact_5360_neg__0__le__iff__le,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.06/5.37 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_0_le_iff_le
% 5.06/5.37 thf(fact_5361_less__neg__neg,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.06/5.37 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_neg_neg
% 5.06/5.37 thf(fact_5362_less__neg__neg,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.06/5.37 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_neg_neg
% 5.06/5.37 thf(fact_5363_less__neg__neg,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.06/5.37 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_neg_neg
% 5.06/5.37 thf(fact_5364_less__neg__neg,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.06/5.37 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_neg_neg
% 5.06/5.37 thf(fact_5365_neg__less__pos,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.06/5.37 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_pos
% 5.06/5.37 thf(fact_5366_neg__less__pos,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.06/5.37 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_pos
% 5.06/5.37 thf(fact_5367_neg__less__pos,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.06/5.37 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_pos
% 5.06/5.37 thf(fact_5368_neg__less__pos,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.06/5.37 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_pos
% 5.06/5.37 thf(fact_5369_neg__0__less__iff__less,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.06/5.37 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_0_less_iff_less
% 5.06/5.37 thf(fact_5370_neg__0__less__iff__less,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.06/5.37 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_0_less_iff_less
% 5.06/5.37 thf(fact_5371_neg__0__less__iff__less,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.06/5.37 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_0_less_iff_less
% 5.06/5.37 thf(fact_5372_neg__0__less__iff__less,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.06/5.37 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_0_less_iff_less
% 5.06/5.37 thf(fact_5373_neg__less__0__iff__less,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.06/5.37 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_0_iff_less
% 5.06/5.37 thf(fact_5374_neg__less__0__iff__less,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.06/5.37 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_0_iff_less
% 5.06/5.37 thf(fact_5375_neg__less__0__iff__less,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.06/5.37 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_0_iff_less
% 5.06/5.37 thf(fact_5376_neg__less__0__iff__less,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.06/5.37 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_less_0_iff_less
% 5.06/5.37 thf(fact_5377_ab__left__minus,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.06/5.37 = zero_zero_real ) ).
% 5.06/5.37
% 5.06/5.37 % ab_left_minus
% 5.06/5.37 thf(fact_5378_ab__left__minus,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.06/5.37 = zero_zero_int ) ).
% 5.06/5.37
% 5.06/5.37 % ab_left_minus
% 5.06/5.37 thf(fact_5379_ab__left__minus,axiom,
% 5.06/5.37 ! [A: complex] :
% 5.06/5.37 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.06/5.37 = zero_zero_complex ) ).
% 5.06/5.37
% 5.06/5.37 % ab_left_minus
% 5.06/5.37 thf(fact_5380_ab__left__minus,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.06/5.37 = zero_zero_rat ) ).
% 5.06/5.37
% 5.06/5.37 % ab_left_minus
% 5.06/5.37 thf(fact_5381_ab__left__minus,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.06/5.37 = zero_z3403309356797280102nteger ) ).
% 5.06/5.37
% 5.06/5.37 % ab_left_minus
% 5.06/5.37 thf(fact_5382_add_Oright__inverse,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.06/5.37 = zero_zero_real ) ).
% 5.06/5.37
% 5.06/5.37 % add.right_inverse
% 5.06/5.37 thf(fact_5383_add_Oright__inverse,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.06/5.37 = zero_zero_int ) ).
% 5.06/5.37
% 5.06/5.37 % add.right_inverse
% 5.06/5.37 thf(fact_5384_add_Oright__inverse,axiom,
% 5.06/5.37 ! [A: complex] :
% 5.06/5.37 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.06/5.37 = zero_zero_complex ) ).
% 5.06/5.37
% 5.06/5.37 % add.right_inverse
% 5.06/5.37 thf(fact_5385_add_Oright__inverse,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.06/5.37 = zero_zero_rat ) ).
% 5.06/5.37
% 5.06/5.37 % add.right_inverse
% 5.06/5.37 thf(fact_5386_add_Oright__inverse,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.06/5.37 = zero_z3403309356797280102nteger ) ).
% 5.06/5.37
% 5.06/5.37 % add.right_inverse
% 5.06/5.37 thf(fact_5387_diff__0,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.06/5.37 = ( uminus_uminus_real @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_0
% 5.06/5.37 thf(fact_5388_diff__0,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.06/5.37 = ( uminus_uminus_int @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_0
% 5.06/5.37 thf(fact_5389_diff__0,axiom,
% 5.06/5.37 ! [A: complex] :
% 5.06/5.37 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_0
% 5.06/5.37 thf(fact_5390_diff__0,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.06/5.37 = ( uminus_uminus_rat @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_0
% 5.06/5.37 thf(fact_5391_diff__0,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_0
% 5.06/5.37 thf(fact_5392_verit__minus__simplify_I3_J,axiom,
% 5.06/5.37 ! [B: real] :
% 5.06/5.37 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.06/5.37 = ( uminus_uminus_real @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % verit_minus_simplify(3)
% 5.06/5.37 thf(fact_5393_verit__minus__simplify_I3_J,axiom,
% 5.06/5.37 ! [B: int] :
% 5.06/5.37 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.06/5.37 = ( uminus_uminus_int @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % verit_minus_simplify(3)
% 5.06/5.37 thf(fact_5394_verit__minus__simplify_I3_J,axiom,
% 5.06/5.37 ! [B: complex] :
% 5.06/5.37 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % verit_minus_simplify(3)
% 5.06/5.37 thf(fact_5395_verit__minus__simplify_I3_J,axiom,
% 5.06/5.37 ! [B: rat] :
% 5.06/5.37 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.06/5.37 = ( uminus_uminus_rat @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % verit_minus_simplify(3)
% 5.06/5.37 thf(fact_5396_verit__minus__simplify_I3_J,axiom,
% 5.06/5.37 ! [B: code_integer] :
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % verit_minus_simplify(3)
% 5.06/5.37 thf(fact_5397_add__neg__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_simps(3)
% 5.06/5.37 thf(fact_5398_add__neg__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_simps(3)
% 5.06/5.37 thf(fact_5399_add__neg__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_simps(3)
% 5.06/5.37 thf(fact_5400_add__neg__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_simps(3)
% 5.06/5.37 thf(fact_5401_add__neg__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_simps(3)
% 5.06/5.37 thf(fact_5402_mult__minus1,axiom,
% 5.06/5.37 ! [Z: real] :
% 5.06/5.37 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.06/5.37 = ( uminus_uminus_real @ Z ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus1
% 5.06/5.37 thf(fact_5403_mult__minus1,axiom,
% 5.06/5.37 ! [Z: int] :
% 5.06/5.37 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.06/5.37 = ( uminus_uminus_int @ Z ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus1
% 5.06/5.37 thf(fact_5404_mult__minus1,axiom,
% 5.06/5.37 ! [Z: complex] :
% 5.06/5.37 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus1
% 5.06/5.37 thf(fact_5405_mult__minus1,axiom,
% 5.06/5.37 ! [Z: rat] :
% 5.06/5.37 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.06/5.37 = ( uminus_uminus_rat @ Z ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus1
% 5.06/5.37 thf(fact_5406_mult__minus1,axiom,
% 5.06/5.37 ! [Z: code_integer] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus1
% 5.06/5.37 thf(fact_5407_mult__minus1__right,axiom,
% 5.06/5.37 ! [Z: real] :
% 5.06/5.37 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.37 = ( uminus_uminus_real @ Z ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus1_right
% 5.06/5.37 thf(fact_5408_mult__minus1__right,axiom,
% 5.06/5.37 ! [Z: int] :
% 5.06/5.37 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = ( uminus_uminus_int @ Z ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus1_right
% 5.06/5.37 thf(fact_5409_mult__minus1__right,axiom,
% 5.06/5.37 ! [Z: complex] :
% 5.06/5.37 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus1_right
% 5.06/5.37 thf(fact_5410_mult__minus1__right,axiom,
% 5.06/5.37 ! [Z: rat] :
% 5.06/5.37 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.37 = ( uminus_uminus_rat @ Z ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus1_right
% 5.06/5.37 thf(fact_5411_mult__minus1__right,axiom,
% 5.06/5.37 ! [Z: code_integer] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_minus1_right
% 5.06/5.37 thf(fact_5412_diff__minus__eq__add,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.06/5.37 = ( plus_plus_real @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_minus_eq_add
% 5.06/5.37 thf(fact_5413_diff__minus__eq__add,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.37 = ( plus_plus_int @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_minus_eq_add
% 5.06/5.37 thf(fact_5414_diff__minus__eq__add,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.06/5.37 = ( plus_plus_complex @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_minus_eq_add
% 5.06/5.37 thf(fact_5415_diff__minus__eq__add,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.06/5.37 = ( plus_plus_rat @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_minus_eq_add
% 5.06/5.37 thf(fact_5416_diff__minus__eq__add,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.37 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_minus_eq_add
% 5.06/5.37 thf(fact_5417_uminus__add__conv__diff,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.06/5.37 = ( minus_minus_real @ B @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % uminus_add_conv_diff
% 5.06/5.37 thf(fact_5418_uminus__add__conv__diff,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.37 = ( minus_minus_int @ B @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % uminus_add_conv_diff
% 5.06/5.37 thf(fact_5419_uminus__add__conv__diff,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.06/5.37 = ( minus_minus_complex @ B @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % uminus_add_conv_diff
% 5.06/5.37 thf(fact_5420_uminus__add__conv__diff,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.06/5.37 = ( minus_minus_rat @ B @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % uminus_add_conv_diff
% 5.06/5.37 thf(fact_5421_uminus__add__conv__diff,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.06/5.37 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % uminus_add_conv_diff
% 5.06/5.37 thf(fact_5422_div__minus1__right,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = ( uminus_uminus_int @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % div_minus1_right
% 5.06/5.37 thf(fact_5423_div__minus1__right,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % div_minus1_right
% 5.06/5.37 thf(fact_5424_divide__minus1,axiom,
% 5.06/5.37 ! [X: real] :
% 5.06/5.37 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.37 = ( uminus_uminus_real @ X ) ) ).
% 5.06/5.37
% 5.06/5.37 % divide_minus1
% 5.06/5.37 thf(fact_5425_divide__minus1,axiom,
% 5.06/5.37 ! [X: complex] :
% 5.06/5.37 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.06/5.37
% 5.06/5.37 % divide_minus1
% 5.06/5.37 thf(fact_5426_divide__minus1,axiom,
% 5.06/5.37 ! [X: rat] :
% 5.06/5.37 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.37 = ( uminus_uminus_rat @ X ) ) ).
% 5.06/5.37
% 5.06/5.37 % divide_minus1
% 5.06/5.37 thf(fact_5427_minus__mod__self1,axiom,
% 5.06/5.37 ! [B: int,A: int] :
% 5.06/5.37 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.06/5.37 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_mod_self1
% 5.06/5.37 thf(fact_5428_minus__mod__self1,axiom,
% 5.06/5.37 ! [B: code_integer,A: code_integer] :
% 5.06/5.37 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.06/5.37 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_mod_self1
% 5.06/5.37 thf(fact_5429_ln__le__cancel__iff,axiom,
% 5.06/5.37 ! [X: real,Y: real] :
% 5.06/5.37 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.37 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.37 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 5.06/5.37 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % ln_le_cancel_iff
% 5.06/5.37 thf(fact_5430_ln__one,axiom,
% 5.06/5.37 ( ( ln_ln_real @ one_one_real )
% 5.06/5.37 = zero_zero_real ) ).
% 5.06/5.37
% 5.06/5.37 % ln_one
% 5.06/5.37 thf(fact_5431_signed__take__bit__of__minus__1,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( bit_ri6519982836138164636nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.37
% 5.06/5.37 % signed_take_bit_of_minus_1
% 5.06/5.37 thf(fact_5432_signed__take__bit__of__minus__1,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % signed_take_bit_of_minus_1
% 5.06/5.37 thf(fact_5433_sum_Odelta_H,axiom,
% 5.06/5.37 ! [S3: set_real,A: real,B: real > complex] :
% 5.06/5.37 ( ( finite_finite_real @ S3 )
% 5.06/5.37 => ( ( ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups5754745047067104278omplex
% 5.06/5.37 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups5754745047067104278omplex
% 5.06/5.37 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_complex ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta'
% 5.06/5.37 thf(fact_5434_sum_Odelta_H,axiom,
% 5.06/5.37 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.06/5.37 ( ( finite_finite_nat @ S3 )
% 5.06/5.37 => ( ( ( member_nat @ A @ S3 )
% 5.06/5.37 => ( ( groups2073611262835488442omplex
% 5.06/5.37 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_nat @ A @ S3 )
% 5.06/5.37 => ( ( groups2073611262835488442omplex
% 5.06/5.37 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_complex ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta'
% 5.06/5.37 thf(fact_5435_sum_Odelta_H,axiom,
% 5.06/5.37 ! [S3: set_int,A: int,B: int > complex] :
% 5.06/5.37 ( ( finite_finite_int @ S3 )
% 5.06/5.37 => ( ( ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups3049146728041665814omplex
% 5.06/5.37 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups3049146728041665814omplex
% 5.06/5.37 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_complex ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta'
% 5.06/5.37 thf(fact_5436_sum_Odelta_H,axiom,
% 5.06/5.37 ! [S3: set_real,A: real,B: real > real] :
% 5.06/5.37 ( ( finite_finite_real @ S3 )
% 5.06/5.37 => ( ( ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups8097168146408367636l_real
% 5.06/5.37 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups8097168146408367636l_real
% 5.06/5.37 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_real ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta'
% 5.06/5.37 thf(fact_5437_sum_Odelta_H,axiom,
% 5.06/5.37 ! [S3: set_int,A: int,B: int > real] :
% 5.06/5.37 ( ( finite_finite_int @ S3 )
% 5.06/5.37 => ( ( ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups8778361861064173332t_real
% 5.06/5.37 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups8778361861064173332t_real
% 5.06/5.37 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_real ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta'
% 5.06/5.37 thf(fact_5438_sum_Odelta_H,axiom,
% 5.06/5.37 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.06/5.37 ( ( finite3207457112153483333omplex @ S3 )
% 5.06/5.37 => ( ( ( member_complex @ A @ S3 )
% 5.06/5.37 => ( ( groups5808333547571424918x_real
% 5.06/5.37 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_complex @ A @ S3 )
% 5.06/5.37 => ( ( groups5808333547571424918x_real
% 5.06/5.37 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_real ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta'
% 5.06/5.37 thf(fact_5439_sum_Odelta_H,axiom,
% 5.06/5.37 ! [S3: set_real,A: real,B: real > rat] :
% 5.06/5.37 ( ( finite_finite_real @ S3 )
% 5.06/5.37 => ( ( ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups1300246762558778688al_rat
% 5.06/5.37 @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups1300246762558778688al_rat
% 5.06/5.37 @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_rat ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta'
% 5.06/5.37 thf(fact_5440_sum_Odelta_H,axiom,
% 5.06/5.37 ! [S3: set_nat,A: nat,B: nat > rat] :
% 5.06/5.37 ( ( finite_finite_nat @ S3 )
% 5.06/5.37 => ( ( ( member_nat @ A @ S3 )
% 5.06/5.37 => ( ( groups2906978787729119204at_rat
% 5.06/5.37 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_nat @ A @ S3 )
% 5.06/5.37 => ( ( groups2906978787729119204at_rat
% 5.06/5.37 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_rat ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta'
% 5.06/5.37 thf(fact_5441_sum_Odelta_H,axiom,
% 5.06/5.37 ! [S3: set_int,A: int,B: int > rat] :
% 5.06/5.37 ( ( finite_finite_int @ S3 )
% 5.06/5.37 => ( ( ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups3906332499630173760nt_rat
% 5.06/5.37 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups3906332499630173760nt_rat
% 5.06/5.37 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_rat ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta'
% 5.06/5.37 thf(fact_5442_sum_Odelta_H,axiom,
% 5.06/5.37 ! [S3: set_complex,A: complex,B: complex > rat] :
% 5.06/5.37 ( ( finite3207457112153483333omplex @ S3 )
% 5.06/5.37 => ( ( ( member_complex @ A @ S3 )
% 5.06/5.37 => ( ( groups5058264527183730370ex_rat
% 5.06/5.37 @ ^ [K3: complex] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_complex @ A @ S3 )
% 5.06/5.37 => ( ( groups5058264527183730370ex_rat
% 5.06/5.37 @ ^ [K3: complex] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_rat ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta'
% 5.06/5.37 thf(fact_5443_sum_Odelta,axiom,
% 5.06/5.37 ! [S3: set_real,A: real,B: real > complex] :
% 5.06/5.37 ( ( finite_finite_real @ S3 )
% 5.06/5.37 => ( ( ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups5754745047067104278omplex
% 5.06/5.37 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups5754745047067104278omplex
% 5.06/5.37 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_complex ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta
% 5.06/5.37 thf(fact_5444_sum_Odelta,axiom,
% 5.06/5.37 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.06/5.37 ( ( finite_finite_nat @ S3 )
% 5.06/5.37 => ( ( ( member_nat @ A @ S3 )
% 5.06/5.37 => ( ( groups2073611262835488442omplex
% 5.06/5.37 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_nat @ A @ S3 )
% 5.06/5.37 => ( ( groups2073611262835488442omplex
% 5.06/5.37 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_complex ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta
% 5.06/5.37 thf(fact_5445_sum_Odelta,axiom,
% 5.06/5.37 ! [S3: set_int,A: int,B: int > complex] :
% 5.06/5.37 ( ( finite_finite_int @ S3 )
% 5.06/5.37 => ( ( ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups3049146728041665814omplex
% 5.06/5.37 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups3049146728041665814omplex
% 5.06/5.37 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_complex ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta
% 5.06/5.37 thf(fact_5446_sum_Odelta,axiom,
% 5.06/5.37 ! [S3: set_real,A: real,B: real > real] :
% 5.06/5.37 ( ( finite_finite_real @ S3 )
% 5.06/5.37 => ( ( ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups8097168146408367636l_real
% 5.06/5.37 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups8097168146408367636l_real
% 5.06/5.37 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_real ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta
% 5.06/5.37 thf(fact_5447_sum_Odelta,axiom,
% 5.06/5.37 ! [S3: set_int,A: int,B: int > real] :
% 5.06/5.37 ( ( finite_finite_int @ S3 )
% 5.06/5.37 => ( ( ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups8778361861064173332t_real
% 5.06/5.37 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups8778361861064173332t_real
% 5.06/5.37 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_real ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta
% 5.06/5.37 thf(fact_5448_sum_Odelta,axiom,
% 5.06/5.37 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.06/5.37 ( ( finite3207457112153483333omplex @ S3 )
% 5.06/5.37 => ( ( ( member_complex @ A @ S3 )
% 5.06/5.37 => ( ( groups5808333547571424918x_real
% 5.06/5.37 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_complex @ A @ S3 )
% 5.06/5.37 => ( ( groups5808333547571424918x_real
% 5.06/5.37 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_real ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta
% 5.06/5.37 thf(fact_5449_sum_Odelta,axiom,
% 5.06/5.37 ! [S3: set_real,A: real,B: real > rat] :
% 5.06/5.37 ( ( finite_finite_real @ S3 )
% 5.06/5.37 => ( ( ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups1300246762558778688al_rat
% 5.06/5.37 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_real @ A @ S3 )
% 5.06/5.37 => ( ( groups1300246762558778688al_rat
% 5.06/5.37 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_rat ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta
% 5.06/5.37 thf(fact_5450_sum_Odelta,axiom,
% 5.06/5.37 ! [S3: set_nat,A: nat,B: nat > rat] :
% 5.06/5.37 ( ( finite_finite_nat @ S3 )
% 5.06/5.37 => ( ( ( member_nat @ A @ S3 )
% 5.06/5.37 => ( ( groups2906978787729119204at_rat
% 5.06/5.37 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_nat @ A @ S3 )
% 5.06/5.37 => ( ( groups2906978787729119204at_rat
% 5.06/5.37 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_rat ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta
% 5.06/5.37 thf(fact_5451_sum_Odelta,axiom,
% 5.06/5.37 ! [S3: set_int,A: int,B: int > rat] :
% 5.06/5.37 ( ( finite_finite_int @ S3 )
% 5.06/5.37 => ( ( ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups3906332499630173760nt_rat
% 5.06/5.37 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_int @ A @ S3 )
% 5.06/5.37 => ( ( groups3906332499630173760nt_rat
% 5.06/5.37 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_rat ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta
% 5.06/5.37 thf(fact_5452_sum_Odelta,axiom,
% 5.06/5.37 ! [S3: set_complex,A: complex,B: complex > rat] :
% 5.06/5.37 ( ( finite3207457112153483333omplex @ S3 )
% 5.06/5.37 => ( ( ( member_complex @ A @ S3 )
% 5.06/5.37 => ( ( groups5058264527183730370ex_rat
% 5.06/5.37 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = ( B @ A ) ) )
% 5.06/5.37 & ( ~ ( member_complex @ A @ S3 )
% 5.06/5.37 => ( ( groups5058264527183730370ex_rat
% 5.06/5.37 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.06/5.37 @ S3 )
% 5.06/5.37 = zero_zero_rat ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.delta
% 5.06/5.37 thf(fact_5453_dbl__simps_I1_J,axiom,
% 5.06/5.37 ! [K: num] :
% 5.06/5.37 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % dbl_simps(1)
% 5.06/5.37 thf(fact_5454_dbl__simps_I1_J,axiom,
% 5.06/5.37 ! [K: num] :
% 5.06/5.37 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % dbl_simps(1)
% 5.06/5.37 thf(fact_5455_dbl__simps_I1_J,axiom,
% 5.06/5.37 ! [K: num] :
% 5.06/5.37 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % dbl_simps(1)
% 5.06/5.37 thf(fact_5456_dbl__simps_I1_J,axiom,
% 5.06/5.37 ! [K: num] :
% 5.06/5.37 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % dbl_simps(1)
% 5.06/5.37 thf(fact_5457_dbl__simps_I1_J,axiom,
% 5.06/5.37 ! [K: num] :
% 5.06/5.37 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % dbl_simps(1)
% 5.06/5.37 thf(fact_5458_add__neg__numeral__special_I7_J,axiom,
% 5.06/5.37 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.37 = zero_zero_real ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(7)
% 5.06/5.37 thf(fact_5459_add__neg__numeral__special_I7_J,axiom,
% 5.06/5.37 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = zero_zero_int ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(7)
% 5.06/5.37 thf(fact_5460_add__neg__numeral__special_I7_J,axiom,
% 5.06/5.37 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.37 = zero_zero_complex ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(7)
% 5.06/5.37 thf(fact_5461_add__neg__numeral__special_I7_J,axiom,
% 5.06/5.37 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.37 = zero_zero_rat ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(7)
% 5.06/5.37 thf(fact_5462_add__neg__numeral__special_I7_J,axiom,
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = zero_z3403309356797280102nteger ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(7)
% 5.06/5.37 thf(fact_5463_add__neg__numeral__special_I8_J,axiom,
% 5.06/5.37 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.06/5.37 = zero_zero_real ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(8)
% 5.06/5.37 thf(fact_5464_add__neg__numeral__special_I8_J,axiom,
% 5.06/5.37 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.06/5.37 = zero_zero_int ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(8)
% 5.06/5.37 thf(fact_5465_add__neg__numeral__special_I8_J,axiom,
% 5.06/5.37 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.06/5.37 = zero_zero_complex ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(8)
% 5.06/5.37 thf(fact_5466_add__neg__numeral__special_I8_J,axiom,
% 5.06/5.37 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.06/5.37 = zero_zero_rat ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(8)
% 5.06/5.37 thf(fact_5467_add__neg__numeral__special_I8_J,axiom,
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.06/5.37 = zero_z3403309356797280102nteger ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(8)
% 5.06/5.37 thf(fact_5468_diff__numeral__special_I12_J,axiom,
% 5.06/5.37 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.37 = zero_zero_real ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(12)
% 5.06/5.37 thf(fact_5469_diff__numeral__special_I12_J,axiom,
% 5.06/5.37 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = zero_zero_int ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(12)
% 5.06/5.37 thf(fact_5470_diff__numeral__special_I12_J,axiom,
% 5.06/5.37 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.37 = zero_zero_complex ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(12)
% 5.06/5.37 thf(fact_5471_diff__numeral__special_I12_J,axiom,
% 5.06/5.37 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.37 = zero_zero_rat ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(12)
% 5.06/5.37 thf(fact_5472_diff__numeral__special_I12_J,axiom,
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = zero_z3403309356797280102nteger ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(12)
% 5.06/5.37 thf(fact_5473_numeral__eq__neg__one__iff,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) )
% 5.06/5.37 = ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.37 = ( N2 = one ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_eq_neg_one_iff
% 5.06/5.37 thf(fact_5474_numeral__eq__neg__one__iff,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.37 = ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = ( N2 = one ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_eq_neg_one_iff
% 5.06/5.37 thf(fact_5475_numeral__eq__neg__one__iff,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.37 = ( N2 = one ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_eq_neg_one_iff
% 5.06/5.37 thf(fact_5476_numeral__eq__neg__one__iff,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.06/5.37 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.37 = ( N2 = one ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_eq_neg_one_iff
% 5.06/5.37 thf(fact_5477_numeral__eq__neg__one__iff,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = ( N2 = one ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_eq_neg_one_iff
% 5.06/5.37 thf(fact_5478_neg__one__eq__numeral__iff,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( ( uminus_uminus_real @ one_one_real )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.37 = ( N2 = one ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_eq_numeral_iff
% 5.06/5.37 thf(fact_5479_neg__one__eq__numeral__iff,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( ( uminus_uminus_int @ one_one_int )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.37 = ( N2 = one ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_eq_numeral_iff
% 5.06/5.37 thf(fact_5480_neg__one__eq__numeral__iff,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.06/5.37 = ( N2 = one ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_eq_numeral_iff
% 5.06/5.37 thf(fact_5481_neg__one__eq__numeral__iff,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.06/5.37 = ( N2 = one ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_eq_numeral_iff
% 5.06/5.37 thf(fact_5482_neg__one__eq__numeral__iff,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.06/5.37 = ( N2 = one ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_eq_numeral_iff
% 5.06/5.37 thf(fact_5483_left__minus__one__mult__self,axiom,
% 5.06/5.37 ! [N2: nat,A: real] :
% 5.06/5.37 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ A ) )
% 5.06/5.37 = A ) ).
% 5.06/5.37
% 5.06/5.37 % left_minus_one_mult_self
% 5.06/5.37 thf(fact_5484_left__minus__one__mult__self,axiom,
% 5.06/5.37 ! [N2: nat,A: int] :
% 5.06/5.37 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ A ) )
% 5.06/5.37 = A ) ).
% 5.06/5.37
% 5.06/5.37 % left_minus_one_mult_self
% 5.06/5.37 thf(fact_5485_left__minus__one__mult__self,axiom,
% 5.06/5.37 ! [N2: nat,A: complex] :
% 5.06/5.37 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ A ) )
% 5.06/5.37 = A ) ).
% 5.06/5.37
% 5.06/5.37 % left_minus_one_mult_self
% 5.06/5.37 thf(fact_5486_left__minus__one__mult__self,axiom,
% 5.06/5.37 ! [N2: nat,A: rat] :
% 5.06/5.37 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ A ) )
% 5.06/5.37 = A ) ).
% 5.06/5.37
% 5.06/5.37 % left_minus_one_mult_self
% 5.06/5.37 thf(fact_5487_left__minus__one__mult__self,axiom,
% 5.06/5.37 ! [N2: nat,A: code_integer] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A ) )
% 5.06/5.37 = A ) ).
% 5.06/5.37
% 5.06/5.37 % left_minus_one_mult_self
% 5.06/5.37 thf(fact_5488_minus__one__mult__self,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) )
% 5.06/5.37 = one_one_real ) ).
% 5.06/5.37
% 5.06/5.37 % minus_one_mult_self
% 5.06/5.37 thf(fact_5489_minus__one__mult__self,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 5.06/5.37 = one_one_int ) ).
% 5.06/5.37
% 5.06/5.37 % minus_one_mult_self
% 5.06/5.37 thf(fact_5490_minus__one__mult__self,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) )
% 5.06/5.37 = one_one_complex ) ).
% 5.06/5.37
% 5.06/5.37 % minus_one_mult_self
% 5.06/5.37 thf(fact_5491_minus__one__mult__self,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) )
% 5.06/5.37 = one_one_rat ) ).
% 5.06/5.37
% 5.06/5.37 % minus_one_mult_self
% 5.06/5.37 thf(fact_5492_minus__one__mult__self,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 5.06/5.37 = one_one_Code_integer ) ).
% 5.06/5.37
% 5.06/5.37 % minus_one_mult_self
% 5.06/5.37 thf(fact_5493_mod__minus1__right,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = zero_zero_int ) ).
% 5.06/5.37
% 5.06/5.37 % mod_minus1_right
% 5.06/5.37 thf(fact_5494_mod__minus1__right,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = zero_z3403309356797280102nteger ) ).
% 5.06/5.37
% 5.06/5.37 % mod_minus1_right
% 5.06/5.37 thf(fact_5495_max__number__of_I4_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.06/5.37 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.06/5.37 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.06/5.37 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(4)
% 5.06/5.37 thf(fact_5496_max__number__of_I4_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.06/5.37 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.06/5.37 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.06/5.37 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(4)
% 5.06/5.37 thf(fact_5497_max__number__of_I4_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.06/5.37 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.06/5.37 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.06/5.37 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(4)
% 5.06/5.37 thf(fact_5498_max__number__of_I4_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.06/5.37 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.06/5.37 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.06/5.37 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(4)
% 5.06/5.37 thf(fact_5499_max__number__of_I3_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.06/5.37 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.06/5.37 = ( numeral_numeral_real @ V ) ) )
% 5.06/5.37 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.06/5.37 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(3)
% 5.06/5.37 thf(fact_5500_max__number__of_I3_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.06/5.37 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.06/5.37 = ( numera6620942414471956472nteger @ V ) ) )
% 5.06/5.37 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.06/5.37 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(3)
% 5.06/5.37 thf(fact_5501_max__number__of_I3_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.06/5.37 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.06/5.37 = ( numeral_numeral_rat @ V ) ) )
% 5.06/5.37 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.06/5.37 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(3)
% 5.06/5.37 thf(fact_5502_max__number__of_I3_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.06/5.37 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.06/5.37 = ( numeral_numeral_int @ V ) ) )
% 5.06/5.37 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.06/5.37 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(3)
% 5.06/5.37 thf(fact_5503_max__number__of_I2_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.06/5.37 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.06/5.37 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.06/5.37 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.06/5.37 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(2)
% 5.06/5.37 thf(fact_5504_max__number__of_I2_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.06/5.37 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.06/5.37 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.06/5.37 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.06/5.37 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(2)
% 5.06/5.37 thf(fact_5505_max__number__of_I2_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.06/5.37 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.06/5.37 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.06/5.37 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.06/5.37 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(2)
% 5.06/5.37 thf(fact_5506_max__number__of_I2_J,axiom,
% 5.06/5.37 ! [U: num,V: num] :
% 5.06/5.37 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.06/5.37 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.06/5.37 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.06/5.37 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.06/5.37 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % max_number_of(2)
% 5.06/5.37 thf(fact_5507_ln__le__zero__iff,axiom,
% 5.06/5.37 ! [X: real] :
% 5.06/5.37 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.37 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.06/5.37 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % ln_le_zero_iff
% 5.06/5.37 thf(fact_5508_ln__ge__zero__iff,axiom,
% 5.06/5.37 ! [X: real] :
% 5.06/5.37 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.06/5.37 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % ln_ge_zero_iff
% 5.06/5.37 thf(fact_5509_semiring__norm_I168_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: real] :
% 5.06/5.37 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.06/5.37 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(168)
% 5.06/5.37 thf(fact_5510_semiring__norm_I168_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: int] :
% 5.06/5.37 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.06/5.37 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(168)
% 5.06/5.37 thf(fact_5511_semiring__norm_I168_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: complex] :
% 5.06/5.37 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.06/5.37 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(168)
% 5.06/5.37 thf(fact_5512_semiring__norm_I168_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: rat] :
% 5.06/5.37 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.06/5.37 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(168)
% 5.06/5.37 thf(fact_5513_semiring__norm_I168_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: code_integer] :
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.06/5.37 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(168)
% 5.06/5.37 thf(fact_5514_diff__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_simps(3)
% 5.06/5.37 thf(fact_5515_diff__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_simps(3)
% 5.06/5.37 thf(fact_5516_diff__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_simps(3)
% 5.06/5.37 thf(fact_5517_diff__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_simps(3)
% 5.06/5.37 thf(fact_5518_diff__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_simps(3)
% 5.06/5.37 thf(fact_5519_diff__numeral__simps_I2_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.37 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_simps(2)
% 5.06/5.37 thf(fact_5520_diff__numeral__simps_I2_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.37 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_simps(2)
% 5.06/5.37 thf(fact_5521_diff__numeral__simps_I2_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.06/5.37 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_simps(2)
% 5.06/5.37 thf(fact_5522_diff__numeral__simps_I2_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.06/5.37 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_simps(2)
% 5.06/5.37 thf(fact_5523_diff__numeral__simps_I2_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.06/5.37 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_simps(2)
% 5.06/5.37 thf(fact_5524_mult__neg__numeral__simps_I1_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.37 = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(1)
% 5.06/5.37 thf(fact_5525_mult__neg__numeral__simps_I1_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.37 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(1)
% 5.06/5.37 thf(fact_5526_mult__neg__numeral__simps_I1_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.06/5.37 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(1)
% 5.06/5.37 thf(fact_5527_mult__neg__numeral__simps_I1_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.06/5.37 = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(1)
% 5.06/5.37 thf(fact_5528_mult__neg__numeral__simps_I1_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.06/5.37 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(1)
% 5.06/5.37 thf(fact_5529_mult__neg__numeral__simps_I2_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(2)
% 5.06/5.37 thf(fact_5530_mult__neg__numeral__simps_I2_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(2)
% 5.06/5.37 thf(fact_5531_mult__neg__numeral__simps_I2_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(2)
% 5.06/5.37 thf(fact_5532_mult__neg__numeral__simps_I2_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(2)
% 5.06/5.37 thf(fact_5533_mult__neg__numeral__simps_I2_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(2)
% 5.06/5.37 thf(fact_5534_mult__neg__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(3)
% 5.06/5.37 thf(fact_5535_mult__neg__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(3)
% 5.06/5.37 thf(fact_5536_mult__neg__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(3)
% 5.06/5.37 thf(fact_5537_mult__neg__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(3)
% 5.06/5.37 thf(fact_5538_mult__neg__numeral__simps_I3_J,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mult_neg_numeral_simps(3)
% 5.06/5.37 thf(fact_5539_semiring__norm_I170_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: real] :
% 5.06/5.37 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 5.06/5.37 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(170)
% 5.06/5.37 thf(fact_5540_semiring__norm_I170_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: int] :
% 5.06/5.37 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 5.06/5.37 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(170)
% 5.06/5.37 thf(fact_5541_semiring__norm_I170_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: complex] :
% 5.06/5.37 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 5.06/5.37 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(170)
% 5.06/5.37 thf(fact_5542_semiring__norm_I170_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: rat] :
% 5.06/5.37 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 5.06/5.37 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(170)
% 5.06/5.37 thf(fact_5543_semiring__norm_I170_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: code_integer] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 5.06/5.37 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(170)
% 5.06/5.37 thf(fact_5544_semiring__norm_I171_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: real] :
% 5.06/5.37 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.06/5.37 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(171)
% 5.06/5.37 thf(fact_5545_semiring__norm_I171_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: int] :
% 5.06/5.37 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.06/5.37 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(171)
% 5.06/5.37 thf(fact_5546_semiring__norm_I171_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: complex] :
% 5.06/5.37 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.06/5.37 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(171)
% 5.06/5.37 thf(fact_5547_semiring__norm_I171_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: rat] :
% 5.06/5.37 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.06/5.37 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(171)
% 5.06/5.37 thf(fact_5548_semiring__norm_I171_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: code_integer] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.06/5.37 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(171)
% 5.06/5.37 thf(fact_5549_semiring__norm_I172_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: real] :
% 5.06/5.37 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.06/5.37 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(172)
% 5.06/5.37 thf(fact_5550_semiring__norm_I172_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: int] :
% 5.06/5.37 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.06/5.37 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(172)
% 5.06/5.37 thf(fact_5551_semiring__norm_I172_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: complex] :
% 5.06/5.37 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.06/5.37 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(172)
% 5.06/5.37 thf(fact_5552_semiring__norm_I172_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: rat] :
% 5.06/5.37 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.06/5.37 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(172)
% 5.06/5.37 thf(fact_5553_semiring__norm_I172_J,axiom,
% 5.06/5.37 ! [V: num,W: num,Y: code_integer] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.06/5.37 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % semiring_norm(172)
% 5.06/5.37 thf(fact_5554_neg__numeral__le__iff,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.37 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_le_iff
% 5.06/5.37 thf(fact_5555_neg__numeral__le__iff,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.06/5.37 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_le_iff
% 5.06/5.37 thf(fact_5556_neg__numeral__le__iff,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.06/5.37 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_le_iff
% 5.06/5.37 thf(fact_5557_neg__numeral__le__iff,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.37 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_le_iff
% 5.06/5.37 thf(fact_5558_neg__numeral__less__iff,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.37 = ( ord_less_num @ N2 @ M ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_iff
% 5.06/5.37 thf(fact_5559_neg__numeral__less__iff,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.37 = ( ord_less_num @ N2 @ M ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_iff
% 5.06/5.37 thf(fact_5560_neg__numeral__less__iff,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.06/5.37 = ( ord_less_num @ N2 @ M ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_iff
% 5.06/5.37 thf(fact_5561_neg__numeral__less__iff,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.06/5.37 = ( ord_less_num @ N2 @ M ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_iff
% 5.06/5.37 thf(fact_5562_not__neg__one__le__neg__numeral__iff,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.06/5.37 = ( M != one ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_neg_one_le_neg_numeral_iff
% 5.06/5.37 thf(fact_5563_not__neg__one__le__neg__numeral__iff,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.06/5.37 = ( M != one ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_neg_one_le_neg_numeral_iff
% 5.06/5.37 thf(fact_5564_not__neg__one__le__neg__numeral__iff,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.06/5.37 = ( M != one ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_neg_one_le_neg_numeral_iff
% 5.06/5.37 thf(fact_5565_not__neg__one__le__neg__numeral__iff,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.06/5.37 = ( M != one ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_neg_one_le_neg_numeral_iff
% 5.06/5.37 thf(fact_5566_le__divide__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [A: real,B: real,W: num] :
% 5.06/5.37 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.06/5.37 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_divide_eq_numeral1(2)
% 5.06/5.37 thf(fact_5567_le__divide__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [A: rat,B: rat,W: num] :
% 5.06/5.37 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.06/5.37 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_divide_eq_numeral1(2)
% 5.06/5.37 thf(fact_5568_divide__le__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [B: real,W: num,A: real] :
% 5.06/5.37 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.06/5.37 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % divide_le_eq_numeral1(2)
% 5.06/5.37 thf(fact_5569_divide__le__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [B: rat,W: num,A: rat] :
% 5.06/5.37 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.06/5.37 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % divide_le_eq_numeral1(2)
% 5.06/5.37 thf(fact_5570_eq__divide__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [A: real,B: real,W: num] :
% 5.06/5.37 ( ( A
% 5.06/5.37 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.06/5.37 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.06/5.37 != zero_zero_real )
% 5.06/5.37 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.06/5.37 = B ) )
% 5.06/5.37 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.06/5.37 = zero_zero_real )
% 5.06/5.37 => ( A = zero_zero_real ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % eq_divide_eq_numeral1(2)
% 5.06/5.37 thf(fact_5571_eq__divide__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [A: complex,B: complex,W: num] :
% 5.06/5.37 ( ( A
% 5.06/5.37 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.06/5.37 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.37 != zero_zero_complex )
% 5.06/5.37 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.37 = B ) )
% 5.06/5.37 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.37 = zero_zero_complex )
% 5.06/5.37 => ( A = zero_zero_complex ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % eq_divide_eq_numeral1(2)
% 5.06/5.37 thf(fact_5572_eq__divide__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [A: rat,B: rat,W: num] :
% 5.06/5.37 ( ( A
% 5.06/5.37 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.06/5.37 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.06/5.37 != zero_zero_rat )
% 5.06/5.37 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.06/5.37 = B ) )
% 5.06/5.37 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.06/5.37 = zero_zero_rat )
% 5.06/5.37 => ( A = zero_zero_rat ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % eq_divide_eq_numeral1(2)
% 5.06/5.37 thf(fact_5573_divide__eq__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [B: real,W: num,A: real] :
% 5.06/5.37 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.06/5.37 = A )
% 5.06/5.37 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.06/5.37 != zero_zero_real )
% 5.06/5.37 => ( B
% 5.06/5.37 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.06/5.37 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.06/5.37 = zero_zero_real )
% 5.06/5.37 => ( A = zero_zero_real ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % divide_eq_eq_numeral1(2)
% 5.06/5.37 thf(fact_5574_divide__eq__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [B: complex,W: num,A: complex] :
% 5.06/5.37 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.37 = A )
% 5.06/5.37 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.37 != zero_zero_complex )
% 5.06/5.37 => ( B
% 5.06/5.37 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.06/5.37 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.37 = zero_zero_complex )
% 5.06/5.37 => ( A = zero_zero_complex ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % divide_eq_eq_numeral1(2)
% 5.06/5.37 thf(fact_5575_divide__eq__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [B: rat,W: num,A: rat] :
% 5.06/5.37 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.06/5.37 = A )
% 5.06/5.37 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.06/5.37 != zero_zero_rat )
% 5.06/5.37 => ( B
% 5.06/5.37 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.06/5.37 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.06/5.37 = zero_zero_rat )
% 5.06/5.37 => ( A = zero_zero_rat ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % divide_eq_eq_numeral1(2)
% 5.06/5.37 thf(fact_5576_neg__numeral__less__neg__one__iff,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.37 = ( M != one ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_neg_one_iff
% 5.06/5.37 thf(fact_5577_neg__numeral__less__neg__one__iff,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = ( M != one ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_neg_one_iff
% 5.06/5.37 thf(fact_5578_neg__numeral__less__neg__one__iff,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.37 = ( M != one ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_neg_one_iff
% 5.06/5.37 thf(fact_5579_neg__numeral__less__neg__one__iff,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = ( M != one ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_neg_one_iff
% 5.06/5.37 thf(fact_5580_less__divide__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [A: real,B: real,W: num] :
% 5.06/5.37 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.06/5.37 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_divide_eq_numeral1(2)
% 5.06/5.37 thf(fact_5581_less__divide__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [A: rat,B: rat,W: num] :
% 5.06/5.37 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.06/5.37 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_divide_eq_numeral1(2)
% 5.06/5.37 thf(fact_5582_divide__less__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [B: real,W: num,A: real] :
% 5.06/5.37 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.06/5.37 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % divide_less_eq_numeral1(2)
% 5.06/5.37 thf(fact_5583_divide__less__eq__numeral1_I2_J,axiom,
% 5.06/5.37 ! [B: rat,W: num,A: rat] :
% 5.06/5.37 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.06/5.37 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % divide_less_eq_numeral1(2)
% 5.06/5.37 thf(fact_5584_power2__minus,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.37 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % power2_minus
% 5.06/5.37 thf(fact_5585_power2__minus,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.37 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % power2_minus
% 5.06/5.37 thf(fact_5586_power2__minus,axiom,
% 5.06/5.37 ! [A: complex] :
% 5.06/5.37 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.37 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % power2_minus
% 5.06/5.37 thf(fact_5587_power2__minus,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.37 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % power2_minus
% 5.06/5.37 thf(fact_5588_power2__minus,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.37 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % power2_minus
% 5.06/5.37 thf(fact_5589_add__neg__numeral__special_I9_J,axiom,
% 5.06/5.37 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(9)
% 5.06/5.37 thf(fact_5590_add__neg__numeral__special_I9_J,axiom,
% 5.06/5.37 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(9)
% 5.06/5.37 thf(fact_5591_add__neg__numeral__special_I9_J,axiom,
% 5.06/5.37 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(9)
% 5.06/5.37 thf(fact_5592_add__neg__numeral__special_I9_J,axiom,
% 5.06/5.37 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(9)
% 5.06/5.37 thf(fact_5593_add__neg__numeral__special_I9_J,axiom,
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_neg_numeral_special(9)
% 5.06/5.37 thf(fact_5594_diff__numeral__special_I10_J,axiom,
% 5.06/5.37 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(10)
% 5.06/5.37 thf(fact_5595_diff__numeral__special_I10_J,axiom,
% 5.06/5.37 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(10)
% 5.06/5.37 thf(fact_5596_diff__numeral__special_I10_J,axiom,
% 5.06/5.37 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(10)
% 5.06/5.37 thf(fact_5597_diff__numeral__special_I10_J,axiom,
% 5.06/5.37 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(10)
% 5.06/5.37 thf(fact_5598_diff__numeral__special_I10_J,axiom,
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(10)
% 5.06/5.37 thf(fact_5599_diff__numeral__special_I11_J,axiom,
% 5.06/5.37 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.37 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(11)
% 5.06/5.37 thf(fact_5600_diff__numeral__special_I11_J,axiom,
% 5.06/5.37 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(11)
% 5.06/5.37 thf(fact_5601_diff__numeral__special_I11_J,axiom,
% 5.06/5.37 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.37 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(11)
% 5.06/5.37 thf(fact_5602_diff__numeral__special_I11_J,axiom,
% 5.06/5.37 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.37 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(11)
% 5.06/5.37 thf(fact_5603_diff__numeral__special_I11_J,axiom,
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(11)
% 5.06/5.37 thf(fact_5604_minus__1__div__2__eq,axiom,
% 5.06/5.37 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.37 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_1_div_2_eq
% 5.06/5.37 thf(fact_5605_minus__1__div__2__eq,axiom,
% 5.06/5.37 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_1_div_2_eq
% 5.06/5.37 thf(fact_5606_minus__1__mod__2__eq,axiom,
% 5.06/5.37 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.37 = one_one_int ) ).
% 5.06/5.37
% 5.06/5.37 % minus_1_mod_2_eq
% 5.06/5.37 thf(fact_5607_minus__1__mod__2__eq,axiom,
% 5.06/5.37 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.37 = one_one_Code_integer ) ).
% 5.06/5.37
% 5.06/5.37 % minus_1_mod_2_eq
% 5.06/5.37 thf(fact_5608_bits__minus__1__mod__2__eq,axiom,
% 5.06/5.37 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.37 = one_one_int ) ).
% 5.06/5.37
% 5.06/5.37 % bits_minus_1_mod_2_eq
% 5.06/5.37 thf(fact_5609_bits__minus__1__mod__2__eq,axiom,
% 5.06/5.37 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.37 = one_one_Code_integer ) ).
% 5.06/5.37
% 5.06/5.37 % bits_minus_1_mod_2_eq
% 5.06/5.37 thf(fact_5610_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.06/5.37 ! [A: real,N2: nat] :
% 5.06/5.37 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.37 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % Power.ring_1_class.power_minus_even
% 5.06/5.37 thf(fact_5611_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.06/5.37 ! [A: int,N2: nat] :
% 5.06/5.37 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.37 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % Power.ring_1_class.power_minus_even
% 5.06/5.37 thf(fact_5612_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.06/5.37 ! [A: complex,N2: nat] :
% 5.06/5.37 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.37 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % Power.ring_1_class.power_minus_even
% 5.06/5.37 thf(fact_5613_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.06/5.37 ! [A: rat,N2: nat] :
% 5.06/5.37 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.37 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % Power.ring_1_class.power_minus_even
% 5.06/5.37 thf(fact_5614_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.06/5.37 ! [A: code_integer,N2: nat] :
% 5.06/5.37 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.37 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % Power.ring_1_class.power_minus_even
% 5.06/5.37 thf(fact_5615_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.06/5.37 ! [N2: nat,A: real] :
% 5.06/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.06/5.37 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % Parity.ring_1_class.power_minus_even
% 5.06/5.37 thf(fact_5616_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.06/5.37 ! [N2: nat,A: int] :
% 5.06/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.06/5.37 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % Parity.ring_1_class.power_minus_even
% 5.06/5.37 thf(fact_5617_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.06/5.37 ! [N2: nat,A: complex] :
% 5.06/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.06/5.37 = ( power_power_complex @ A @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % Parity.ring_1_class.power_minus_even
% 5.06/5.37 thf(fact_5618_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.06/5.37 ! [N2: nat,A: rat] :
% 5.06/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.06/5.37 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % Parity.ring_1_class.power_minus_even
% 5.06/5.37 thf(fact_5619_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.06/5.37 ! [N2: nat,A: code_integer] :
% 5.06/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.06/5.37 = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % Parity.ring_1_class.power_minus_even
% 5.06/5.37 thf(fact_5620_power__minus__odd,axiom,
% 5.06/5.37 ! [N2: nat,A: real] :
% 5.06/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.06/5.37 = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % power_minus_odd
% 5.06/5.37 thf(fact_5621_power__minus__odd,axiom,
% 5.06/5.37 ! [N2: nat,A: int] :
% 5.06/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.06/5.37 = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % power_minus_odd
% 5.06/5.37 thf(fact_5622_power__minus__odd,axiom,
% 5.06/5.37 ! [N2: nat,A: complex] :
% 5.06/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % power_minus_odd
% 5.06/5.37 thf(fact_5623_power__minus__odd,axiom,
% 5.06/5.37 ! [N2: nat,A: rat] :
% 5.06/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.06/5.37 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % power_minus_odd
% 5.06/5.37 thf(fact_5624_power__minus__odd,axiom,
% 5.06/5.37 ! [N2: nat,A: code_integer] :
% 5.06/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % power_minus_odd
% 5.06/5.37 thf(fact_5625_diff__numeral__special_I4_J,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(4)
% 5.06/5.37 thf(fact_5626_diff__numeral__special_I4_J,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(4)
% 5.06/5.37 thf(fact_5627_diff__numeral__special_I4_J,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(4)
% 5.06/5.37 thf(fact_5628_diff__numeral__special_I4_J,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(4)
% 5.06/5.37 thf(fact_5629_diff__numeral__special_I4_J,axiom,
% 5.06/5.37 ! [M: num] :
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(4)
% 5.06/5.37 thf(fact_5630_diff__numeral__special_I3_J,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.37 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(3)
% 5.06/5.37 thf(fact_5631_diff__numeral__special_I3_J,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.37 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(3)
% 5.06/5.37 thf(fact_5632_diff__numeral__special_I3_J,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.06/5.37 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(3)
% 5.06/5.37 thf(fact_5633_diff__numeral__special_I3_J,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.06/5.37 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(3)
% 5.06/5.37 thf(fact_5634_diff__numeral__special_I3_J,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.06/5.37 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % diff_numeral_special(3)
% 5.06/5.37 thf(fact_5635_signed__take__bit__Suc__minus__bit0,axiom,
% 5.06/5.37 ! [N2: nat,K: num] :
% 5.06/5.37 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.06/5.37 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % signed_take_bit_Suc_minus_bit0
% 5.06/5.37 thf(fact_5636_dbl__simps_I4_J,axiom,
% 5.06/5.37 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % dbl_simps(4)
% 5.06/5.37 thf(fact_5637_dbl__simps_I4_J,axiom,
% 5.06/5.37 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % dbl_simps(4)
% 5.06/5.37 thf(fact_5638_dbl__simps_I4_J,axiom,
% 5.06/5.37 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % dbl_simps(4)
% 5.06/5.37 thf(fact_5639_dbl__simps_I4_J,axiom,
% 5.06/5.37 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % dbl_simps(4)
% 5.06/5.37 thf(fact_5640_dbl__simps_I4_J,axiom,
% 5.06/5.37 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % dbl_simps(4)
% 5.06/5.37 thf(fact_5641_power__minus1__even,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.37 = one_one_real ) ).
% 5.06/5.37
% 5.06/5.37 % power_minus1_even
% 5.06/5.37 thf(fact_5642_power__minus1__even,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.37 = one_one_int ) ).
% 5.06/5.37
% 5.06/5.37 % power_minus1_even
% 5.06/5.37 thf(fact_5643_power__minus1__even,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.37 = one_one_complex ) ).
% 5.06/5.37
% 5.06/5.37 % power_minus1_even
% 5.06/5.37 thf(fact_5644_power__minus1__even,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.37 = one_one_rat ) ).
% 5.06/5.37
% 5.06/5.37 % power_minus1_even
% 5.06/5.37 thf(fact_5645_power__minus1__even,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.37 = one_one_Code_integer ) ).
% 5.06/5.37
% 5.06/5.37 % power_minus1_even
% 5.06/5.37 thf(fact_5646_neg__one__even__power,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.06/5.37 = one_one_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_even_power
% 5.06/5.37 thf(fact_5647_neg__one__even__power,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.06/5.37 = one_one_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_even_power
% 5.06/5.37 thf(fact_5648_neg__one__even__power,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.06/5.37 = one_one_complex ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_even_power
% 5.06/5.37 thf(fact_5649_neg__one__even__power,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.06/5.37 = one_one_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_even_power
% 5.06/5.37 thf(fact_5650_neg__one__even__power,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.06/5.37 = one_one_Code_integer ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_even_power
% 5.06/5.37 thf(fact_5651_neg__one__odd__power,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.06/5.37 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_odd_power
% 5.06/5.37 thf(fact_5652_neg__one__odd__power,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.06/5.37 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_odd_power
% 5.06/5.37 thf(fact_5653_neg__one__odd__power,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_odd_power
% 5.06/5.37 thf(fact_5654_neg__one__odd__power,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.06/5.37 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_odd_power
% 5.06/5.37 thf(fact_5655_neg__one__odd__power,axiom,
% 5.06/5.37 ! [N2: nat] :
% 5.06/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.37 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_one_odd_power
% 5.06/5.37 thf(fact_5656_signed__take__bit__0,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % signed_take_bit_0
% 5.06/5.37 thf(fact_5657_signed__take__bit__0,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.06/5.37 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % signed_take_bit_0
% 5.06/5.37 thf(fact_5658_signed__take__bit__minus,axiom,
% 5.06/5.37 ! [N2: nat,K: int] :
% 5.06/5.37 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) )
% 5.06/5.37 = ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % signed_take_bit_minus
% 5.06/5.37 thf(fact_5659_sum__negf,axiom,
% 5.06/5.37 ! [F: int > int,A2: set_int] :
% 5.06/5.37 ( ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [X2: int] : ( uminus_uminus_int @ ( F @ X2 ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( uminus_uminus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_negf
% 5.06/5.37 thf(fact_5660_sum__negf,axiom,
% 5.06/5.37 ! [F: complex > complex,A2: set_complex] :
% 5.06/5.37 ( ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [X2: complex] : ( uminus1482373934393186551omplex @ ( F @ X2 ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( groups7754918857620584856omplex @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_negf
% 5.06/5.37 thf(fact_5661_sum__negf,axiom,
% 5.06/5.37 ! [F: nat > real,A2: set_nat] :
% 5.06/5.37 ( ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [X2: nat] : ( uminus_uminus_real @ ( F @ X2 ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( uminus_uminus_real @ ( groups6591440286371151544t_real @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_negf
% 5.06/5.37 thf(fact_5662_sum_Oswap,axiom,
% 5.06/5.37 ! [G: int > int > int,B3: set_int,A2: set_int] :
% 5.06/5.37 ( ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [I5: int] : ( groups4538972089207619220nt_int @ ( G @ I5 ) @ B3 )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [J3: int] :
% 5.06/5.37 ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [I5: int] : ( G @ I5 @ J3 )
% 5.06/5.37 @ A2 )
% 5.06/5.37 @ B3 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap
% 5.06/5.37 thf(fact_5663_sum_Oswap,axiom,
% 5.06/5.37 ! [G: complex > complex > complex,B3: set_complex,A2: set_complex] :
% 5.06/5.37 ( ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [I5: complex] : ( groups7754918857620584856omplex @ ( G @ I5 ) @ B3 )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [J3: complex] :
% 5.06/5.37 ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [I5: complex] : ( G @ I5 @ J3 )
% 5.06/5.37 @ A2 )
% 5.06/5.37 @ B3 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap
% 5.06/5.37 thf(fact_5664_sum_Oswap,axiom,
% 5.06/5.37 ! [G: nat > nat > nat,B3: set_nat,A2: set_nat] :
% 5.06/5.37 ( ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [I5: nat] : ( groups3542108847815614940at_nat @ ( G @ I5 ) @ B3 )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [J3: nat] :
% 5.06/5.37 ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [I5: nat] : ( G @ I5 @ J3 )
% 5.06/5.37 @ A2 )
% 5.06/5.37 @ B3 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap
% 5.06/5.37 thf(fact_5665_sum_Oswap,axiom,
% 5.06/5.37 ! [G: nat > nat > real,B3: set_nat,A2: set_nat] :
% 5.06/5.37 ( ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [I5: nat] : ( groups6591440286371151544t_real @ ( G @ I5 ) @ B3 )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [J3: nat] :
% 5.06/5.37 ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [I5: nat] : ( G @ I5 @ J3 )
% 5.06/5.37 @ A2 )
% 5.06/5.37 @ B3 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap
% 5.06/5.37 thf(fact_5666_prod_Ocase__distrib,axiom,
% 5.06/5.37 ! [H2: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 5.06/5.37 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.06/5.37 = ( produc4947309494688390418_int_o
% 5.06/5.37 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.06/5.37 @ Prod ) ) ).
% 5.06/5.37
% 5.06/5.37 % prod.case_distrib
% 5.06/5.37 thf(fact_5667_prod_Ocase__distrib,axiom,
% 5.06/5.37 ! [H2: $o > int,F: int > int > $o,Prod: product_prod_int_int] :
% 5.06/5.37 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.06/5.37 = ( produc8211389475949308722nt_int
% 5.06/5.37 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.06/5.37 @ Prod ) ) ).
% 5.06/5.37
% 5.06/5.37 % prod.case_distrib
% 5.06/5.37 thf(fact_5668_prod_Ocase__distrib,axiom,
% 5.06/5.37 ! [H2: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 5.06/5.37 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.06/5.37 = ( produc4947309494688390418_int_o
% 5.06/5.37 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.06/5.37 @ Prod ) ) ).
% 5.06/5.37
% 5.06/5.37 % prod.case_distrib
% 5.06/5.37 thf(fact_5669_prod_Ocase__distrib,axiom,
% 5.06/5.37 ! [H2: int > int,F: int > int > int,Prod: product_prod_int_int] :
% 5.06/5.37 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.06/5.37 = ( produc8211389475949308722nt_int
% 5.06/5.37 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.06/5.37 @ Prod ) ) ).
% 5.06/5.37
% 5.06/5.37 % prod.case_distrib
% 5.06/5.37 thf(fact_5670_prod_Ocase__distrib,axiom,
% 5.06/5.37 ! [H2: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.06/5.37 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.06/5.37 = ( produc4947309494688390418_int_o
% 5.06/5.37 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.06/5.37 @ Prod ) ) ).
% 5.06/5.37
% 5.06/5.37 % prod.case_distrib
% 5.06/5.37 thf(fact_5671_prod_Ocase__distrib,axiom,
% 5.06/5.37 ! [H2: product_prod_int_int > int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.06/5.37 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.06/5.37 = ( produc8211389475949308722nt_int
% 5.06/5.37 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.06/5.37 @ Prod ) ) ).
% 5.06/5.37
% 5.06/5.37 % prod.case_distrib
% 5.06/5.37 thf(fact_5672_prod_Ocase__distrib,axiom,
% 5.06/5.37 ! [H2: $o > product_prod_int_int,F: int > int > $o,Prod: product_prod_int_int] :
% 5.06/5.37 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.06/5.37 = ( produc4245557441103728435nt_int
% 5.06/5.37 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.06/5.37 @ Prod ) ) ).
% 5.06/5.37
% 5.06/5.37 % prod.case_distrib
% 5.06/5.37 thf(fact_5673_prod_Ocase__distrib,axiom,
% 5.06/5.37 ! [H2: int > product_prod_int_int,F: int > int > int,Prod: product_prod_int_int] :
% 5.06/5.37 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.06/5.37 = ( produc4245557441103728435nt_int
% 5.06/5.37 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.06/5.37 @ Prod ) ) ).
% 5.06/5.37
% 5.06/5.37 % prod.case_distrib
% 5.06/5.37 thf(fact_5674_prod_Ocase__distrib,axiom,
% 5.06/5.37 ! [H2: product_prod_int_int > product_prod_int_int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.06/5.37 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.06/5.37 = ( produc4245557441103728435nt_int
% 5.06/5.37 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.06/5.37 @ Prod ) ) ).
% 5.06/5.37
% 5.06/5.37 % prod.case_distrib
% 5.06/5.37 thf(fact_5675_prod_Ocase__distrib,axiom,
% 5.06/5.37 ! [H2: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 5.06/5.37 ( ( H2 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 5.06/5.37 = ( produc8739625826339149834_nat_o
% 5.06/5.37 @ ^ [X15: nat,X24: nat] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.06/5.37 @ Prod ) ) ).
% 5.06/5.37
% 5.06/5.37 % prod.case_distrib
% 5.06/5.37 thf(fact_5676_le__minus__iff,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.06/5.37 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_minus_iff
% 5.06/5.37 thf(fact_5677_le__minus__iff,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.37 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_minus_iff
% 5.06/5.37 thf(fact_5678_le__minus__iff,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.06/5.37 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_minus_iff
% 5.06/5.37 thf(fact_5679_le__minus__iff,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.37 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_minus_iff
% 5.06/5.37 thf(fact_5680_minus__le__iff,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.06/5.37 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_le_iff
% 5.06/5.37 thf(fact_5681_minus__le__iff,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.06/5.37 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_le_iff
% 5.06/5.37 thf(fact_5682_minus__le__iff,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.06/5.37 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_le_iff
% 5.06/5.37 thf(fact_5683_minus__le__iff,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.37 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_le_iff
% 5.06/5.37 thf(fact_5684_le__imp__neg__le,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.37 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_imp_neg_le
% 5.06/5.37 thf(fact_5685_le__imp__neg__le,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.06/5.37 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_imp_neg_le
% 5.06/5.37 thf(fact_5686_le__imp__neg__le,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.37 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_imp_neg_le
% 5.06/5.37 thf(fact_5687_le__imp__neg__le,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( ord_less_eq_int @ A @ B )
% 5.06/5.37 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_imp_neg_le
% 5.06/5.37 thf(fact_5688_compl__le__swap2,axiom,
% 5.06/5.37 ! [Y: set_int,X: set_int] :
% 5.06/5.37 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X )
% 5.06/5.37 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 5.06/5.37
% 5.06/5.37 % compl_le_swap2
% 5.06/5.37 thf(fact_5689_compl__le__swap1,axiom,
% 5.06/5.37 ! [Y: set_int,X: set_int] :
% 5.06/5.37 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) )
% 5.06/5.37 => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % compl_le_swap1
% 5.06/5.37 thf(fact_5690_compl__mono,axiom,
% 5.06/5.37 ! [X: set_int,Y: set_int] :
% 5.06/5.37 ( ( ord_less_eq_set_int @ X @ Y )
% 5.06/5.37 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % compl_mono
% 5.06/5.37 thf(fact_5691_less__minus__iff,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.06/5.37 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_minus_iff
% 5.06/5.37 thf(fact_5692_less__minus__iff,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.37 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_minus_iff
% 5.06/5.37 thf(fact_5693_less__minus__iff,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.06/5.37 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_minus_iff
% 5.06/5.37 thf(fact_5694_less__minus__iff,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.37 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_minus_iff
% 5.06/5.37 thf(fact_5695_minus__less__iff,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.06/5.37 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_less_iff
% 5.06/5.37 thf(fact_5696_minus__less__iff,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.37 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_less_iff
% 5.06/5.37 thf(fact_5697_minus__less__iff,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.06/5.37 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_less_iff
% 5.06/5.37 thf(fact_5698_minus__less__iff,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.06/5.37 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_less_iff
% 5.06/5.37 thf(fact_5699_verit__negate__coefficient_I2_J,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( ord_less_real @ A @ B )
% 5.06/5.37 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % verit_negate_coefficient(2)
% 5.06/5.37 thf(fact_5700_verit__negate__coefficient_I2_J,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( ord_less_int @ A @ B )
% 5.06/5.37 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % verit_negate_coefficient(2)
% 5.06/5.37 thf(fact_5701_verit__negate__coefficient_I2_J,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( ord_less_rat @ A @ B )
% 5.06/5.37 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % verit_negate_coefficient(2)
% 5.06/5.37 thf(fact_5702_verit__negate__coefficient_I2_J,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.06/5.37 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % verit_negate_coefficient(2)
% 5.06/5.37 thf(fact_5703_numeral__neq__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( numeral_numeral_real @ M )
% 5.06/5.37 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_neq_neg_numeral
% 5.06/5.37 thf(fact_5704_numeral__neq__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( numeral_numeral_int @ M )
% 5.06/5.37 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_neq_neg_numeral
% 5.06/5.37 thf(fact_5705_numeral__neq__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( numera6690914467698888265omplex @ M )
% 5.06/5.37 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_neq_neg_numeral
% 5.06/5.37 thf(fact_5706_numeral__neq__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( numeral_numeral_rat @ M )
% 5.06/5.37 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_neq_neg_numeral
% 5.06/5.37 thf(fact_5707_numeral__neq__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( numera6620942414471956472nteger @ M )
% 5.06/5.37 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_neq_neg_numeral
% 5.06/5.37 thf(fact_5708_neg__numeral__neq__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.06/5.37 != ( numeral_numeral_real @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_neq_numeral
% 5.06/5.37 thf(fact_5709_neg__numeral__neq__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.06/5.37 != ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_neq_numeral
% 5.06/5.37 thf(fact_5710_neg__numeral__neq__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.06/5.37 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_neq_numeral
% 5.06/5.37 thf(fact_5711_neg__numeral__neq__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.06/5.37 != ( numeral_numeral_rat @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_neq_numeral
% 5.06/5.37 thf(fact_5712_neg__numeral__neq__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.06/5.37 != ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_neq_numeral
% 5.06/5.37 thf(fact_5713_minus__mult__commute,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.06/5.37 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_mult_commute
% 5.06/5.37 thf(fact_5714_minus__mult__commute,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.37 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_mult_commute
% 5.06/5.37 thf(fact_5715_minus__mult__commute,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.06/5.37 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_mult_commute
% 5.06/5.37 thf(fact_5716_minus__mult__commute,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.06/5.37 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_mult_commute
% 5.06/5.37 thf(fact_5717_minus__mult__commute,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.06/5.37 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_mult_commute
% 5.06/5.37 thf(fact_5718_square__eq__iff,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( ( times_times_real @ A @ A )
% 5.06/5.37 = ( times_times_real @ B @ B ) )
% 5.06/5.37 = ( ( A = B )
% 5.06/5.37 | ( A
% 5.06/5.37 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % square_eq_iff
% 5.06/5.37 thf(fact_5719_square__eq__iff,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( ( times_times_int @ A @ A )
% 5.06/5.37 = ( times_times_int @ B @ B ) )
% 5.06/5.37 = ( ( A = B )
% 5.06/5.37 | ( A
% 5.06/5.37 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % square_eq_iff
% 5.06/5.37 thf(fact_5720_square__eq__iff,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( ( times_times_complex @ A @ A )
% 5.06/5.37 = ( times_times_complex @ B @ B ) )
% 5.06/5.37 = ( ( A = B )
% 5.06/5.37 | ( A
% 5.06/5.37 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % square_eq_iff
% 5.06/5.37 thf(fact_5721_square__eq__iff,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( ( times_times_rat @ A @ A )
% 5.06/5.37 = ( times_times_rat @ B @ B ) )
% 5.06/5.37 = ( ( A = B )
% 5.06/5.37 | ( A
% 5.06/5.37 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % square_eq_iff
% 5.06/5.37 thf(fact_5722_square__eq__iff,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.06/5.37 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.06/5.37 = ( ( A = B )
% 5.06/5.37 | ( A
% 5.06/5.37 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % square_eq_iff
% 5.06/5.37 thf(fact_5723_is__num__normalize_I8_J,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.06/5.37 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % is_num_normalize(8)
% 5.06/5.37 thf(fact_5724_is__num__normalize_I8_J,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.06/5.37 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % is_num_normalize(8)
% 5.06/5.37 thf(fact_5725_is__num__normalize_I8_J,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.06/5.37 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % is_num_normalize(8)
% 5.06/5.37 thf(fact_5726_is__num__normalize_I8_J,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.06/5.37 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % is_num_normalize(8)
% 5.06/5.37 thf(fact_5727_is__num__normalize_I8_J,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.06/5.37 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % is_num_normalize(8)
% 5.06/5.37 thf(fact_5728_add_Oinverse__distrib__swap,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.06/5.37 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add.inverse_distrib_swap
% 5.06/5.37 thf(fact_5729_add_Oinverse__distrib__swap,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.06/5.37 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add.inverse_distrib_swap
% 5.06/5.37 thf(fact_5730_add_Oinverse__distrib__swap,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.06/5.37 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add.inverse_distrib_swap
% 5.06/5.37 thf(fact_5731_add_Oinverse__distrib__swap,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.06/5.37 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add.inverse_distrib_swap
% 5.06/5.37 thf(fact_5732_add_Oinverse__distrib__swap,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.06/5.37 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add.inverse_distrib_swap
% 5.06/5.37 thf(fact_5733_group__cancel_Oneg1,axiom,
% 5.06/5.37 ! [A2: real,K: real,A: real] :
% 5.06/5.37 ( ( A2
% 5.06/5.37 = ( plus_plus_real @ K @ A ) )
% 5.06/5.37 => ( ( uminus_uminus_real @ A2 )
% 5.06/5.37 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % group_cancel.neg1
% 5.06/5.37 thf(fact_5734_group__cancel_Oneg1,axiom,
% 5.06/5.37 ! [A2: int,K: int,A: int] :
% 5.06/5.37 ( ( A2
% 5.06/5.37 = ( plus_plus_int @ K @ A ) )
% 5.06/5.37 => ( ( uminus_uminus_int @ A2 )
% 5.06/5.37 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % group_cancel.neg1
% 5.06/5.37 thf(fact_5735_group__cancel_Oneg1,axiom,
% 5.06/5.37 ! [A2: complex,K: complex,A: complex] :
% 5.06/5.37 ( ( A2
% 5.06/5.37 = ( plus_plus_complex @ K @ A ) )
% 5.06/5.37 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.06/5.37 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % group_cancel.neg1
% 5.06/5.37 thf(fact_5736_group__cancel_Oneg1,axiom,
% 5.06/5.37 ! [A2: rat,K: rat,A: rat] :
% 5.06/5.37 ( ( A2
% 5.06/5.37 = ( plus_plus_rat @ K @ A ) )
% 5.06/5.37 => ( ( uminus_uminus_rat @ A2 )
% 5.06/5.37 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % group_cancel.neg1
% 5.06/5.37 thf(fact_5737_group__cancel_Oneg1,axiom,
% 5.06/5.37 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.06/5.37 ( ( A2
% 5.06/5.37 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.06/5.37 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.06/5.37 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % group_cancel.neg1
% 5.06/5.37 thf(fact_5738_one__neq__neg__one,axiom,
% 5.06/5.37 ( one_one_real
% 5.06/5.37 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % one_neq_neg_one
% 5.06/5.37 thf(fact_5739_one__neq__neg__one,axiom,
% 5.06/5.37 ( one_one_int
% 5.06/5.37 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % one_neq_neg_one
% 5.06/5.37 thf(fact_5740_one__neq__neg__one,axiom,
% 5.06/5.37 ( one_one_complex
% 5.06/5.37 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.37
% 5.06/5.37 % one_neq_neg_one
% 5.06/5.37 thf(fact_5741_one__neq__neg__one,axiom,
% 5.06/5.37 ( one_one_rat
% 5.06/5.37 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % one_neq_neg_one
% 5.06/5.37 thf(fact_5742_one__neq__neg__one,axiom,
% 5.06/5.37 ( one_one_Code_integer
% 5.06/5.37 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.37
% 5.06/5.37 % one_neq_neg_one
% 5.06/5.37 thf(fact_5743_minus__diff__minus,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.06/5.37 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_minus
% 5.06/5.37 thf(fact_5744_minus__diff__minus,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_minus
% 5.06/5.37 thf(fact_5745_minus__diff__minus,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.06/5.37 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_minus
% 5.06/5.37 thf(fact_5746_minus__diff__minus,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.06/5.37 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_minus
% 5.06/5.37 thf(fact_5747_minus__diff__minus,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_minus
% 5.06/5.37 thf(fact_5748_minus__diff__commute,axiom,
% 5.06/5.37 ! [B: real,A: real] :
% 5.06/5.37 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.06/5.37 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_commute
% 5.06/5.37 thf(fact_5749_minus__diff__commute,axiom,
% 5.06/5.37 ! [B: int,A: int] :
% 5.06/5.37 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.06/5.37 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_commute
% 5.06/5.37 thf(fact_5750_minus__diff__commute,axiom,
% 5.06/5.37 ! [B: complex,A: complex] :
% 5.06/5.37 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.06/5.37 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_commute
% 5.06/5.37 thf(fact_5751_minus__diff__commute,axiom,
% 5.06/5.37 ! [B: rat,A: rat] :
% 5.06/5.37 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.06/5.37 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_commute
% 5.06/5.37 thf(fact_5752_minus__diff__commute,axiom,
% 5.06/5.37 ! [B: code_integer,A: code_integer] :
% 5.06/5.37 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.06/5.37 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_diff_commute
% 5.06/5.37 thf(fact_5753_div__minus__right,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.37 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % div_minus_right
% 5.06/5.37 thf(fact_5754_div__minus__right,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.37 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % div_minus_right
% 5.06/5.37 thf(fact_5755_minus__divide__left,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.37 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_divide_left
% 5.06/5.37 thf(fact_5756_minus__divide__left,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.06/5.37 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_divide_left
% 5.06/5.37 thf(fact_5757_minus__divide__left,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.06/5.37 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_divide_left
% 5.06/5.37 thf(fact_5758_minus__divide__divide,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.06/5.37 = ( divide_divide_real @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_divide_divide
% 5.06/5.37 thf(fact_5759_minus__divide__divide,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.06/5.37 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_divide_divide
% 5.06/5.37 thf(fact_5760_minus__divide__divide,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.06/5.37 = ( divide_divide_rat @ A @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_divide_divide
% 5.06/5.37 thf(fact_5761_minus__divide__right,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.37 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_divide_right
% 5.06/5.37 thf(fact_5762_minus__divide__right,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.06/5.37 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_divide_right
% 5.06/5.37 thf(fact_5763_minus__divide__right,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.06/5.37 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % minus_divide_right
% 5.06/5.37 thf(fact_5764_old_Oprod_Ocase,axiom,
% 5.06/5.37 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 5.06/5.37 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.06/5.37 = ( F @ X1 @ X22 ) ) ).
% 5.06/5.37
% 5.06/5.37 % old.prod.case
% 5.06/5.37 thf(fact_5765_old_Oprod_Ocase,axiom,
% 5.06/5.37 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 5.06/5.37 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.06/5.37 = ( F @ X1 @ X22 ) ) ).
% 5.06/5.37
% 5.06/5.37 % old.prod.case
% 5.06/5.37 thf(fact_5766_old_Oprod_Ocase,axiom,
% 5.06/5.37 ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 5.06/5.37 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.06/5.37 = ( F @ X1 @ X22 ) ) ).
% 5.06/5.37
% 5.06/5.37 % old.prod.case
% 5.06/5.37 thf(fact_5767_old_Oprod_Ocase,axiom,
% 5.06/5.37 ! [F: int > int > $o,X1: int,X22: int] :
% 5.06/5.37 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.06/5.37 = ( F @ X1 @ X22 ) ) ).
% 5.06/5.37
% 5.06/5.37 % old.prod.case
% 5.06/5.37 thf(fact_5768_old_Oprod_Ocase,axiom,
% 5.06/5.37 ! [F: int > int > int,X1: int,X22: int] :
% 5.06/5.37 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.06/5.37 = ( F @ X1 @ X22 ) ) ).
% 5.06/5.37
% 5.06/5.37 % old.prod.case
% 5.06/5.37 thf(fact_5769_mod__minus__right,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.37 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mod_minus_right
% 5.06/5.37 thf(fact_5770_mod__minus__right,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.37 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mod_minus_right
% 5.06/5.37 thf(fact_5771_mod__minus__cong,axiom,
% 5.06/5.37 ! [A: int,B: int,A6: int] :
% 5.06/5.37 ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.37 = ( modulo_modulo_int @ A6 @ B ) )
% 5.06/5.37 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.37 = ( modulo_modulo_int @ ( uminus_uminus_int @ A6 ) @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mod_minus_cong
% 5.06/5.37 thf(fact_5772_mod__minus__cong,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer,A6: code_integer] :
% 5.06/5.37 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.06/5.37 = ( modulo364778990260209775nteger @ A6 @ B ) )
% 5.06/5.37 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.06/5.37 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A6 ) @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % mod_minus_cong
% 5.06/5.37 thf(fact_5773_mod__minus__eq,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.06/5.37 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % mod_minus_eq
% 5.06/5.37 thf(fact_5774_mod__minus__eq,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.06/5.37 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.06/5.37
% 5.06/5.37 % mod_minus_eq
% 5.06/5.37 thf(fact_5775_sum__mono,axiom,
% 5.06/5.37 ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 5.06/5.37 ( ! [I3: complex] :
% 5.06/5.37 ( ( member_complex @ I3 @ K5 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono
% 5.06/5.37 thf(fact_5776_sum__mono,axiom,
% 5.06/5.37 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.06/5.37 ( ! [I3: real] :
% 5.06/5.37 ( ( member_real @ I3 @ K5 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono
% 5.06/5.37 thf(fact_5777_sum__mono,axiom,
% 5.06/5.37 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.06/5.37 ( ! [I3: nat] :
% 5.06/5.37 ( ( member_nat @ I3 @ K5 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono
% 5.06/5.37 thf(fact_5778_sum__mono,axiom,
% 5.06/5.37 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.06/5.37 ( ! [I3: int] :
% 5.06/5.37 ( ( member_int @ I3 @ K5 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono
% 5.06/5.37 thf(fact_5779_sum__mono,axiom,
% 5.06/5.37 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.06/5.37 ( ! [I3: complex] :
% 5.06/5.37 ( ( member_complex @ I3 @ K5 )
% 5.06/5.37 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono
% 5.06/5.37 thf(fact_5780_sum__mono,axiom,
% 5.06/5.37 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.06/5.37 ( ! [I3: real] :
% 5.06/5.37 ( ( member_real @ I3 @ K5 )
% 5.06/5.37 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono
% 5.06/5.37 thf(fact_5781_sum__mono,axiom,
% 5.06/5.37 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.06/5.37 ( ! [I3: int] :
% 5.06/5.37 ( ( member_int @ I3 @ K5 )
% 5.06/5.37 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono
% 5.06/5.37 thf(fact_5782_sum__mono,axiom,
% 5.06/5.37 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.06/5.37 ( ! [I3: complex] :
% 5.06/5.37 ( ( member_complex @ I3 @ K5 )
% 5.06/5.37 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono
% 5.06/5.37 thf(fact_5783_sum__mono,axiom,
% 5.06/5.37 ! [K5: set_real,F: real > int,G: real > int] :
% 5.06/5.37 ( ! [I3: real] :
% 5.06/5.37 ( ( member_real @ I3 @ K5 )
% 5.06/5.37 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono
% 5.06/5.37 thf(fact_5784_sum__mono,axiom,
% 5.06/5.37 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.06/5.37 ( ! [I3: nat] :
% 5.06/5.37 ( ( member_nat @ I3 @ K5 )
% 5.06/5.37 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono
% 5.06/5.37 thf(fact_5785_sum__product,axiom,
% 5.06/5.37 ! [F: int > int,A2: set_int,G: int > int,B3: set_int] :
% 5.06/5.37 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B3 ) )
% 5.06/5.37 = ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [I5: int] :
% 5.06/5.37 ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [J3: int] : ( times_times_int @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.06/5.37 @ B3 )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_product
% 5.06/5.37 thf(fact_5786_sum__product,axiom,
% 5.06/5.37 ! [F: complex > complex,A2: set_complex,G: complex > complex,B3: set_complex] :
% 5.06/5.37 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B3 ) )
% 5.06/5.37 = ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [I5: complex] :
% 5.06/5.37 ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.06/5.37 @ B3 )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_product
% 5.06/5.37 thf(fact_5787_sum__product,axiom,
% 5.06/5.37 ! [F: nat > nat,A2: set_nat,G: nat > nat,B3: set_nat] :
% 5.06/5.37 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
% 5.06/5.37 = ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [I5: nat] :
% 5.06/5.37 ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.06/5.37 @ B3 )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_product
% 5.06/5.37 thf(fact_5788_sum__product,axiom,
% 5.06/5.37 ! [F: nat > real,A2: set_nat,G: nat > real,B3: set_nat] :
% 5.06/5.37 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B3 ) )
% 5.06/5.37 = ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [I5: nat] :
% 5.06/5.37 ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [J3: nat] : ( times_times_real @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.06/5.37 @ B3 )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_product
% 5.06/5.37 thf(fact_5789_sum__distrib__right,axiom,
% 5.06/5.37 ! [F: int > int,A2: set_int,R2: int] :
% 5.06/5.37 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R2 )
% 5.06/5.37 = ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [N: int] : ( times_times_int @ ( F @ N ) @ R2 )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_distrib_right
% 5.06/5.37 thf(fact_5790_sum__distrib__right,axiom,
% 5.06/5.37 ! [F: complex > complex,A2: set_complex,R2: complex] :
% 5.06/5.37 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R2 )
% 5.06/5.37 = ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [N: complex] : ( times_times_complex @ ( F @ N ) @ R2 )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_distrib_right
% 5.06/5.37 thf(fact_5791_sum__distrib__right,axiom,
% 5.06/5.37 ! [F: nat > nat,A2: set_nat,R2: nat] :
% 5.06/5.37 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R2 )
% 5.06/5.37 = ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [N: nat] : ( times_times_nat @ ( F @ N ) @ R2 )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_distrib_right
% 5.06/5.37 thf(fact_5792_sum__distrib__right,axiom,
% 5.06/5.37 ! [F: nat > real,A2: set_nat,R2: real] :
% 5.06/5.37 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R2 )
% 5.06/5.37 = ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ R2 )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_distrib_right
% 5.06/5.37 thf(fact_5793_sum__distrib__left,axiom,
% 5.06/5.37 ! [R2: int,F: int > int,A2: set_int] :
% 5.06/5.37 ( ( times_times_int @ R2 @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.06/5.37 = ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [N: int] : ( times_times_int @ R2 @ ( F @ N ) )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_distrib_left
% 5.06/5.37 thf(fact_5794_sum__distrib__left,axiom,
% 5.06/5.37 ! [R2: complex,F: complex > complex,A2: set_complex] :
% 5.06/5.37 ( ( times_times_complex @ R2 @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.06/5.37 = ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [N: complex] : ( times_times_complex @ R2 @ ( F @ N ) )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_distrib_left
% 5.06/5.37 thf(fact_5795_sum__distrib__left,axiom,
% 5.06/5.37 ! [R2: nat,F: nat > nat,A2: set_nat] :
% 5.06/5.37 ( ( times_times_nat @ R2 @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.06/5.37 = ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [N: nat] : ( times_times_nat @ R2 @ ( F @ N ) )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_distrib_left
% 5.06/5.37 thf(fact_5796_sum__distrib__left,axiom,
% 5.06/5.37 ! [R2: real,F: nat > real,A2: set_nat] :
% 5.06/5.37 ( ( times_times_real @ R2 @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.06/5.37 = ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [N: nat] : ( times_times_real @ R2 @ ( F @ N ) )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_distrib_left
% 5.06/5.37 thf(fact_5797_sum_Odistrib,axiom,
% 5.06/5.37 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.06/5.37 ( ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [X2: int] : ( plus_plus_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.distrib
% 5.06/5.37 thf(fact_5798_sum_Odistrib,axiom,
% 5.06/5.37 ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 5.06/5.37 ( ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [X2: complex] : ( plus_plus_complex @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.distrib
% 5.06/5.37 thf(fact_5799_sum_Odistrib,axiom,
% 5.06/5.37 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.06/5.37 ( ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.distrib
% 5.06/5.37 thf(fact_5800_sum_Odistrib,axiom,
% 5.06/5.37 ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 5.06/5.37 ( ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [X2: nat] : ( plus_plus_real @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.distrib
% 5.06/5.37 thf(fact_5801_sum__subtractf,axiom,
% 5.06/5.37 ! [F: int > int,G: int > int,A2: set_int] :
% 5.06/5.37 ( ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [X2: int] : ( minus_minus_int @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_subtractf
% 5.06/5.37 thf(fact_5802_sum__subtractf,axiom,
% 5.06/5.37 ! [F: complex > complex,G: complex > complex,A2: set_complex] :
% 5.06/5.37 ( ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [X2: complex] : ( minus_minus_complex @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_subtractf
% 5.06/5.37 thf(fact_5803_sum__subtractf,axiom,
% 5.06/5.37 ! [F: nat > real,G: nat > real,A2: set_nat] :
% 5.06/5.37 ( ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [X2: nat] : ( minus_minus_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_subtractf
% 5.06/5.37 thf(fact_5804_sum__divide__distrib,axiom,
% 5.06/5.37 ! [F: complex > complex,A2: set_complex,R2: complex] :
% 5.06/5.37 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R2 )
% 5.06/5.37 = ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [N: complex] : ( divide1717551699836669952omplex @ ( F @ N ) @ R2 )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_divide_distrib
% 5.06/5.37 thf(fact_5805_sum__divide__distrib,axiom,
% 5.06/5.37 ! [F: nat > real,A2: set_nat,R2: real] :
% 5.06/5.37 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R2 )
% 5.06/5.37 = ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ R2 )
% 5.06/5.37 @ A2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_divide_distrib
% 5.06/5.37 thf(fact_5806_sum_Oswap__restrict,axiom,
% 5.06/5.37 ! [A2: set_real,B3: set_int,G: real > int > int,R: real > int > $o] :
% 5.06/5.37 ( ( finite_finite_real @ A2 )
% 5.06/5.37 => ( ( finite_finite_int @ B3 )
% 5.06/5.37 => ( ( groups1932886352136224148al_int
% 5.06/5.37 @ ^ [X2: real] :
% 5.06/5.37 ( groups4538972089207619220nt_int @ ( G @ X2 )
% 5.06/5.37 @ ( collect_int
% 5.06/5.37 @ ^ [Y2: int] :
% 5.06/5.37 ( ( member_int @ Y2 @ B3 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [Y2: int] :
% 5.06/5.37 ( groups1932886352136224148al_int
% 5.06/5.37 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.06/5.37 @ ( collect_real
% 5.06/5.37 @ ^ [X2: real] :
% 5.06/5.37 ( ( member_real @ X2 @ A2 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ B3 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap_restrict
% 5.06/5.37 thf(fact_5807_sum_Oswap__restrict,axiom,
% 5.06/5.37 ! [A2: set_nat,B3: set_int,G: nat > int > int,R: nat > int > $o] :
% 5.06/5.37 ( ( finite_finite_nat @ A2 )
% 5.06/5.37 => ( ( finite_finite_int @ B3 )
% 5.06/5.37 => ( ( groups3539618377306564664at_int
% 5.06/5.37 @ ^ [X2: nat] :
% 5.06/5.37 ( groups4538972089207619220nt_int @ ( G @ X2 )
% 5.06/5.37 @ ( collect_int
% 5.06/5.37 @ ^ [Y2: int] :
% 5.06/5.37 ( ( member_int @ Y2 @ B3 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [Y2: int] :
% 5.06/5.37 ( groups3539618377306564664at_int
% 5.06/5.37 @ ^ [X2: nat] : ( G @ X2 @ Y2 )
% 5.06/5.37 @ ( collect_nat
% 5.06/5.37 @ ^ [X2: nat] :
% 5.06/5.37 ( ( member_nat @ X2 @ A2 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ B3 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap_restrict
% 5.06/5.37 thf(fact_5808_sum_Oswap__restrict,axiom,
% 5.06/5.37 ! [A2: set_complex,B3: set_int,G: complex > int > int,R: complex > int > $o] :
% 5.06/5.37 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.37 => ( ( finite_finite_int @ B3 )
% 5.06/5.37 => ( ( groups5690904116761175830ex_int
% 5.06/5.37 @ ^ [X2: complex] :
% 5.06/5.37 ( groups4538972089207619220nt_int @ ( G @ X2 )
% 5.06/5.37 @ ( collect_int
% 5.06/5.37 @ ^ [Y2: int] :
% 5.06/5.37 ( ( member_int @ Y2 @ B3 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [Y2: int] :
% 5.06/5.37 ( groups5690904116761175830ex_int
% 5.06/5.37 @ ^ [X2: complex] : ( G @ X2 @ Y2 )
% 5.06/5.37 @ ( collect_complex
% 5.06/5.37 @ ^ [X2: complex] :
% 5.06/5.37 ( ( member_complex @ X2 @ A2 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ B3 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap_restrict
% 5.06/5.37 thf(fact_5809_sum_Oswap__restrict,axiom,
% 5.06/5.37 ! [A2: set_real,B3: set_complex,G: real > complex > complex,R: real > complex > $o] :
% 5.06/5.37 ( ( finite_finite_real @ A2 )
% 5.06/5.37 => ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.37 => ( ( groups5754745047067104278omplex
% 5.06/5.37 @ ^ [X2: real] :
% 5.06/5.37 ( groups7754918857620584856omplex @ ( G @ X2 )
% 5.06/5.37 @ ( collect_complex
% 5.06/5.37 @ ^ [Y2: complex] :
% 5.06/5.37 ( ( member_complex @ Y2 @ B3 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [Y2: complex] :
% 5.06/5.37 ( groups5754745047067104278omplex
% 5.06/5.37 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.06/5.37 @ ( collect_real
% 5.06/5.37 @ ^ [X2: real] :
% 5.06/5.37 ( ( member_real @ X2 @ A2 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ B3 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap_restrict
% 5.06/5.37 thf(fact_5810_sum_Oswap__restrict,axiom,
% 5.06/5.37 ! [A2: set_nat,B3: set_complex,G: nat > complex > complex,R: nat > complex > $o] :
% 5.06/5.37 ( ( finite_finite_nat @ A2 )
% 5.06/5.37 => ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.37 => ( ( groups2073611262835488442omplex
% 5.06/5.37 @ ^ [X2: nat] :
% 5.06/5.37 ( groups7754918857620584856omplex @ ( G @ X2 )
% 5.06/5.37 @ ( collect_complex
% 5.06/5.37 @ ^ [Y2: complex] :
% 5.06/5.37 ( ( member_complex @ Y2 @ B3 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [Y2: complex] :
% 5.06/5.37 ( groups2073611262835488442omplex
% 5.06/5.37 @ ^ [X2: nat] : ( G @ X2 @ Y2 )
% 5.06/5.37 @ ( collect_nat
% 5.06/5.37 @ ^ [X2: nat] :
% 5.06/5.37 ( ( member_nat @ X2 @ A2 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ B3 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap_restrict
% 5.06/5.37 thf(fact_5811_sum_Oswap__restrict,axiom,
% 5.06/5.37 ! [A2: set_int,B3: set_complex,G: int > complex > complex,R: int > complex > $o] :
% 5.06/5.37 ( ( finite_finite_int @ A2 )
% 5.06/5.37 => ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.37 => ( ( groups3049146728041665814omplex
% 5.06/5.37 @ ^ [X2: int] :
% 5.06/5.37 ( groups7754918857620584856omplex @ ( G @ X2 )
% 5.06/5.37 @ ( collect_complex
% 5.06/5.37 @ ^ [Y2: complex] :
% 5.06/5.37 ( ( member_complex @ Y2 @ B3 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups7754918857620584856omplex
% 5.06/5.37 @ ^ [Y2: complex] :
% 5.06/5.37 ( groups3049146728041665814omplex
% 5.06/5.37 @ ^ [X2: int] : ( G @ X2 @ Y2 )
% 5.06/5.37 @ ( collect_int
% 5.06/5.37 @ ^ [X2: int] :
% 5.06/5.37 ( ( member_int @ X2 @ A2 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ B3 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap_restrict
% 5.06/5.37 thf(fact_5812_sum_Oswap__restrict,axiom,
% 5.06/5.37 ! [A2: set_real,B3: set_nat,G: real > nat > nat,R: real > nat > $o] :
% 5.06/5.37 ( ( finite_finite_real @ A2 )
% 5.06/5.37 => ( ( finite_finite_nat @ B3 )
% 5.06/5.37 => ( ( groups1935376822645274424al_nat
% 5.06/5.37 @ ^ [X2: real] :
% 5.06/5.37 ( groups3542108847815614940at_nat @ ( G @ X2 )
% 5.06/5.37 @ ( collect_nat
% 5.06/5.37 @ ^ [Y2: nat] :
% 5.06/5.37 ( ( member_nat @ Y2 @ B3 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [Y2: nat] :
% 5.06/5.37 ( groups1935376822645274424al_nat
% 5.06/5.37 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.06/5.37 @ ( collect_real
% 5.06/5.37 @ ^ [X2: real] :
% 5.06/5.37 ( ( member_real @ X2 @ A2 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ B3 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap_restrict
% 5.06/5.37 thf(fact_5813_sum_Oswap__restrict,axiom,
% 5.06/5.37 ! [A2: set_int,B3: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 5.06/5.37 ( ( finite_finite_int @ A2 )
% 5.06/5.37 => ( ( finite_finite_nat @ B3 )
% 5.06/5.37 => ( ( groups4541462559716669496nt_nat
% 5.06/5.37 @ ^ [X2: int] :
% 5.06/5.37 ( groups3542108847815614940at_nat @ ( G @ X2 )
% 5.06/5.37 @ ( collect_nat
% 5.06/5.37 @ ^ [Y2: nat] :
% 5.06/5.37 ( ( member_nat @ Y2 @ B3 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [Y2: nat] :
% 5.06/5.37 ( groups4541462559716669496nt_nat
% 5.06/5.37 @ ^ [X2: int] : ( G @ X2 @ Y2 )
% 5.06/5.37 @ ( collect_int
% 5.06/5.37 @ ^ [X2: int] :
% 5.06/5.37 ( ( member_int @ X2 @ A2 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ B3 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap_restrict
% 5.06/5.37 thf(fact_5814_sum_Oswap__restrict,axiom,
% 5.06/5.37 ! [A2: set_complex,B3: set_nat,G: complex > nat > nat,R: complex > nat > $o] :
% 5.06/5.37 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.37 => ( ( finite_finite_nat @ B3 )
% 5.06/5.37 => ( ( groups5693394587270226106ex_nat
% 5.06/5.37 @ ^ [X2: complex] :
% 5.06/5.37 ( groups3542108847815614940at_nat @ ( G @ X2 )
% 5.06/5.37 @ ( collect_nat
% 5.06/5.37 @ ^ [Y2: nat] :
% 5.06/5.37 ( ( member_nat @ Y2 @ B3 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [Y2: nat] :
% 5.06/5.37 ( groups5693394587270226106ex_nat
% 5.06/5.37 @ ^ [X2: complex] : ( G @ X2 @ Y2 )
% 5.06/5.37 @ ( collect_complex
% 5.06/5.37 @ ^ [X2: complex] :
% 5.06/5.37 ( ( member_complex @ X2 @ A2 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ B3 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap_restrict
% 5.06/5.37 thf(fact_5815_sum_Oswap__restrict,axiom,
% 5.06/5.37 ! [A2: set_real,B3: set_nat,G: real > nat > real,R: real > nat > $o] :
% 5.06/5.37 ( ( finite_finite_real @ A2 )
% 5.06/5.37 => ( ( finite_finite_nat @ B3 )
% 5.06/5.37 => ( ( groups8097168146408367636l_real
% 5.06/5.37 @ ^ [X2: real] :
% 5.06/5.37 ( groups6591440286371151544t_real @ ( G @ X2 )
% 5.06/5.37 @ ( collect_nat
% 5.06/5.37 @ ^ [Y2: nat] :
% 5.06/5.37 ( ( member_nat @ Y2 @ B3 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ A2 )
% 5.06/5.37 = ( groups6591440286371151544t_real
% 5.06/5.37 @ ^ [Y2: nat] :
% 5.06/5.37 ( groups8097168146408367636l_real
% 5.06/5.37 @ ^ [X2: real] : ( G @ X2 @ Y2 )
% 5.06/5.37 @ ( collect_real
% 5.06/5.37 @ ^ [X2: real] :
% 5.06/5.37 ( ( member_real @ X2 @ A2 )
% 5.06/5.37 & ( R @ X2 @ Y2 ) ) ) )
% 5.06/5.37 @ B3 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum.swap_restrict
% 5.06/5.37 thf(fact_5816_mod__sum__eq,axiom,
% 5.06/5.37 ! [F: int > int,A: int,A2: set_int] :
% 5.06/5.37 ( ( modulo_modulo_int
% 5.06/5.37 @ ( groups4538972089207619220nt_int
% 5.06/5.37 @ ^ [I5: int] : ( modulo_modulo_int @ ( F @ I5 ) @ A )
% 5.06/5.37 @ A2 )
% 5.06/5.37 @ A )
% 5.06/5.37 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % mod_sum_eq
% 5.06/5.37 thf(fact_5817_mod__sum__eq,axiom,
% 5.06/5.37 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.06/5.37 ( ( modulo_modulo_nat
% 5.06/5.37 @ ( groups3542108847815614940at_nat
% 5.06/5.37 @ ^ [I5: nat] : ( modulo_modulo_nat @ ( F @ I5 ) @ A )
% 5.06/5.37 @ A2 )
% 5.06/5.37 @ A )
% 5.06/5.37 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 5.06/5.37
% 5.06/5.37 % mod_sum_eq
% 5.06/5.37 thf(fact_5818_cond__case__prod__eta,axiom,
% 5.06/5.37 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.06/5.37 ( ! [X3: nat,Y5: nat] :
% 5.06/5.37 ( ( F @ X3 @ Y5 )
% 5.06/5.37 = ( G @ ( product_Pair_nat_nat @ X3 @ Y5 ) ) )
% 5.06/5.37 => ( ( produc27273713700761075at_nat @ F )
% 5.06/5.37 = G ) ) ).
% 5.06/5.37
% 5.06/5.37 % cond_case_prod_eta
% 5.06/5.37 thf(fact_5819_cond__case__prod__eta,axiom,
% 5.06/5.37 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.06/5.37 ( ! [X3: nat,Y5: nat] :
% 5.06/5.37 ( ( F @ X3 @ Y5 )
% 5.06/5.37 = ( G @ ( product_Pair_nat_nat @ X3 @ Y5 ) ) )
% 5.06/5.37 => ( ( produc8739625826339149834_nat_o @ F )
% 5.06/5.37 = G ) ) ).
% 5.06/5.37
% 5.06/5.37 % cond_case_prod_eta
% 5.06/5.37 thf(fact_5820_cond__case__prod__eta,axiom,
% 5.06/5.37 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.06/5.37 ( ! [X3: int,Y5: int] :
% 5.06/5.37 ( ( F @ X3 @ Y5 )
% 5.06/5.37 = ( G @ ( product_Pair_int_int @ X3 @ Y5 ) ) )
% 5.06/5.37 => ( ( produc4245557441103728435nt_int @ F )
% 5.06/5.37 = G ) ) ).
% 5.06/5.37
% 5.06/5.37 % cond_case_prod_eta
% 5.06/5.37 thf(fact_5821_cond__case__prod__eta,axiom,
% 5.06/5.37 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 5.06/5.37 ( ! [X3: int,Y5: int] :
% 5.06/5.37 ( ( F @ X3 @ Y5 )
% 5.06/5.37 = ( G @ ( product_Pair_int_int @ X3 @ Y5 ) ) )
% 5.06/5.37 => ( ( produc4947309494688390418_int_o @ F )
% 5.06/5.37 = G ) ) ).
% 5.06/5.37
% 5.06/5.37 % cond_case_prod_eta
% 5.06/5.37 thf(fact_5822_cond__case__prod__eta,axiom,
% 5.06/5.37 ! [F: int > int > int,G: product_prod_int_int > int] :
% 5.06/5.37 ( ! [X3: int,Y5: int] :
% 5.06/5.37 ( ( F @ X3 @ Y5 )
% 5.06/5.37 = ( G @ ( product_Pair_int_int @ X3 @ Y5 ) ) )
% 5.06/5.37 => ( ( produc8211389475949308722nt_int @ F )
% 5.06/5.37 = G ) ) ).
% 5.06/5.37
% 5.06/5.37 % cond_case_prod_eta
% 5.06/5.37 thf(fact_5823_case__prod__eta,axiom,
% 5.06/5.37 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.06/5.37 ( ( produc27273713700761075at_nat
% 5.06/5.37 @ ^ [X2: nat,Y2: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y2 ) ) )
% 5.06/5.37 = F ) ).
% 5.06/5.37
% 5.06/5.37 % case_prod_eta
% 5.06/5.37 thf(fact_5824_case__prod__eta,axiom,
% 5.06/5.37 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.06/5.37 ( ( produc8739625826339149834_nat_o
% 5.06/5.37 @ ^ [X2: nat,Y2: nat] : ( F @ ( product_Pair_nat_nat @ X2 @ Y2 ) ) )
% 5.06/5.37 = F ) ).
% 5.06/5.37
% 5.06/5.37 % case_prod_eta
% 5.06/5.37 thf(fact_5825_case__prod__eta,axiom,
% 5.06/5.37 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.06/5.37 ( ( produc4245557441103728435nt_int
% 5.06/5.37 @ ^ [X2: int,Y2: int] : ( F @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 5.06/5.37 = F ) ).
% 5.06/5.37
% 5.06/5.37 % case_prod_eta
% 5.06/5.37 thf(fact_5826_case__prod__eta,axiom,
% 5.06/5.37 ! [F: product_prod_int_int > $o] :
% 5.06/5.37 ( ( produc4947309494688390418_int_o
% 5.06/5.37 @ ^ [X2: int,Y2: int] : ( F @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 5.06/5.37 = F ) ).
% 5.06/5.37
% 5.06/5.37 % case_prod_eta
% 5.06/5.37 thf(fact_5827_case__prod__eta,axiom,
% 5.06/5.37 ! [F: product_prod_int_int > int] :
% 5.06/5.37 ( ( produc8211389475949308722nt_int
% 5.06/5.37 @ ^ [X2: int,Y2: int] : ( F @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 5.06/5.37 = F ) ).
% 5.06/5.37
% 5.06/5.37 % case_prod_eta
% 5.06/5.37 thf(fact_5828_case__prodE2,axiom,
% 5.06/5.37 ! [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] :
% 5.06/5.37 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 5.06/5.37 => ~ ! [X3: nat,Y5: nat] :
% 5.06/5.37 ( ( Z
% 5.06/5.37 = ( product_Pair_nat_nat @ X3 @ Y5 ) )
% 5.06/5.37 => ~ ( Q @ ( P @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % case_prodE2
% 5.06/5.37 thf(fact_5829_case__prodE2,axiom,
% 5.06/5.37 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 5.06/5.37 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 5.06/5.37 => ~ ! [X3: nat,Y5: nat] :
% 5.06/5.37 ( ( Z
% 5.06/5.37 = ( product_Pair_nat_nat @ X3 @ Y5 ) )
% 5.06/5.37 => ~ ( Q @ ( P @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % case_prodE2
% 5.06/5.37 thf(fact_5830_case__prodE2,axiom,
% 5.06/5.37 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 5.06/5.37 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 5.06/5.37 => ~ ! [X3: int,Y5: int] :
% 5.06/5.37 ( ( Z
% 5.06/5.37 = ( product_Pair_int_int @ X3 @ Y5 ) )
% 5.06/5.37 => ~ ( Q @ ( P @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % case_prodE2
% 5.06/5.37 thf(fact_5831_case__prodE2,axiom,
% 5.06/5.37 ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 5.06/5.37 ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 5.06/5.37 => ~ ! [X3: int,Y5: int] :
% 5.06/5.37 ( ( Z
% 5.06/5.37 = ( product_Pair_int_int @ X3 @ Y5 ) )
% 5.06/5.37 => ~ ( Q @ ( P @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % case_prodE2
% 5.06/5.37 thf(fact_5832_case__prodE2,axiom,
% 5.06/5.37 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 5.06/5.37 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 5.06/5.37 => ~ ! [X3: int,Y5: int] :
% 5.06/5.37 ( ( Z
% 5.06/5.37 = ( product_Pair_int_int @ X3 @ Y5 ) )
% 5.06/5.37 => ~ ( Q @ ( P @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % case_prodE2
% 5.06/5.37 thf(fact_5833_sum__nonneg,axiom,
% 5.06/5.37 ! [A2: set_complex,F: complex > real] :
% 5.06/5.37 ( ! [X3: complex] :
% 5.06/5.37 ( ( member_complex @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.06/5.37 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonneg
% 5.06/5.37 thf(fact_5834_sum__nonneg,axiom,
% 5.06/5.37 ! [A2: set_real,F: real > real] :
% 5.06/5.37 ( ! [X3: real] :
% 5.06/5.37 ( ( member_real @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.06/5.37 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonneg
% 5.06/5.37 thf(fact_5835_sum__nonneg,axiom,
% 5.06/5.37 ! [A2: set_int,F: int > real] :
% 5.06/5.37 ( ! [X3: int] :
% 5.06/5.37 ( ( member_int @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.06/5.37 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonneg
% 5.06/5.37 thf(fact_5836_sum__nonneg,axiom,
% 5.06/5.37 ! [A2: set_complex,F: complex > rat] :
% 5.06/5.37 ( ! [X3: complex] :
% 5.06/5.37 ( ( member_complex @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.37 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonneg
% 5.06/5.37 thf(fact_5837_sum__nonneg,axiom,
% 5.06/5.37 ! [A2: set_real,F: real > rat] :
% 5.06/5.37 ( ! [X3: real] :
% 5.06/5.37 ( ( member_real @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.37 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonneg
% 5.06/5.37 thf(fact_5838_sum__nonneg,axiom,
% 5.06/5.37 ! [A2: set_nat,F: nat > rat] :
% 5.06/5.37 ( ! [X3: nat] :
% 5.06/5.37 ( ( member_nat @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.37 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonneg
% 5.06/5.37 thf(fact_5839_sum__nonneg,axiom,
% 5.06/5.37 ! [A2: set_int,F: int > rat] :
% 5.06/5.37 ( ! [X3: int] :
% 5.06/5.37 ( ( member_int @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.37 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonneg
% 5.06/5.37 thf(fact_5840_sum__nonneg,axiom,
% 5.06/5.37 ! [A2: set_complex,F: complex > nat] :
% 5.06/5.37 ( ! [X3: complex] :
% 5.06/5.37 ( ( member_complex @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.06/5.37 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonneg
% 5.06/5.37 thf(fact_5841_sum__nonneg,axiom,
% 5.06/5.37 ! [A2: set_real,F: real > nat] :
% 5.06/5.37 ( ! [X3: real] :
% 5.06/5.37 ( ( member_real @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.06/5.37 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonneg
% 5.06/5.37 thf(fact_5842_sum__nonneg,axiom,
% 5.06/5.37 ! [A2: set_int,F: int > nat] :
% 5.06/5.37 ( ! [X3: int] :
% 5.06/5.37 ( ( member_int @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.06/5.37 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonneg
% 5.06/5.37 thf(fact_5843_sum__nonpos,axiom,
% 5.06/5.37 ! [A2: set_complex,F: complex > real] :
% 5.06/5.37 ( ! [X3: complex] :
% 5.06/5.37 ( ( member_complex @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.06/5.37 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonpos
% 5.06/5.37 thf(fact_5844_sum__nonpos,axiom,
% 5.06/5.37 ! [A2: set_real,F: real > real] :
% 5.06/5.37 ( ! [X3: real] :
% 5.06/5.37 ( ( member_real @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.06/5.37 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonpos
% 5.06/5.37 thf(fact_5845_sum__nonpos,axiom,
% 5.06/5.37 ! [A2: set_int,F: int > real] :
% 5.06/5.37 ( ! [X3: int] :
% 5.06/5.37 ( ( member_int @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 5.06/5.37 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonpos
% 5.06/5.37 thf(fact_5846_sum__nonpos,axiom,
% 5.06/5.37 ! [A2: set_complex,F: complex > rat] :
% 5.06/5.37 ( ! [X3: complex] :
% 5.06/5.37 ( ( member_complex @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.06/5.37 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonpos
% 5.06/5.37 thf(fact_5847_sum__nonpos,axiom,
% 5.06/5.37 ! [A2: set_real,F: real > rat] :
% 5.06/5.37 ( ! [X3: real] :
% 5.06/5.37 ( ( member_real @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.06/5.37 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonpos
% 5.06/5.37 thf(fact_5848_sum__nonpos,axiom,
% 5.06/5.37 ! [A2: set_nat,F: nat > rat] :
% 5.06/5.37 ( ! [X3: nat] :
% 5.06/5.37 ( ( member_nat @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.06/5.37 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonpos
% 5.06/5.37 thf(fact_5849_sum__nonpos,axiom,
% 5.06/5.37 ! [A2: set_int,F: int > rat] :
% 5.06/5.37 ( ! [X3: int] :
% 5.06/5.37 ( ( member_int @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.06/5.37 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonpos
% 5.06/5.37 thf(fact_5850_sum__nonpos,axiom,
% 5.06/5.37 ! [A2: set_complex,F: complex > nat] :
% 5.06/5.37 ( ! [X3: complex] :
% 5.06/5.37 ( ( member_complex @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.06/5.37 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonpos
% 5.06/5.37 thf(fact_5851_sum__nonpos,axiom,
% 5.06/5.37 ! [A2: set_real,F: real > nat] :
% 5.06/5.37 ( ! [X3: real] :
% 5.06/5.37 ( ( member_real @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.06/5.37 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonpos
% 5.06/5.37 thf(fact_5852_sum__nonpos,axiom,
% 5.06/5.37 ! [A2: set_int,F: int > nat] :
% 5.06/5.37 ( ! [X3: int] :
% 5.06/5.37 ( ( member_int @ X3 @ A2 )
% 5.06/5.37 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.06/5.37 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_nonpos
% 5.06/5.37 thf(fact_5853_ln__add__one__self__le__self2,axiom,
% 5.06/5.37 ! [X: real] :
% 5.06/5.37 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.37 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.06/5.37
% 5.06/5.37 % ln_add_one_self_le_self2
% 5.06/5.37 thf(fact_5854_sum__mono__inv,axiom,
% 5.06/5.37 ! [F: real > rat,I6: set_real,G: real > rat,I2: real] :
% 5.06/5.37 ( ( ( groups1300246762558778688al_rat @ F @ I6 )
% 5.06/5.37 = ( groups1300246762558778688al_rat @ G @ I6 ) )
% 5.06/5.37 => ( ! [I3: real] :
% 5.06/5.37 ( ( member_real @ I3 @ I6 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ( member_real @ I2 @ I6 )
% 5.06/5.37 => ( ( finite_finite_real @ I6 )
% 5.06/5.37 => ( ( F @ I2 )
% 5.06/5.37 = ( G @ I2 ) ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono_inv
% 5.06/5.37 thf(fact_5855_sum__mono__inv,axiom,
% 5.06/5.37 ! [F: nat > rat,I6: set_nat,G: nat > rat,I2: nat] :
% 5.06/5.37 ( ( ( groups2906978787729119204at_rat @ F @ I6 )
% 5.06/5.37 = ( groups2906978787729119204at_rat @ G @ I6 ) )
% 5.06/5.37 => ( ! [I3: nat] :
% 5.06/5.37 ( ( member_nat @ I3 @ I6 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ( member_nat @ I2 @ I6 )
% 5.06/5.37 => ( ( finite_finite_nat @ I6 )
% 5.06/5.37 => ( ( F @ I2 )
% 5.06/5.37 = ( G @ I2 ) ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono_inv
% 5.06/5.37 thf(fact_5856_sum__mono__inv,axiom,
% 5.06/5.37 ! [F: int > rat,I6: set_int,G: int > rat,I2: int] :
% 5.06/5.37 ( ( ( groups3906332499630173760nt_rat @ F @ I6 )
% 5.06/5.37 = ( groups3906332499630173760nt_rat @ G @ I6 ) )
% 5.06/5.37 => ( ! [I3: int] :
% 5.06/5.37 ( ( member_int @ I3 @ I6 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ( member_int @ I2 @ I6 )
% 5.06/5.37 => ( ( finite_finite_int @ I6 )
% 5.06/5.37 => ( ( F @ I2 )
% 5.06/5.37 = ( G @ I2 ) ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono_inv
% 5.06/5.37 thf(fact_5857_sum__mono__inv,axiom,
% 5.06/5.37 ! [F: complex > rat,I6: set_complex,G: complex > rat,I2: complex] :
% 5.06/5.37 ( ( ( groups5058264527183730370ex_rat @ F @ I6 )
% 5.06/5.37 = ( groups5058264527183730370ex_rat @ G @ I6 ) )
% 5.06/5.37 => ( ! [I3: complex] :
% 5.06/5.37 ( ( member_complex @ I3 @ I6 )
% 5.06/5.37 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ( member_complex @ I2 @ I6 )
% 5.06/5.37 => ( ( finite3207457112153483333omplex @ I6 )
% 5.06/5.37 => ( ( F @ I2 )
% 5.06/5.37 = ( G @ I2 ) ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono_inv
% 5.06/5.37 thf(fact_5858_sum__mono__inv,axiom,
% 5.06/5.37 ! [F: real > nat,I6: set_real,G: real > nat,I2: real] :
% 5.06/5.37 ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 5.06/5.37 = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 5.06/5.37 => ( ! [I3: real] :
% 5.06/5.37 ( ( member_real @ I3 @ I6 )
% 5.06/5.37 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ( member_real @ I2 @ I6 )
% 5.06/5.37 => ( ( finite_finite_real @ I6 )
% 5.06/5.37 => ( ( F @ I2 )
% 5.06/5.37 = ( G @ I2 ) ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono_inv
% 5.06/5.37 thf(fact_5859_sum__mono__inv,axiom,
% 5.06/5.37 ! [F: int > nat,I6: set_int,G: int > nat,I2: int] :
% 5.06/5.37 ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 5.06/5.37 = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 5.06/5.37 => ( ! [I3: int] :
% 5.06/5.37 ( ( member_int @ I3 @ I6 )
% 5.06/5.37 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ( member_int @ I2 @ I6 )
% 5.06/5.37 => ( ( finite_finite_int @ I6 )
% 5.06/5.37 => ( ( F @ I2 )
% 5.06/5.37 = ( G @ I2 ) ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono_inv
% 5.06/5.37 thf(fact_5860_sum__mono__inv,axiom,
% 5.06/5.37 ! [F: complex > nat,I6: set_complex,G: complex > nat,I2: complex] :
% 5.06/5.37 ( ( ( groups5693394587270226106ex_nat @ F @ I6 )
% 5.06/5.37 = ( groups5693394587270226106ex_nat @ G @ I6 ) )
% 5.06/5.37 => ( ! [I3: complex] :
% 5.06/5.37 ( ( member_complex @ I3 @ I6 )
% 5.06/5.37 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ( member_complex @ I2 @ I6 )
% 5.06/5.37 => ( ( finite3207457112153483333omplex @ I6 )
% 5.06/5.37 => ( ( F @ I2 )
% 5.06/5.37 = ( G @ I2 ) ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono_inv
% 5.06/5.37 thf(fact_5861_sum__mono__inv,axiom,
% 5.06/5.37 ! [F: real > int,I6: set_real,G: real > int,I2: real] :
% 5.06/5.37 ( ( ( groups1932886352136224148al_int @ F @ I6 )
% 5.06/5.37 = ( groups1932886352136224148al_int @ G @ I6 ) )
% 5.06/5.37 => ( ! [I3: real] :
% 5.06/5.37 ( ( member_real @ I3 @ I6 )
% 5.06/5.37 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ( member_real @ I2 @ I6 )
% 5.06/5.37 => ( ( finite_finite_real @ I6 )
% 5.06/5.37 => ( ( F @ I2 )
% 5.06/5.37 = ( G @ I2 ) ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono_inv
% 5.06/5.37 thf(fact_5862_sum__mono__inv,axiom,
% 5.06/5.37 ! [F: nat > int,I6: set_nat,G: nat > int,I2: nat] :
% 5.06/5.37 ( ( ( groups3539618377306564664at_int @ F @ I6 )
% 5.06/5.37 = ( groups3539618377306564664at_int @ G @ I6 ) )
% 5.06/5.37 => ( ! [I3: nat] :
% 5.06/5.37 ( ( member_nat @ I3 @ I6 )
% 5.06/5.37 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ( member_nat @ I2 @ I6 )
% 5.06/5.37 => ( ( finite_finite_nat @ I6 )
% 5.06/5.37 => ( ( F @ I2 )
% 5.06/5.37 = ( G @ I2 ) ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono_inv
% 5.06/5.37 thf(fact_5863_sum__mono__inv,axiom,
% 5.06/5.37 ! [F: complex > int,I6: set_complex,G: complex > int,I2: complex] :
% 5.06/5.37 ( ( ( groups5690904116761175830ex_int @ F @ I6 )
% 5.06/5.37 = ( groups5690904116761175830ex_int @ G @ I6 ) )
% 5.06/5.37 => ( ! [I3: complex] :
% 5.06/5.37 ( ( member_complex @ I3 @ I6 )
% 5.06/5.37 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.06/5.37 => ( ( member_complex @ I2 @ I6 )
% 5.06/5.37 => ( ( finite3207457112153483333omplex @ I6 )
% 5.06/5.37 => ( ( F @ I2 )
% 5.06/5.37 = ( G @ I2 ) ) ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % sum_mono_inv
% 5.06/5.37 thf(fact_5864_neg__numeral__le__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_le_numeral
% 5.06/5.37 thf(fact_5865_neg__numeral__le__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_le_numeral
% 5.06/5.37 thf(fact_5866_neg__numeral__le__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_le_numeral
% 5.06/5.37 thf(fact_5867_neg__numeral__le__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_le_numeral
% 5.06/5.37 thf(fact_5868_not__numeral__le__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_numeral_le_neg_numeral
% 5.06/5.37 thf(fact_5869_not__numeral__le__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_numeral_le_neg_numeral
% 5.06/5.37 thf(fact_5870_not__numeral__le__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_numeral_le_neg_numeral
% 5.06/5.37 thf(fact_5871_not__numeral__le__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_numeral_le_neg_numeral
% 5.06/5.37 thf(fact_5872_zero__neq__neg__numeral,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( zero_zero_real
% 5.06/5.37 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % zero_neq_neg_numeral
% 5.06/5.37 thf(fact_5873_zero__neq__neg__numeral,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( zero_zero_int
% 5.06/5.37 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % zero_neq_neg_numeral
% 5.06/5.37 thf(fact_5874_zero__neq__neg__numeral,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( zero_zero_complex
% 5.06/5.37 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % zero_neq_neg_numeral
% 5.06/5.37 thf(fact_5875_zero__neq__neg__numeral,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( zero_zero_rat
% 5.06/5.37 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % zero_neq_neg_numeral
% 5.06/5.37 thf(fact_5876_zero__neq__neg__numeral,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( zero_z3403309356797280102nteger
% 5.06/5.37 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % zero_neq_neg_numeral
% 5.06/5.37 thf(fact_5877_neg__numeral__less__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_numeral
% 5.06/5.37 thf(fact_5878_neg__numeral__less__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_numeral
% 5.06/5.37 thf(fact_5879_neg__numeral__less__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_numeral
% 5.06/5.37 thf(fact_5880_neg__numeral__less__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_numeral_less_numeral
% 5.06/5.37 thf(fact_5881_not__numeral__less__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_numeral_less_neg_numeral
% 5.06/5.37 thf(fact_5882_not__numeral__less__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_numeral_less_neg_numeral
% 5.06/5.37 thf(fact_5883_not__numeral__less__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_numeral_less_neg_numeral
% 5.06/5.37 thf(fact_5884_not__numeral__less__neg__numeral,axiom,
% 5.06/5.37 ! [M: num,N2: num] :
% 5.06/5.37 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % not_numeral_less_neg_numeral
% 5.06/5.37 thf(fact_5885_le__minus__one__simps_I4_J,axiom,
% 5.06/5.37 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_minus_one_simps(4)
% 5.06/5.37 thf(fact_5886_le__minus__one__simps_I4_J,axiom,
% 5.06/5.37 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_minus_one_simps(4)
% 5.06/5.37 thf(fact_5887_le__minus__one__simps_I4_J,axiom,
% 5.06/5.37 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_minus_one_simps(4)
% 5.06/5.37 thf(fact_5888_le__minus__one__simps_I4_J,axiom,
% 5.06/5.37 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % le_minus_one_simps(4)
% 5.06/5.37 thf(fact_5889_le__minus__one__simps_I2_J,axiom,
% 5.06/5.37 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.06/5.37
% 5.06/5.37 % le_minus_one_simps(2)
% 5.06/5.37 thf(fact_5890_le__minus__one__simps_I2_J,axiom,
% 5.06/5.37 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.06/5.37
% 5.06/5.37 % le_minus_one_simps(2)
% 5.06/5.37 thf(fact_5891_le__minus__one__simps_I2_J,axiom,
% 5.06/5.37 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.06/5.37
% 5.06/5.37 % le_minus_one_simps(2)
% 5.06/5.37 thf(fact_5892_le__minus__one__simps_I2_J,axiom,
% 5.06/5.37 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.06/5.37
% 5.06/5.37 % le_minus_one_simps(2)
% 5.06/5.37 thf(fact_5893_add__eq__0__iff,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( ( plus_plus_real @ A @ B )
% 5.06/5.37 = zero_zero_real )
% 5.06/5.37 = ( B
% 5.06/5.37 = ( uminus_uminus_real @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_eq_0_iff
% 5.06/5.37 thf(fact_5894_add__eq__0__iff,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( ( plus_plus_int @ A @ B )
% 5.06/5.37 = zero_zero_int )
% 5.06/5.37 = ( B
% 5.06/5.37 = ( uminus_uminus_int @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_eq_0_iff
% 5.06/5.37 thf(fact_5895_add__eq__0__iff,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( ( plus_plus_complex @ A @ B )
% 5.06/5.37 = zero_zero_complex )
% 5.06/5.37 = ( B
% 5.06/5.37 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_eq_0_iff
% 5.06/5.37 thf(fact_5896_add__eq__0__iff,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( ( plus_plus_rat @ A @ B )
% 5.06/5.37 = zero_zero_rat )
% 5.06/5.37 = ( B
% 5.06/5.37 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_eq_0_iff
% 5.06/5.37 thf(fact_5897_add__eq__0__iff,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.06/5.37 = zero_z3403309356797280102nteger )
% 5.06/5.37 = ( B
% 5.06/5.37 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % add_eq_0_iff
% 5.06/5.37 thf(fact_5898_ab__group__add__class_Oab__left__minus,axiom,
% 5.06/5.37 ! [A: real] :
% 5.06/5.37 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.06/5.37 = zero_zero_real ) ).
% 5.06/5.37
% 5.06/5.37 % ab_group_add_class.ab_left_minus
% 5.06/5.37 thf(fact_5899_ab__group__add__class_Oab__left__minus,axiom,
% 5.06/5.37 ! [A: int] :
% 5.06/5.37 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.06/5.37 = zero_zero_int ) ).
% 5.06/5.37
% 5.06/5.37 % ab_group_add_class.ab_left_minus
% 5.06/5.37 thf(fact_5900_ab__group__add__class_Oab__left__minus,axiom,
% 5.06/5.37 ! [A: complex] :
% 5.06/5.37 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.06/5.37 = zero_zero_complex ) ).
% 5.06/5.37
% 5.06/5.37 % ab_group_add_class.ab_left_minus
% 5.06/5.37 thf(fact_5901_ab__group__add__class_Oab__left__minus,axiom,
% 5.06/5.37 ! [A: rat] :
% 5.06/5.37 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.06/5.37 = zero_zero_rat ) ).
% 5.06/5.37
% 5.06/5.37 % ab_group_add_class.ab_left_minus
% 5.06/5.37 thf(fact_5902_ab__group__add__class_Oab__left__minus,axiom,
% 5.06/5.37 ! [A: code_integer] :
% 5.06/5.37 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.06/5.37 = zero_z3403309356797280102nteger ) ).
% 5.06/5.37
% 5.06/5.37 % ab_group_add_class.ab_left_minus
% 5.06/5.37 thf(fact_5903_add_Oinverse__unique,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( ( plus_plus_real @ A @ B )
% 5.06/5.37 = zero_zero_real )
% 5.06/5.37 => ( ( uminus_uminus_real @ A )
% 5.06/5.37 = B ) ) ).
% 5.06/5.37
% 5.06/5.37 % add.inverse_unique
% 5.06/5.37 thf(fact_5904_add_Oinverse__unique,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( ( plus_plus_int @ A @ B )
% 5.06/5.37 = zero_zero_int )
% 5.06/5.37 => ( ( uminus_uminus_int @ A )
% 5.06/5.37 = B ) ) ).
% 5.06/5.37
% 5.06/5.37 % add.inverse_unique
% 5.06/5.37 thf(fact_5905_add_Oinverse__unique,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( ( plus_plus_complex @ A @ B )
% 5.06/5.37 = zero_zero_complex )
% 5.06/5.37 => ( ( uminus1482373934393186551omplex @ A )
% 5.06/5.37 = B ) ) ).
% 5.06/5.37
% 5.06/5.37 % add.inverse_unique
% 5.06/5.37 thf(fact_5906_add_Oinverse__unique,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( ( plus_plus_rat @ A @ B )
% 5.06/5.37 = zero_zero_rat )
% 5.06/5.37 => ( ( uminus_uminus_rat @ A )
% 5.06/5.37 = B ) ) ).
% 5.06/5.37
% 5.06/5.37 % add.inverse_unique
% 5.06/5.37 thf(fact_5907_add_Oinverse__unique,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.06/5.37 = zero_z3403309356797280102nteger )
% 5.06/5.37 => ( ( uminus1351360451143612070nteger @ A )
% 5.06/5.37 = B ) ) ).
% 5.06/5.37
% 5.06/5.37 % add.inverse_unique
% 5.06/5.37 thf(fact_5908_eq__neg__iff__add__eq__0,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( A
% 5.06/5.37 = ( uminus_uminus_real @ B ) )
% 5.06/5.37 = ( ( plus_plus_real @ A @ B )
% 5.06/5.37 = zero_zero_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % eq_neg_iff_add_eq_0
% 5.06/5.37 thf(fact_5909_eq__neg__iff__add__eq__0,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( A
% 5.06/5.37 = ( uminus_uminus_int @ B ) )
% 5.06/5.37 = ( ( plus_plus_int @ A @ B )
% 5.06/5.37 = zero_zero_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % eq_neg_iff_add_eq_0
% 5.06/5.37 thf(fact_5910_eq__neg__iff__add__eq__0,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( A
% 5.06/5.37 = ( uminus1482373934393186551omplex @ B ) )
% 5.06/5.37 = ( ( plus_plus_complex @ A @ B )
% 5.06/5.37 = zero_zero_complex ) ) ).
% 5.06/5.37
% 5.06/5.37 % eq_neg_iff_add_eq_0
% 5.06/5.37 thf(fact_5911_eq__neg__iff__add__eq__0,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( A
% 5.06/5.37 = ( uminus_uminus_rat @ B ) )
% 5.06/5.37 = ( ( plus_plus_rat @ A @ B )
% 5.06/5.37 = zero_zero_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % eq_neg_iff_add_eq_0
% 5.06/5.37 thf(fact_5912_eq__neg__iff__add__eq__0,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( A
% 5.06/5.37 = ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.37 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.06/5.37 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.37
% 5.06/5.37 % eq_neg_iff_add_eq_0
% 5.06/5.37 thf(fact_5913_neg__eq__iff__add__eq__0,axiom,
% 5.06/5.37 ! [A: real,B: real] :
% 5.06/5.37 ( ( ( uminus_uminus_real @ A )
% 5.06/5.37 = B )
% 5.06/5.37 = ( ( plus_plus_real @ A @ B )
% 5.06/5.37 = zero_zero_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_eq_iff_add_eq_0
% 5.06/5.37 thf(fact_5914_neg__eq__iff__add__eq__0,axiom,
% 5.06/5.37 ! [A: int,B: int] :
% 5.06/5.37 ( ( ( uminus_uminus_int @ A )
% 5.06/5.37 = B )
% 5.06/5.37 = ( ( plus_plus_int @ A @ B )
% 5.06/5.37 = zero_zero_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_eq_iff_add_eq_0
% 5.06/5.37 thf(fact_5915_neg__eq__iff__add__eq__0,axiom,
% 5.06/5.37 ! [A: complex,B: complex] :
% 5.06/5.37 ( ( ( uminus1482373934393186551omplex @ A )
% 5.06/5.37 = B )
% 5.06/5.37 = ( ( plus_plus_complex @ A @ B )
% 5.06/5.37 = zero_zero_complex ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_eq_iff_add_eq_0
% 5.06/5.37 thf(fact_5916_neg__eq__iff__add__eq__0,axiom,
% 5.06/5.37 ! [A: rat,B: rat] :
% 5.06/5.37 ( ( ( uminus_uminus_rat @ A )
% 5.06/5.37 = B )
% 5.06/5.37 = ( ( plus_plus_rat @ A @ B )
% 5.06/5.37 = zero_zero_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_eq_iff_add_eq_0
% 5.06/5.37 thf(fact_5917_neg__eq__iff__add__eq__0,axiom,
% 5.06/5.37 ! [A: code_integer,B: code_integer] :
% 5.06/5.37 ( ( ( uminus1351360451143612070nteger @ A )
% 5.06/5.37 = B )
% 5.06/5.37 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.06/5.37 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.37
% 5.06/5.37 % neg_eq_iff_add_eq_0
% 5.06/5.37 thf(fact_5918_zero__neq__neg__one,axiom,
% 5.06/5.37 ( zero_zero_real
% 5.06/5.37 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % zero_neq_neg_one
% 5.06/5.37 thf(fact_5919_zero__neq__neg__one,axiom,
% 5.06/5.37 ( zero_zero_int
% 5.06/5.37 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % zero_neq_neg_one
% 5.06/5.37 thf(fact_5920_zero__neq__neg__one,axiom,
% 5.06/5.37 ( zero_zero_complex
% 5.06/5.37 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.37
% 5.06/5.37 % zero_neq_neg_one
% 5.06/5.37 thf(fact_5921_zero__neq__neg__one,axiom,
% 5.06/5.37 ( zero_zero_rat
% 5.06/5.37 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % zero_neq_neg_one
% 5.06/5.37 thf(fact_5922_zero__neq__neg__one,axiom,
% 5.06/5.37 ( zero_z3403309356797280102nteger
% 5.06/5.37 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.37
% 5.06/5.37 % zero_neq_neg_one
% 5.06/5.37 thf(fact_5923_less__minus__one__simps_I4_J,axiom,
% 5.06/5.37 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_minus_one_simps(4)
% 5.06/5.37 thf(fact_5924_less__minus__one__simps_I4_J,axiom,
% 5.06/5.37 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_minus_one_simps(4)
% 5.06/5.37 thf(fact_5925_less__minus__one__simps_I4_J,axiom,
% 5.06/5.37 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_minus_one_simps(4)
% 5.06/5.37 thf(fact_5926_less__minus__one__simps_I4_J,axiom,
% 5.06/5.37 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.37
% 5.06/5.37 % less_minus_one_simps(4)
% 5.06/5.37 thf(fact_5927_less__minus__one__simps_I2_J,axiom,
% 5.06/5.37 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.06/5.37
% 5.06/5.37 % less_minus_one_simps(2)
% 5.06/5.37 thf(fact_5928_less__minus__one__simps_I2_J,axiom,
% 5.06/5.37 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.06/5.37
% 5.06/5.37 % less_minus_one_simps(2)
% 5.06/5.37 thf(fact_5929_less__minus__one__simps_I2_J,axiom,
% 5.06/5.37 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.06/5.37
% 5.06/5.37 % less_minus_one_simps(2)
% 5.06/5.37 thf(fact_5930_less__minus__one__simps_I2_J,axiom,
% 5.06/5.37 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.06/5.37
% 5.06/5.37 % less_minus_one_simps(2)
% 5.06/5.37 thf(fact_5931_numeral__times__minus__swap,axiom,
% 5.06/5.37 ! [W: num,X: real] :
% 5.06/5.37 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 5.06/5.37 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_times_minus_swap
% 5.06/5.37 thf(fact_5932_numeral__times__minus__swap,axiom,
% 5.06/5.37 ! [W: num,X: int] :
% 5.06/5.37 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 5.06/5.37 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_times_minus_swap
% 5.06/5.37 thf(fact_5933_numeral__times__minus__swap,axiom,
% 5.06/5.37 ! [W: num,X: complex] :
% 5.06/5.37 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 5.06/5.37 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_times_minus_swap
% 5.06/5.37 thf(fact_5934_numeral__times__minus__swap,axiom,
% 5.06/5.37 ! [W: num,X: rat] :
% 5.06/5.37 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 5.06/5.37 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_times_minus_swap
% 5.06/5.37 thf(fact_5935_numeral__times__minus__swap,axiom,
% 5.06/5.37 ! [W: num,X: code_integer] :
% 5.06/5.37 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 5.06/5.37 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_times_minus_swap
% 5.06/5.37 thf(fact_5936_nonzero__minus__divide__divide,axiom,
% 5.06/5.37 ! [B: real,A: real] :
% 5.06/5.37 ( ( B != zero_zero_real )
% 5.06/5.37 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.06/5.37 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % nonzero_minus_divide_divide
% 5.06/5.37 thf(fact_5937_nonzero__minus__divide__divide,axiom,
% 5.06/5.37 ! [B: complex,A: complex] :
% 5.06/5.37 ( ( B != zero_zero_complex )
% 5.06/5.37 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.06/5.37 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % nonzero_minus_divide_divide
% 5.06/5.37 thf(fact_5938_nonzero__minus__divide__divide,axiom,
% 5.06/5.37 ! [B: rat,A: rat] :
% 5.06/5.37 ( ( B != zero_zero_rat )
% 5.06/5.37 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.06/5.37 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % nonzero_minus_divide_divide
% 5.06/5.37 thf(fact_5939_nonzero__minus__divide__right,axiom,
% 5.06/5.37 ! [B: real,A: real] :
% 5.06/5.37 ( ( B != zero_zero_real )
% 5.06/5.37 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.37 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % nonzero_minus_divide_right
% 5.06/5.37 thf(fact_5940_nonzero__minus__divide__right,axiom,
% 5.06/5.37 ! [B: complex,A: complex] :
% 5.06/5.37 ( ( B != zero_zero_complex )
% 5.06/5.37 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.06/5.37 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % nonzero_minus_divide_right
% 5.06/5.37 thf(fact_5941_nonzero__minus__divide__right,axiom,
% 5.06/5.37 ! [B: rat,A: rat] :
% 5.06/5.37 ( ( B != zero_zero_rat )
% 5.06/5.37 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.06/5.37 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % nonzero_minus_divide_right
% 5.06/5.37 thf(fact_5942_numeral__neq__neg__one,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( numeral_numeral_real @ N2 )
% 5.06/5.37 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_neq_neg_one
% 5.06/5.37 thf(fact_5943_numeral__neq__neg__one,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( numeral_numeral_int @ N2 )
% 5.06/5.37 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_neq_neg_one
% 5.06/5.37 thf(fact_5944_numeral__neq__neg__one,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( numera6690914467698888265omplex @ N2 )
% 5.06/5.37 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_neq_neg_one
% 5.06/5.37 thf(fact_5945_numeral__neq__neg__one,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( numeral_numeral_rat @ N2 )
% 5.06/5.37 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_neq_neg_one
% 5.06/5.37 thf(fact_5946_numeral__neq__neg__one,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( ( numera6620942414471956472nteger @ N2 )
% 5.06/5.37 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.37
% 5.06/5.37 % numeral_neq_neg_one
% 5.06/5.37 thf(fact_5947_one__neq__neg__numeral,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( one_one_real
% 5.06/5.37 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % one_neq_neg_numeral
% 5.06/5.37 thf(fact_5948_one__neq__neg__numeral,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( one_one_int
% 5.06/5.37 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % one_neq_neg_numeral
% 5.06/5.37 thf(fact_5949_one__neq__neg__numeral,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( one_one_complex
% 5.06/5.37 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % one_neq_neg_numeral
% 5.06/5.37 thf(fact_5950_one__neq__neg__numeral,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( one_one_rat
% 5.06/5.37 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % one_neq_neg_numeral
% 5.06/5.37 thf(fact_5951_one__neq__neg__numeral,axiom,
% 5.06/5.37 ! [N2: num] :
% 5.06/5.37 ( one_one_Code_integer
% 5.06/5.37 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % one_neq_neg_numeral
% 5.06/5.37 thf(fact_5952_square__eq__1__iff,axiom,
% 5.06/5.37 ! [X: real] :
% 5.06/5.37 ( ( ( times_times_real @ X @ X )
% 5.06/5.37 = one_one_real )
% 5.06/5.37 = ( ( X = one_one_real )
% 5.06/5.37 | ( X
% 5.06/5.37 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.06/5.37
% 5.06/5.37 % square_eq_1_iff
% 5.06/5.37 thf(fact_5953_square__eq__1__iff,axiom,
% 5.06/5.37 ! [X: int] :
% 5.06/5.37 ( ( ( times_times_int @ X @ X )
% 5.06/5.37 = one_one_int )
% 5.06/5.37 = ( ( X = one_one_int )
% 5.06/5.38 | ( X
% 5.06/5.38 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % square_eq_1_iff
% 5.06/5.38 thf(fact_5954_square__eq__1__iff,axiom,
% 5.06/5.38 ! [X: complex] :
% 5.06/5.38 ( ( ( times_times_complex @ X @ X )
% 5.06/5.38 = one_one_complex )
% 5.06/5.38 = ( ( X = one_one_complex )
% 5.06/5.38 | ( X
% 5.06/5.38 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % square_eq_1_iff
% 5.06/5.38 thf(fact_5955_square__eq__1__iff,axiom,
% 5.06/5.38 ! [X: rat] :
% 5.06/5.38 ( ( ( times_times_rat @ X @ X )
% 5.06/5.38 = one_one_rat )
% 5.06/5.38 = ( ( X = one_one_rat )
% 5.06/5.38 | ( X
% 5.06/5.38 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % square_eq_1_iff
% 5.06/5.38 thf(fact_5956_square__eq__1__iff,axiom,
% 5.06/5.38 ! [X: code_integer] :
% 5.06/5.38 ( ( ( times_3573771949741848930nteger @ X @ X )
% 5.06/5.38 = one_one_Code_integer )
% 5.06/5.38 = ( ( X = one_one_Code_integer )
% 5.06/5.38 | ( X
% 5.06/5.38 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % square_eq_1_iff
% 5.06/5.38 thf(fact_5957_group__cancel_Osub2,axiom,
% 5.06/5.38 ! [B3: real,K: real,B: real,A: real] :
% 5.06/5.38 ( ( B3
% 5.06/5.38 = ( plus_plus_real @ K @ B ) )
% 5.06/5.38 => ( ( minus_minus_real @ A @ B3 )
% 5.06/5.38 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % group_cancel.sub2
% 5.06/5.38 thf(fact_5958_group__cancel_Osub2,axiom,
% 5.06/5.38 ! [B3: int,K: int,B: int,A: int] :
% 5.06/5.38 ( ( B3
% 5.06/5.38 = ( plus_plus_int @ K @ B ) )
% 5.06/5.38 => ( ( minus_minus_int @ A @ B3 )
% 5.06/5.38 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % group_cancel.sub2
% 5.06/5.38 thf(fact_5959_group__cancel_Osub2,axiom,
% 5.06/5.38 ! [B3: complex,K: complex,B: complex,A: complex] :
% 5.06/5.38 ( ( B3
% 5.06/5.38 = ( plus_plus_complex @ K @ B ) )
% 5.06/5.38 => ( ( minus_minus_complex @ A @ B3 )
% 5.06/5.38 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % group_cancel.sub2
% 5.06/5.38 thf(fact_5960_group__cancel_Osub2,axiom,
% 5.06/5.38 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.06/5.38 ( ( B3
% 5.06/5.38 = ( plus_plus_rat @ K @ B ) )
% 5.06/5.38 => ( ( minus_minus_rat @ A @ B3 )
% 5.06/5.38 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % group_cancel.sub2
% 5.06/5.38 thf(fact_5961_group__cancel_Osub2,axiom,
% 5.06/5.38 ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.06/5.38 ( ( B3
% 5.06/5.38 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.06/5.38 => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 5.06/5.38 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % group_cancel.sub2
% 5.06/5.38 thf(fact_5962_diff__conv__add__uminus,axiom,
% 5.06/5.38 ( minus_minus_real
% 5.06/5.38 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % diff_conv_add_uminus
% 5.06/5.38 thf(fact_5963_diff__conv__add__uminus,axiom,
% 5.06/5.38 ( minus_minus_int
% 5.06/5.38 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % diff_conv_add_uminus
% 5.06/5.38 thf(fact_5964_diff__conv__add__uminus,axiom,
% 5.06/5.38 ( minus_minus_complex
% 5.06/5.38 = ( ^ [A4: complex,B4: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % diff_conv_add_uminus
% 5.06/5.38 thf(fact_5965_diff__conv__add__uminus,axiom,
% 5.06/5.38 ( minus_minus_rat
% 5.06/5.38 = ( ^ [A4: rat,B4: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % diff_conv_add_uminus
% 5.06/5.38 thf(fact_5966_diff__conv__add__uminus,axiom,
% 5.06/5.38 ( minus_8373710615458151222nteger
% 5.06/5.38 = ( ^ [A4: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % diff_conv_add_uminus
% 5.06/5.38 thf(fact_5967_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.06/5.38 ( minus_minus_real
% 5.06/5.38 = ( ^ [A4: real,B4: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.06/5.38 thf(fact_5968_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.06/5.38 ( minus_minus_int
% 5.06/5.38 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.06/5.38 thf(fact_5969_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.06/5.38 ( minus_minus_complex
% 5.06/5.38 = ( ^ [A4: complex,B4: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.06/5.38 thf(fact_5970_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.06/5.38 ( minus_minus_rat
% 5.06/5.38 = ( ^ [A4: rat,B4: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.06/5.38 thf(fact_5971_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.06/5.38 ( minus_8373710615458151222nteger
% 5.06/5.38 = ( ^ [A4: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.06/5.38 thf(fact_5972_dvd__neg__div,axiom,
% 5.06/5.38 ! [B: real,A: real] :
% 5.06/5.38 ( ( dvd_dvd_real @ B @ A )
% 5.06/5.38 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.06/5.38 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % dvd_neg_div
% 5.06/5.38 thf(fact_5973_dvd__neg__div,axiom,
% 5.06/5.38 ! [B: int,A: int] :
% 5.06/5.38 ( ( dvd_dvd_int @ B @ A )
% 5.06/5.38 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.38 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % dvd_neg_div
% 5.06/5.38 thf(fact_5974_dvd__neg__div,axiom,
% 5.06/5.38 ! [B: complex,A: complex] :
% 5.06/5.38 ( ( dvd_dvd_complex @ B @ A )
% 5.06/5.38 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % dvd_neg_div
% 5.06/5.38 thf(fact_5975_dvd__neg__div,axiom,
% 5.06/5.38 ! [B: rat,A: rat] :
% 5.06/5.38 ( ( dvd_dvd_rat @ B @ A )
% 5.06/5.38 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.06/5.38 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % dvd_neg_div
% 5.06/5.38 thf(fact_5976_dvd__neg__div,axiom,
% 5.06/5.38 ! [B: code_integer,A: code_integer] :
% 5.06/5.38 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.06/5.38 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.06/5.38 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % dvd_neg_div
% 5.06/5.38 thf(fact_5977_dvd__div__neg,axiom,
% 5.06/5.38 ! [B: real,A: real] :
% 5.06/5.38 ( ( dvd_dvd_real @ B @ A )
% 5.06/5.38 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.06/5.38 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % dvd_div_neg
% 5.06/5.38 thf(fact_5978_dvd__div__neg,axiom,
% 5.06/5.38 ! [B: int,A: int] :
% 5.06/5.38 ( ( dvd_dvd_int @ B @ A )
% 5.06/5.38 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.38 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % dvd_div_neg
% 5.06/5.38 thf(fact_5979_dvd__div__neg,axiom,
% 5.06/5.38 ! [B: complex,A: complex] :
% 5.06/5.38 ( ( dvd_dvd_complex @ B @ A )
% 5.06/5.38 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % dvd_div_neg
% 5.06/5.38 thf(fact_5980_dvd__div__neg,axiom,
% 5.06/5.38 ! [B: rat,A: rat] :
% 5.06/5.38 ( ( dvd_dvd_rat @ B @ A )
% 5.06/5.38 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.06/5.38 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % dvd_div_neg
% 5.06/5.38 thf(fact_5981_dvd__div__neg,axiom,
% 5.06/5.38 ! [B: code_integer,A: code_integer] :
% 5.06/5.38 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.06/5.38 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.06/5.38 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % dvd_div_neg
% 5.06/5.38 thf(fact_5982_subset__Compl__self__eq,axiom,
% 5.06/5.38 ! [A2: set_nat] :
% 5.06/5.38 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.06/5.38 = ( A2 = bot_bot_set_nat ) ) ).
% 5.06/5.38
% 5.06/5.38 % subset_Compl_self_eq
% 5.06/5.38 thf(fact_5983_subset__Compl__self__eq,axiom,
% 5.06/5.38 ! [A2: set_real] :
% 5.06/5.38 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 5.06/5.38 = ( A2 = bot_bot_set_real ) ) ).
% 5.06/5.38
% 5.06/5.38 % subset_Compl_self_eq
% 5.06/5.38 thf(fact_5984_subset__Compl__self__eq,axiom,
% 5.06/5.38 ! [A2: set_int] :
% 5.06/5.38 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.06/5.38 = ( A2 = bot_bot_set_int ) ) ).
% 5.06/5.38
% 5.06/5.38 % subset_Compl_self_eq
% 5.06/5.38 thf(fact_5985_real__minus__mult__self__le,axiom,
% 5.06/5.38 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 5.06/5.38
% 5.06/5.38 % real_minus_mult_self_le
% 5.06/5.38 thf(fact_5986_zmult__eq__1__iff,axiom,
% 5.06/5.38 ! [M: int,N2: int] :
% 5.06/5.38 ( ( ( times_times_int @ M @ N2 )
% 5.06/5.38 = one_one_int )
% 5.06/5.38 = ( ( ( M = one_one_int )
% 5.06/5.38 & ( N2 = one_one_int ) )
% 5.06/5.38 | ( ( M
% 5.06/5.38 = ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.38 & ( N2
% 5.06/5.38 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % zmult_eq_1_iff
% 5.06/5.38 thf(fact_5987_pos__zmult__eq__1__iff__lemma,axiom,
% 5.06/5.38 ! [M: int,N2: int] :
% 5.06/5.38 ( ( ( times_times_int @ M @ N2 )
% 5.06/5.38 = one_one_int )
% 5.06/5.38 => ( ( M = one_one_int )
% 5.06/5.38 | ( M
% 5.06/5.38 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % pos_zmult_eq_1_iff_lemma
% 5.06/5.38 thf(fact_5988_minus__int__code_I2_J,axiom,
% 5.06/5.38 ! [L2: int] :
% 5.06/5.38 ( ( minus_minus_int @ zero_zero_int @ L2 )
% 5.06/5.38 = ( uminus_uminus_int @ L2 ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_int_code(2)
% 5.06/5.38 thf(fact_5989_sum_Ointer__filter,axiom,
% 5.06/5.38 ! [A2: set_real,G: real > complex,P: real > $o] :
% 5.06/5.38 ( ( finite_finite_real @ A2 )
% 5.06/5.38 => ( ( groups5754745047067104278omplex @ G
% 5.06/5.38 @ ( collect_real
% 5.06/5.38 @ ^ [X2: real] :
% 5.06/5.38 ( ( member_real @ X2 @ A2 )
% 5.06/5.38 & ( P @ X2 ) ) ) )
% 5.06/5.38 = ( groups5754745047067104278omplex
% 5.06/5.38 @ ^ [X2: real] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 5.06/5.38 @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.inter_filter
% 5.06/5.38 thf(fact_5990_sum_Ointer__filter,axiom,
% 5.06/5.38 ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ( groups2073611262835488442omplex @ G
% 5.06/5.38 @ ( collect_nat
% 5.06/5.38 @ ^ [X2: nat] :
% 5.06/5.38 ( ( member_nat @ X2 @ A2 )
% 5.06/5.38 & ( P @ X2 ) ) ) )
% 5.06/5.38 = ( groups2073611262835488442omplex
% 5.06/5.38 @ ^ [X2: nat] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 5.06/5.38 @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.inter_filter
% 5.06/5.38 thf(fact_5991_sum_Ointer__filter,axiom,
% 5.06/5.38 ! [A2: set_int,G: int > complex,P: int > $o] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups3049146728041665814omplex @ G
% 5.06/5.38 @ ( collect_int
% 5.06/5.38 @ ^ [X2: int] :
% 5.06/5.38 ( ( member_int @ X2 @ A2 )
% 5.06/5.38 & ( P @ X2 ) ) ) )
% 5.06/5.38 = ( groups3049146728041665814omplex
% 5.06/5.38 @ ^ [X2: int] : ( if_complex @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_complex )
% 5.06/5.38 @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.inter_filter
% 5.06/5.38 thf(fact_5992_sum_Ointer__filter,axiom,
% 5.06/5.38 ! [A2: set_real,G: real > real,P: real > $o] :
% 5.06/5.38 ( ( finite_finite_real @ A2 )
% 5.06/5.38 => ( ( groups8097168146408367636l_real @ G
% 5.06/5.38 @ ( collect_real
% 5.06/5.38 @ ^ [X2: real] :
% 5.06/5.38 ( ( member_real @ X2 @ A2 )
% 5.06/5.38 & ( P @ X2 ) ) ) )
% 5.06/5.38 = ( groups8097168146408367636l_real
% 5.06/5.38 @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 5.06/5.38 @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.inter_filter
% 5.06/5.38 thf(fact_5993_sum_Ointer__filter,axiom,
% 5.06/5.38 ! [A2: set_int,G: int > real,P: int > $o] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups8778361861064173332t_real @ G
% 5.06/5.38 @ ( collect_int
% 5.06/5.38 @ ^ [X2: int] :
% 5.06/5.38 ( ( member_int @ X2 @ A2 )
% 5.06/5.38 & ( P @ X2 ) ) ) )
% 5.06/5.38 = ( groups8778361861064173332t_real
% 5.06/5.38 @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 5.06/5.38 @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.inter_filter
% 5.06/5.38 thf(fact_5994_sum_Ointer__filter,axiom,
% 5.06/5.38 ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( groups5808333547571424918x_real @ G
% 5.06/5.38 @ ( collect_complex
% 5.06/5.38 @ ^ [X2: complex] :
% 5.06/5.38 ( ( member_complex @ X2 @ A2 )
% 5.06/5.38 & ( P @ X2 ) ) ) )
% 5.06/5.38 = ( groups5808333547571424918x_real
% 5.06/5.38 @ ^ [X2: complex] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_real )
% 5.06/5.38 @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.inter_filter
% 5.06/5.38 thf(fact_5995_sum_Ointer__filter,axiom,
% 5.06/5.38 ! [A2: set_real,G: real > rat,P: real > $o] :
% 5.06/5.38 ( ( finite_finite_real @ A2 )
% 5.06/5.38 => ( ( groups1300246762558778688al_rat @ G
% 5.06/5.38 @ ( collect_real
% 5.06/5.38 @ ^ [X2: real] :
% 5.06/5.38 ( ( member_real @ X2 @ A2 )
% 5.06/5.38 & ( P @ X2 ) ) ) )
% 5.06/5.38 = ( groups1300246762558778688al_rat
% 5.06/5.38 @ ^ [X2: real] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 5.06/5.38 @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.inter_filter
% 5.06/5.38 thf(fact_5996_sum_Ointer__filter,axiom,
% 5.06/5.38 ! [A2: set_nat,G: nat > rat,P: nat > $o] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ( groups2906978787729119204at_rat @ G
% 5.06/5.38 @ ( collect_nat
% 5.06/5.38 @ ^ [X2: nat] :
% 5.06/5.38 ( ( member_nat @ X2 @ A2 )
% 5.06/5.38 & ( P @ X2 ) ) ) )
% 5.06/5.38 = ( groups2906978787729119204at_rat
% 5.06/5.38 @ ^ [X2: nat] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 5.06/5.38 @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.inter_filter
% 5.06/5.38 thf(fact_5997_sum_Ointer__filter,axiom,
% 5.06/5.38 ! [A2: set_int,G: int > rat,P: int > $o] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups3906332499630173760nt_rat @ G
% 5.06/5.38 @ ( collect_int
% 5.06/5.38 @ ^ [X2: int] :
% 5.06/5.38 ( ( member_int @ X2 @ A2 )
% 5.06/5.38 & ( P @ X2 ) ) ) )
% 5.06/5.38 = ( groups3906332499630173760nt_rat
% 5.06/5.38 @ ^ [X2: int] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 5.06/5.38 @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.inter_filter
% 5.06/5.38 thf(fact_5998_sum_Ointer__filter,axiom,
% 5.06/5.38 ! [A2: set_complex,G: complex > rat,P: complex > $o] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( groups5058264527183730370ex_rat @ G
% 5.06/5.38 @ ( collect_complex
% 5.06/5.38 @ ^ [X2: complex] :
% 5.06/5.38 ( ( member_complex @ X2 @ A2 )
% 5.06/5.38 & ( P @ X2 ) ) ) )
% 5.06/5.38 = ( groups5058264527183730370ex_rat
% 5.06/5.38 @ ^ [X2: complex] : ( if_rat @ ( P @ X2 ) @ ( G @ X2 ) @ zero_zero_rat )
% 5.06/5.38 @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.inter_filter
% 5.06/5.38 thf(fact_5999_minus__real__def,axiom,
% 5.06/5.38 ( minus_minus_real
% 5.06/5.38 = ( ^ [X2: real,Y2: real] : ( plus_plus_real @ X2 @ ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_real_def
% 5.06/5.38 thf(fact_6000_ln__one__minus__pos__upper__bound,axiom,
% 5.06/5.38 ! [X: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.38 => ( ( ord_less_real @ X @ one_one_real )
% 5.06/5.38 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_one_minus_pos_upper_bound
% 5.06/5.38 thf(fact_6001_sum__le__included,axiom,
% 5.06/5.38 ! [S2: set_int,T: set_int,G: int > real,I2: int > int,F: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ( finite_finite_int @ T )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ T )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ S2 )
% 5.06/5.38 => ? [Xa: int] :
% 5.06/5.38 ( ( member_int @ Xa @ T )
% 5.06/5.38 & ( ( I2 @ Xa )
% 5.06/5.38 = X3 )
% 5.06/5.38 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.06/5.38 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S2 ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_le_included
% 5.06/5.38 thf(fact_6002_sum__le__included,axiom,
% 5.06/5.38 ! [S2: set_int,T: set_complex,G: complex > real,I2: complex > int,F: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ T )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ T )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ S2 )
% 5.06/5.38 => ? [Xa: complex] :
% 5.06/5.38 ( ( member_complex @ Xa @ T )
% 5.06/5.38 & ( ( I2 @ Xa )
% 5.06/5.38 = X3 )
% 5.06/5.38 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.06/5.38 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_le_included
% 5.06/5.38 thf(fact_6003_sum__le__included,axiom,
% 5.06/5.38 ! [S2: set_complex,T: set_int,G: int > real,I2: int > complex,F: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ S2 )
% 5.06/5.38 => ( ( finite_finite_int @ T )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ T )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S2 )
% 5.06/5.38 => ? [Xa: int] :
% 5.06/5.38 ( ( member_int @ Xa @ T )
% 5.06/5.38 & ( ( I2 @ Xa )
% 5.06/5.38 = X3 )
% 5.06/5.38 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.06/5.38 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_le_included
% 5.06/5.38 thf(fact_6004_sum__le__included,axiom,
% 5.06/5.38 ! [S2: set_complex,T: set_complex,G: complex > real,I2: complex > complex,F: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ S2 )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ T )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ T )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S2 )
% 5.06/5.38 => ? [Xa: complex] :
% 5.06/5.38 ( ( member_complex @ Xa @ T )
% 5.06/5.38 & ( ( I2 @ Xa )
% 5.06/5.38 = X3 )
% 5.06/5.38 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.06/5.38 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S2 ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_le_included
% 5.06/5.38 thf(fact_6005_sum__le__included,axiom,
% 5.06/5.38 ! [S2: set_nat,T: set_nat,G: nat > rat,I2: nat > nat,F: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ S2 )
% 5.06/5.38 => ( ( finite_finite_nat @ T )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ T )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ S2 )
% 5.06/5.38 => ? [Xa: nat] :
% 5.06/5.38 ( ( member_nat @ Xa @ T )
% 5.06/5.38 & ( ( I2 @ Xa )
% 5.06/5.38 = X3 )
% 5.06/5.38 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.06/5.38 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_le_included
% 5.06/5.38 thf(fact_6006_sum__le__included,axiom,
% 5.06/5.38 ! [S2: set_nat,T: set_int,G: int > rat,I2: int > nat,F: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ S2 )
% 5.06/5.38 => ( ( finite_finite_int @ T )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ T )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ S2 )
% 5.06/5.38 => ? [Xa: int] :
% 5.06/5.38 ( ( member_int @ Xa @ T )
% 5.06/5.38 & ( ( I2 @ Xa )
% 5.06/5.38 = X3 )
% 5.06/5.38 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.06/5.38 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_le_included
% 5.06/5.38 thf(fact_6007_sum__le__included,axiom,
% 5.06/5.38 ! [S2: set_nat,T: set_complex,G: complex > rat,I2: complex > nat,F: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ S2 )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ T )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ T )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ S2 )
% 5.06/5.38 => ? [Xa: complex] :
% 5.06/5.38 ( ( member_complex @ Xa @ T )
% 5.06/5.38 & ( ( I2 @ Xa )
% 5.06/5.38 = X3 )
% 5.06/5.38 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.06/5.38 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_le_included
% 5.06/5.38 thf(fact_6008_sum__le__included,axiom,
% 5.06/5.38 ! [S2: set_int,T: set_nat,G: nat > rat,I2: nat > int,F: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ( finite_finite_nat @ T )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ T )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ S2 )
% 5.06/5.38 => ? [Xa: nat] :
% 5.06/5.38 ( ( member_nat @ Xa @ T )
% 5.06/5.38 & ( ( I2 @ Xa )
% 5.06/5.38 = X3 )
% 5.06/5.38 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.06/5.38 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_le_included
% 5.06/5.38 thf(fact_6009_sum__le__included,axiom,
% 5.06/5.38 ! [S2: set_int,T: set_int,G: int > rat,I2: int > int,F: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ( finite_finite_int @ T )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ T )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ S2 )
% 5.06/5.38 => ? [Xa: int] :
% 5.06/5.38 ( ( member_int @ Xa @ T )
% 5.06/5.38 & ( ( I2 @ Xa )
% 5.06/5.38 = X3 )
% 5.06/5.38 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.06/5.38 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_le_included
% 5.06/5.38 thf(fact_6010_sum__le__included,axiom,
% 5.06/5.38 ! [S2: set_int,T: set_complex,G: complex > rat,I2: complex > int,F: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ T )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ T )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ S2 )
% 5.06/5.38 => ? [Xa: complex] :
% 5.06/5.38 ( ( member_complex @ Xa @ T )
% 5.06/5.38 & ( ( I2 @ Xa )
% 5.06/5.38 = X3 )
% 5.06/5.38 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 5.06/5.38 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_le_included
% 5.06/5.38 thf(fact_6011_sum__nonneg__eq__0__iff,axiom,
% 5.06/5.38 ! [A2: set_real,F: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ A2 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 5.06/5.38 = zero_zero_real )
% 5.06/5.38 = ( ! [X2: real] :
% 5.06/5.38 ( ( member_real @ X2 @ A2 )
% 5.06/5.38 => ( ( F @ X2 )
% 5.06/5.38 = zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_eq_0_iff
% 5.06/5.38 thf(fact_6012_sum__nonneg__eq__0__iff,axiom,
% 5.06/5.38 ! [A2: set_int,F: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 5.06/5.38 = zero_zero_real )
% 5.06/5.38 = ( ! [X2: int] :
% 5.06/5.38 ( ( member_int @ X2 @ A2 )
% 5.06/5.38 => ( ( F @ X2 )
% 5.06/5.38 = zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_eq_0_iff
% 5.06/5.38 thf(fact_6013_sum__nonneg__eq__0__iff,axiom,
% 5.06/5.38 ! [A2: set_complex,F: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 5.06/5.38 = zero_zero_real )
% 5.06/5.38 = ( ! [X2: complex] :
% 5.06/5.38 ( ( member_complex @ X2 @ A2 )
% 5.06/5.38 => ( ( F @ X2 )
% 5.06/5.38 = zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_eq_0_iff
% 5.06/5.38 thf(fact_6014_sum__nonneg__eq__0__iff,axiom,
% 5.06/5.38 ! [A2: set_real,F: real > rat] :
% 5.06/5.38 ( ( finite_finite_real @ A2 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 5.06/5.38 = zero_zero_rat )
% 5.06/5.38 = ( ! [X2: real] :
% 5.06/5.38 ( ( member_real @ X2 @ A2 )
% 5.06/5.38 => ( ( F @ X2 )
% 5.06/5.38 = zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_eq_0_iff
% 5.06/5.38 thf(fact_6015_sum__nonneg__eq__0__iff,axiom,
% 5.06/5.38 ! [A2: set_nat,F: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 5.06/5.38 = zero_zero_rat )
% 5.06/5.38 = ( ! [X2: nat] :
% 5.06/5.38 ( ( member_nat @ X2 @ A2 )
% 5.06/5.38 => ( ( F @ X2 )
% 5.06/5.38 = zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_eq_0_iff
% 5.06/5.38 thf(fact_6016_sum__nonneg__eq__0__iff,axiom,
% 5.06/5.38 ! [A2: set_int,F: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 5.06/5.38 = zero_zero_rat )
% 5.06/5.38 = ( ! [X2: int] :
% 5.06/5.38 ( ( member_int @ X2 @ A2 )
% 5.06/5.38 => ( ( F @ X2 )
% 5.06/5.38 = zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_eq_0_iff
% 5.06/5.38 thf(fact_6017_sum__nonneg__eq__0__iff,axiom,
% 5.06/5.38 ! [A2: set_complex,F: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 5.06/5.38 = zero_zero_rat )
% 5.06/5.38 = ( ! [X2: complex] :
% 5.06/5.38 ( ( member_complex @ X2 @ A2 )
% 5.06/5.38 => ( ( F @ X2 )
% 5.06/5.38 = zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_eq_0_iff
% 5.06/5.38 thf(fact_6018_sum__nonneg__eq__0__iff,axiom,
% 5.06/5.38 ! [A2: set_real,F: real > nat] :
% 5.06/5.38 ( ( finite_finite_real @ A2 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 5.06/5.38 = zero_zero_nat )
% 5.06/5.38 = ( ! [X2: real] :
% 5.06/5.38 ( ( member_real @ X2 @ A2 )
% 5.06/5.38 => ( ( F @ X2 )
% 5.06/5.38 = zero_zero_nat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_eq_0_iff
% 5.06/5.38 thf(fact_6019_sum__nonneg__eq__0__iff,axiom,
% 5.06/5.38 ! [A2: set_int,F: int > nat] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.06/5.38 = zero_zero_nat )
% 5.06/5.38 = ( ! [X2: int] :
% 5.06/5.38 ( ( member_int @ X2 @ A2 )
% 5.06/5.38 => ( ( F @ X2 )
% 5.06/5.38 = zero_zero_nat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_eq_0_iff
% 5.06/5.38 thf(fact_6020_sum__nonneg__eq__0__iff,axiom,
% 5.06/5.38 ! [A2: set_complex,F: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.06/5.38 = zero_zero_nat )
% 5.06/5.38 = ( ! [X2: complex] :
% 5.06/5.38 ( ( member_complex @ X2 @ A2 )
% 5.06/5.38 => ( ( F @ X2 )
% 5.06/5.38 = zero_zero_nat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_eq_0_iff
% 5.06/5.38 thf(fact_6021_sum__strict__mono__ex1,axiom,
% 5.06/5.38 ! [A2: set_int,F: int > real,G: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ? [X5: int] :
% 5.06/5.38 ( ( member_int @ X5 @ A2 )
% 5.06/5.38 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.06/5.38 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono_ex1
% 5.06/5.38 thf(fact_6022_sum__strict__mono__ex1,axiom,
% 5.06/5.38 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ? [X5: complex] :
% 5.06/5.38 ( ( member_complex @ X5 @ A2 )
% 5.06/5.38 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.06/5.38 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono_ex1
% 5.06/5.38 thf(fact_6023_sum__strict__mono__ex1,axiom,
% 5.06/5.38 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ? [X5: nat] :
% 5.06/5.38 ( ( member_nat @ X5 @ A2 )
% 5.06/5.38 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.06/5.38 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono_ex1
% 5.06/5.38 thf(fact_6024_sum__strict__mono__ex1,axiom,
% 5.06/5.38 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ? [X5: int] :
% 5.06/5.38 ( ( member_int @ X5 @ A2 )
% 5.06/5.38 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.06/5.38 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono_ex1
% 5.06/5.38 thf(fact_6025_sum__strict__mono__ex1,axiom,
% 5.06/5.38 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ? [X5: complex] :
% 5.06/5.38 ( ( member_complex @ X5 @ A2 )
% 5.06/5.38 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.06/5.38 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono_ex1
% 5.06/5.38 thf(fact_6026_sum__strict__mono__ex1,axiom,
% 5.06/5.38 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ? [X5: int] :
% 5.06/5.38 ( ( member_int @ X5 @ A2 )
% 5.06/5.38 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.06/5.38 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono_ex1
% 5.06/5.38 thf(fact_6027_sum__strict__mono__ex1,axiom,
% 5.06/5.38 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ? [X5: complex] :
% 5.06/5.38 ( ( member_complex @ X5 @ A2 )
% 5.06/5.38 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.06/5.38 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono_ex1
% 5.06/5.38 thf(fact_6028_sum__strict__mono__ex1,axiom,
% 5.06/5.38 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ? [X5: nat] :
% 5.06/5.38 ( ( member_nat @ X5 @ A2 )
% 5.06/5.38 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.06/5.38 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono_ex1
% 5.06/5.38 thf(fact_6029_sum__strict__mono__ex1,axiom,
% 5.06/5.38 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ? [X5: complex] :
% 5.06/5.38 ( ( member_complex @ X5 @ A2 )
% 5.06/5.38 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.06/5.38 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono_ex1
% 5.06/5.38 thf(fact_6030_sum__strict__mono__ex1,axiom,
% 5.06/5.38 ! [A2: set_int,F: int > int,G: int > int] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ? [X5: int] :
% 5.06/5.38 ( ( member_int @ X5 @ A2 )
% 5.06/5.38 & ( ord_less_int @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 5.06/5.38 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono_ex1
% 5.06/5.38 thf(fact_6031_sum_Orelated,axiom,
% 5.06/5.38 ! [R: complex > complex > $o,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.06/5.38 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.06/5.38 => ( ! [X16: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.06/5.38 ( ( ( R @ X16 @ X23 )
% 5.06/5.38 & ( R @ Y15 @ Y23 ) )
% 5.06/5.38 => ( R @ ( plus_plus_complex @ X16 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.06/5.38 => ( ( finite_finite_nat @ S3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ S3 )
% 5.06/5.38 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( R @ ( groups2073611262835488442omplex @ H2 @ S3 ) @ ( groups2073611262835488442omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.related
% 5.06/5.38 thf(fact_6032_sum_Orelated,axiom,
% 5.06/5.38 ! [R: complex > complex > $o,S3: set_int,H2: int > complex,G: int > complex] :
% 5.06/5.38 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.06/5.38 => ( ! [X16: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.06/5.38 ( ( ( R @ X16 @ X23 )
% 5.06/5.38 & ( R @ Y15 @ Y23 ) )
% 5.06/5.38 => ( R @ ( plus_plus_complex @ X16 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.06/5.38 => ( ( finite_finite_int @ S3 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ S3 )
% 5.06/5.38 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( R @ ( groups3049146728041665814omplex @ H2 @ S3 ) @ ( groups3049146728041665814omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.related
% 5.06/5.38 thf(fact_6033_sum_Orelated,axiom,
% 5.06/5.38 ! [R: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 5.06/5.38 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.06/5.38 => ( ! [X16: real,Y15: real,X23: real,Y23: real] :
% 5.06/5.38 ( ( ( R @ X16 @ X23 )
% 5.06/5.38 & ( R @ Y15 @ Y23 ) )
% 5.06/5.38 => ( R @ ( plus_plus_real @ X16 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.06/5.38 => ( ( finite_finite_int @ S3 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ S3 )
% 5.06/5.38 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( R @ ( groups8778361861064173332t_real @ H2 @ S3 ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.related
% 5.06/5.38 thf(fact_6034_sum_Orelated,axiom,
% 5.06/5.38 ! [R: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.06/5.38 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.06/5.38 => ( ! [X16: real,Y15: real,X23: real,Y23: real] :
% 5.06/5.38 ( ( ( R @ X16 @ X23 )
% 5.06/5.38 & ( R @ Y15 @ Y23 ) )
% 5.06/5.38 => ( R @ ( plus_plus_real @ X16 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ S3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( R @ ( groups5808333547571424918x_real @ H2 @ S3 ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.related
% 5.06/5.38 thf(fact_6035_sum_Orelated,axiom,
% 5.06/5.38 ! [R: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.06/5.38 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.06/5.38 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.06/5.38 ( ( ( R @ X16 @ X23 )
% 5.06/5.38 & ( R @ Y15 @ Y23 ) )
% 5.06/5.38 => ( R @ ( plus_plus_rat @ X16 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.06/5.38 => ( ( finite_finite_nat @ S3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ S3 )
% 5.06/5.38 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( R @ ( groups2906978787729119204at_rat @ H2 @ S3 ) @ ( groups2906978787729119204at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.related
% 5.06/5.38 thf(fact_6036_sum_Orelated,axiom,
% 5.06/5.38 ! [R: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 5.06/5.38 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.06/5.38 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.06/5.38 ( ( ( R @ X16 @ X23 )
% 5.06/5.38 & ( R @ Y15 @ Y23 ) )
% 5.06/5.38 => ( R @ ( plus_plus_rat @ X16 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.06/5.38 => ( ( finite_finite_int @ S3 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ S3 )
% 5.06/5.38 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( R @ ( groups3906332499630173760nt_rat @ H2 @ S3 ) @ ( groups3906332499630173760nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.related
% 5.06/5.38 thf(fact_6037_sum_Orelated,axiom,
% 5.06/5.38 ! [R: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.06/5.38 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.06/5.38 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.06/5.38 ( ( ( R @ X16 @ X23 )
% 5.06/5.38 & ( R @ Y15 @ Y23 ) )
% 5.06/5.38 => ( R @ ( plus_plus_rat @ X16 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ S3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( R @ ( groups5058264527183730370ex_rat @ H2 @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.related
% 5.06/5.38 thf(fact_6038_sum_Orelated,axiom,
% 5.06/5.38 ! [R: nat > nat > $o,S3: set_int,H2: int > nat,G: int > nat] :
% 5.06/5.38 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.06/5.38 => ( ! [X16: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.06/5.38 ( ( ( R @ X16 @ X23 )
% 5.06/5.38 & ( R @ Y15 @ Y23 ) )
% 5.06/5.38 => ( R @ ( plus_plus_nat @ X16 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.06/5.38 => ( ( finite_finite_int @ S3 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ S3 )
% 5.06/5.38 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( R @ ( groups4541462559716669496nt_nat @ H2 @ S3 ) @ ( groups4541462559716669496nt_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.related
% 5.06/5.38 thf(fact_6039_sum_Orelated,axiom,
% 5.06/5.38 ! [R: nat > nat > $o,S3: set_complex,H2: complex > nat,G: complex > nat] :
% 5.06/5.38 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.06/5.38 => ( ! [X16: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.06/5.38 ( ( ( R @ X16 @ X23 )
% 5.06/5.38 & ( R @ Y15 @ Y23 ) )
% 5.06/5.38 => ( R @ ( plus_plus_nat @ X16 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ S3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( R @ ( groups5693394587270226106ex_nat @ H2 @ S3 ) @ ( groups5693394587270226106ex_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.related
% 5.06/5.38 thf(fact_6040_sum_Orelated,axiom,
% 5.06/5.38 ! [R: int > int > $o,S3: set_nat,H2: nat > int,G: nat > int] :
% 5.06/5.38 ( ( R @ zero_zero_int @ zero_zero_int )
% 5.06/5.38 => ( ! [X16: int,Y15: int,X23: int,Y23: int] :
% 5.06/5.38 ( ( ( R @ X16 @ X23 )
% 5.06/5.38 & ( R @ Y15 @ Y23 ) )
% 5.06/5.38 => ( R @ ( plus_plus_int @ X16 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 5.06/5.38 => ( ( finite_finite_nat @ S3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ S3 )
% 5.06/5.38 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( R @ ( groups3539618377306564664at_int @ H2 @ S3 ) @ ( groups3539618377306564664at_int @ G @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.related
% 5.06/5.38 thf(fact_6041_sum__strict__mono,axiom,
% 5.06/5.38 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( A2 != bot_bot_set_complex )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono
% 5.06/5.38 thf(fact_6042_sum__strict__mono,axiom,
% 5.06/5.38 ! [A2: set_int,F: int > real,G: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( A2 != bot_bot_set_int )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono
% 5.06/5.38 thf(fact_6043_sum__strict__mono,axiom,
% 5.06/5.38 ! [A2: set_real,F: real > real,G: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ A2 )
% 5.06/5.38 => ( ( A2 != bot_bot_set_real )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono
% 5.06/5.38 thf(fact_6044_sum__strict__mono,axiom,
% 5.06/5.38 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( A2 != bot_bot_set_complex )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono
% 5.06/5.38 thf(fact_6045_sum__strict__mono,axiom,
% 5.06/5.38 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ( A2 != bot_bot_set_nat )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono
% 5.06/5.38 thf(fact_6046_sum__strict__mono,axiom,
% 5.06/5.38 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( A2 != bot_bot_set_int )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono
% 5.06/5.38 thf(fact_6047_sum__strict__mono,axiom,
% 5.06/5.38 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.06/5.38 ( ( finite_finite_real @ A2 )
% 5.06/5.38 => ( ( A2 != bot_bot_set_real )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono
% 5.06/5.38 thf(fact_6048_sum__strict__mono,axiom,
% 5.06/5.38 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( A2 != bot_bot_set_complex )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono
% 5.06/5.38 thf(fact_6049_sum__strict__mono,axiom,
% 5.06/5.38 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( A2 != bot_bot_set_int )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono
% 5.06/5.38 thf(fact_6050_sum__strict__mono,axiom,
% 5.06/5.38 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.06/5.38 ( ( finite_finite_real @ A2 )
% 5.06/5.38 => ( ( A2 != bot_bot_set_real )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ A2 )
% 5.06/5.38 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono
% 5.06/5.38 thf(fact_6051_ln__bound,axiom,
% 5.06/5.38 ! [X: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.38 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_bound
% 5.06/5.38 thf(fact_6052_ln__ge__zero,axiom,
% 5.06/5.38 ! [X: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_ge_zero
% 5.06/5.38 thf(fact_6053_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.06/5.38 ! [S4: set_real,T4: set_real,S3: set_real,I2: real > real,J: real > real,T3: set_real,G: real > complex,H2: real > complex] :
% 5.06/5.38 ( ( finite_finite_real @ S4 )
% 5.06/5.38 => ( ( finite_finite_real @ T4 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.06/5.38 => ( ( I2 @ ( J @ A3 ) )
% 5.06/5.38 = A3 ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.06/5.38 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.06/5.38 => ( ( J @ ( I2 @ B2 ) )
% 5.06/5.38 = B2 ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.06/5.38 => ( member_real @ ( I2 @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ S4 )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ T4 )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ S3 )
% 5.06/5.38 => ( ( H2 @ ( J @ A3 ) )
% 5.06/5.38 = ( G @ A3 ) ) )
% 5.06/5.38 => ( ( groups5754745047067104278omplex @ G @ S3 )
% 5.06/5.38 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.reindex_bij_witness_not_neutral
% 5.06/5.38 thf(fact_6054_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.06/5.38 ! [S4: set_real,T4: set_int,S3: set_real,I2: int > real,J: real > int,T3: set_int,G: real > complex,H2: int > complex] :
% 5.06/5.38 ( ( finite_finite_real @ S4 )
% 5.06/5.38 => ( ( finite_finite_int @ T4 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.06/5.38 => ( ( I2 @ ( J @ A3 ) )
% 5.06/5.38 = A3 ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.06/5.38 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.06/5.38 => ( ( J @ ( I2 @ B2 ) )
% 5.06/5.38 = B2 ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.06/5.38 => ( member_real @ ( I2 @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ S4 )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ T4 )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ S3 )
% 5.06/5.38 => ( ( H2 @ ( J @ A3 ) )
% 5.06/5.38 = ( G @ A3 ) ) )
% 5.06/5.38 => ( ( groups5754745047067104278omplex @ G @ S3 )
% 5.06/5.38 = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.reindex_bij_witness_not_neutral
% 5.06/5.38 thf(fact_6055_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.06/5.38 ! [S4: set_int,T4: set_real,S3: set_int,I2: real > int,J: int > real,T3: set_real,G: int > complex,H2: real > complex] :
% 5.06/5.38 ( ( finite_finite_int @ S4 )
% 5.06/5.38 => ( ( finite_finite_real @ T4 )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.06/5.38 => ( ( I2 @ ( J @ A3 ) )
% 5.06/5.38 = A3 ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.06/5.38 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.06/5.38 => ( ( J @ ( I2 @ B2 ) )
% 5.06/5.38 = B2 ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.06/5.38 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S3 @ S4 ) ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ S4 )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ T4 )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ S3 )
% 5.06/5.38 => ( ( H2 @ ( J @ A3 ) )
% 5.06/5.38 = ( G @ A3 ) ) )
% 5.06/5.38 => ( ( groups3049146728041665814omplex @ G @ S3 )
% 5.06/5.38 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.reindex_bij_witness_not_neutral
% 5.06/5.38 thf(fact_6056_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.06/5.38 ! [S4: set_int,T4: set_int,S3: set_int,I2: int > int,J: int > int,T3: set_int,G: int > complex,H2: int > complex] :
% 5.06/5.38 ( ( finite_finite_int @ S4 )
% 5.06/5.38 => ( ( finite_finite_int @ T4 )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.06/5.38 => ( ( I2 @ ( J @ A3 ) )
% 5.06/5.38 = A3 ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.06/5.38 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.06/5.38 => ( ( J @ ( I2 @ B2 ) )
% 5.06/5.38 = B2 ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.06/5.38 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S3 @ S4 ) ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ S4 )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ T4 )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ S3 )
% 5.06/5.38 => ( ( H2 @ ( J @ A3 ) )
% 5.06/5.38 = ( G @ A3 ) ) )
% 5.06/5.38 => ( ( groups3049146728041665814omplex @ G @ S3 )
% 5.06/5.38 = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.reindex_bij_witness_not_neutral
% 5.06/5.38 thf(fact_6057_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.06/5.38 ! [S4: set_real,T4: set_real,S3: set_real,I2: real > real,J: real > real,T3: set_real,G: real > real,H2: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ S4 )
% 5.06/5.38 => ( ( finite_finite_real @ T4 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.06/5.38 => ( ( I2 @ ( J @ A3 ) )
% 5.06/5.38 = A3 ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.06/5.38 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.06/5.38 => ( ( J @ ( I2 @ B2 ) )
% 5.06/5.38 = B2 ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.06/5.38 => ( member_real @ ( I2 @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ S4 )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ T4 )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ S3 )
% 5.06/5.38 => ( ( H2 @ ( J @ A3 ) )
% 5.06/5.38 = ( G @ A3 ) ) )
% 5.06/5.38 => ( ( groups8097168146408367636l_real @ G @ S3 )
% 5.06/5.38 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.reindex_bij_witness_not_neutral
% 5.06/5.38 thf(fact_6058_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.06/5.38 ! [S4: set_real,T4: set_int,S3: set_real,I2: int > real,J: real > int,T3: set_int,G: real > real,H2: int > real] :
% 5.06/5.38 ( ( finite_finite_real @ S4 )
% 5.06/5.38 => ( ( finite_finite_int @ T4 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.06/5.38 => ( ( I2 @ ( J @ A3 ) )
% 5.06/5.38 = A3 ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.06/5.38 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.06/5.38 => ( ( J @ ( I2 @ B2 ) )
% 5.06/5.38 = B2 ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.06/5.38 => ( member_real @ ( I2 @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ S4 )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ T4 )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ S3 )
% 5.06/5.38 => ( ( H2 @ ( J @ A3 ) )
% 5.06/5.38 = ( G @ A3 ) ) )
% 5.06/5.38 => ( ( groups8097168146408367636l_real @ G @ S3 )
% 5.06/5.38 = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.reindex_bij_witness_not_neutral
% 5.06/5.38 thf(fact_6059_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.06/5.38 ! [S4: set_real,T4: set_complex,S3: set_real,I2: complex > real,J: real > complex,T3: set_complex,G: real > real,H2: complex > real] :
% 5.06/5.38 ( ( finite_finite_real @ S4 )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ T4 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.06/5.38 => ( ( I2 @ ( J @ A3 ) )
% 5.06/5.38 = A3 ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 5.06/5.38 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.06/5.38 => ( ( J @ ( I2 @ B2 ) )
% 5.06/5.38 = B2 ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.06/5.38 => ( member_real @ ( I2 @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ S4 )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ T4 )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ S3 )
% 5.06/5.38 => ( ( H2 @ ( J @ A3 ) )
% 5.06/5.38 = ( G @ A3 ) ) )
% 5.06/5.38 => ( ( groups8097168146408367636l_real @ G @ S3 )
% 5.06/5.38 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.reindex_bij_witness_not_neutral
% 5.06/5.38 thf(fact_6060_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.06/5.38 ! [S4: set_int,T4: set_real,S3: set_int,I2: real > int,J: int > real,T3: set_real,G: int > real,H2: real > real] :
% 5.06/5.38 ( ( finite_finite_int @ S4 )
% 5.06/5.38 => ( ( finite_finite_real @ T4 )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.06/5.38 => ( ( I2 @ ( J @ A3 ) )
% 5.06/5.38 = A3 ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.06/5.38 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.06/5.38 => ( ( J @ ( I2 @ B2 ) )
% 5.06/5.38 = B2 ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.06/5.38 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S3 @ S4 ) ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ S4 )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ T4 )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ S3 )
% 5.06/5.38 => ( ( H2 @ ( J @ A3 ) )
% 5.06/5.38 = ( G @ A3 ) ) )
% 5.06/5.38 => ( ( groups8778361861064173332t_real @ G @ S3 )
% 5.06/5.38 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.reindex_bij_witness_not_neutral
% 5.06/5.38 thf(fact_6061_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.06/5.38 ! [S4: set_int,T4: set_int,S3: set_int,I2: int > int,J: int > int,T3: set_int,G: int > real,H2: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ S4 )
% 5.06/5.38 => ( ( finite_finite_int @ T4 )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.06/5.38 => ( ( I2 @ ( J @ A3 ) )
% 5.06/5.38 = A3 ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.06/5.38 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.06/5.38 => ( ( J @ ( I2 @ B2 ) )
% 5.06/5.38 = B2 ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.06/5.38 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S3 @ S4 ) ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ S4 )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [B2: int] :
% 5.06/5.38 ( ( member_int @ B2 @ T4 )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ S3 )
% 5.06/5.38 => ( ( H2 @ ( J @ A3 ) )
% 5.06/5.38 = ( G @ A3 ) ) )
% 5.06/5.38 => ( ( groups8778361861064173332t_real @ G @ S3 )
% 5.06/5.38 = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.reindex_bij_witness_not_neutral
% 5.06/5.38 thf(fact_6062_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.06/5.38 ! [S4: set_int,T4: set_complex,S3: set_int,I2: complex > int,J: int > complex,T3: set_complex,G: int > real,H2: complex > real] :
% 5.06/5.38 ( ( finite_finite_int @ S4 )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ T4 )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.06/5.38 => ( ( I2 @ ( J @ A3 ) )
% 5.06/5.38 = A3 ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S4 ) )
% 5.06/5.38 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.06/5.38 => ( ( J @ ( I2 @ B2 ) )
% 5.06/5.38 = B2 ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.06/5.38 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S3 @ S4 ) ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ S4 )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ T4 )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [A3: int] :
% 5.06/5.38 ( ( member_int @ A3 @ S3 )
% 5.06/5.38 => ( ( H2 @ ( J @ A3 ) )
% 5.06/5.38 = ( G @ A3 ) ) )
% 5.06/5.38 => ( ( groups8778361861064173332t_real @ G @ S3 )
% 5.06/5.38 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.reindex_bij_witness_not_neutral
% 5.06/5.38 thf(fact_6063_neg__numeral__le__zero,axiom,
% 5.06/5.38 ! [N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_zero
% 5.06/5.38 thf(fact_6064_neg__numeral__le__zero,axiom,
% 5.06/5.38 ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_zero
% 5.06/5.38 thf(fact_6065_neg__numeral__le__zero,axiom,
% 5.06/5.38 ! [N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_zero
% 5.06/5.38 thf(fact_6066_neg__numeral__le__zero,axiom,
% 5.06/5.38 ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_zero
% 5.06/5.38 thf(fact_6067_not__zero__le__neg__numeral,axiom,
% 5.06/5.38 ! [N2: num] :
% 5.06/5.38 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_zero_le_neg_numeral
% 5.06/5.38 thf(fact_6068_not__zero__le__neg__numeral,axiom,
% 5.06/5.38 ! [N2: num] :
% 5.06/5.38 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_zero_le_neg_numeral
% 5.06/5.38 thf(fact_6069_not__zero__le__neg__numeral,axiom,
% 5.06/5.38 ! [N2: num] :
% 5.06/5.38 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_zero_le_neg_numeral
% 5.06/5.38 thf(fact_6070_not__zero__le__neg__numeral,axiom,
% 5.06/5.38 ! [N2: num] :
% 5.06/5.38 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_zero_le_neg_numeral
% 5.06/5.38 thf(fact_6071_neg__numeral__less__zero,axiom,
% 5.06/5.38 ! [N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_less_zero
% 5.06/5.38 thf(fact_6072_neg__numeral__less__zero,axiom,
% 5.06/5.38 ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_less_zero
% 5.06/5.38 thf(fact_6073_neg__numeral__less__zero,axiom,
% 5.06/5.38 ! [N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_less_zero
% 5.06/5.38 thf(fact_6074_neg__numeral__less__zero,axiom,
% 5.06/5.38 ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_less_zero
% 5.06/5.38 thf(fact_6075_not__zero__less__neg__numeral,axiom,
% 5.06/5.38 ! [N2: num] :
% 5.06/5.38 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_zero_less_neg_numeral
% 5.06/5.38 thf(fact_6076_not__zero__less__neg__numeral,axiom,
% 5.06/5.38 ! [N2: num] :
% 5.06/5.38 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_zero_less_neg_numeral
% 5.06/5.38 thf(fact_6077_not__zero__less__neg__numeral,axiom,
% 5.06/5.38 ! [N2: num] :
% 5.06/5.38 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_zero_less_neg_numeral
% 5.06/5.38 thf(fact_6078_not__zero__less__neg__numeral,axiom,
% 5.06/5.38 ! [N2: num] :
% 5.06/5.38 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_zero_less_neg_numeral
% 5.06/5.38 thf(fact_6079_le__minus__one__simps_I1_J,axiom,
% 5.06/5.38 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.06/5.38
% 5.06/5.38 % le_minus_one_simps(1)
% 5.06/5.38 thf(fact_6080_le__minus__one__simps_I1_J,axiom,
% 5.06/5.38 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.06/5.38
% 5.06/5.38 % le_minus_one_simps(1)
% 5.06/5.38 thf(fact_6081_le__minus__one__simps_I1_J,axiom,
% 5.06/5.38 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.06/5.38
% 5.06/5.38 % le_minus_one_simps(1)
% 5.06/5.38 thf(fact_6082_le__minus__one__simps_I1_J,axiom,
% 5.06/5.38 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.06/5.38
% 5.06/5.38 % le_minus_one_simps(1)
% 5.06/5.38 thf(fact_6083_le__minus__one__simps_I3_J,axiom,
% 5.06/5.38 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.38
% 5.06/5.38 % le_minus_one_simps(3)
% 5.06/5.38 thf(fact_6084_le__minus__one__simps_I3_J,axiom,
% 5.06/5.38 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.38
% 5.06/5.38 % le_minus_one_simps(3)
% 5.06/5.38 thf(fact_6085_le__minus__one__simps_I3_J,axiom,
% 5.06/5.38 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.38
% 5.06/5.38 % le_minus_one_simps(3)
% 5.06/5.38 thf(fact_6086_le__minus__one__simps_I3_J,axiom,
% 5.06/5.38 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.38
% 5.06/5.38 % le_minus_one_simps(3)
% 5.06/5.38 thf(fact_6087_less__minus__one__simps_I1_J,axiom,
% 5.06/5.38 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.06/5.38
% 5.06/5.38 % less_minus_one_simps(1)
% 5.06/5.38 thf(fact_6088_less__minus__one__simps_I1_J,axiom,
% 5.06/5.38 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.06/5.38
% 5.06/5.38 % less_minus_one_simps(1)
% 5.06/5.38 thf(fact_6089_less__minus__one__simps_I1_J,axiom,
% 5.06/5.38 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.06/5.38
% 5.06/5.38 % less_minus_one_simps(1)
% 5.06/5.38 thf(fact_6090_less__minus__one__simps_I1_J,axiom,
% 5.06/5.38 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.06/5.38
% 5.06/5.38 % less_minus_one_simps(1)
% 5.06/5.38 thf(fact_6091_less__minus__one__simps_I3_J,axiom,
% 5.06/5.38 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.38
% 5.06/5.38 % less_minus_one_simps(3)
% 5.06/5.38 thf(fact_6092_less__minus__one__simps_I3_J,axiom,
% 5.06/5.38 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.38
% 5.06/5.38 % less_minus_one_simps(3)
% 5.06/5.38 thf(fact_6093_less__minus__one__simps_I3_J,axiom,
% 5.06/5.38 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.38
% 5.06/5.38 % less_minus_one_simps(3)
% 5.06/5.38 thf(fact_6094_less__minus__one__simps_I3_J,axiom,
% 5.06/5.38 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.38
% 5.06/5.38 % less_minus_one_simps(3)
% 5.06/5.38 thf(fact_6095_neg__numeral__le__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_one
% 5.06/5.38 thf(fact_6096_neg__numeral__le__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_one
% 5.06/5.38 thf(fact_6097_neg__numeral__le__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_one
% 5.06/5.38 thf(fact_6098_neg__numeral__le__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_one
% 5.06/5.38 thf(fact_6099_neg__one__le__numeral,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_le_numeral
% 5.06/5.38 thf(fact_6100_neg__one__le__numeral,axiom,
% 5.06/5.38 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_le_numeral
% 5.06/5.38 thf(fact_6101_neg__one__le__numeral,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_le_numeral
% 5.06/5.38 thf(fact_6102_neg__one__le__numeral,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_le_numeral
% 5.06/5.38 thf(fact_6103_neg__numeral__le__neg__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_neg_one
% 5.06/5.38 thf(fact_6104_neg__numeral__le__neg__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_neg_one
% 5.06/5.38 thf(fact_6105_neg__numeral__le__neg__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_neg_one
% 5.06/5.38 thf(fact_6106_neg__numeral__le__neg__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_le_neg_one
% 5.06/5.38 thf(fact_6107_not__numeral__le__neg__one,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_numeral_le_neg_one
% 5.06/5.38 thf(fact_6108_not__numeral__le__neg__one,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_numeral_le_neg_one
% 5.06/5.38 thf(fact_6109_not__numeral__le__neg__one,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_numeral_le_neg_one
% 5.06/5.38 thf(fact_6110_not__numeral__le__neg__one,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_numeral_le_neg_one
% 5.06/5.38 thf(fact_6111_not__one__le__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_one_le_neg_numeral
% 5.06/5.38 thf(fact_6112_not__one__le__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_one_le_neg_numeral
% 5.06/5.38 thf(fact_6113_not__one__le__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_one_le_neg_numeral
% 5.06/5.38 thf(fact_6114_not__one__le__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_one_le_neg_numeral
% 5.06/5.38 thf(fact_6115_neg__numeral__less__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_less_one
% 5.06/5.38 thf(fact_6116_neg__numeral__less__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_less_one
% 5.06/5.38 thf(fact_6117_neg__numeral__less__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_less_one
% 5.06/5.38 thf(fact_6118_neg__numeral__less__one,axiom,
% 5.06/5.38 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.06/5.38
% 5.06/5.38 % neg_numeral_less_one
% 5.06/5.38 thf(fact_6119_neg__one__less__numeral,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_less_numeral
% 5.06/5.38 thf(fact_6120_neg__one__less__numeral,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_less_numeral
% 5.06/5.38 thf(fact_6121_neg__one__less__numeral,axiom,
% 5.06/5.38 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_less_numeral
% 5.06/5.38 thf(fact_6122_neg__one__less__numeral,axiom,
% 5.06/5.38 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_less_numeral
% 5.06/5.38 thf(fact_6123_not__numeral__less__neg__one,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_numeral_less_neg_one
% 5.06/5.38 thf(fact_6124_not__numeral__less__neg__one,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_numeral_less_neg_one
% 5.06/5.38 thf(fact_6125_not__numeral__less__neg__one,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_numeral_less_neg_one
% 5.06/5.38 thf(fact_6126_not__numeral__less__neg__one,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_numeral_less_neg_one
% 5.06/5.38 thf(fact_6127_not__one__less__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_one_less_neg_numeral
% 5.06/5.38 thf(fact_6128_not__one__less__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_one_less_neg_numeral
% 5.06/5.38 thf(fact_6129_not__one__less__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_one_less_neg_numeral
% 5.06/5.38 thf(fact_6130_not__one__less__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_one_less_neg_numeral
% 5.06/5.38 thf(fact_6131_not__neg__one__less__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_neg_one_less_neg_numeral
% 5.06/5.38 thf(fact_6132_not__neg__one__less__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_neg_one_less_neg_numeral
% 5.06/5.38 thf(fact_6133_not__neg__one__less__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_neg_one_less_neg_numeral
% 5.06/5.38 thf(fact_6134_not__neg__one__less__neg__numeral,axiom,
% 5.06/5.38 ! [M: num] :
% 5.06/5.38 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % not_neg_one_less_neg_numeral
% 5.06/5.38 thf(fact_6135_nonzero__neg__divide__eq__eq2,axiom,
% 5.06/5.38 ! [B: real,C: real,A: real] :
% 5.06/5.38 ( ( B != zero_zero_real )
% 5.06/5.38 => ( ( C
% 5.06/5.38 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.06/5.38 = ( ( times_times_real @ C @ B )
% 5.06/5.38 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % nonzero_neg_divide_eq_eq2
% 5.06/5.38 thf(fact_6136_nonzero__neg__divide__eq__eq2,axiom,
% 5.06/5.38 ! [B: complex,C: complex,A: complex] :
% 5.06/5.38 ( ( B != zero_zero_complex )
% 5.06/5.38 => ( ( C
% 5.06/5.38 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.06/5.38 = ( ( times_times_complex @ C @ B )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % nonzero_neg_divide_eq_eq2
% 5.06/5.38 thf(fact_6137_nonzero__neg__divide__eq__eq2,axiom,
% 5.06/5.38 ! [B: rat,C: rat,A: rat] :
% 5.06/5.38 ( ( B != zero_zero_rat )
% 5.06/5.38 => ( ( C
% 5.06/5.38 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.06/5.38 = ( ( times_times_rat @ C @ B )
% 5.06/5.38 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % nonzero_neg_divide_eq_eq2
% 5.06/5.38 thf(fact_6138_nonzero__neg__divide__eq__eq,axiom,
% 5.06/5.38 ! [B: real,A: real,C: real] :
% 5.06/5.38 ( ( B != zero_zero_real )
% 5.06/5.38 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.38 = C )
% 5.06/5.38 = ( ( uminus_uminus_real @ A )
% 5.06/5.38 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % nonzero_neg_divide_eq_eq
% 5.06/5.38 thf(fact_6139_nonzero__neg__divide__eq__eq,axiom,
% 5.06/5.38 ! [B: complex,A: complex,C: complex] :
% 5.06/5.38 ( ( B != zero_zero_complex )
% 5.06/5.38 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.06/5.38 = C )
% 5.06/5.38 = ( ( uminus1482373934393186551omplex @ A )
% 5.06/5.38 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % nonzero_neg_divide_eq_eq
% 5.06/5.38 thf(fact_6140_nonzero__neg__divide__eq__eq,axiom,
% 5.06/5.38 ! [B: rat,A: rat,C: rat] :
% 5.06/5.38 ( ( B != zero_zero_rat )
% 5.06/5.38 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.06/5.38 = C )
% 5.06/5.38 = ( ( uminus_uminus_rat @ A )
% 5.06/5.38 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % nonzero_neg_divide_eq_eq
% 5.06/5.38 thf(fact_6141_minus__divide__eq__eq,axiom,
% 5.06/5.38 ! [B: real,C: real,A: real] :
% 5.06/5.38 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.06/5.38 = A )
% 5.06/5.38 = ( ( ( C != zero_zero_real )
% 5.06/5.38 => ( ( uminus_uminus_real @ B )
% 5.06/5.38 = ( times_times_real @ A @ C ) ) )
% 5.06/5.38 & ( ( C = zero_zero_real )
% 5.06/5.38 => ( A = zero_zero_real ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_eq_eq
% 5.06/5.38 thf(fact_6142_minus__divide__eq__eq,axiom,
% 5.06/5.38 ! [B: complex,C: complex,A: complex] :
% 5.06/5.38 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.06/5.38 = A )
% 5.06/5.38 = ( ( ( C != zero_zero_complex )
% 5.06/5.38 => ( ( uminus1482373934393186551omplex @ B )
% 5.06/5.38 = ( times_times_complex @ A @ C ) ) )
% 5.06/5.38 & ( ( C = zero_zero_complex )
% 5.06/5.38 => ( A = zero_zero_complex ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_eq_eq
% 5.06/5.38 thf(fact_6143_minus__divide__eq__eq,axiom,
% 5.06/5.38 ! [B: rat,C: rat,A: rat] :
% 5.06/5.38 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.38 = A )
% 5.06/5.38 = ( ( ( C != zero_zero_rat )
% 5.06/5.38 => ( ( uminus_uminus_rat @ B )
% 5.06/5.38 = ( times_times_rat @ A @ C ) ) )
% 5.06/5.38 & ( ( C = zero_zero_rat )
% 5.06/5.38 => ( A = zero_zero_rat ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_eq_eq
% 5.06/5.38 thf(fact_6144_eq__minus__divide__eq,axiom,
% 5.06/5.38 ! [A: real,B: real,C: real] :
% 5.06/5.38 ( ( A
% 5.06/5.38 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.06/5.38 = ( ( ( C != zero_zero_real )
% 5.06/5.38 => ( ( times_times_real @ A @ C )
% 5.06/5.38 = ( uminus_uminus_real @ B ) ) )
% 5.06/5.38 & ( ( C = zero_zero_real )
% 5.06/5.38 => ( A = zero_zero_real ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % eq_minus_divide_eq
% 5.06/5.38 thf(fact_6145_eq__minus__divide__eq,axiom,
% 5.06/5.38 ! [A: complex,B: complex,C: complex] :
% 5.06/5.38 ( ( A
% 5.06/5.38 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.06/5.38 = ( ( ( C != zero_zero_complex )
% 5.06/5.38 => ( ( times_times_complex @ A @ C )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.06/5.38 & ( ( C = zero_zero_complex )
% 5.06/5.38 => ( A = zero_zero_complex ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % eq_minus_divide_eq
% 5.06/5.38 thf(fact_6146_eq__minus__divide__eq,axiom,
% 5.06/5.38 ! [A: rat,B: rat,C: rat] :
% 5.06/5.38 ( ( A
% 5.06/5.38 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.06/5.38 = ( ( ( C != zero_zero_rat )
% 5.06/5.38 => ( ( times_times_rat @ A @ C )
% 5.06/5.38 = ( uminus_uminus_rat @ B ) ) )
% 5.06/5.38 & ( ( C = zero_zero_rat )
% 5.06/5.38 => ( A = zero_zero_rat ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % eq_minus_divide_eq
% 5.06/5.38 thf(fact_6147_mult__1s__ring__1_I1_J,axiom,
% 5.06/5.38 ! [B: real] :
% 5.06/5.38 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.06/5.38 = ( uminus_uminus_real @ B ) ) ).
% 5.06/5.38
% 5.06/5.38 % mult_1s_ring_1(1)
% 5.06/5.38 thf(fact_6148_mult__1s__ring__1_I1_J,axiom,
% 5.06/5.38 ! [B: int] :
% 5.06/5.38 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.06/5.38 = ( uminus_uminus_int @ B ) ) ).
% 5.06/5.38
% 5.06/5.38 % mult_1s_ring_1(1)
% 5.06/5.38 thf(fact_6149_mult__1s__ring__1_I1_J,axiom,
% 5.06/5.38 ! [B: complex] :
% 5.06/5.38 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.06/5.38
% 5.06/5.38 % mult_1s_ring_1(1)
% 5.06/5.38 thf(fact_6150_mult__1s__ring__1_I1_J,axiom,
% 5.06/5.38 ! [B: rat] :
% 5.06/5.38 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.06/5.38 = ( uminus_uminus_rat @ B ) ) ).
% 5.06/5.38
% 5.06/5.38 % mult_1s_ring_1(1)
% 5.06/5.38 thf(fact_6151_mult__1s__ring__1_I1_J,axiom,
% 5.06/5.38 ! [B: code_integer] :
% 5.06/5.38 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.06/5.38 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.06/5.38
% 5.06/5.38 % mult_1s_ring_1(1)
% 5.06/5.38 thf(fact_6152_mult__1s__ring__1_I2_J,axiom,
% 5.06/5.38 ! [B: real] :
% 5.06/5.38 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.06/5.38 = ( uminus_uminus_real @ B ) ) ).
% 5.06/5.38
% 5.06/5.38 % mult_1s_ring_1(2)
% 5.06/5.38 thf(fact_6153_mult__1s__ring__1_I2_J,axiom,
% 5.06/5.38 ! [B: int] :
% 5.06/5.38 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.06/5.38 = ( uminus_uminus_int @ B ) ) ).
% 5.06/5.38
% 5.06/5.38 % mult_1s_ring_1(2)
% 5.06/5.38 thf(fact_6154_mult__1s__ring__1_I2_J,axiom,
% 5.06/5.38 ! [B: complex] :
% 5.06/5.38 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.06/5.38
% 5.06/5.38 % mult_1s_ring_1(2)
% 5.06/5.38 thf(fact_6155_mult__1s__ring__1_I2_J,axiom,
% 5.06/5.38 ! [B: rat] :
% 5.06/5.38 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.06/5.38 = ( uminus_uminus_rat @ B ) ) ).
% 5.06/5.38
% 5.06/5.38 % mult_1s_ring_1(2)
% 5.06/5.38 thf(fact_6156_mult__1s__ring__1_I2_J,axiom,
% 5.06/5.38 ! [B: code_integer] :
% 5.06/5.38 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.06/5.38 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.06/5.38
% 5.06/5.38 % mult_1s_ring_1(2)
% 5.06/5.38 thf(fact_6157_divide__eq__minus__1__iff,axiom,
% 5.06/5.38 ! [A: real,B: real] :
% 5.06/5.38 ( ( ( divide_divide_real @ A @ B )
% 5.06/5.38 = ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.38 = ( ( B != zero_zero_real )
% 5.06/5.38 & ( A
% 5.06/5.38 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % divide_eq_minus_1_iff
% 5.06/5.38 thf(fact_6158_divide__eq__minus__1__iff,axiom,
% 5.06/5.38 ! [A: complex,B: complex] :
% 5.06/5.38 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.38 = ( ( B != zero_zero_complex )
% 5.06/5.38 & ( A
% 5.06/5.38 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % divide_eq_minus_1_iff
% 5.06/5.38 thf(fact_6159_divide__eq__minus__1__iff,axiom,
% 5.06/5.38 ! [A: rat,B: rat] :
% 5.06/5.38 ( ( ( divide_divide_rat @ A @ B )
% 5.06/5.38 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.38 = ( ( B != zero_zero_rat )
% 5.06/5.38 & ( A
% 5.06/5.38 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % divide_eq_minus_1_iff
% 5.06/5.38 thf(fact_6160_uminus__numeral__One,axiom,
% 5.06/5.38 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.06/5.38 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.38
% 5.06/5.38 % uminus_numeral_One
% 5.06/5.38 thf(fact_6161_uminus__numeral__One,axiom,
% 5.06/5.38 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.06/5.38 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.38
% 5.06/5.38 % uminus_numeral_One
% 5.06/5.38 thf(fact_6162_uminus__numeral__One,axiom,
% 5.06/5.38 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.38
% 5.06/5.38 % uminus_numeral_One
% 5.06/5.38 thf(fact_6163_uminus__numeral__One,axiom,
% 5.06/5.38 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.06/5.38 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.38
% 5.06/5.38 % uminus_numeral_One
% 5.06/5.38 thf(fact_6164_uminus__numeral__One,axiom,
% 5.06/5.38 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.06/5.38 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.38
% 5.06/5.38 % uminus_numeral_One
% 5.06/5.38 thf(fact_6165_power__minus,axiom,
% 5.06/5.38 ! [A: real,N2: nat] :
% 5.06/5.38 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.06/5.38 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power_minus
% 5.06/5.38 thf(fact_6166_power__minus,axiom,
% 5.06/5.38 ! [A: int,N2: nat] :
% 5.06/5.38 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.06/5.38 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power_minus
% 5.06/5.38 thf(fact_6167_power__minus,axiom,
% 5.06/5.38 ! [A: complex,N2: nat] :
% 5.06/5.38 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.06/5.38 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power_minus
% 5.06/5.38 thf(fact_6168_power__minus,axiom,
% 5.06/5.38 ! [A: rat,N2: nat] :
% 5.06/5.38 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.06/5.38 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power_minus
% 5.06/5.38 thf(fact_6169_power__minus,axiom,
% 5.06/5.38 ! [A: code_integer,N2: nat] :
% 5.06/5.38 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.06/5.38 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power_minus
% 5.06/5.38 thf(fact_6170_power__minus__Bit0,axiom,
% 5.06/5.38 ! [X: real,K: num] :
% 5.06/5.38 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.06/5.38 = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power_minus_Bit0
% 5.06/5.38 thf(fact_6171_power__minus__Bit0,axiom,
% 5.06/5.38 ! [X: int,K: num] :
% 5.06/5.38 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.06/5.38 = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power_minus_Bit0
% 5.06/5.38 thf(fact_6172_power__minus__Bit0,axiom,
% 5.06/5.38 ! [X: complex,K: num] :
% 5.06/5.38 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.06/5.38 = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power_minus_Bit0
% 5.06/5.38 thf(fact_6173_power__minus__Bit0,axiom,
% 5.06/5.38 ! [X: rat,K: num] :
% 5.06/5.38 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.06/5.38 = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power_minus_Bit0
% 5.06/5.38 thf(fact_6174_power__minus__Bit0,axiom,
% 5.06/5.38 ! [X: code_integer,K: num] :
% 5.06/5.38 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.06/5.38 = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power_minus_Bit0
% 5.06/5.38 thf(fact_6175_sum__nonneg__0,axiom,
% 5.06/5.38 ! [S2: set_real,F: real > real,I2: real] :
% 5.06/5.38 ( ( finite_finite_real @ S2 )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups8097168146408367636l_real @ F @ S2 )
% 5.06/5.38 = zero_zero_real )
% 5.06/5.38 => ( ( member_real @ I2 @ S2 )
% 5.06/5.38 => ( ( F @ I2 )
% 5.06/5.38 = zero_zero_real ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_0
% 5.06/5.38 thf(fact_6176_sum__nonneg__0,axiom,
% 5.06/5.38 ! [S2: set_int,F: int > real,I2: int] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups8778361861064173332t_real @ F @ S2 )
% 5.06/5.38 = zero_zero_real )
% 5.06/5.38 => ( ( member_int @ I2 @ S2 )
% 5.06/5.38 => ( ( F @ I2 )
% 5.06/5.38 = zero_zero_real ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_0
% 5.06/5.38 thf(fact_6177_sum__nonneg__0,axiom,
% 5.06/5.38 ! [S2: set_complex,F: complex > real,I2: complex] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ S2 )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups5808333547571424918x_real @ F @ S2 )
% 5.06/5.38 = zero_zero_real )
% 5.06/5.38 => ( ( member_complex @ I2 @ S2 )
% 5.06/5.38 => ( ( F @ I2 )
% 5.06/5.38 = zero_zero_real ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_0
% 5.06/5.38 thf(fact_6178_sum__nonneg__0,axiom,
% 5.06/5.38 ! [S2: set_real,F: real > rat,I2: real] :
% 5.06/5.38 ( ( finite_finite_real @ S2 )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.06/5.38 = zero_zero_rat )
% 5.06/5.38 => ( ( member_real @ I2 @ S2 )
% 5.06/5.38 => ( ( F @ I2 )
% 5.06/5.38 = zero_zero_rat ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_0
% 5.06/5.38 thf(fact_6179_sum__nonneg__0,axiom,
% 5.06/5.38 ! [S2: set_nat,F: nat > rat,I2: nat] :
% 5.06/5.38 ( ( finite_finite_nat @ S2 )
% 5.06/5.38 => ( ! [I3: nat] :
% 5.06/5.38 ( ( member_nat @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.06/5.38 = zero_zero_rat )
% 5.06/5.38 => ( ( member_nat @ I2 @ S2 )
% 5.06/5.38 => ( ( F @ I2 )
% 5.06/5.38 = zero_zero_rat ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_0
% 5.06/5.38 thf(fact_6180_sum__nonneg__0,axiom,
% 5.06/5.38 ! [S2: set_int,F: int > rat,I2: int] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.06/5.38 = zero_zero_rat )
% 5.06/5.38 => ( ( member_int @ I2 @ S2 )
% 5.06/5.38 => ( ( F @ I2 )
% 5.06/5.38 = zero_zero_rat ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_0
% 5.06/5.38 thf(fact_6181_sum__nonneg__0,axiom,
% 5.06/5.38 ! [S2: set_complex,F: complex > rat,I2: complex] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ S2 )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups5058264527183730370ex_rat @ F @ S2 )
% 5.06/5.38 = zero_zero_rat )
% 5.06/5.38 => ( ( member_complex @ I2 @ S2 )
% 5.06/5.38 => ( ( F @ I2 )
% 5.06/5.38 = zero_zero_rat ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_0
% 5.06/5.38 thf(fact_6182_sum__nonneg__0,axiom,
% 5.06/5.38 ! [S2: set_real,F: real > nat,I2: real] :
% 5.06/5.38 ( ( finite_finite_real @ S2 )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups1935376822645274424al_nat @ F @ S2 )
% 5.06/5.38 = zero_zero_nat )
% 5.06/5.38 => ( ( member_real @ I2 @ S2 )
% 5.06/5.38 => ( ( F @ I2 )
% 5.06/5.38 = zero_zero_nat ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_0
% 5.06/5.38 thf(fact_6183_sum__nonneg__0,axiom,
% 5.06/5.38 ! [S2: set_int,F: int > nat,I2: int] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 5.06/5.38 = zero_zero_nat )
% 5.06/5.38 => ( ( member_int @ I2 @ S2 )
% 5.06/5.38 => ( ( F @ I2 )
% 5.06/5.38 = zero_zero_nat ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_0
% 5.06/5.38 thf(fact_6184_sum__nonneg__0,axiom,
% 5.06/5.38 ! [S2: set_complex,F: complex > nat,I2: complex] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ S2 )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups5693394587270226106ex_nat @ F @ S2 )
% 5.06/5.38 = zero_zero_nat )
% 5.06/5.38 => ( ( member_complex @ I2 @ S2 )
% 5.06/5.38 => ( ( F @ I2 )
% 5.06/5.38 = zero_zero_nat ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_0
% 5.06/5.38 thf(fact_6185_sum__nonneg__leq__bound,axiom,
% 5.06/5.38 ! [S2: set_real,F: real > real,B3: real,I2: real] :
% 5.06/5.38 ( ( finite_finite_real @ S2 )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups8097168146408367636l_real @ F @ S2 )
% 5.06/5.38 = B3 )
% 5.06/5.38 => ( ( member_real @ I2 @ S2 )
% 5.06/5.38 => ( ord_less_eq_real @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_leq_bound
% 5.06/5.38 thf(fact_6186_sum__nonneg__leq__bound,axiom,
% 5.06/5.38 ! [S2: set_int,F: int > real,B3: real,I2: int] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups8778361861064173332t_real @ F @ S2 )
% 5.06/5.38 = B3 )
% 5.06/5.38 => ( ( member_int @ I2 @ S2 )
% 5.06/5.38 => ( ord_less_eq_real @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_leq_bound
% 5.06/5.38 thf(fact_6187_sum__nonneg__leq__bound,axiom,
% 5.06/5.38 ! [S2: set_complex,F: complex > real,B3: real,I2: complex] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ S2 )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups5808333547571424918x_real @ F @ S2 )
% 5.06/5.38 = B3 )
% 5.06/5.38 => ( ( member_complex @ I2 @ S2 )
% 5.06/5.38 => ( ord_less_eq_real @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_leq_bound
% 5.06/5.38 thf(fact_6188_sum__nonneg__leq__bound,axiom,
% 5.06/5.38 ! [S2: set_real,F: real > rat,B3: rat,I2: real] :
% 5.06/5.38 ( ( finite_finite_real @ S2 )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.06/5.38 = B3 )
% 5.06/5.38 => ( ( member_real @ I2 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_leq_bound
% 5.06/5.38 thf(fact_6189_sum__nonneg__leq__bound,axiom,
% 5.06/5.38 ! [S2: set_nat,F: nat > rat,B3: rat,I2: nat] :
% 5.06/5.38 ( ( finite_finite_nat @ S2 )
% 5.06/5.38 => ( ! [I3: nat] :
% 5.06/5.38 ( ( member_nat @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.06/5.38 = B3 )
% 5.06/5.38 => ( ( member_nat @ I2 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_leq_bound
% 5.06/5.38 thf(fact_6190_sum__nonneg__leq__bound,axiom,
% 5.06/5.38 ! [S2: set_int,F: int > rat,B3: rat,I2: int] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.06/5.38 = B3 )
% 5.06/5.38 => ( ( member_int @ I2 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_leq_bound
% 5.06/5.38 thf(fact_6191_sum__nonneg__leq__bound,axiom,
% 5.06/5.38 ! [S2: set_complex,F: complex > rat,B3: rat,I2: complex] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ S2 )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups5058264527183730370ex_rat @ F @ S2 )
% 5.06/5.38 = B3 )
% 5.06/5.38 => ( ( member_complex @ I2 @ S2 )
% 5.06/5.38 => ( ord_less_eq_rat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_leq_bound
% 5.06/5.38 thf(fact_6192_sum__nonneg__leq__bound,axiom,
% 5.06/5.38 ! [S2: set_real,F: real > nat,B3: nat,I2: real] :
% 5.06/5.38 ( ( finite_finite_real @ S2 )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups1935376822645274424al_nat @ F @ S2 )
% 5.06/5.38 = B3 )
% 5.06/5.38 => ( ( member_real @ I2 @ S2 )
% 5.06/5.38 => ( ord_less_eq_nat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_leq_bound
% 5.06/5.38 thf(fact_6193_sum__nonneg__leq__bound,axiom,
% 5.06/5.38 ! [S2: set_int,F: int > nat,B3: nat,I2: int] :
% 5.06/5.38 ( ( finite_finite_int @ S2 )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 5.06/5.38 = B3 )
% 5.06/5.38 => ( ( member_int @ I2 @ S2 )
% 5.06/5.38 => ( ord_less_eq_nat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_leq_bound
% 5.06/5.38 thf(fact_6194_sum__nonneg__leq__bound,axiom,
% 5.06/5.38 ! [S2: set_complex,F: complex > nat,B3: nat,I2: complex] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ S2 )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ S2 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ( ( groups5693394587270226106ex_nat @ F @ S2 )
% 5.06/5.38 = B3 )
% 5.06/5.38 => ( ( member_complex @ I2 @ S2 )
% 5.06/5.38 => ( ord_less_eq_nat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_nonneg_leq_bound
% 5.06/5.38 thf(fact_6195_sum_Osetdiff__irrelevant,axiom,
% 5.06/5.38 ! [A2: set_int,G: int > complex] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups3049146728041665814omplex @ G
% 5.06/5.38 @ ( minus_minus_set_int @ A2
% 5.06/5.38 @ ( collect_int
% 5.06/5.38 @ ^ [X2: int] :
% 5.06/5.38 ( ( G @ X2 )
% 5.06/5.38 = zero_zero_complex ) ) ) )
% 5.06/5.38 = ( groups3049146728041665814omplex @ G @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.setdiff_irrelevant
% 5.06/5.38 thf(fact_6196_sum_Osetdiff__irrelevant,axiom,
% 5.06/5.38 ! [A2: set_int,G: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups8778361861064173332t_real @ G
% 5.06/5.38 @ ( minus_minus_set_int @ A2
% 5.06/5.38 @ ( collect_int
% 5.06/5.38 @ ^ [X2: int] :
% 5.06/5.38 ( ( G @ X2 )
% 5.06/5.38 = zero_zero_real ) ) ) )
% 5.06/5.38 = ( groups8778361861064173332t_real @ G @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.setdiff_irrelevant
% 5.06/5.38 thf(fact_6197_sum_Osetdiff__irrelevant,axiom,
% 5.06/5.38 ! [A2: set_complex,G: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( groups5808333547571424918x_real @ G
% 5.06/5.38 @ ( minus_811609699411566653omplex @ A2
% 5.06/5.38 @ ( collect_complex
% 5.06/5.38 @ ^ [X2: complex] :
% 5.06/5.38 ( ( G @ X2 )
% 5.06/5.38 = zero_zero_real ) ) ) )
% 5.06/5.38 = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.setdiff_irrelevant
% 5.06/5.38 thf(fact_6198_sum_Osetdiff__irrelevant,axiom,
% 5.06/5.38 ! [A2: set_int,G: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups3906332499630173760nt_rat @ G
% 5.06/5.38 @ ( minus_minus_set_int @ A2
% 5.06/5.38 @ ( collect_int
% 5.06/5.38 @ ^ [X2: int] :
% 5.06/5.38 ( ( G @ X2 )
% 5.06/5.38 = zero_zero_rat ) ) ) )
% 5.06/5.38 = ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.setdiff_irrelevant
% 5.06/5.38 thf(fact_6199_sum_Osetdiff__irrelevant,axiom,
% 5.06/5.38 ! [A2: set_complex,G: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( groups5058264527183730370ex_rat @ G
% 5.06/5.38 @ ( minus_811609699411566653omplex @ A2
% 5.06/5.38 @ ( collect_complex
% 5.06/5.38 @ ^ [X2: complex] :
% 5.06/5.38 ( ( G @ X2 )
% 5.06/5.38 = zero_zero_rat ) ) ) )
% 5.06/5.38 = ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.setdiff_irrelevant
% 5.06/5.38 thf(fact_6200_sum_Osetdiff__irrelevant,axiom,
% 5.06/5.38 ! [A2: set_int,G: int > nat] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups4541462559716669496nt_nat @ G
% 5.06/5.38 @ ( minus_minus_set_int @ A2
% 5.06/5.38 @ ( collect_int
% 5.06/5.38 @ ^ [X2: int] :
% 5.06/5.38 ( ( G @ X2 )
% 5.06/5.38 = zero_zero_nat ) ) ) )
% 5.06/5.38 = ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.setdiff_irrelevant
% 5.06/5.38 thf(fact_6201_sum_Osetdiff__irrelevant,axiom,
% 5.06/5.38 ! [A2: set_complex,G: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( groups5693394587270226106ex_nat @ G
% 5.06/5.38 @ ( minus_811609699411566653omplex @ A2
% 5.06/5.38 @ ( collect_complex
% 5.06/5.38 @ ^ [X2: complex] :
% 5.06/5.38 ( ( G @ X2 )
% 5.06/5.38 = zero_zero_nat ) ) ) )
% 5.06/5.38 = ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.setdiff_irrelevant
% 5.06/5.38 thf(fact_6202_sum_Osetdiff__irrelevant,axiom,
% 5.06/5.38 ! [A2: set_complex,G: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( groups5690904116761175830ex_int @ G
% 5.06/5.38 @ ( minus_811609699411566653omplex @ A2
% 5.06/5.38 @ ( collect_complex
% 5.06/5.38 @ ^ [X2: complex] :
% 5.06/5.38 ( ( G @ X2 )
% 5.06/5.38 = zero_zero_int ) ) ) )
% 5.06/5.38 = ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.setdiff_irrelevant
% 5.06/5.38 thf(fact_6203_sum_Osetdiff__irrelevant,axiom,
% 5.06/5.38 ! [A2: set_nat,G: nat > complex] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ( groups2073611262835488442omplex @ G
% 5.06/5.38 @ ( minus_minus_set_nat @ A2
% 5.06/5.38 @ ( collect_nat
% 5.06/5.38 @ ^ [X2: nat] :
% 5.06/5.38 ( ( G @ X2 )
% 5.06/5.38 = zero_zero_complex ) ) ) )
% 5.06/5.38 = ( groups2073611262835488442omplex @ G @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.setdiff_irrelevant
% 5.06/5.38 thf(fact_6204_sum_Osetdiff__irrelevant,axiom,
% 5.06/5.38 ! [A2: set_nat,G: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ( groups2906978787729119204at_rat @ G
% 5.06/5.38 @ ( minus_minus_set_nat @ A2
% 5.06/5.38 @ ( collect_nat
% 5.06/5.38 @ ^ [X2: nat] :
% 5.06/5.38 ( ( G @ X2 )
% 5.06/5.38 = zero_zero_rat ) ) ) )
% 5.06/5.38 = ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.setdiff_irrelevant
% 5.06/5.38 thf(fact_6205_real__0__less__add__iff,axiom,
% 5.06/5.38 ! [X: real,Y: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 5.06/5.38 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 5.06/5.38
% 5.06/5.38 % real_0_less_add_iff
% 5.06/5.38 thf(fact_6206_real__add__less__0__iff,axiom,
% 5.06/5.38 ! [X: real,Y: real] :
% 5.06/5.38 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.06/5.38 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % real_add_less_0_iff
% 5.06/5.38 thf(fact_6207_real__add__le__0__iff,axiom,
% 5.06/5.38 ! [X: real,Y: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.06/5.38 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % real_add_le_0_iff
% 5.06/5.38 thf(fact_6208_real__0__le__add__iff,axiom,
% 5.06/5.38 ! [X: real,Y: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 5.06/5.38 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 5.06/5.38
% 5.06/5.38 % real_0_le_add_iff
% 5.06/5.38 thf(fact_6209_zmod__zminus2__eq__if,axiom,
% 5.06/5.38 ! [A: int,B: int] :
% 5.06/5.38 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.38 = zero_zero_int )
% 5.06/5.38 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 & ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.38 != zero_zero_int )
% 5.06/5.38 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.38 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % zmod_zminus2_eq_if
% 5.06/5.38 thf(fact_6210_zmod__zminus1__eq__if,axiom,
% 5.06/5.38 ! [A: int,B: int] :
% 5.06/5.38 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.38 = zero_zero_int )
% 5.06/5.38 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 & ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.38 != zero_zero_int )
% 5.06/5.38 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.38 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % zmod_zminus1_eq_if
% 5.06/5.38 thf(fact_6211_sum__pos2,axiom,
% 5.06/5.38 ! [I6: set_real,I2: real,F: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ I6 )
% 5.06/5.38 => ( ( member_real @ I2 @ I6 )
% 5.06/5.38 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos2
% 5.06/5.38 thf(fact_6212_sum__pos2,axiom,
% 5.06/5.38 ! [I6: set_int,I2: int,F: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ I6 )
% 5.06/5.38 => ( ( member_int @ I2 @ I6 )
% 5.06/5.38 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos2
% 5.06/5.38 thf(fact_6213_sum__pos2,axiom,
% 5.06/5.38 ! [I6: set_complex,I2: complex,F: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ I6 )
% 5.06/5.38 => ( ( member_complex @ I2 @ I6 )
% 5.06/5.38 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos2
% 5.06/5.38 thf(fact_6214_sum__pos2,axiom,
% 5.06/5.38 ! [I6: set_real,I2: real,F: real > rat] :
% 5.06/5.38 ( ( finite_finite_real @ I6 )
% 5.06/5.38 => ( ( member_real @ I2 @ I6 )
% 5.06/5.38 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos2
% 5.06/5.38 thf(fact_6215_sum__pos2,axiom,
% 5.06/5.38 ! [I6: set_nat,I2: nat,F: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ I6 )
% 5.06/5.38 => ( ( member_nat @ I2 @ I6 )
% 5.06/5.38 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.06/5.38 => ( ! [I3: nat] :
% 5.06/5.38 ( ( member_nat @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos2
% 5.06/5.38 thf(fact_6216_sum__pos2,axiom,
% 5.06/5.38 ! [I6: set_int,I2: int,F: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ I6 )
% 5.06/5.38 => ( ( member_int @ I2 @ I6 )
% 5.06/5.38 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos2
% 5.06/5.38 thf(fact_6217_sum__pos2,axiom,
% 5.06/5.38 ! [I6: set_complex,I2: complex,F: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ I6 )
% 5.06/5.38 => ( ( member_complex @ I2 @ I6 )
% 5.06/5.38 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos2
% 5.06/5.38 thf(fact_6218_sum__pos2,axiom,
% 5.06/5.38 ! [I6: set_real,I2: real,F: real > nat] :
% 5.06/5.38 ( ( finite_finite_real @ I6 )
% 5.06/5.38 => ( ( member_real @ I2 @ I6 )
% 5.06/5.38 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos2
% 5.06/5.38 thf(fact_6219_sum__pos2,axiom,
% 5.06/5.38 ! [I6: set_int,I2: int,F: int > nat] :
% 5.06/5.38 ( ( finite_finite_int @ I6 )
% 5.06/5.38 => ( ( member_int @ I2 @ I6 )
% 5.06/5.38 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos2
% 5.06/5.38 thf(fact_6220_sum__pos2,axiom,
% 5.06/5.38 ! [I6: set_complex,I2: complex,F: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ I6 )
% 5.06/5.38 => ( ( member_complex @ I2 @ I6 )
% 5.06/5.38 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos2
% 5.06/5.38 thf(fact_6221_sum__pos,axiom,
% 5.06/5.38 ! [I6: set_complex,F: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ I6 )
% 5.06/5.38 => ( ( I6 != bot_bot_set_complex )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos
% 5.06/5.38 thf(fact_6222_sum__pos,axiom,
% 5.06/5.38 ! [I6: set_int,F: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ I6 )
% 5.06/5.38 => ( ( I6 != bot_bot_set_int )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos
% 5.06/5.38 thf(fact_6223_sum__pos,axiom,
% 5.06/5.38 ! [I6: set_real,F: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ I6 )
% 5.06/5.38 => ( ( I6 != bot_bot_set_real )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos
% 5.06/5.38 thf(fact_6224_sum__pos,axiom,
% 5.06/5.38 ! [I6: set_complex,F: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ I6 )
% 5.06/5.38 => ( ( I6 != bot_bot_set_complex )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos
% 5.06/5.38 thf(fact_6225_sum__pos,axiom,
% 5.06/5.38 ! [I6: set_nat,F: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ I6 )
% 5.06/5.38 => ( ( I6 != bot_bot_set_nat )
% 5.06/5.38 => ( ! [I3: nat] :
% 5.06/5.38 ( ( member_nat @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos
% 5.06/5.38 thf(fact_6226_sum__pos,axiom,
% 5.06/5.38 ! [I6: set_int,F: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ I6 )
% 5.06/5.38 => ( ( I6 != bot_bot_set_int )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos
% 5.06/5.38 thf(fact_6227_sum__pos,axiom,
% 5.06/5.38 ! [I6: set_real,F: real > rat] :
% 5.06/5.38 ( ( finite_finite_real @ I6 )
% 5.06/5.38 => ( ( I6 != bot_bot_set_real )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos
% 5.06/5.38 thf(fact_6228_sum__pos,axiom,
% 5.06/5.38 ! [I6: set_complex,F: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ I6 )
% 5.06/5.38 => ( ( I6 != bot_bot_set_complex )
% 5.06/5.38 => ( ! [I3: complex] :
% 5.06/5.38 ( ( member_complex @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos
% 5.06/5.38 thf(fact_6229_sum__pos,axiom,
% 5.06/5.38 ! [I6: set_int,F: int > nat] :
% 5.06/5.38 ( ( finite_finite_int @ I6 )
% 5.06/5.38 => ( ( I6 != bot_bot_set_int )
% 5.06/5.38 => ( ! [I3: int] :
% 5.06/5.38 ( ( member_int @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos
% 5.06/5.38 thf(fact_6230_sum__pos,axiom,
% 5.06/5.38 ! [I6: set_real,F: real > nat] :
% 5.06/5.38 ( ( finite_finite_real @ I6 )
% 5.06/5.38 => ( ( I6 != bot_bot_set_real )
% 5.06/5.38 => ( ! [I3: real] :
% 5.06/5.38 ( ( member_real @ I3 @ I6 )
% 5.06/5.38 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_pos
% 5.06/5.38 thf(fact_6231_ln__ge__zero__imp__ge__one,axiom,
% 5.06/5.38 ! [X: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.06/5.38 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.38 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_ge_zero_imp_ge_one
% 5.06/5.38 thf(fact_6232_sum_Omono__neutral__cong__right,axiom,
% 5.06/5.38 ! [T3: set_real,S3: set_real,G: real > complex,H2: real > complex] :
% 5.06/5.38 ( ( finite_finite_real @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups5754745047067104278omplex @ G @ T3 )
% 5.06/5.38 = ( groups5754745047067104278omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_right
% 5.06/5.38 thf(fact_6233_sum_Omono__neutral__cong__right,axiom,
% 5.06/5.38 ! [T3: set_real,S3: set_real,G: real > real,H2: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups8097168146408367636l_real @ G @ T3 )
% 5.06/5.38 = ( groups8097168146408367636l_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_right
% 5.06/5.38 thf(fact_6234_sum_Omono__neutral__cong__right,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > real,H2: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 5.06/5.38 = ( groups5808333547571424918x_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_right
% 5.06/5.38 thf(fact_6235_sum_Omono__neutral__cong__right,axiom,
% 5.06/5.38 ! [T3: set_real,S3: set_real,G: real > rat,H2: real > rat] :
% 5.06/5.38 ( ( finite_finite_real @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups1300246762558778688al_rat @ G @ T3 )
% 5.06/5.38 = ( groups1300246762558778688al_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_right
% 5.06/5.38 thf(fact_6236_sum_Omono__neutral__cong__right,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 5.06/5.38 = ( groups5058264527183730370ex_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_right
% 5.06/5.38 thf(fact_6237_sum_Omono__neutral__cong__right,axiom,
% 5.06/5.38 ! [T3: set_real,S3: set_real,G: real > nat,H2: real > nat] :
% 5.06/5.38 ( ( finite_finite_real @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups1935376822645274424al_nat @ G @ T3 )
% 5.06/5.38 = ( groups1935376822645274424al_nat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_right
% 5.06/5.38 thf(fact_6238_sum_Omono__neutral__cong__right,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > nat,H2: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 5.06/5.38 = ( groups5693394587270226106ex_nat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_right
% 5.06/5.38 thf(fact_6239_sum_Omono__neutral__cong__right,axiom,
% 5.06/5.38 ! [T3: set_real,S3: set_real,G: real > int,H2: real > int] :
% 5.06/5.38 ( ( finite_finite_real @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups1932886352136224148al_int @ G @ T3 )
% 5.06/5.38 = ( groups1932886352136224148al_int @ H2 @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_right
% 5.06/5.38 thf(fact_6240_sum_Omono__neutral__cong__right,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > int,H2: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 5.06/5.38 = ( groups5690904116761175830ex_int @ H2 @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_right
% 5.06/5.38 thf(fact_6241_sum_Omono__neutral__cong__right,axiom,
% 5.06/5.38 ! [T3: set_nat,S3: set_nat,G: nat > complex,H2: nat > complex] :
% 5.06/5.38 ( ( finite_finite_nat @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups2073611262835488442omplex @ G @ T3 )
% 5.06/5.38 = ( groups2073611262835488442omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_right
% 5.06/5.38 thf(fact_6242_sum_Omono__neutral__cong__left,axiom,
% 5.06/5.38 ! [T3: set_real,S3: set_real,H2: real > complex,G: real > complex] :
% 5.06/5.38 ( ( finite_finite_real @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.06/5.38 => ( ( H2 @ X3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups5754745047067104278omplex @ G @ S3 )
% 5.06/5.38 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_left
% 5.06/5.38 thf(fact_6243_sum_Omono__neutral__cong__left,axiom,
% 5.06/5.38 ! [T3: set_real,S3: set_real,H2: real > real,G: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.06/5.38 => ( ( H2 @ X3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups8097168146408367636l_real @ G @ S3 )
% 5.06/5.38 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_left
% 5.06/5.38 thf(fact_6244_sum_Omono__neutral__cong__left,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( H2 @ X3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups5808333547571424918x_real @ G @ S3 )
% 5.06/5.38 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_left
% 5.06/5.38 thf(fact_6245_sum_Omono__neutral__cong__left,axiom,
% 5.06/5.38 ! [T3: set_real,S3: set_real,H2: real > rat,G: real > rat] :
% 5.06/5.38 ( ( finite_finite_real @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.06/5.38 => ( ( H2 @ X3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups1300246762558778688al_rat @ G @ S3 )
% 5.06/5.38 = ( groups1300246762558778688al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_left
% 5.06/5.38 thf(fact_6246_sum_Omono__neutral__cong__left,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( H2 @ X3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups5058264527183730370ex_rat @ G @ S3 )
% 5.06/5.38 = ( groups5058264527183730370ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_left
% 5.06/5.38 thf(fact_6247_sum_Omono__neutral__cong__left,axiom,
% 5.06/5.38 ! [T3: set_real,S3: set_real,H2: real > nat,G: real > nat] :
% 5.06/5.38 ( ( finite_finite_real @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.06/5.38 => ( ( H2 @ X3 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups1935376822645274424al_nat @ G @ S3 )
% 5.06/5.38 = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_left
% 5.06/5.38 thf(fact_6248_sum_Omono__neutral__cong__left,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,H2: complex > nat,G: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( H2 @ X3 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups5693394587270226106ex_nat @ G @ S3 )
% 5.06/5.38 = ( groups5693394587270226106ex_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_left
% 5.06/5.38 thf(fact_6249_sum_Omono__neutral__cong__left,axiom,
% 5.06/5.38 ! [T3: set_real,S3: set_real,H2: real > int,G: real > int] :
% 5.06/5.38 ( ( finite_finite_real @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 5.06/5.38 => ( ( H2 @ X3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups1932886352136224148al_int @ G @ S3 )
% 5.06/5.38 = ( groups1932886352136224148al_int @ H2 @ T3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_left
% 5.06/5.38 thf(fact_6250_sum_Omono__neutral__cong__left,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,H2: complex > int,G: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( H2 @ X3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups5690904116761175830ex_int @ G @ S3 )
% 5.06/5.38 = ( groups5690904116761175830ex_int @ H2 @ T3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_left
% 5.06/5.38 thf(fact_6251_sum_Omono__neutral__cong__left,axiom,
% 5.06/5.38 ! [T3: set_nat,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.06/5.38 ( ( finite_finite_nat @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.06/5.38 => ( ( H2 @ X3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ S3 )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = ( H2 @ X3 ) ) )
% 5.06/5.38 => ( ( groups2073611262835488442omplex @ G @ S3 )
% 5.06/5.38 = ( groups2073611262835488442omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_cong_left
% 5.06/5.38 thf(fact_6252_sum_Omono__neutral__right,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 5.06/5.38 = ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_right
% 5.06/5.38 thf(fact_6253_sum_Omono__neutral__right,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 5.06/5.38 = ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_right
% 5.06/5.38 thf(fact_6254_sum_Omono__neutral__right,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 5.06/5.38 = ( groups5693394587270226106ex_nat @ G @ S3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_right
% 5.06/5.38 thf(fact_6255_sum_Omono__neutral__right,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 5.06/5.38 = ( groups5690904116761175830ex_int @ G @ S3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_right
% 5.06/5.38 thf(fact_6256_sum_Omono__neutral__right,axiom,
% 5.06/5.38 ! [T3: set_nat,S3: set_nat,G: nat > complex] :
% 5.06/5.38 ( ( finite_finite_nat @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ( groups2073611262835488442omplex @ G @ T3 )
% 5.06/5.38 = ( groups2073611262835488442omplex @ G @ S3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_right
% 5.06/5.38 thf(fact_6257_sum_Omono__neutral__right,axiom,
% 5.06/5.38 ! [T3: set_nat,S3: set_nat,G: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ( groups2906978787729119204at_rat @ G @ T3 )
% 5.06/5.38 = ( groups2906978787729119204at_rat @ G @ S3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_right
% 5.06/5.38 thf(fact_6258_sum_Omono__neutral__right,axiom,
% 5.06/5.38 ! [T3: set_nat,S3: set_nat,G: nat > int] :
% 5.06/5.38 ( ( finite_finite_nat @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ( groups3539618377306564664at_int @ G @ T3 )
% 5.06/5.38 = ( groups3539618377306564664at_int @ G @ S3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_right
% 5.06/5.38 thf(fact_6259_sum_Omono__neutral__right,axiom,
% 5.06/5.38 ! [T3: set_int,S3: set_int,G: int > complex] :
% 5.06/5.38 ( ( finite_finite_int @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ( groups3049146728041665814omplex @ G @ T3 )
% 5.06/5.38 = ( groups3049146728041665814omplex @ G @ S3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_right
% 5.06/5.38 thf(fact_6260_sum_Omono__neutral__right,axiom,
% 5.06/5.38 ! [T3: set_int,S3: set_int,G: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ( groups8778361861064173332t_real @ G @ T3 )
% 5.06/5.38 = ( groups8778361861064173332t_real @ G @ S3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_right
% 5.06/5.38 thf(fact_6261_sum_Omono__neutral__right,axiom,
% 5.06/5.38 ! [T3: set_int,S3: set_int,G: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ( groups3906332499630173760nt_rat @ G @ T3 )
% 5.06/5.38 = ( groups3906332499630173760nt_rat @ G @ S3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_right
% 5.06/5.38 thf(fact_6262_sum_Omono__neutral__left,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ( groups5808333547571424918x_real @ G @ S3 )
% 5.06/5.38 = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_left
% 5.06/5.38 thf(fact_6263_sum_Omono__neutral__left,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ( groups5058264527183730370ex_rat @ G @ S3 )
% 5.06/5.38 = ( groups5058264527183730370ex_rat @ G @ T3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_left
% 5.06/5.38 thf(fact_6264_sum_Omono__neutral__left,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ( groups5693394587270226106ex_nat @ G @ S3 )
% 5.06/5.38 = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_left
% 5.06/5.38 thf(fact_6265_sum_Omono__neutral__left,axiom,
% 5.06/5.38 ! [T3: set_complex,S3: set_complex,G: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ T3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ( groups5690904116761175830ex_int @ G @ S3 )
% 5.06/5.38 = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_left
% 5.06/5.38 thf(fact_6266_sum_Omono__neutral__left,axiom,
% 5.06/5.38 ! [T3: set_nat,S3: set_nat,G: nat > complex] :
% 5.06/5.38 ( ( finite_finite_nat @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ( groups2073611262835488442omplex @ G @ S3 )
% 5.06/5.38 = ( groups2073611262835488442omplex @ G @ T3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_left
% 5.06/5.38 thf(fact_6267_sum_Omono__neutral__left,axiom,
% 5.06/5.38 ! [T3: set_nat,S3: set_nat,G: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ( groups2906978787729119204at_rat @ G @ S3 )
% 5.06/5.38 = ( groups2906978787729119204at_rat @ G @ T3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_left
% 5.06/5.38 thf(fact_6268_sum_Omono__neutral__left,axiom,
% 5.06/5.38 ! [T3: set_nat,S3: set_nat,G: nat > int] :
% 5.06/5.38 ( ( finite_finite_nat @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ( groups3539618377306564664at_int @ G @ S3 )
% 5.06/5.38 = ( groups3539618377306564664at_int @ G @ T3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_left
% 5.06/5.38 thf(fact_6269_sum_Omono__neutral__left,axiom,
% 5.06/5.38 ! [T3: set_int,S3: set_int,G: int > complex] :
% 5.06/5.38 ( ( finite_finite_int @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ( groups3049146728041665814omplex @ G @ S3 )
% 5.06/5.38 = ( groups3049146728041665814omplex @ G @ T3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_left
% 5.06/5.38 thf(fact_6270_sum_Omono__neutral__left,axiom,
% 5.06/5.38 ! [T3: set_int,S3: set_int,G: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ( groups8778361861064173332t_real @ G @ S3 )
% 5.06/5.38 = ( groups8778361861064173332t_real @ G @ T3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_left
% 5.06/5.38 thf(fact_6271_sum_Omono__neutral__left,axiom,
% 5.06/5.38 ! [T3: set_int,S3: set_int,G: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ T3 )
% 5.06/5.38 => ( ( ord_less_eq_set_int @ S3 @ T3 )
% 5.06/5.38 => ( ! [X3: int] :
% 5.06/5.38 ( ( member_int @ X3 @ ( minus_minus_set_int @ T3 @ S3 ) )
% 5.06/5.38 => ( ( G @ X3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ( groups3906332499630173760nt_rat @ G @ S3 )
% 5.06/5.38 = ( groups3906332499630173760nt_rat @ G @ T3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.mono_neutral_left
% 5.06/5.38 thf(fact_6272_sum_Osame__carrierI,axiom,
% 5.06/5.38 ! [C2: set_real,A2: set_real,B3: set_real,G: real > complex,H2: real > complex] :
% 5.06/5.38 ( ( finite_finite_real @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ( ( groups5754745047067104278omplex @ G @ C2 )
% 5.06/5.38 = ( groups5754745047067104278omplex @ H2 @ C2 ) )
% 5.06/5.38 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.06/5.38 = ( groups5754745047067104278omplex @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrierI
% 5.06/5.38 thf(fact_6273_sum_Osame__carrierI,axiom,
% 5.06/5.38 ! [C2: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ( ( groups8097168146408367636l_real @ G @ C2 )
% 5.06/5.38 = ( groups8097168146408367636l_real @ H2 @ C2 ) )
% 5.06/5.38 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.06/5.38 = ( groups8097168146408367636l_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrierI
% 5.06/5.38 thf(fact_6274_sum_Osame__carrierI,axiom,
% 5.06/5.38 ! [C2: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: complex] :
% 5.06/5.38 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ( ( groups5808333547571424918x_real @ G @ C2 )
% 5.06/5.38 = ( groups5808333547571424918x_real @ H2 @ C2 ) )
% 5.06/5.38 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.06/5.38 = ( groups5808333547571424918x_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrierI
% 5.06/5.38 thf(fact_6275_sum_Osame__carrierI,axiom,
% 5.06/5.38 ! [C2: set_real,A2: set_real,B3: set_real,G: real > rat,H2: real > rat] :
% 5.06/5.38 ( ( finite_finite_real @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ( ( groups1300246762558778688al_rat @ G @ C2 )
% 5.06/5.38 = ( groups1300246762558778688al_rat @ H2 @ C2 ) )
% 5.06/5.38 => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.06/5.38 = ( groups1300246762558778688al_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrierI
% 5.06/5.38 thf(fact_6276_sum_Osame__carrierI,axiom,
% 5.06/5.38 ! [C2: set_complex,A2: set_complex,B3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: complex] :
% 5.06/5.38 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ( ( groups5058264527183730370ex_rat @ G @ C2 )
% 5.06/5.38 = ( groups5058264527183730370ex_rat @ H2 @ C2 ) )
% 5.06/5.38 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.06/5.38 = ( groups5058264527183730370ex_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrierI
% 5.06/5.38 thf(fact_6277_sum_Osame__carrierI,axiom,
% 5.06/5.38 ! [C2: set_real,A2: set_real,B3: set_real,G: real > nat,H2: real > nat] :
% 5.06/5.38 ( ( finite_finite_real @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ( ( groups1935376822645274424al_nat @ G @ C2 )
% 5.06/5.38 = ( groups1935376822645274424al_nat @ H2 @ C2 ) )
% 5.06/5.38 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.06/5.38 = ( groups1935376822645274424al_nat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrierI
% 5.06/5.38 thf(fact_6278_sum_Osame__carrierI,axiom,
% 5.06/5.38 ! [C2: set_complex,A2: set_complex,B3: set_complex,G: complex > nat,H2: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: complex] :
% 5.06/5.38 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ( ( groups5693394587270226106ex_nat @ G @ C2 )
% 5.06/5.38 = ( groups5693394587270226106ex_nat @ H2 @ C2 ) )
% 5.06/5.38 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.06/5.38 = ( groups5693394587270226106ex_nat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrierI
% 5.06/5.38 thf(fact_6279_sum_Osame__carrierI,axiom,
% 5.06/5.38 ! [C2: set_real,A2: set_real,B3: set_real,G: real > int,H2: real > int] :
% 5.06/5.38 ( ( finite_finite_real @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ( ( groups1932886352136224148al_int @ G @ C2 )
% 5.06/5.38 = ( groups1932886352136224148al_int @ H2 @ C2 ) )
% 5.06/5.38 => ( ( groups1932886352136224148al_int @ G @ A2 )
% 5.06/5.38 = ( groups1932886352136224148al_int @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrierI
% 5.06/5.38 thf(fact_6280_sum_Osame__carrierI,axiom,
% 5.06/5.38 ! [C2: set_complex,A2: set_complex,B3: set_complex,G: complex > int,H2: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: complex] :
% 5.06/5.38 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ( ( groups5690904116761175830ex_int @ G @ C2 )
% 5.06/5.38 = ( groups5690904116761175830ex_int @ H2 @ C2 ) )
% 5.06/5.38 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.06/5.38 = ( groups5690904116761175830ex_int @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrierI
% 5.06/5.38 thf(fact_6281_sum_Osame__carrierI,axiom,
% 5.06/5.38 ! [C2: set_nat,A2: set_nat,B3: set_nat,G: nat > complex,H2: nat > complex] :
% 5.06/5.38 ( ( finite_finite_nat @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: nat] :
% 5.06/5.38 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [B2: nat] :
% 5.06/5.38 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ( ( groups2073611262835488442omplex @ G @ C2 )
% 5.06/5.38 = ( groups2073611262835488442omplex @ H2 @ C2 ) )
% 5.06/5.38 => ( ( groups2073611262835488442omplex @ G @ A2 )
% 5.06/5.38 = ( groups2073611262835488442omplex @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrierI
% 5.06/5.38 thf(fact_6282_sum_Osame__carrier,axiom,
% 5.06/5.38 ! [C2: set_real,A2: set_real,B3: set_real,G: real > complex,H2: real > complex] :
% 5.06/5.38 ( ( finite_finite_real @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.06/5.38 = ( groups5754745047067104278omplex @ H2 @ B3 ) )
% 5.06/5.38 = ( ( groups5754745047067104278omplex @ G @ C2 )
% 5.06/5.38 = ( groups5754745047067104278omplex @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrier
% 5.06/5.38 thf(fact_6283_sum_Osame__carrier,axiom,
% 5.06/5.38 ! [C2: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.06/5.38 = ( groups8097168146408367636l_real @ H2 @ B3 ) )
% 5.06/5.38 = ( ( groups8097168146408367636l_real @ G @ C2 )
% 5.06/5.38 = ( groups8097168146408367636l_real @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrier
% 5.06/5.38 thf(fact_6284_sum_Osame__carrier,axiom,
% 5.06/5.38 ! [C2: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: complex] :
% 5.06/5.38 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_real ) )
% 5.06/5.38 => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.06/5.38 = ( groups5808333547571424918x_real @ H2 @ B3 ) )
% 5.06/5.38 = ( ( groups5808333547571424918x_real @ G @ C2 )
% 5.06/5.38 = ( groups5808333547571424918x_real @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrier
% 5.06/5.38 thf(fact_6285_sum_Osame__carrier,axiom,
% 5.06/5.38 ! [C2: set_real,A2: set_real,B3: set_real,G: real > rat,H2: real > rat] :
% 5.06/5.38 ( ( finite_finite_real @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.06/5.38 = ( groups1300246762558778688al_rat @ H2 @ B3 ) )
% 5.06/5.38 = ( ( groups1300246762558778688al_rat @ G @ C2 )
% 5.06/5.38 = ( groups1300246762558778688al_rat @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrier
% 5.06/5.38 thf(fact_6286_sum_Osame__carrier,axiom,
% 5.06/5.38 ! [C2: set_complex,A2: set_complex,B3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: complex] :
% 5.06/5.38 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_rat ) )
% 5.06/5.38 => ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.06/5.38 = ( groups5058264527183730370ex_rat @ H2 @ B3 ) )
% 5.06/5.38 = ( ( groups5058264527183730370ex_rat @ G @ C2 )
% 5.06/5.38 = ( groups5058264527183730370ex_rat @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrier
% 5.06/5.38 thf(fact_6287_sum_Osame__carrier,axiom,
% 5.06/5.38 ! [C2: set_real,A2: set_real,B3: set_real,G: real > nat,H2: real > nat] :
% 5.06/5.38 ( ( finite_finite_real @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.06/5.38 = ( groups1935376822645274424al_nat @ H2 @ B3 ) )
% 5.06/5.38 = ( ( groups1935376822645274424al_nat @ G @ C2 )
% 5.06/5.38 = ( groups1935376822645274424al_nat @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrier
% 5.06/5.38 thf(fact_6288_sum_Osame__carrier,axiom,
% 5.06/5.38 ! [C2: set_complex,A2: set_complex,B3: set_complex,G: complex > nat,H2: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: complex] :
% 5.06/5.38 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_nat ) )
% 5.06/5.38 => ( ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.06/5.38 = ( groups5693394587270226106ex_nat @ H2 @ B3 ) )
% 5.06/5.38 = ( ( groups5693394587270226106ex_nat @ G @ C2 )
% 5.06/5.38 = ( groups5693394587270226106ex_nat @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrier
% 5.06/5.38 thf(fact_6289_sum_Osame__carrier,axiom,
% 5.06/5.38 ! [C2: set_real,A2: set_real,B3: set_real,G: real > int,H2: real > int] :
% 5.06/5.38 ( ( finite_finite_real @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: real] :
% 5.06/5.38 ( ( member_real @ A3 @ ( minus_minus_set_real @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ( ( groups1932886352136224148al_int @ G @ A2 )
% 5.06/5.38 = ( groups1932886352136224148al_int @ H2 @ B3 ) )
% 5.06/5.38 = ( ( groups1932886352136224148al_int @ G @ C2 )
% 5.06/5.38 = ( groups1932886352136224148al_int @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrier
% 5.06/5.38 thf(fact_6290_sum_Osame__carrier,axiom,
% 5.06/5.38 ! [C2: set_complex,A2: set_complex,B3: set_complex,G: complex > int,H2: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: complex] :
% 5.06/5.38 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_int ) )
% 5.06/5.38 => ( ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.06/5.38 = ( groups5690904116761175830ex_int @ H2 @ B3 ) )
% 5.06/5.38 = ( ( groups5690904116761175830ex_int @ G @ C2 )
% 5.06/5.38 = ( groups5690904116761175830ex_int @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrier
% 5.06/5.38 thf(fact_6291_sum_Osame__carrier,axiom,
% 5.06/5.38 ! [C2: set_nat,A2: set_nat,B3: set_nat,G: nat > complex,H2: nat > complex] :
% 5.06/5.38 ( ( finite_finite_nat @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ B3 @ C2 )
% 5.06/5.38 => ( ! [A3: nat] :
% 5.06/5.38 ( ( member_nat @ A3 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 5.06/5.38 => ( ( G @ A3 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ! [B2: nat] :
% 5.06/5.38 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ C2 @ B3 ) )
% 5.06/5.38 => ( ( H2 @ B2 )
% 5.06/5.38 = zero_zero_complex ) )
% 5.06/5.38 => ( ( ( groups2073611262835488442omplex @ G @ A2 )
% 5.06/5.38 = ( groups2073611262835488442omplex @ H2 @ B3 ) )
% 5.06/5.38 = ( ( groups2073611262835488442omplex @ G @ C2 )
% 5.06/5.38 = ( groups2073611262835488442omplex @ H2 @ C2 ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.same_carrier
% 5.06/5.38 thf(fact_6292_sum_Osubset__diff,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,G: complex > real] :
% 5.06/5.38 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.06/5.38 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5808333547571424918x_real @ G @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.subset_diff
% 5.06/5.38 thf(fact_6293_sum_Osubset__diff,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,G: complex > rat] :
% 5.06/5.38 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.06/5.38 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5058264527183730370ex_rat @ G @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.subset_diff
% 5.06/5.38 thf(fact_6294_sum_Osubset__diff,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,G: complex > nat] :
% 5.06/5.38 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.06/5.38 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5693394587270226106ex_nat @ G @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.subset_diff
% 5.06/5.38 thf(fact_6295_sum_Osubset__diff,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,G: complex > int] :
% 5.06/5.38 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.06/5.38 => ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.06/5.38 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5690904116761175830ex_int @ G @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.subset_diff
% 5.06/5.38 thf(fact_6296_sum_Osubset__diff,axiom,
% 5.06/5.38 ! [B3: set_nat,A2: set_nat,G: nat > rat] :
% 5.06/5.38 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.06/5.38 => ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 5.06/5.38 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups2906978787729119204at_rat @ G @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.subset_diff
% 5.06/5.38 thf(fact_6297_sum_Osubset__diff,axiom,
% 5.06/5.38 ! [B3: set_nat,A2: set_nat,G: nat > int] :
% 5.06/5.38 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.06/5.38 => ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 5.06/5.38 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups3539618377306564664at_int @ G @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.subset_diff
% 5.06/5.38 thf(fact_6298_sum_Osubset__diff,axiom,
% 5.06/5.38 ! [B3: set_int,A2: set_int,G: int > real] :
% 5.06/5.38 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.06/5.38 => ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.06/5.38 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups8778361861064173332t_real @ G @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.subset_diff
% 5.06/5.38 thf(fact_6299_sum_Osubset__diff,axiom,
% 5.06/5.38 ! [B3: set_int,A2: set_int,G: int > rat] :
% 5.06/5.38 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.06/5.38 => ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.06/5.38 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ G @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.subset_diff
% 5.06/5.38 thf(fact_6300_sum_Osubset__diff,axiom,
% 5.06/5.38 ! [B3: set_int,A2: set_int,G: int > nat] :
% 5.06/5.38 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.06/5.38 => ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.06/5.38 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ G @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.subset_diff
% 5.06/5.38 thf(fact_6301_sum_Osubset__diff,axiom,
% 5.06/5.38 ! [B3: set_int,A2: set_int,G: int > int] :
% 5.06/5.38 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.06/5.38 => ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 5.06/5.38 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4538972089207619220nt_int @ G @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum.subset_diff
% 5.06/5.38 thf(fact_6302_sum__diff,axiom,
% 5.06/5.38 ! [A2: set_complex,B3: set_complex,F: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.06/5.38 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.06/5.38 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_diff
% 5.06/5.38 thf(fact_6303_sum__diff,axiom,
% 5.06/5.38 ! [A2: set_complex,B3: set_complex,F: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.06/5.38 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.06/5.38 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_diff
% 5.06/5.38 thf(fact_6304_sum__diff,axiom,
% 5.06/5.38 ! [A2: set_complex,B3: set_complex,F: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.06/5.38 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.06/5.38 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_diff
% 5.06/5.38 thf(fact_6305_sum__diff,axiom,
% 5.06/5.38 ! [A2: set_nat,B3: set_nat,F: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.06/5.38 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.06/5.38 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_diff
% 5.06/5.38 thf(fact_6306_sum__diff,axiom,
% 5.06/5.38 ! [A2: set_nat,B3: set_nat,F: nat > int] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.06/5.38 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.06/5.38 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_diff
% 5.06/5.38 thf(fact_6307_sum__diff,axiom,
% 5.06/5.38 ! [A2: set_int,B3: set_int,F: int > real] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.06/5.38 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.06/5.38 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_diff
% 5.06/5.38 thf(fact_6308_sum__diff,axiom,
% 5.06/5.38 ! [A2: set_int,B3: set_int,F: int > rat] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.06/5.38 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.06/5.38 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_diff
% 5.06/5.38 thf(fact_6309_sum__diff,axiom,
% 5.06/5.38 ! [A2: set_int,B3: set_int,F: int > int] :
% 5.06/5.38 ( ( finite_finite_int @ A2 )
% 5.06/5.38 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.06/5.38 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.06/5.38 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_diff
% 5.06/5.38 thf(fact_6310_sum__diff,axiom,
% 5.06/5.38 ! [A2: set_complex,B3: set_complex,F: complex > complex] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.06/5.38 => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.06/5.38 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_diff
% 5.06/5.38 thf(fact_6311_sum__diff,axiom,
% 5.06/5.38 ! [A2: set_nat,B3: set_nat,F: nat > real] :
% 5.06/5.38 ( ( finite_finite_nat @ A2 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.06/5.38 => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.06/5.38 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_diff
% 5.06/5.38 thf(fact_6312_ln__add__one__self__le__self,axiom,
% 5.06/5.38 ! [X: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.38 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_add_one_self_le_self
% 5.06/5.38 thf(fact_6313_ln__mult,axiom,
% 5.06/5.38 ! [X: real,Y: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.38 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.38 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 5.06/5.38 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_mult
% 5.06/5.38 thf(fact_6314_ln__eq__minus__one,axiom,
% 5.06/5.38 ! [X: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.38 => ( ( ( ln_ln_real @ X )
% 5.06/5.38 = ( minus_minus_real @ X @ one_one_real ) )
% 5.06/5.38 => ( X = one_one_real ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_eq_minus_one
% 5.06/5.38 thf(fact_6315_ln__div,axiom,
% 5.06/5.38 ! [X: real,Y: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.38 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.38 => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y ) )
% 5.06/5.38 = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_div
% 5.06/5.38 thf(fact_6316_pos__minus__divide__less__eq,axiom,
% 5.06/5.38 ! [C: real,B: real,A: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.06/5.38 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % pos_minus_divide_less_eq
% 5.06/5.38 thf(fact_6317_pos__minus__divide__less__eq,axiom,
% 5.06/5.38 ! [C: rat,B: rat,A: rat] :
% 5.06/5.38 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.06/5.38 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % pos_minus_divide_less_eq
% 5.06/5.38 thf(fact_6318_pos__less__minus__divide__eq,axiom,
% 5.06/5.38 ! [C: real,A: real,B: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.06/5.38 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % pos_less_minus_divide_eq
% 5.06/5.38 thf(fact_6319_pos__less__minus__divide__eq,axiom,
% 5.06/5.38 ! [C: rat,A: rat,B: rat] :
% 5.06/5.38 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.06/5.38 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % pos_less_minus_divide_eq
% 5.06/5.38 thf(fact_6320_neg__minus__divide__less__eq,axiom,
% 5.06/5.38 ! [C: real,B: real,A: real] :
% 5.06/5.38 ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.06/5.38 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_minus_divide_less_eq
% 5.06/5.38 thf(fact_6321_neg__minus__divide__less__eq,axiom,
% 5.06/5.38 ! [C: rat,B: rat,A: rat] :
% 5.06/5.38 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.06/5.38 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_minus_divide_less_eq
% 5.06/5.38 thf(fact_6322_neg__less__minus__divide__eq,axiom,
% 5.06/5.38 ! [C: real,A: real,B: real] :
% 5.06/5.38 ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.06/5.38 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_less_minus_divide_eq
% 5.06/5.38 thf(fact_6323_neg__less__minus__divide__eq,axiom,
% 5.06/5.38 ! [C: rat,A: rat,B: rat] :
% 5.06/5.38 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.06/5.38 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_less_minus_divide_eq
% 5.06/5.38 thf(fact_6324_minus__divide__less__eq,axiom,
% 5.06/5.38 ! [B: real,C: real,A: real] :
% 5.06/5.38 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.06/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_less_eq
% 5.06/5.38 thf(fact_6325_minus__divide__less__eq,axiom,
% 5.06/5.38 ! [B: rat,C: rat,A: rat] :
% 5.06/5.38 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.06/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_less_eq
% 5.06/5.38 thf(fact_6326_less__minus__divide__eq,axiom,
% 5.06/5.38 ! [A: real,B: real,C: real] :
% 5.06/5.38 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.06/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % less_minus_divide_eq
% 5.06/5.38 thf(fact_6327_less__minus__divide__eq,axiom,
% 5.06/5.38 ! [A: rat,B: rat,C: rat] :
% 5.06/5.38 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.06/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % less_minus_divide_eq
% 5.06/5.38 thf(fact_6328_eq__divide__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [W: num,B: real,C: real] :
% 5.06/5.38 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.06/5.38 = ( divide_divide_real @ B @ C ) )
% 5.06/5.38 = ( ( ( C != zero_zero_real )
% 5.06/5.38 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.06/5.38 = B ) )
% 5.06/5.38 & ( ( C = zero_zero_real )
% 5.06/5.38 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.06/5.38 = zero_zero_real ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % eq_divide_eq_numeral(2)
% 5.06/5.38 thf(fact_6329_eq__divide__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [W: num,B: complex,C: complex] :
% 5.06/5.38 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.38 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.06/5.38 = ( ( ( C != zero_zero_complex )
% 5.06/5.38 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.06/5.38 = B ) )
% 5.06/5.38 & ( ( C = zero_zero_complex )
% 5.06/5.38 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.38 = zero_zero_complex ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % eq_divide_eq_numeral(2)
% 5.06/5.38 thf(fact_6330_eq__divide__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [W: num,B: rat,C: rat] :
% 5.06/5.38 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.06/5.38 = ( divide_divide_rat @ B @ C ) )
% 5.06/5.38 = ( ( ( C != zero_zero_rat )
% 5.06/5.38 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.06/5.38 = B ) )
% 5.06/5.38 & ( ( C = zero_zero_rat )
% 5.06/5.38 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.06/5.38 = zero_zero_rat ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % eq_divide_eq_numeral(2)
% 5.06/5.38 thf(fact_6331_divide__eq__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [B: real,C: real,W: num] :
% 5.06/5.38 ( ( ( divide_divide_real @ B @ C )
% 5.06/5.38 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.06/5.38 = ( ( ( C != zero_zero_real )
% 5.06/5.38 => ( B
% 5.06/5.38 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ( C = zero_zero_real )
% 5.06/5.38 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.06/5.38 = zero_zero_real ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % divide_eq_eq_numeral(2)
% 5.06/5.38 thf(fact_6332_divide__eq__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [B: complex,C: complex,W: num] :
% 5.06/5.38 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.38 = ( ( ( C != zero_zero_complex )
% 5.06/5.38 => ( B
% 5.06/5.38 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ( C = zero_zero_complex )
% 5.06/5.38 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.38 = zero_zero_complex ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % divide_eq_eq_numeral(2)
% 5.06/5.38 thf(fact_6333_divide__eq__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [B: rat,C: rat,W: num] :
% 5.06/5.38 ( ( ( divide_divide_rat @ B @ C )
% 5.06/5.38 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.06/5.38 = ( ( ( C != zero_zero_rat )
% 5.06/5.38 => ( B
% 5.06/5.38 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ( C = zero_zero_rat )
% 5.06/5.38 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.06/5.38 = zero_zero_rat ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % divide_eq_eq_numeral(2)
% 5.06/5.38 thf(fact_6334_minus__divide__add__eq__iff,axiom,
% 5.06/5.38 ! [Z: real,X: real,Y: real] :
% 5.06/5.38 ( ( Z != zero_zero_real )
% 5.06/5.38 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 5.06/5.38 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_add_eq_iff
% 5.06/5.38 thf(fact_6335_minus__divide__add__eq__iff,axiom,
% 5.06/5.38 ! [Z: complex,X: complex,Y: complex] :
% 5.06/5.38 ( ( Z != zero_zero_complex )
% 5.06/5.38 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 5.06/5.38 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_add_eq_iff
% 5.06/5.38 thf(fact_6336_minus__divide__add__eq__iff,axiom,
% 5.06/5.38 ! [Z: rat,X: rat,Y: rat] :
% 5.06/5.38 ( ( Z != zero_zero_rat )
% 5.06/5.38 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 5.06/5.38 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_add_eq_iff
% 5.06/5.38 thf(fact_6337_add__divide__eq__if__simps_I3_J,axiom,
% 5.06/5.38 ! [Z: real,A: real,B: real] :
% 5.06/5.38 ( ( ( Z = zero_zero_real )
% 5.06/5.38 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.06/5.38 = B ) )
% 5.06/5.38 & ( ( Z != zero_zero_real )
% 5.06/5.38 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.06/5.38 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_divide_eq_if_simps(3)
% 5.06/5.38 thf(fact_6338_add__divide__eq__if__simps_I3_J,axiom,
% 5.06/5.38 ! [Z: complex,A: complex,B: complex] :
% 5.06/5.38 ( ( ( Z = zero_zero_complex )
% 5.06/5.38 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.06/5.38 = B ) )
% 5.06/5.38 & ( ( Z != zero_zero_complex )
% 5.06/5.38 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.06/5.38 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_divide_eq_if_simps(3)
% 5.06/5.38 thf(fact_6339_add__divide__eq__if__simps_I3_J,axiom,
% 5.06/5.38 ! [Z: rat,A: rat,B: rat] :
% 5.06/5.38 ( ( ( Z = zero_zero_rat )
% 5.06/5.38 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.06/5.38 = B ) )
% 5.06/5.38 & ( ( Z != zero_zero_rat )
% 5.06/5.38 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.06/5.38 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_divide_eq_if_simps(3)
% 5.06/5.38 thf(fact_6340_add__divide__eq__if__simps_I6_J,axiom,
% 5.06/5.38 ! [Z: real,A: real,B: real] :
% 5.06/5.38 ( ( ( Z = zero_zero_real )
% 5.06/5.38 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.06/5.38 = ( uminus_uminus_real @ B ) ) )
% 5.06/5.38 & ( ( Z != zero_zero_real )
% 5.06/5.38 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.06/5.38 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_divide_eq_if_simps(6)
% 5.06/5.38 thf(fact_6341_add__divide__eq__if__simps_I6_J,axiom,
% 5.06/5.38 ! [Z: complex,A: complex,B: complex] :
% 5.06/5.38 ( ( ( Z = zero_zero_complex )
% 5.06/5.38 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.06/5.38 & ( ( Z != zero_zero_complex )
% 5.06/5.38 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.06/5.38 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_divide_eq_if_simps(6)
% 5.06/5.38 thf(fact_6342_add__divide__eq__if__simps_I6_J,axiom,
% 5.06/5.38 ! [Z: rat,A: rat,B: rat] :
% 5.06/5.38 ( ( ( Z = zero_zero_rat )
% 5.06/5.38 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.06/5.38 = ( uminus_uminus_rat @ B ) ) )
% 5.06/5.38 & ( ( Z != zero_zero_rat )
% 5.06/5.38 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.06/5.38 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_divide_eq_if_simps(6)
% 5.06/5.38 thf(fact_6343_add__divide__eq__if__simps_I5_J,axiom,
% 5.06/5.38 ! [Z: real,A: real,B: real] :
% 5.06/5.38 ( ( ( Z = zero_zero_real )
% 5.06/5.38 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.06/5.38 = ( uminus_uminus_real @ B ) ) )
% 5.06/5.38 & ( ( Z != zero_zero_real )
% 5.06/5.38 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.06/5.38 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_divide_eq_if_simps(5)
% 5.06/5.38 thf(fact_6344_add__divide__eq__if__simps_I5_J,axiom,
% 5.06/5.38 ! [Z: complex,A: complex,B: complex] :
% 5.06/5.38 ( ( ( Z = zero_zero_complex )
% 5.06/5.38 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.06/5.38 & ( ( Z != zero_zero_complex )
% 5.06/5.38 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.06/5.38 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_divide_eq_if_simps(5)
% 5.06/5.38 thf(fact_6345_add__divide__eq__if__simps_I5_J,axiom,
% 5.06/5.38 ! [Z: rat,A: rat,B: rat] :
% 5.06/5.38 ( ( ( Z = zero_zero_rat )
% 5.06/5.38 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.06/5.38 = ( uminus_uminus_rat @ B ) ) )
% 5.06/5.38 & ( ( Z != zero_zero_rat )
% 5.06/5.38 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.06/5.38 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_divide_eq_if_simps(5)
% 5.06/5.38 thf(fact_6346_minus__divide__diff__eq__iff,axiom,
% 5.06/5.38 ! [Z: real,X: real,Y: real] :
% 5.06/5.38 ( ( Z != zero_zero_real )
% 5.06/5.38 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 5.06/5.38 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_diff_eq_iff
% 5.06/5.38 thf(fact_6347_minus__divide__diff__eq__iff,axiom,
% 5.06/5.38 ! [Z: complex,X: complex,Y: complex] :
% 5.06/5.38 ( ( Z != zero_zero_complex )
% 5.06/5.38 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 5.06/5.38 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_diff_eq_iff
% 5.06/5.38 thf(fact_6348_minus__divide__diff__eq__iff,axiom,
% 5.06/5.38 ! [Z: rat,X: rat,Y: rat] :
% 5.06/5.38 ( ( Z != zero_zero_rat )
% 5.06/5.38 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 5.06/5.38 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_diff_eq_iff
% 5.06/5.38 thf(fact_6349_even__minus,axiom,
% 5.06/5.38 ! [A: int] :
% 5.06/5.38 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.06/5.38 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.06/5.38
% 5.06/5.38 % even_minus
% 5.06/5.38 thf(fact_6350_even__minus,axiom,
% 5.06/5.38 ! [A: code_integer] :
% 5.06/5.38 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.06/5.38 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.06/5.38
% 5.06/5.38 % even_minus
% 5.06/5.38 thf(fact_6351_power2__eq__iff,axiom,
% 5.06/5.38 ! [X: real,Y: real] :
% 5.06/5.38 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.38 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.38 = ( ( X = Y )
% 5.06/5.38 | ( X
% 5.06/5.38 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power2_eq_iff
% 5.06/5.38 thf(fact_6352_power2__eq__iff,axiom,
% 5.06/5.38 ! [X: int,Y: int] :
% 5.06/5.38 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.38 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.38 = ( ( X = Y )
% 5.06/5.38 | ( X
% 5.06/5.38 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power2_eq_iff
% 5.06/5.38 thf(fact_6353_power2__eq__iff,axiom,
% 5.06/5.38 ! [X: complex,Y: complex] :
% 5.06/5.38 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.38 = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.38 = ( ( X = Y )
% 5.06/5.38 | ( X
% 5.06/5.38 = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power2_eq_iff
% 5.06/5.38 thf(fact_6354_power2__eq__iff,axiom,
% 5.06/5.38 ! [X: rat,Y: rat] :
% 5.06/5.38 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.38 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.38 = ( ( X = Y )
% 5.06/5.38 | ( X
% 5.06/5.38 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power2_eq_iff
% 5.06/5.38 thf(fact_6355_power2__eq__iff,axiom,
% 5.06/5.38 ! [X: code_integer,Y: code_integer] :
% 5.06/5.38 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.38 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.38 = ( ( X = Y )
% 5.06/5.38 | ( X
% 5.06/5.38 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power2_eq_iff
% 5.06/5.38 thf(fact_6356_verit__less__mono__div__int2,axiom,
% 5.06/5.38 ! [A2: int,B3: int,N2: int] :
% 5.06/5.38 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.06/5.38 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N2 ) )
% 5.06/5.38 => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N2 ) @ ( divide_divide_int @ A2 @ N2 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % verit_less_mono_div_int2
% 5.06/5.38 thf(fact_6357_sum__mono2,axiom,
% 5.06/5.38 ! [B3: set_real,A2: set_real,F: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.06/5.38 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_mono2
% 5.06/5.38 thf(fact_6358_sum__mono2,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,F: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B2 ) ) )
% 5.06/5.38 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_mono2
% 5.06/5.38 thf(fact_6359_sum__mono2,axiom,
% 5.06/5.38 ! [B3: set_real,A2: set_real,F: real > rat] :
% 5.06/5.38 ( ( finite_finite_real @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.06/5.38 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_mono2
% 5.06/5.38 thf(fact_6360_sum__mono2,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,F: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.06/5.38 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_mono2
% 5.06/5.38 thf(fact_6361_sum__mono2,axiom,
% 5.06/5.38 ! [B3: set_nat,A2: set_nat,F: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.06/5.38 => ( ! [B2: nat] :
% 5.06/5.38 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B2 ) ) )
% 5.06/5.38 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_mono2
% 5.06/5.38 thf(fact_6362_sum__mono2,axiom,
% 5.06/5.38 ! [B3: set_real,A2: set_real,F: real > nat] :
% 5.06/5.38 ( ( finite_finite_real @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B2 ) ) )
% 5.06/5.38 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_mono2
% 5.06/5.38 thf(fact_6363_sum__mono2,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B2 ) ) )
% 5.06/5.38 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_mono2
% 5.06/5.38 thf(fact_6364_sum__mono2,axiom,
% 5.06/5.38 ! [B3: set_real,A2: set_real,F: real > int] :
% 5.06/5.38 ( ( finite_finite_real @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.06/5.38 => ( ! [B2: real] :
% 5.06/5.38 ( ( member_real @ B2 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.06/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B2 ) ) )
% 5.06/5.38 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_mono2
% 5.06/5.38 thf(fact_6365_sum__mono2,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,F: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.06/5.38 => ( ! [B2: complex] :
% 5.06/5.38 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.06/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B2 ) ) )
% 5.06/5.38 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_mono2
% 5.06/5.38 thf(fact_6366_sum__mono2,axiom,
% 5.06/5.38 ! [B3: set_nat,A2: set_nat,F: nat > int] :
% 5.06/5.38 ( ( finite_finite_nat @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.06/5.38 => ( ! [B2: nat] :
% 5.06/5.38 ( ( member_nat @ B2 @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 5.06/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B2 ) ) )
% 5.06/5.38 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_mono2
% 5.06/5.38 thf(fact_6367_ln__le__minus__one,axiom,
% 5.06/5.38 ! [X: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.38 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_le_minus_one
% 5.06/5.38 thf(fact_6368_ln__diff__le,axiom,
% 5.06/5.38 ! [X: real,Y: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.38 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.38 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_diff_le
% 5.06/5.38 thf(fact_6369_le__minus__divide__eq,axiom,
% 5.06/5.38 ! [A: real,B: real,C: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.06/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % le_minus_divide_eq
% 5.06/5.38 thf(fact_6370_le__minus__divide__eq,axiom,
% 5.06/5.38 ! [A: rat,B: rat,C: rat] :
% 5.06/5.38 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.06/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % le_minus_divide_eq
% 5.06/5.38 thf(fact_6371_minus__divide__le__eq,axiom,
% 5.06/5.38 ! [B: real,C: real,A: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.06/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_le_eq
% 5.06/5.38 thf(fact_6372_minus__divide__le__eq,axiom,
% 5.06/5.38 ! [B: rat,C: rat,A: rat] :
% 5.06/5.38 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.06/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_divide_le_eq
% 5.06/5.38 thf(fact_6373_neg__le__minus__divide__eq,axiom,
% 5.06/5.38 ! [C: real,A: real,B: real] :
% 5.06/5.38 ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.06/5.38 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_le_minus_divide_eq
% 5.06/5.38 thf(fact_6374_neg__le__minus__divide__eq,axiom,
% 5.06/5.38 ! [C: rat,A: rat,B: rat] :
% 5.06/5.38 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.06/5.38 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_le_minus_divide_eq
% 5.06/5.38 thf(fact_6375_neg__minus__divide__le__eq,axiom,
% 5.06/5.38 ! [C: real,B: real,A: real] :
% 5.06/5.38 ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.06/5.38 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_minus_divide_le_eq
% 5.06/5.38 thf(fact_6376_neg__minus__divide__le__eq,axiom,
% 5.06/5.38 ! [C: rat,B: rat,A: rat] :
% 5.06/5.38 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.06/5.38 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_minus_divide_le_eq
% 5.06/5.38 thf(fact_6377_pos__le__minus__divide__eq,axiom,
% 5.06/5.38 ! [C: real,A: real,B: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.06/5.38 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % pos_le_minus_divide_eq
% 5.06/5.38 thf(fact_6378_pos__le__minus__divide__eq,axiom,
% 5.06/5.38 ! [C: rat,A: rat,B: rat] :
% 5.06/5.38 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.06/5.38 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % pos_le_minus_divide_eq
% 5.06/5.38 thf(fact_6379_pos__minus__divide__le__eq,axiom,
% 5.06/5.38 ! [C: real,B: real,A: real] :
% 5.06/5.38 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.06/5.38 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % pos_minus_divide_le_eq
% 5.06/5.38 thf(fact_6380_pos__minus__divide__le__eq,axiom,
% 5.06/5.38 ! [C: rat,B: rat,A: rat] :
% 5.06/5.38 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.06/5.38 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % pos_minus_divide_le_eq
% 5.06/5.38 thf(fact_6381_less__divide__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [W: num,B: real,C: real] :
% 5.06/5.38 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.06/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % less_divide_eq_numeral(2)
% 5.06/5.38 thf(fact_6382_less__divide__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [W: num,B: rat,C: rat] :
% 5.06/5.38 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % less_divide_eq_numeral(2)
% 5.06/5.38 thf(fact_6383_divide__less__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [B: real,C: real,W: num] :
% 5.06/5.38 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.06/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % divide_less_eq_numeral(2)
% 5.06/5.38 thf(fact_6384_divide__less__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [B: rat,C: rat,W: num] :
% 5.06/5.38 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.06/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % divide_less_eq_numeral(2)
% 5.06/5.38 thf(fact_6385_power2__eq__1__iff,axiom,
% 5.06/5.38 ! [A: real] :
% 5.06/5.38 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.38 = one_one_real )
% 5.06/5.38 = ( ( A = one_one_real )
% 5.06/5.38 | ( A
% 5.06/5.38 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power2_eq_1_iff
% 5.06/5.38 thf(fact_6386_power2__eq__1__iff,axiom,
% 5.06/5.38 ! [A: int] :
% 5.06/5.38 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.38 = one_one_int )
% 5.06/5.38 = ( ( A = one_one_int )
% 5.06/5.38 | ( A
% 5.06/5.38 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power2_eq_1_iff
% 5.06/5.38 thf(fact_6387_power2__eq__1__iff,axiom,
% 5.06/5.38 ! [A: complex] :
% 5.06/5.38 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.38 = one_one_complex )
% 5.06/5.38 = ( ( A = one_one_complex )
% 5.06/5.38 | ( A
% 5.06/5.38 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power2_eq_1_iff
% 5.06/5.38 thf(fact_6388_power2__eq__1__iff,axiom,
% 5.06/5.38 ! [A: rat] :
% 5.06/5.38 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.38 = one_one_rat )
% 5.06/5.38 = ( ( A = one_one_rat )
% 5.06/5.38 | ( A
% 5.06/5.38 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power2_eq_1_iff
% 5.06/5.38 thf(fact_6389_power2__eq__1__iff,axiom,
% 5.06/5.38 ! [A: code_integer] :
% 5.06/5.38 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.38 = one_one_Code_integer )
% 5.06/5.38 = ( ( A = one_one_Code_integer )
% 5.06/5.38 | ( A
% 5.06/5.38 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % power2_eq_1_iff
% 5.06/5.38 thf(fact_6390_uminus__power__if,axiom,
% 5.06/5.38 ! [N2: nat,A: real] :
% 5.06/5.38 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.06/5.38 = ( power_power_real @ A @ N2 ) ) )
% 5.06/5.38 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.06/5.38 = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % uminus_power_if
% 5.06/5.38 thf(fact_6391_uminus__power__if,axiom,
% 5.06/5.38 ! [N2: nat,A: int] :
% 5.06/5.38 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.06/5.38 = ( power_power_int @ A @ N2 ) ) )
% 5.06/5.38 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.06/5.38 = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % uminus_power_if
% 5.06/5.38 thf(fact_6392_uminus__power__if,axiom,
% 5.06/5.38 ! [N2: nat,A: complex] :
% 5.06/5.38 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.06/5.38 = ( power_power_complex @ A @ N2 ) ) )
% 5.06/5.38 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % uminus_power_if
% 5.06/5.38 thf(fact_6393_uminus__power__if,axiom,
% 5.06/5.38 ! [N2: nat,A: rat] :
% 5.06/5.38 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.06/5.38 = ( power_power_rat @ A @ N2 ) ) )
% 5.06/5.38 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.06/5.38 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % uminus_power_if
% 5.06/5.38 thf(fact_6394_uminus__power__if,axiom,
% 5.06/5.38 ! [N2: nat,A: code_integer] :
% 5.06/5.38 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.06/5.38 = ( power_8256067586552552935nteger @ A @ N2 ) ) )
% 5.06/5.38 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.06/5.38 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % uminus_power_if
% 5.06/5.38 thf(fact_6395_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.06/5.38 ! [K: nat,N2: nat] :
% 5.06/5.38 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.38 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.06/5.38 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_power_add_eq_neg_one_power_diff
% 5.06/5.38 thf(fact_6396_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.06/5.38 ! [K: nat,N2: nat] :
% 5.06/5.38 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.38 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.06/5.38 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_power_add_eq_neg_one_power_diff
% 5.06/5.38 thf(fact_6397_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.06/5.38 ! [K: nat,N2: nat] :
% 5.06/5.38 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.38 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.06/5.38 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_power_add_eq_neg_one_power_diff
% 5.06/5.38 thf(fact_6398_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.06/5.38 ! [K: nat,N2: nat] :
% 5.06/5.38 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.38 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.06/5.38 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_power_add_eq_neg_one_power_diff
% 5.06/5.38 thf(fact_6399_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.06/5.38 ! [K: nat,N2: nat] :
% 5.06/5.38 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.38 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.06/5.38 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % neg_one_power_add_eq_neg_one_power_diff
% 5.06/5.38 thf(fact_6400_realpow__square__minus__le,axiom,
% 5.06/5.38 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % realpow_square_minus_le
% 5.06/5.38 thf(fact_6401_ln__one__minus__pos__lower__bound,axiom,
% 5.06/5.38 ! [X: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.38 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.38 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % ln_one_minus_pos_lower_bound
% 5.06/5.38 thf(fact_6402_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.06/5.38 ! [N2: nat,K: int] :
% 5.06/5.38 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.06/5.38 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K ) ) ).
% 5.06/5.38
% 5.06/5.38 % signed_take_bit_int_less_eq_self_iff
% 5.06/5.38 thf(fact_6403_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.06/5.38 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ).
% 5.06/5.38
% 5.06/5.38 % signed_take_bit_int_greater_eq_minus_exp
% 5.06/5.38 thf(fact_6404_signed__take__bit__int__greater__self__iff,axiom,
% 5.06/5.38 ! [K: int,N2: nat] :
% 5.06/5.38 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.06/5.38 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % signed_take_bit_int_greater_self_iff
% 5.06/5.38 thf(fact_6405_minus__mod__int__eq,axiom,
% 5.06/5.38 ! [L2: int,K: int] :
% 5.06/5.38 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.06/5.38 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.06/5.38 = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_mod_int_eq
% 5.06/5.38 thf(fact_6406_zmod__minus1,axiom,
% 5.06/5.38 ! [B: int] :
% 5.06/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.38 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.06/5.38 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % zmod_minus1
% 5.06/5.38 thf(fact_6407_sum__strict__mono2,axiom,
% 5.06/5.38 ! [B3: set_real,A2: set_real,B: real,F: real > real] :
% 5.06/5.38 ( ( finite_finite_real @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.06/5.38 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.06/5.38 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ B3 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono2
% 5.06/5.38 thf(fact_6408_sum__strict__mono2,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.06/5.38 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.06/5.38 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ B3 )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono2
% 5.06/5.38 thf(fact_6409_sum__strict__mono2,axiom,
% 5.06/5.38 ! [B3: set_real,A2: set_real,B: real,F: real > rat] :
% 5.06/5.38 ( ( finite_finite_real @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.06/5.38 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.06/5.38 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ B3 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono2
% 5.06/5.38 thf(fact_6410_sum__strict__mono2,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.06/5.38 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.06/5.38 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ B3 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono2
% 5.06/5.38 thf(fact_6411_sum__strict__mono2,axiom,
% 5.06/5.38 ! [B3: set_nat,A2: set_nat,B: nat,F: nat > rat] :
% 5.06/5.38 ( ( finite_finite_nat @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.06/5.38 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 5.06/5.38 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ B3 )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono2
% 5.06/5.38 thf(fact_6412_sum__strict__mono2,axiom,
% 5.06/5.38 ! [B3: set_real,A2: set_real,B: real,F: real > nat] :
% 5.06/5.38 ( ( finite_finite_real @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.06/5.38 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.06/5.38 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ B3 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono2
% 5.06/5.38 thf(fact_6413_sum__strict__mono2,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.06/5.38 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.06/5.38 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ B3 )
% 5.06/5.38 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono2
% 5.06/5.38 thf(fact_6414_sum__strict__mono2,axiom,
% 5.06/5.38 ! [B3: set_real,A2: set_real,B: real,F: real > int] :
% 5.06/5.38 ( ( finite_finite_real @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.06/5.38 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.06/5.38 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.06/5.38 => ( ! [X3: real] :
% 5.06/5.38 ( ( member_real @ X3 @ B3 )
% 5.06/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono2
% 5.06/5.38 thf(fact_6415_sum__strict__mono2,axiom,
% 5.06/5.38 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > int] :
% 5.06/5.38 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.38 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.06/5.38 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.06/5.38 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.06/5.38 => ( ! [X3: complex] :
% 5.06/5.38 ( ( member_complex @ X3 @ B3 )
% 5.06/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono2
% 5.06/5.38 thf(fact_6416_sum__strict__mono2,axiom,
% 5.06/5.38 ! [B3: set_nat,A2: set_nat,B: nat,F: nat > int] :
% 5.06/5.38 ( ( finite_finite_nat @ B3 )
% 5.06/5.38 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.06/5.38 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 5.06/5.38 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.06/5.38 => ( ! [X3: nat] :
% 5.06/5.38 ( ( member_nat @ X3 @ B3 )
% 5.06/5.38 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.06/5.38 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % sum_strict_mono2
% 5.06/5.38 thf(fact_6417_zdiv__zminus1__eq__if,axiom,
% 5.06/5.38 ! [B: int,A: int] :
% 5.06/5.38 ( ( B != zero_zero_int )
% 5.06/5.38 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.38 = zero_zero_int )
% 5.06/5.38 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.38 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.06/5.38 & ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.38 != zero_zero_int )
% 5.06/5.38 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.38 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % zdiv_zminus1_eq_if
% 5.06/5.38 thf(fact_6418_zdiv__zminus2__eq__if,axiom,
% 5.06/5.38 ! [B: int,A: int] :
% 5.06/5.38 ( ( B != zero_zero_int )
% 5.06/5.38 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.38 = zero_zero_int )
% 5.06/5.38 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.38 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.06/5.38 & ( ( ( modulo_modulo_int @ A @ B )
% 5.06/5.38 != zero_zero_int )
% 5.06/5.38 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.06/5.38 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % zdiv_zminus2_eq_if
% 5.06/5.38 thf(fact_6419_zminus1__lemma,axiom,
% 5.06/5.38 ! [A: int,B: int,Q2: int,R2: int] :
% 5.06/5.38 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.06/5.38 => ( ( B != zero_zero_int )
% 5.06/5.38 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R2 ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % zminus1_lemma
% 5.06/5.38 thf(fact_6420_le__divide__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [W: num,B: real,C: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.06/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % le_divide_eq_numeral(2)
% 5.06/5.38 thf(fact_6421_le__divide__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [W: num,B: rat,C: rat] :
% 5.06/5.38 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.06/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % le_divide_eq_numeral(2)
% 5.06/5.38 thf(fact_6422_divide__le__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [B: real,C: real,W: num] :
% 5.06/5.38 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.06/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.38 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.06/5.38 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.06/5.38 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % divide_le_eq_numeral(2)
% 5.06/5.38 thf(fact_6423_divide__le__eq__numeral_I2_J,axiom,
% 5.06/5.38 ! [B: rat,C: rat,W: num] :
% 5.06/5.38 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.06/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.06/5.38 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.06/5.38 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.06/5.38 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % divide_le_eq_numeral(2)
% 5.06/5.38 thf(fact_6424_square__le__1,axiom,
% 5.06/5.38 ! [X: real] :
% 5.06/5.38 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.38 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.38 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % square_le_1
% 5.06/5.38 thf(fact_6425_square__le__1,axiom,
% 5.06/5.38 ! [X: code_integer] :
% 5.06/5.38 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.06/5.38 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 5.06/5.38 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % square_le_1
% 5.06/5.38 thf(fact_6426_square__le__1,axiom,
% 5.06/5.38 ! [X: rat] :
% 5.06/5.38 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 5.06/5.38 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 5.06/5.38 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % square_le_1
% 5.06/5.38 thf(fact_6427_square__le__1,axiom,
% 5.06/5.38 ! [X: int] :
% 5.06/5.38 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.06/5.38 => ( ( ord_less_eq_int @ X @ one_one_int )
% 5.06/5.38 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % square_le_1
% 5.06/5.38 thf(fact_6428_minus__power__mult__self,axiom,
% 5.06/5.38 ! [A: real,N2: nat] :
% 5.06/5.38 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 5.06/5.38 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_power_mult_self
% 5.06/5.38 thf(fact_6429_minus__power__mult__self,axiom,
% 5.06/5.38 ! [A: int,N2: nat] :
% 5.06/5.38 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.06/5.38 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_power_mult_self
% 5.06/5.38 thf(fact_6430_minus__power__mult__self,axiom,
% 5.06/5.38 ! [A: complex,N2: nat] :
% 5.06/5.38 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) )
% 5.06/5.38 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_power_mult_self
% 5.06/5.38 thf(fact_6431_minus__power__mult__self,axiom,
% 5.06/5.38 ! [A: rat,N2: nat] :
% 5.06/5.38 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 5.06/5.38 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_power_mult_self
% 5.06/5.38 thf(fact_6432_minus__power__mult__self,axiom,
% 5.06/5.38 ! [A: code_integer,N2: nat] :
% 5.06/5.38 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.06/5.38 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_power_mult_self
% 5.06/5.38 thf(fact_6433_minus__one__power__iff,axiom,
% 5.06/5.38 ! [N2: nat] :
% 5.06/5.38 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.06/5.38 = one_one_real ) )
% 5.06/5.38 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.06/5.38 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_one_power_iff
% 5.06/5.38 thf(fact_6434_minus__one__power__iff,axiom,
% 5.06/5.38 ! [N2: nat] :
% 5.06/5.38 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.06/5.38 = one_one_int ) )
% 5.06/5.38 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.06/5.38 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_one_power_iff
% 5.06/5.38 thf(fact_6435_minus__one__power__iff,axiom,
% 5.06/5.38 ! [N2: nat] :
% 5.06/5.38 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.06/5.38 = one_one_complex ) )
% 5.06/5.38 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.06/5.38 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_one_power_iff
% 5.06/5.38 thf(fact_6436_minus__one__power__iff,axiom,
% 5.06/5.38 ! [N2: nat] :
% 5.06/5.38 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.06/5.38 = one_one_rat ) )
% 5.06/5.38 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.06/5.38 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_one_power_iff
% 5.06/5.38 thf(fact_6437_minus__one__power__iff,axiom,
% 5.06/5.38 ! [N2: nat] :
% 5.06/5.38 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.06/5.38 = one_one_Code_integer ) )
% 5.06/5.38 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.38 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.06/5.38 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_one_power_iff
% 5.06/5.38 thf(fact_6438_signed__take__bit__int__eq__self,axiom,
% 5.06/5.38 ! [N2: nat,K: int] :
% 5.06/5.38 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.06/5.38 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.38 => ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.06/5.38 = K ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % signed_take_bit_int_eq_self
% 5.06/5.38 thf(fact_6439_signed__take__bit__int__eq__self__iff,axiom,
% 5.06/5.38 ! [N2: nat,K: int] :
% 5.06/5.38 ( ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.06/5.38 = K )
% 5.06/5.38 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.06/5.38 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % signed_take_bit_int_eq_self_iff
% 5.06/5.38 thf(fact_6440_minus__1__div__exp__eq__int,axiom,
% 5.06/5.38 ! [N2: nat] :
% 5.06/5.38 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.38 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.38
% 5.06/5.38 % minus_1_div_exp_eq_int
% 5.06/5.38 thf(fact_6441_div__pos__neg__trivial,axiom,
% 5.06/5.38 ! [K: int,L2: int] :
% 5.06/5.38 ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.38 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.06/5.38 => ( ( divide_divide_int @ K @ L2 )
% 5.06/5.38 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % div_pos_neg_trivial
% 5.06/5.38 thf(fact_6442_add__0__iff,axiom,
% 5.06/5.38 ! [B: complex,A: complex] :
% 5.06/5.38 ( ( B
% 5.06/5.38 = ( plus_plus_complex @ B @ A ) )
% 5.06/5.38 = ( A = zero_zero_complex ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_0_iff
% 5.06/5.38 thf(fact_6443_add__0__iff,axiom,
% 5.06/5.38 ! [B: real,A: real] :
% 5.06/5.38 ( ( B
% 5.06/5.38 = ( plus_plus_real @ B @ A ) )
% 5.06/5.38 = ( A = zero_zero_real ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_0_iff
% 5.06/5.38 thf(fact_6444_add__0__iff,axiom,
% 5.06/5.38 ! [B: rat,A: rat] :
% 5.06/5.38 ( ( B
% 5.06/5.38 = ( plus_plus_rat @ B @ A ) )
% 5.06/5.38 = ( A = zero_zero_rat ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_0_iff
% 5.06/5.38 thf(fact_6445_add__0__iff,axiom,
% 5.06/5.38 ! [B: nat,A: nat] :
% 5.06/5.38 ( ( B
% 5.06/5.38 = ( plus_plus_nat @ B @ A ) )
% 5.06/5.38 = ( A = zero_zero_nat ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_0_iff
% 5.06/5.38 thf(fact_6446_add__0__iff,axiom,
% 5.06/5.38 ! [B: int,A: int] :
% 5.06/5.38 ( ( B
% 5.06/5.38 = ( plus_plus_int @ B @ A ) )
% 5.06/5.38 = ( A = zero_zero_int ) ) ).
% 5.06/5.38
% 5.06/5.38 % add_0_iff
% 5.06/5.38 thf(fact_6447_crossproduct__noteq,axiom,
% 5.06/5.38 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.38 ( ( ( A != B )
% 5.06/5.38 & ( C != D ) )
% 5.06/5.38 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.06/5.38 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % crossproduct_noteq
% 5.06/5.38 thf(fact_6448_crossproduct__noteq,axiom,
% 5.06/5.38 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.06/5.38 ( ( ( A != B )
% 5.06/5.38 & ( C != D ) )
% 5.06/5.38 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.06/5.38 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % crossproduct_noteq
% 5.06/5.38 thf(fact_6449_crossproduct__noteq,axiom,
% 5.06/5.38 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.06/5.38 ( ( ( A != B )
% 5.06/5.38 & ( C != D ) )
% 5.06/5.38 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.06/5.38 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % crossproduct_noteq
% 5.06/5.38 thf(fact_6450_crossproduct__noteq,axiom,
% 5.06/5.38 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.38 ( ( ( A != B )
% 5.06/5.38 & ( C != D ) )
% 5.06/5.38 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.06/5.38 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % crossproduct_noteq
% 5.06/5.38 thf(fact_6451_crossproduct__eq,axiom,
% 5.06/5.38 ! [W: real,Y: real,X: real,Z: real] :
% 5.06/5.38 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X @ Z ) )
% 5.06/5.38 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y ) ) )
% 5.06/5.38 = ( ( W = X )
% 5.06/5.38 | ( Y = Z ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % crossproduct_eq
% 5.06/5.38 thf(fact_6452_crossproduct__eq,axiom,
% 5.06/5.38 ! [W: rat,Y: rat,X: rat,Z: rat] :
% 5.06/5.38 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 5.06/5.38 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 5.06/5.38 = ( ( W = X )
% 5.06/5.38 | ( Y = Z ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % crossproduct_eq
% 5.06/5.38 thf(fact_6453_crossproduct__eq,axiom,
% 5.06/5.38 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 5.06/5.38 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 5.06/5.38 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 5.06/5.38 = ( ( W = X )
% 5.06/5.38 | ( Y = Z ) ) ) ).
% 5.06/5.38
% 5.06/5.38 % crossproduct_eq
% 5.06/5.38 thf(fact_6454_crossproduct__eq,axiom,
% 5.06/5.38 ! [W: int,Y: int,X: int,Z: int] :
% 5.06/5.38 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 5.06/5.39 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 5.06/5.39 = ( ( W = X )
% 5.06/5.39 | ( Y = Z ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % crossproduct_eq
% 5.06/5.39 thf(fact_6455_power__minus1__odd,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.39 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_minus1_odd
% 5.06/5.39 thf(fact_6456_power__minus1__odd,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.39 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_minus1_odd
% 5.06/5.39 thf(fact_6457_power__minus1__odd,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.39 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_minus1_odd
% 5.06/5.39 thf(fact_6458_power__minus1__odd,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.39 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_minus1_odd
% 5.06/5.39 thf(fact_6459_power__minus1__odd,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_minus1_odd
% 5.06/5.39 thf(fact_6460_int__bit__induct,axiom,
% 5.06/5.39 ! [P: int > $o,K: int] :
% 5.06/5.39 ( ( P @ zero_zero_int )
% 5.06/5.39 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.39 => ( ! [K2: int] :
% 5.06/5.39 ( ( P @ K2 )
% 5.06/5.39 => ( ( K2 != zero_zero_int )
% 5.06/5.39 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.39 => ( ! [K2: int] :
% 5.06/5.39 ( ( P @ K2 )
% 5.06/5.39 => ( ( K2
% 5.06/5.39 != ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.39 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.06/5.39 => ( P @ K ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % int_bit_induct
% 5.06/5.39 thf(fact_6461_divmod__step__nat__def,axiom,
% 5.06/5.39 ( unique5026877609467782581ep_nat
% 5.06/5.39 = ( ^ [L: num] :
% 5.06/5.39 ( produc2626176000494625587at_nat
% 5.06/5.39 @ ^ [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 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_step_nat_def
% 5.06/5.39 thf(fact_6462_ln__one__plus__pos__lower__bound,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.39 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.39 => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % ln_one_plus_pos_lower_bound
% 5.06/5.39 thf(fact_6463_signed__take__bit__int__greater__eq,axiom,
% 5.06/5.39 ! [K: int,N2: nat] :
% 5.06/5.39 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.39 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % signed_take_bit_int_greater_eq
% 5.06/5.39 thf(fact_6464_divmod__step__int__def,axiom,
% 5.06/5.39 ( unique5024387138958732305ep_int
% 5.06/5.39 = ( ^ [L: num] :
% 5.06/5.39 ( produc4245557441103728435nt_int
% 5.06/5.39 @ ^ [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 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_step_int_def
% 5.06/5.39 thf(fact_6465_ln__2__less__1,axiom,
% 5.06/5.39 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.06/5.39
% 5.06/5.39 % ln_2_less_1
% 5.06/5.39 thf(fact_6466_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.39 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.39 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.06/5.39 thf(fact_6467_tanh__ln__real,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.39 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 5.06/5.39 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % tanh_ln_real
% 5.06/5.39 thf(fact_6468_divmod__algorithm__code_I5_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( produc4245557441103728435nt_int
% 5.06/5.39 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.06/5.39 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(5)
% 5.06/5.39 thf(fact_6469_divmod__algorithm__code_I5_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( produc2626176000494625587at_nat
% 5.06/5.39 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.06/5.39 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(5)
% 5.06/5.39 thf(fact_6470_divmod__algorithm__code_I5_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( produc6916734918728496179nteger
% 5.06/5.39 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 5.06/5.39 @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(5)
% 5.06/5.39 thf(fact_6471_divmod__nat__if,axiom,
% 5.06/5.39 ( divmod_nat
% 5.06/5.39 = ( ^ [M6: nat,N: nat] :
% 5.06/5.39 ( if_Pro6206227464963214023at_nat
% 5.06/5.39 @ ( ( N = zero_zero_nat )
% 5.06/5.39 | ( ord_less_nat @ M6 @ N ) )
% 5.06/5.39 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 5.06/5.39 @ ( produc2626176000494625587at_nat
% 5.06/5.39 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.06/5.39 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_nat_if
% 5.06/5.39 thf(fact_6472_signed__take__bit__Suc__minus__bit1,axiom,
% 5.06/5.39 ! [N2: nat,K: num] :
% 5.06/5.39 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.06/5.39 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % signed_take_bit_Suc_minus_bit1
% 5.06/5.39 thf(fact_6473_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.39 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ln_one_plus_x_minus_x_bound
% 5.06/5.39 thf(fact_6474_semiring__norm_I90_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ( bit1 @ M )
% 5.06/5.39 = ( bit1 @ N2 ) )
% 5.06/5.39 = ( M = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(90)
% 5.06/5.39 thf(fact_6475_abs__abs,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.06/5.39 = ( abs_abs_real @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_abs
% 5.06/5.39 thf(fact_6476_abs__abs,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.06/5.39 = ( abs_abs_int @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_abs
% 5.06/5.39 thf(fact_6477_abs__abs,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.06/5.39 = ( abs_abs_rat @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_abs
% 5.06/5.39 thf(fact_6478_abs__abs,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.06/5.39 = ( abs_abs_Code_integer @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_abs
% 5.06/5.39 thf(fact_6479_case__prodI,axiom,
% 5.06/5.39 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.06/5.39 ( ( F @ A @ B )
% 5.06/5.39 => ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI
% 5.06/5.39 thf(fact_6480_case__prodI,axiom,
% 5.06/5.39 ! [F: num > num > $o,A: num,B: num] :
% 5.06/5.39 ( ( F @ A @ B )
% 5.06/5.39 => ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI
% 5.06/5.39 thf(fact_6481_case__prodI,axiom,
% 5.06/5.39 ! [F: nat > num > $o,A: nat,B: num] :
% 5.06/5.39 ( ( F @ A @ B )
% 5.06/5.39 => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI
% 5.06/5.39 thf(fact_6482_case__prodI,axiom,
% 5.06/5.39 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.06/5.39 ( ( F @ A @ B )
% 5.06/5.39 => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI
% 5.06/5.39 thf(fact_6483_case__prodI,axiom,
% 5.06/5.39 ! [F: int > int > $o,A: int,B: int] :
% 5.06/5.39 ( ( F @ A @ B )
% 5.06/5.39 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI
% 5.06/5.39 thf(fact_6484_case__prodI2,axiom,
% 5.06/5.39 ! [P4: produc6271795597528267376eger_o,C: code_integer > $o > $o] :
% 5.06/5.39 ( ! [A3: code_integer,B2: $o] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( produc6677183202524767010eger_o @ A3 @ B2 ) )
% 5.06/5.39 => ( C @ A3 @ B2 ) )
% 5.06/5.39 => ( produc7828578312038201481er_o_o @ C @ P4 ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI2
% 5.06/5.39 thf(fact_6485_case__prodI2,axiom,
% 5.06/5.39 ! [P4: product_prod_num_num,C: num > num > $o] :
% 5.06/5.39 ( ! [A3: num,B2: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_num_num @ A3 @ B2 ) )
% 5.06/5.39 => ( C @ A3 @ B2 ) )
% 5.06/5.39 => ( produc5703948589228662326_num_o @ C @ P4 ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI2
% 5.06/5.39 thf(fact_6486_case__prodI2,axiom,
% 5.06/5.39 ! [P4: product_prod_nat_num,C: nat > num > $o] :
% 5.06/5.39 ( ! [A3: nat,B2: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_nat_num @ A3 @ B2 ) )
% 5.06/5.39 => ( C @ A3 @ B2 ) )
% 5.06/5.39 => ( produc4927758841916487424_num_o @ C @ P4 ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI2
% 5.06/5.39 thf(fact_6487_case__prodI2,axiom,
% 5.06/5.39 ! [P4: product_prod_nat_nat,C: nat > nat > $o] :
% 5.06/5.39 ( ! [A3: nat,B2: nat] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_nat_nat @ A3 @ B2 ) )
% 5.06/5.39 => ( C @ A3 @ B2 ) )
% 5.06/5.39 => ( produc6081775807080527818_nat_o @ C @ P4 ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI2
% 5.06/5.39 thf(fact_6488_case__prodI2,axiom,
% 5.06/5.39 ! [P4: product_prod_int_int,C: int > int > $o] :
% 5.06/5.39 ( ! [A3: int,B2: int] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_int_int @ A3 @ B2 ) )
% 5.06/5.39 => ( C @ A3 @ B2 ) )
% 5.06/5.39 => ( produc4947309494688390418_int_o @ C @ P4 ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI2
% 5.06/5.39 thf(fact_6489_mem__case__prodI,axiom,
% 5.06/5.39 ! [Z: complex,C: code_integer > $o > set_complex,A: code_integer,B: $o] :
% 5.06/5.39 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.06/5.39 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI
% 5.06/5.39 thf(fact_6490_mem__case__prodI,axiom,
% 5.06/5.39 ! [Z: real,C: code_integer > $o > set_real,A: code_integer,B: $o] :
% 5.06/5.39 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.06/5.39 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI
% 5.06/5.39 thf(fact_6491_mem__case__prodI,axiom,
% 5.06/5.39 ! [Z: nat,C: code_integer > $o > set_nat,A: code_integer,B: $o] :
% 5.06/5.39 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.06/5.39 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI
% 5.06/5.39 thf(fact_6492_mem__case__prodI,axiom,
% 5.06/5.39 ! [Z: int,C: code_integer > $o > set_int,A: code_integer,B: $o] :
% 5.06/5.39 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.06/5.39 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI
% 5.06/5.39 thf(fact_6493_mem__case__prodI,axiom,
% 5.06/5.39 ! [Z: complex,C: num > num > set_complex,A: num,B: num] :
% 5.06/5.39 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.06/5.39 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI
% 5.06/5.39 thf(fact_6494_mem__case__prodI,axiom,
% 5.06/5.39 ! [Z: real,C: num > num > set_real,A: num,B: num] :
% 5.06/5.39 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.06/5.39 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI
% 5.06/5.39 thf(fact_6495_mem__case__prodI,axiom,
% 5.06/5.39 ! [Z: nat,C: num > num > set_nat,A: num,B: num] :
% 5.06/5.39 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.06/5.39 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI
% 5.06/5.39 thf(fact_6496_mem__case__prodI,axiom,
% 5.06/5.39 ! [Z: int,C: num > num > set_int,A: num,B: num] :
% 5.06/5.39 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.06/5.39 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI
% 5.06/5.39 thf(fact_6497_mem__case__prodI,axiom,
% 5.06/5.39 ! [Z: complex,C: nat > num > set_complex,A: nat,B: num] :
% 5.06/5.39 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.06/5.39 => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI
% 5.06/5.39 thf(fact_6498_mem__case__prodI,axiom,
% 5.06/5.39 ! [Z: real,C: nat > num > set_real,A: nat,B: num] :
% 5.06/5.39 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.06/5.39 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI
% 5.06/5.39 thf(fact_6499_mem__case__prodI2,axiom,
% 5.06/5.39 ! [P4: produc6271795597528267376eger_o,Z: complex,C: code_integer > $o > set_complex] :
% 5.06/5.39 ( ! [A3: code_integer,B2: $o] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( produc6677183202524767010eger_o @ A3 @ B2 ) )
% 5.06/5.39 => ( member_complex @ Z @ ( C @ A3 @ B2 ) ) )
% 5.06/5.39 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI2
% 5.06/5.39 thf(fact_6500_mem__case__prodI2,axiom,
% 5.06/5.39 ! [P4: produc6271795597528267376eger_o,Z: real,C: code_integer > $o > set_real] :
% 5.06/5.39 ( ! [A3: code_integer,B2: $o] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( produc6677183202524767010eger_o @ A3 @ B2 ) )
% 5.06/5.39 => ( member_real @ Z @ ( C @ A3 @ B2 ) ) )
% 5.06/5.39 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI2
% 5.06/5.39 thf(fact_6501_mem__case__prodI2,axiom,
% 5.06/5.39 ! [P4: produc6271795597528267376eger_o,Z: nat,C: code_integer > $o > set_nat] :
% 5.06/5.39 ( ! [A3: code_integer,B2: $o] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( produc6677183202524767010eger_o @ A3 @ B2 ) )
% 5.06/5.39 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 5.06/5.39 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI2
% 5.06/5.39 thf(fact_6502_mem__case__prodI2,axiom,
% 5.06/5.39 ! [P4: produc6271795597528267376eger_o,Z: int,C: code_integer > $o > set_int] :
% 5.06/5.39 ( ! [A3: code_integer,B2: $o] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( produc6677183202524767010eger_o @ A3 @ B2 ) )
% 5.06/5.39 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 5.06/5.39 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI2
% 5.06/5.39 thf(fact_6503_mem__case__prodI2,axiom,
% 5.06/5.39 ! [P4: product_prod_num_num,Z: complex,C: num > num > set_complex] :
% 5.06/5.39 ( ! [A3: num,B2: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_num_num @ A3 @ B2 ) )
% 5.06/5.39 => ( member_complex @ Z @ ( C @ A3 @ B2 ) ) )
% 5.06/5.39 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI2
% 5.06/5.39 thf(fact_6504_mem__case__prodI2,axiom,
% 5.06/5.39 ! [P4: product_prod_num_num,Z: real,C: num > num > set_real] :
% 5.06/5.39 ( ! [A3: num,B2: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_num_num @ A3 @ B2 ) )
% 5.06/5.39 => ( member_real @ Z @ ( C @ A3 @ B2 ) ) )
% 5.06/5.39 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI2
% 5.06/5.39 thf(fact_6505_mem__case__prodI2,axiom,
% 5.06/5.39 ! [P4: product_prod_num_num,Z: nat,C: num > num > set_nat] :
% 5.06/5.39 ( ! [A3: num,B2: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_num_num @ A3 @ B2 ) )
% 5.06/5.39 => ( member_nat @ Z @ ( C @ A3 @ B2 ) ) )
% 5.06/5.39 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI2
% 5.06/5.39 thf(fact_6506_mem__case__prodI2,axiom,
% 5.06/5.39 ! [P4: product_prod_num_num,Z: int,C: num > num > set_int] :
% 5.06/5.39 ( ! [A3: num,B2: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_num_num @ A3 @ B2 ) )
% 5.06/5.39 => ( member_int @ Z @ ( C @ A3 @ B2 ) ) )
% 5.06/5.39 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI2
% 5.06/5.39 thf(fact_6507_mem__case__prodI2,axiom,
% 5.06/5.39 ! [P4: product_prod_nat_num,Z: complex,C: nat > num > set_complex] :
% 5.06/5.39 ( ! [A3: nat,B2: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_nat_num @ A3 @ B2 ) )
% 5.06/5.39 => ( member_complex @ Z @ ( C @ A3 @ B2 ) ) )
% 5.06/5.39 => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI2
% 5.06/5.39 thf(fact_6508_mem__case__prodI2,axiom,
% 5.06/5.39 ! [P4: product_prod_nat_num,Z: real,C: nat > num > set_real] :
% 5.06/5.39 ( ! [A3: nat,B2: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_nat_num @ A3 @ B2 ) )
% 5.06/5.39 => ( member_real @ Z @ ( C @ A3 @ B2 ) ) )
% 5.06/5.39 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodI2
% 5.06/5.39 thf(fact_6509_case__prodI2_H,axiom,
% 5.06/5.39 ! [P4: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 5.06/5.39 ( ! [A3: nat,B2: nat] :
% 5.06/5.39 ( ( ( product_Pair_nat_nat @ A3 @ B2 )
% 5.06/5.39 = P4 )
% 5.06/5.39 => ( C @ A3 @ B2 @ X ) )
% 5.06/5.39 => ( produc8739625826339149834_nat_o @ C @ P4 @ X ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodI2'
% 5.06/5.39 thf(fact_6510_abs__0,axiom,
% 5.06/5.39 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.06/5.39 = zero_z3403309356797280102nteger ) ).
% 5.06/5.39
% 5.06/5.39 % abs_0
% 5.06/5.39 thf(fact_6511_abs__0,axiom,
% 5.06/5.39 ( ( abs_abs_complex @ zero_zero_complex )
% 5.06/5.39 = zero_zero_complex ) ).
% 5.06/5.39
% 5.06/5.39 % abs_0
% 5.06/5.39 thf(fact_6512_abs__0,axiom,
% 5.06/5.39 ( ( abs_abs_real @ zero_zero_real )
% 5.06/5.39 = zero_zero_real ) ).
% 5.06/5.39
% 5.06/5.39 % abs_0
% 5.06/5.39 thf(fact_6513_abs__0,axiom,
% 5.06/5.39 ( ( abs_abs_rat @ zero_zero_rat )
% 5.06/5.39 = zero_zero_rat ) ).
% 5.06/5.39
% 5.06/5.39 % abs_0
% 5.06/5.39 thf(fact_6514_abs__0,axiom,
% 5.06/5.39 ( ( abs_abs_int @ zero_zero_int )
% 5.06/5.39 = zero_zero_int ) ).
% 5.06/5.39
% 5.06/5.39 % abs_0
% 5.06/5.39 thf(fact_6515_semiring__norm_I89_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( bit1 @ M )
% 5.06/5.39 != ( bit0 @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(89)
% 5.06/5.39 thf(fact_6516_semiring__norm_I88_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( bit0 @ M )
% 5.06/5.39 != ( bit1 @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(88)
% 5.06/5.39 thf(fact_6517_semiring__norm_I86_J,axiom,
% 5.06/5.39 ! [M: num] :
% 5.06/5.39 ( ( bit1 @ M )
% 5.06/5.39 != one ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(86)
% 5.06/5.39 thf(fact_6518_semiring__norm_I84_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( one
% 5.06/5.39 != ( bit1 @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(84)
% 5.06/5.39 thf(fact_6519_abs__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 5.06/5.39 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_numeral
% 5.06/5.39 thf(fact_6520_abs__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( abs_abs_real @ ( numeral_numeral_real @ N2 ) )
% 5.06/5.39 = ( numeral_numeral_real @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_numeral
% 5.06/5.39 thf(fact_6521_abs__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.06/5.39 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_numeral
% 5.06/5.39 thf(fact_6522_abs__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( abs_abs_int @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.39 = ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_numeral
% 5.06/5.39 thf(fact_6523_abs__mult__self__eq,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.06/5.39 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_self_eq
% 5.06/5.39 thf(fact_6524_abs__mult__self__eq,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.06/5.39 = ( times_times_real @ A @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_self_eq
% 5.06/5.39 thf(fact_6525_abs__mult__self__eq,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.06/5.39 = ( times_times_rat @ A @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_self_eq
% 5.06/5.39 thf(fact_6526_abs__mult__self__eq,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.06/5.39 = ( times_times_int @ A @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_self_eq
% 5.06/5.39 thf(fact_6527_abs__add__abs,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.06/5.39 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_add_abs
% 5.06/5.39 thf(fact_6528_abs__add__abs,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.06/5.39 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_add_abs
% 5.06/5.39 thf(fact_6529_abs__add__abs,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.06/5.39 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_add_abs
% 5.06/5.39 thf(fact_6530_abs__add__abs,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.06/5.39 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_add_abs
% 5.06/5.39 thf(fact_6531_abs__1,axiom,
% 5.06/5.39 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.06/5.39 = one_one_Code_integer ) ).
% 5.06/5.39
% 5.06/5.39 % abs_1
% 5.06/5.39 thf(fact_6532_abs__1,axiom,
% 5.06/5.39 ( ( abs_abs_complex @ one_one_complex )
% 5.06/5.39 = one_one_complex ) ).
% 5.06/5.39
% 5.06/5.39 % abs_1
% 5.06/5.39 thf(fact_6533_abs__1,axiom,
% 5.06/5.39 ( ( abs_abs_real @ one_one_real )
% 5.06/5.39 = one_one_real ) ).
% 5.06/5.39
% 5.06/5.39 % abs_1
% 5.06/5.39 thf(fact_6534_abs__1,axiom,
% 5.06/5.39 ( ( abs_abs_rat @ one_one_rat )
% 5.06/5.39 = one_one_rat ) ).
% 5.06/5.39
% 5.06/5.39 % abs_1
% 5.06/5.39 thf(fact_6535_abs__1,axiom,
% 5.06/5.39 ( ( abs_abs_int @ one_one_int )
% 5.06/5.39 = one_one_int ) ).
% 5.06/5.39
% 5.06/5.39 % abs_1
% 5.06/5.39 thf(fact_6536_abs__divide,axiom,
% 5.06/5.39 ! [A: complex,B: complex] :
% 5.06/5.39 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.06/5.39 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_divide
% 5.06/5.39 thf(fact_6537_abs__divide,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.39 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_divide
% 5.06/5.39 thf(fact_6538_abs__divide,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.06/5.39 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_divide
% 5.06/5.39 thf(fact_6539_abs__minus,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.06/5.39 = ( abs_abs_real @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus
% 5.06/5.39 thf(fact_6540_abs__minus,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.06/5.39 = ( abs_abs_int @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus
% 5.06/5.39 thf(fact_6541_abs__minus,axiom,
% 5.06/5.39 ! [A: complex] :
% 5.06/5.39 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.06/5.39 = ( abs_abs_complex @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus
% 5.06/5.39 thf(fact_6542_abs__minus,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.06/5.39 = ( abs_abs_rat @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus
% 5.06/5.39 thf(fact_6543_abs__minus,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.06/5.39 = ( abs_abs_Code_integer @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus
% 5.06/5.39 thf(fact_6544_abs__dvd__iff,axiom,
% 5.06/5.39 ! [M: real,K: real] :
% 5.06/5.39 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.06/5.39 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_dvd_iff
% 5.06/5.39 thf(fact_6545_abs__dvd__iff,axiom,
% 5.06/5.39 ! [M: int,K: int] :
% 5.06/5.39 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.06/5.39 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_dvd_iff
% 5.06/5.39 thf(fact_6546_abs__dvd__iff,axiom,
% 5.06/5.39 ! [M: rat,K: rat] :
% 5.06/5.39 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 5.06/5.39 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_dvd_iff
% 5.06/5.39 thf(fact_6547_abs__dvd__iff,axiom,
% 5.06/5.39 ! [M: code_integer,K: code_integer] :
% 5.06/5.39 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.06/5.39 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_dvd_iff
% 5.06/5.39 thf(fact_6548_dvd__abs__iff,axiom,
% 5.06/5.39 ! [M: real,K: real] :
% 5.06/5.39 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.06/5.39 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_abs_iff
% 5.06/5.39 thf(fact_6549_dvd__abs__iff,axiom,
% 5.06/5.39 ! [M: int,K: int] :
% 5.06/5.39 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.06/5.39 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_abs_iff
% 5.06/5.39 thf(fact_6550_dvd__abs__iff,axiom,
% 5.06/5.39 ! [M: rat,K: rat] :
% 5.06/5.39 ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 5.06/5.39 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_abs_iff
% 5.06/5.39 thf(fact_6551_dvd__abs__iff,axiom,
% 5.06/5.39 ! [M: code_integer,K: code_integer] :
% 5.06/5.39 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.06/5.39 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_abs_iff
% 5.06/5.39 thf(fact_6552_abs__bool__eq,axiom,
% 5.06/5.39 ! [P: $o] :
% 5.06/5.39 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.06/5.39 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_bool_eq
% 5.06/5.39 thf(fact_6553_abs__bool__eq,axiom,
% 5.06/5.39 ! [P: $o] :
% 5.06/5.39 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.06/5.39 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_bool_eq
% 5.06/5.39 thf(fact_6554_abs__bool__eq,axiom,
% 5.06/5.39 ! [P: $o] :
% 5.06/5.39 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.06/5.39 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_bool_eq
% 5.06/5.39 thf(fact_6555_abs__bool__eq,axiom,
% 5.06/5.39 ! [P: $o] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.06/5.39 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_bool_eq
% 5.06/5.39 thf(fact_6556_tanh__real__le__iff,axiom,
% 5.06/5.39 ! [X: real,Y: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 5.06/5.39 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.06/5.39
% 5.06/5.39 % tanh_real_le_iff
% 5.06/5.39 thf(fact_6557_semiring__norm_I80_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( ord_less_num @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(80)
% 5.06/5.39 thf(fact_6558_semiring__norm_I73_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(73)
% 5.06/5.39 thf(fact_6559_abs__sum__abs,axiom,
% 5.06/5.39 ! [F: int > int,A2: set_int] :
% 5.06/5.39 ( ( abs_abs_int
% 5.06/5.39 @ ( groups4538972089207619220nt_int
% 5.06/5.39 @ ^ [A4: int] : ( abs_abs_int @ ( F @ A4 ) )
% 5.06/5.39 @ A2 ) )
% 5.06/5.39 = ( groups4538972089207619220nt_int
% 5.06/5.39 @ ^ [A4: int] : ( abs_abs_int @ ( F @ A4 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_sum_abs
% 5.06/5.39 thf(fact_6560_abs__sum__abs,axiom,
% 5.06/5.39 ! [F: nat > real,A2: set_nat] :
% 5.06/5.39 ( ( abs_abs_real
% 5.06/5.39 @ ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [A4: nat] : ( abs_abs_real @ ( F @ A4 ) )
% 5.06/5.39 @ A2 ) )
% 5.06/5.39 = ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [A4: nat] : ( abs_abs_real @ ( F @ A4 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_sum_abs
% 5.06/5.39 thf(fact_6561_abs__of__nonneg,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.06/5.39 => ( ( abs_abs_Code_integer @ A )
% 5.06/5.39 = A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nonneg
% 5.06/5.39 thf(fact_6562_abs__of__nonneg,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.39 => ( ( abs_abs_real @ A )
% 5.06/5.39 = A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nonneg
% 5.06/5.39 thf(fact_6563_abs__of__nonneg,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.39 => ( ( abs_abs_rat @ A )
% 5.06/5.39 = A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nonneg
% 5.06/5.39 thf(fact_6564_abs__of__nonneg,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.39 => ( ( abs_abs_int @ A )
% 5.06/5.39 = A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nonneg
% 5.06/5.39 thf(fact_6565_abs__le__self__iff,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.06/5.39 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_self_iff
% 5.06/5.39 thf(fact_6566_abs__le__self__iff,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.06/5.39 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_self_iff
% 5.06/5.39 thf(fact_6567_abs__le__self__iff,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.06/5.39 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_self_iff
% 5.06/5.39 thf(fact_6568_abs__le__self__iff,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.06/5.39 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_self_iff
% 5.06/5.39 thf(fact_6569_abs__le__zero__iff,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.06/5.39 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_zero_iff
% 5.06/5.39 thf(fact_6570_abs__le__zero__iff,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.06/5.39 = ( A = zero_zero_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_zero_iff
% 5.06/5.39 thf(fact_6571_abs__le__zero__iff,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.06/5.39 = ( A = zero_zero_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_zero_iff
% 5.06/5.39 thf(fact_6572_abs__le__zero__iff,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.06/5.39 = ( A = zero_zero_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_zero_iff
% 5.06/5.39 thf(fact_6573_zero__less__abs__iff,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.06/5.39 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_less_abs_iff
% 5.06/5.39 thf(fact_6574_zero__less__abs__iff,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.06/5.39 = ( A != zero_zero_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_less_abs_iff
% 5.06/5.39 thf(fact_6575_zero__less__abs__iff,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.06/5.39 = ( A != zero_zero_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_less_abs_iff
% 5.06/5.39 thf(fact_6576_zero__less__abs__iff,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.06/5.39 = ( A != zero_zero_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_less_abs_iff
% 5.06/5.39 thf(fact_6577_abs__neg__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.39 = ( numeral_numeral_real @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_neg_numeral
% 5.06/5.39 thf(fact_6578_abs__neg__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.39 = ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_neg_numeral
% 5.06/5.39 thf(fact_6579_abs__neg__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.06/5.39 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_neg_numeral
% 5.06/5.39 thf(fact_6580_abs__neg__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.06/5.39 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_neg_numeral
% 5.06/5.39 thf(fact_6581_abs__neg__one,axiom,
% 5.06/5.39 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.39 = one_one_real ) ).
% 5.06/5.39
% 5.06/5.39 % abs_neg_one
% 5.06/5.39 thf(fact_6582_abs__neg__one,axiom,
% 5.06/5.39 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.39 = one_one_int ) ).
% 5.06/5.39
% 5.06/5.39 % abs_neg_one
% 5.06/5.39 thf(fact_6583_abs__neg__one,axiom,
% 5.06/5.39 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.39 = one_one_rat ) ).
% 5.06/5.39
% 5.06/5.39 % abs_neg_one
% 5.06/5.39 thf(fact_6584_abs__neg__one,axiom,
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.39 = one_one_Code_integer ) ).
% 5.06/5.39
% 5.06/5.39 % abs_neg_one
% 5.06/5.39 thf(fact_6585_abs__power__minus,axiom,
% 5.06/5.39 ! [A: real,N2: nat] :
% 5.06/5.39 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 5.06/5.39 = ( abs_abs_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_power_minus
% 5.06/5.39 thf(fact_6586_abs__power__minus,axiom,
% 5.06/5.39 ! [A: int,N2: nat] :
% 5.06/5.39 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.06/5.39 = ( abs_abs_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_power_minus
% 5.06/5.39 thf(fact_6587_abs__power__minus,axiom,
% 5.06/5.39 ! [A: rat,N2: nat] :
% 5.06/5.39 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 5.06/5.39 = ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_power_minus
% 5.06/5.39 thf(fact_6588_abs__power__minus,axiom,
% 5.06/5.39 ! [A: code_integer,N2: nat] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.06/5.39 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_power_minus
% 5.06/5.39 thf(fact_6589_semiring__norm_I7_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(7)
% 5.06/5.39 thf(fact_6590_semiring__norm_I9_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(9)
% 5.06/5.39 thf(fact_6591_semiring__norm_I14_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(14)
% 5.06/5.39 thf(fact_6592_semiring__norm_I15_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(15)
% 5.06/5.39 thf(fact_6593_semiring__norm_I81_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( ord_less_num @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(81)
% 5.06/5.39 thf(fact_6594_semiring__norm_I72_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(72)
% 5.06/5.39 thf(fact_6595_semiring__norm_I77_J,axiom,
% 5.06/5.39 ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(77)
% 5.06/5.39 thf(fact_6596_semiring__norm_I70_J,axiom,
% 5.06/5.39 ! [M: num] :
% 5.06/5.39 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(70)
% 5.06/5.39 thf(fact_6597_tanh__real__nonneg__iff,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.06/5.39 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.06/5.39
% 5.06/5.39 % tanh_real_nonneg_iff
% 5.06/5.39 thf(fact_6598_tanh__real__nonpos__iff,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.06/5.39 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % tanh_real_nonpos_iff
% 5.06/5.39 thf(fact_6599_sum__abs,axiom,
% 5.06/5.39 ! [F: int > int,A2: set_int] :
% 5.06/5.39 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.06/5.39 @ ( groups4538972089207619220nt_int
% 5.06/5.39 @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_abs
% 5.06/5.39 thf(fact_6600_sum__abs,axiom,
% 5.06/5.39 ! [F: nat > real,A2: set_nat] :
% 5.06/5.39 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.06/5.39 @ ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_abs
% 5.06/5.39 thf(fact_6601_zero__le__divide__abs__iff,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.06/5.39 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.39 | ( B = zero_zero_real ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_le_divide_abs_iff
% 5.06/5.39 thf(fact_6602_zero__le__divide__abs__iff,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.06/5.39 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.39 | ( B = zero_zero_rat ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_le_divide_abs_iff
% 5.06/5.39 thf(fact_6603_divide__le__0__abs__iff,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.06/5.39 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.39 | ( B = zero_zero_real ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divide_le_0_abs_iff
% 5.06/5.39 thf(fact_6604_divide__le__0__abs__iff,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.06/5.39 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.39 | ( B = zero_zero_rat ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divide_le_0_abs_iff
% 5.06/5.39 thf(fact_6605_abs__of__nonpos,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.39 => ( ( abs_abs_real @ A )
% 5.06/5.39 = ( uminus_uminus_real @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nonpos
% 5.06/5.39 thf(fact_6606_abs__of__nonpos,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.06/5.39 => ( ( abs_abs_Code_integer @ A )
% 5.06/5.39 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nonpos
% 5.06/5.39 thf(fact_6607_abs__of__nonpos,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.06/5.39 => ( ( abs_abs_rat @ A )
% 5.06/5.39 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nonpos
% 5.06/5.39 thf(fact_6608_abs__of__nonpos,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.06/5.39 => ( ( abs_abs_int @ A )
% 5.06/5.39 = ( uminus_uminus_int @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nonpos
% 5.06/5.39 thf(fact_6609_zdiv__numeral__Bit1,axiom,
% 5.06/5.39 ! [V: num,W: num] :
% 5.06/5.39 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.06/5.39 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % zdiv_numeral_Bit1
% 5.06/5.39 thf(fact_6610_semiring__norm_I10_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(10)
% 5.06/5.39 thf(fact_6611_semiring__norm_I8_J,axiom,
% 5.06/5.39 ! [M: num] :
% 5.06/5.39 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.06/5.39 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(8)
% 5.06/5.39 thf(fact_6612_semiring__norm_I5_J,axiom,
% 5.06/5.39 ! [M: num] :
% 5.06/5.39 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.06/5.39 = ( bit1 @ M ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(5)
% 5.06/5.39 thf(fact_6613_semiring__norm_I4_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( plus_plus_num @ one @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( bit0 @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(4)
% 5.06/5.39 thf(fact_6614_semiring__norm_I3_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( plus_plus_num @ one @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( bit1 @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(3)
% 5.06/5.39 thf(fact_6615_sum__abs__ge__zero,axiom,
% 5.06/5.39 ! [F: int > int,A2: set_int] :
% 5.06/5.39 ( ord_less_eq_int @ zero_zero_int
% 5.06/5.39 @ ( groups4538972089207619220nt_int
% 5.06/5.39 @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_abs_ge_zero
% 5.06/5.39 thf(fact_6616_sum__abs__ge__zero,axiom,
% 5.06/5.39 ! [F: nat > real,A2: set_nat] :
% 5.06/5.39 ( ord_less_eq_real @ zero_zero_real
% 5.06/5.39 @ ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_abs_ge_zero
% 5.06/5.39 thf(fact_6617_semiring__norm_I16_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(16)
% 5.06/5.39 thf(fact_6618_semiring__norm_I79_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(79)
% 5.06/5.39 thf(fact_6619_semiring__norm_I74_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( ord_less_num @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % semiring_norm(74)
% 5.06/5.39 thf(fact_6620_numeral__div__minus__numeral,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.39 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_div_minus_numeral
% 5.06/5.39 thf(fact_6621_minus__numeral__div__numeral,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.39 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % minus_numeral_div_numeral
% 5.06/5.39 thf(fact_6622_zero__less__power__abs__iff,axiom,
% 5.06/5.39 ! [A: code_integer,N2: nat] :
% 5.06/5.39 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) )
% 5.06/5.39 = ( ( A != zero_z3403309356797280102nteger )
% 5.06/5.39 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_less_power_abs_iff
% 5.06/5.39 thf(fact_6623_zero__less__power__abs__iff,axiom,
% 5.06/5.39 ! [A: real,N2: nat] :
% 5.06/5.39 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 5.06/5.39 = ( ( A != zero_zero_real )
% 5.06/5.39 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_less_power_abs_iff
% 5.06/5.39 thf(fact_6624_zero__less__power__abs__iff,axiom,
% 5.06/5.39 ! [A: rat,N2: nat] :
% 5.06/5.39 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) )
% 5.06/5.39 = ( ( A != zero_zero_rat )
% 5.06/5.39 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_less_power_abs_iff
% 5.06/5.39 thf(fact_6625_zero__less__power__abs__iff,axiom,
% 5.06/5.39 ! [A: int,N2: nat] :
% 5.06/5.39 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 5.06/5.39 = ( ( A != zero_zero_int )
% 5.06/5.39 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_less_power_abs_iff
% 5.06/5.39 thf(fact_6626_abs__power2,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_power2
% 5.06/5.39 thf(fact_6627_abs__power2,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_power2
% 5.06/5.39 thf(fact_6628_abs__power2,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_power2
% 5.06/5.39 thf(fact_6629_abs__power2,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_power2
% 5.06/5.39 thf(fact_6630_power2__abs,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power2_abs
% 5.06/5.39 thf(fact_6631_power2__abs,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power2_abs
% 5.06/5.39 thf(fact_6632_power2__abs,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power2_abs
% 5.06/5.39 thf(fact_6633_power2__abs,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power2_abs
% 5.06/5.39 thf(fact_6634_sum_Ocl__ivl__Suc,axiom,
% 5.06/5.39 ! [N2: nat,M: nat,G: nat > complex] :
% 5.06/5.39 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.06/5.39 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = zero_zero_complex ) )
% 5.06/5.39 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.06/5.39 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.cl_ivl_Suc
% 5.06/5.39 thf(fact_6635_sum_Ocl__ivl__Suc,axiom,
% 5.06/5.39 ! [N2: nat,M: nat,G: nat > rat] :
% 5.06/5.39 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = zero_zero_rat ) )
% 5.06/5.39 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.cl_ivl_Suc
% 5.06/5.39 thf(fact_6636_sum_Ocl__ivl__Suc,axiom,
% 5.06/5.39 ! [N2: nat,M: nat,G: nat > int] :
% 5.06/5.39 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.06/5.39 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = zero_zero_int ) )
% 5.06/5.39 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.06/5.39 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.cl_ivl_Suc
% 5.06/5.39 thf(fact_6637_sum_Ocl__ivl__Suc,axiom,
% 5.06/5.39 ! [N2: nat,M: nat,G: nat > nat] :
% 5.06/5.39 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.06/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = zero_zero_nat ) )
% 5.06/5.39 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.06/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.cl_ivl_Suc
% 5.06/5.39 thf(fact_6638_sum_Ocl__ivl__Suc,axiom,
% 5.06/5.39 ! [N2: nat,M: nat,G: nat > real] :
% 5.06/5.39 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.06/5.39 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = zero_zero_real ) )
% 5.06/5.39 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.06/5.39 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.cl_ivl_Suc
% 5.06/5.39 thf(fact_6639_dvd__numeral__simp,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.39 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N2 @ M ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_numeral_simp
% 5.06/5.39 thf(fact_6640_dvd__numeral__simp,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.06/5.39 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N2 @ M ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_numeral_simp
% 5.06/5.39 thf(fact_6641_dvd__numeral__simp,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.06/5.39 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N2 @ M ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_numeral_simp
% 5.06/5.39 thf(fact_6642_divmod__algorithm__code_I2_J,axiom,
% 5.06/5.39 ! [M: num] :
% 5.06/5.39 ( ( unique5052692396658037445od_int @ M @ one )
% 5.06/5.39 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(2)
% 5.06/5.39 thf(fact_6643_divmod__algorithm__code_I2_J,axiom,
% 5.06/5.39 ! [M: num] :
% 5.06/5.39 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.06/5.39 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(2)
% 5.06/5.39 thf(fact_6644_divmod__algorithm__code_I2_J,axiom,
% 5.06/5.39 ! [M: num] :
% 5.06/5.39 ( ( unique3479559517661332726nteger @ M @ one )
% 5.06/5.39 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(2)
% 5.06/5.39 thf(fact_6645_sum__zero__power,axiom,
% 5.06/5.39 ! [A2: set_nat,C: nat > complex] :
% 5.06/5.39 ( ( ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups2073611262835488442omplex
% 5.06/5.39 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( C @ zero_zero_nat ) ) )
% 5.06/5.39 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups2073611262835488442omplex
% 5.06/5.39 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = zero_zero_complex ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_zero_power
% 5.06/5.39 thf(fact_6646_sum__zero__power,axiom,
% 5.06/5.39 ! [A2: set_nat,C: nat > rat] :
% 5.06/5.39 ( ( ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( C @ zero_zero_nat ) ) )
% 5.06/5.39 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = zero_zero_rat ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_zero_power
% 5.06/5.39 thf(fact_6647_sum__zero__power,axiom,
% 5.06/5.39 ! [A2: set_nat,C: nat > real] :
% 5.06/5.39 ( ( ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( C @ zero_zero_nat ) ) )
% 5.06/5.39 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = zero_zero_real ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_zero_power
% 5.06/5.39 thf(fact_6648_power__even__abs__numeral,axiom,
% 5.06/5.39 ! [W: num,A: rat] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.39 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.39 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_even_abs_numeral
% 5.06/5.39 thf(fact_6649_power__even__abs__numeral,axiom,
% 5.06/5.39 ! [W: num,A: code_integer] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.39 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.39 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_even_abs_numeral
% 5.06/5.39 thf(fact_6650_power__even__abs__numeral,axiom,
% 5.06/5.39 ! [W: num,A: real] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.39 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.39 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_even_abs_numeral
% 5.06/5.39 thf(fact_6651_power__even__abs__numeral,axiom,
% 5.06/5.39 ! [W: num,A: int] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.39 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.06/5.39 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_even_abs_numeral
% 5.06/5.39 thf(fact_6652_div__Suc__eq__div__add3,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 5.06/5.39 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % div_Suc_eq_div_add3
% 5.06/5.39 thf(fact_6653_Suc__div__eq__add3__div__numeral,axiom,
% 5.06/5.39 ! [M: nat,V: num] :
% 5.06/5.39 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.06/5.39 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Suc_div_eq_add3_div_numeral
% 5.06/5.39 thf(fact_6654_divmod__algorithm__code_I3_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(3)
% 5.06/5.39 thf(fact_6655_divmod__algorithm__code_I3_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(3)
% 5.06/5.39 thf(fact_6656_divmod__algorithm__code_I3_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(3)
% 5.06/5.39 thf(fact_6657_mod__Suc__eq__mod__add3,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 5.06/5.39 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mod_Suc_eq_mod_add3
% 5.06/5.39 thf(fact_6658_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.06/5.39 ! [M: nat,V: num] :
% 5.06/5.39 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.06/5.39 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Suc_mod_eq_add3_mod_numeral
% 5.06/5.39 thf(fact_6659_divmod__algorithm__code_I4_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(4)
% 5.06/5.39 thf(fact_6660_divmod__algorithm__code_I4_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(4)
% 5.06/5.39 thf(fact_6661_divmod__algorithm__code_I4_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(4)
% 5.06/5.39 thf(fact_6662_sum__zero__power_H,axiom,
% 5.06/5.39 ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 5.06/5.39 ( ( ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups2073611262835488442omplex
% 5.06/5.39 @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.06/5.39 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups2073611262835488442omplex
% 5.06/5.39 @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = zero_zero_complex ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_zero_power'
% 5.06/5.39 thf(fact_6663_sum__zero__power_H,axiom,
% 5.06/5.39 ! [A2: set_nat,C: nat > rat,D: nat > rat] :
% 5.06/5.39 ( ( ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.06/5.39 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = zero_zero_rat ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_zero_power'
% 5.06/5.39 thf(fact_6664_sum__zero__power_H,axiom,
% 5.06/5.39 ! [A2: set_nat,C: nat > real,D: nat > real] :
% 5.06/5.39 ( ( ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.06/5.39 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.06/5.39 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.06/5.39 => ( ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = zero_zero_real ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_zero_power'
% 5.06/5.39 thf(fact_6665_minus__one__div__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.39 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % minus_one_div_numeral
% 5.06/5.39 thf(fact_6666_one__div__minus__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.39 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % one_div_minus_numeral
% 5.06/5.39 thf(fact_6667_zmod__numeral__Bit1,axiom,
% 5.06/5.39 ! [V: num,W: num] :
% 5.06/5.39 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.06/5.39 = ( 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 ) ) ).
% 5.06/5.39
% 5.06/5.39 % zmod_numeral_Bit1
% 5.06/5.39 thf(fact_6668_divmod__algorithm__code_I8_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ( ord_less_num @ M @ N2 )
% 5.06/5.39 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.06/5.39 & ( ~ ( ord_less_num @ M @ N2 )
% 5.06/5.39 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(8)
% 5.06/5.39 thf(fact_6669_divmod__algorithm__code_I8_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ( ord_less_num @ M @ N2 )
% 5.06/5.39 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.06/5.39 & ( ~ ( ord_less_num @ M @ N2 )
% 5.06/5.39 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(8)
% 5.06/5.39 thf(fact_6670_divmod__algorithm__code_I8_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ( ord_less_num @ M @ N2 )
% 5.06/5.39 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.06/5.39 & ( ~ ( ord_less_num @ M @ N2 )
% 5.06/5.39 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(8)
% 5.06/5.39 thf(fact_6671_divmod__algorithm__code_I7_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.06/5.39 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.06/5.39 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.06/5.39 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(7)
% 5.06/5.39 thf(fact_6672_divmod__algorithm__code_I7_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.06/5.39 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.06/5.39 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.06/5.39 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(7)
% 5.06/5.39 thf(fact_6673_divmod__algorithm__code_I7_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.06/5.39 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.06/5.39 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.06/5.39 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(7)
% 5.06/5.39 thf(fact_6674_signed__take__bit__Suc__bit1,axiom,
% 5.06/5.39 ! [N2: nat,K: num] :
% 5.06/5.39 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.06/5.39 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % signed_take_bit_Suc_bit1
% 5.06/5.39 thf(fact_6675_divmod__algorithm__code_I6_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( produc4245557441103728435nt_int
% 5.06/5.39 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.06/5.39 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(6)
% 5.06/5.39 thf(fact_6676_divmod__algorithm__code_I6_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( produc2626176000494625587at_nat
% 5.06/5.39 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.06/5.39 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(6)
% 5.06/5.39 thf(fact_6677_divmod__algorithm__code_I6_J,axiom,
% 5.06/5.39 ! [M: num,N2: num] :
% 5.06/5.39 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.39 = ( produc6916734918728496179nteger
% 5.06/5.39 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 5.06/5.39 @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_algorithm_code(6)
% 5.06/5.39 thf(fact_6678_Collect__neg__eq,axiom,
% 5.06/5.39 ! [P: product_prod_int_int > $o] :
% 5.06/5.39 ( ( collec213857154873943460nt_int
% 5.06/5.39 @ ^ [X2: product_prod_int_int] :
% 5.06/5.39 ~ ( P @ X2 ) )
% 5.06/5.39 = ( uminus6221592323253981072nt_int @ ( collec213857154873943460nt_int @ P ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Collect_neg_eq
% 5.06/5.39 thf(fact_6679_Collect__neg__eq,axiom,
% 5.06/5.39 ! [P: complex > $o] :
% 5.06/5.39 ( ( collect_complex
% 5.06/5.39 @ ^ [X2: complex] :
% 5.06/5.39 ~ ( P @ X2 ) )
% 5.06/5.39 = ( uminus8566677241136511917omplex @ ( collect_complex @ P ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Collect_neg_eq
% 5.06/5.39 thf(fact_6680_Collect__neg__eq,axiom,
% 5.06/5.39 ! [P: set_nat > $o] :
% 5.06/5.39 ( ( collect_set_nat
% 5.06/5.39 @ ^ [X2: set_nat] :
% 5.06/5.39 ~ ( P @ X2 ) )
% 5.06/5.39 = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Collect_neg_eq
% 5.06/5.39 thf(fact_6681_Collect__neg__eq,axiom,
% 5.06/5.39 ! [P: nat > $o] :
% 5.06/5.39 ( ( collect_nat
% 5.06/5.39 @ ^ [X2: nat] :
% 5.06/5.39 ~ ( P @ X2 ) )
% 5.06/5.39 = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Collect_neg_eq
% 5.06/5.39 thf(fact_6682_Collect__neg__eq,axiom,
% 5.06/5.39 ! [P: int > $o] :
% 5.06/5.39 ( ( collect_int
% 5.06/5.39 @ ^ [X2: int] :
% 5.06/5.39 ~ ( P @ X2 ) )
% 5.06/5.39 = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Collect_neg_eq
% 5.06/5.39 thf(fact_6683_Compl__eq,axiom,
% 5.06/5.39 ( uminus612125837232591019t_real
% 5.06/5.39 = ( ^ [A5: set_real] :
% 5.06/5.39 ( collect_real
% 5.06/5.39 @ ^ [X2: real] :
% 5.06/5.39 ~ ( member_real @ X2 @ A5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Compl_eq
% 5.06/5.39 thf(fact_6684_Compl__eq,axiom,
% 5.06/5.39 ( uminus6221592323253981072nt_int
% 5.06/5.39 = ( ^ [A5: set_Pr958786334691620121nt_int] :
% 5.06/5.39 ( collec213857154873943460nt_int
% 5.06/5.39 @ ^ [X2: product_prod_int_int] :
% 5.06/5.39 ~ ( member5262025264175285858nt_int @ X2 @ A5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Compl_eq
% 5.06/5.39 thf(fact_6685_Compl__eq,axiom,
% 5.06/5.39 ( uminus8566677241136511917omplex
% 5.06/5.39 = ( ^ [A5: set_complex] :
% 5.06/5.39 ( collect_complex
% 5.06/5.39 @ ^ [X2: complex] :
% 5.06/5.39 ~ ( member_complex @ X2 @ A5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Compl_eq
% 5.06/5.39 thf(fact_6686_Compl__eq,axiom,
% 5.06/5.39 ( uminus613421341184616069et_nat
% 5.06/5.39 = ( ^ [A5: set_set_nat] :
% 5.06/5.39 ( collect_set_nat
% 5.06/5.39 @ ^ [X2: set_nat] :
% 5.06/5.39 ~ ( member_set_nat @ X2 @ A5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Compl_eq
% 5.06/5.39 thf(fact_6687_Compl__eq,axiom,
% 5.06/5.39 ( uminus5710092332889474511et_nat
% 5.06/5.39 = ( ^ [A5: set_nat] :
% 5.06/5.39 ( collect_nat
% 5.06/5.39 @ ^ [X2: nat] :
% 5.06/5.39 ~ ( member_nat @ X2 @ A5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Compl_eq
% 5.06/5.39 thf(fact_6688_Compl__eq,axiom,
% 5.06/5.39 ( uminus1532241313380277803et_int
% 5.06/5.39 = ( ^ [A5: set_int] :
% 5.06/5.39 ( collect_int
% 5.06/5.39 @ ^ [X2: int] :
% 5.06/5.39 ~ ( member_int @ X2 @ A5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Compl_eq
% 5.06/5.39 thf(fact_6689_uminus__set__def,axiom,
% 5.06/5.39 ( uminus612125837232591019t_real
% 5.06/5.39 = ( ^ [A5: set_real] :
% 5.06/5.39 ( collect_real
% 5.06/5.39 @ ( uminus_uminus_real_o
% 5.06/5.39 @ ^ [X2: real] : ( member_real @ X2 @ A5 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % uminus_set_def
% 5.06/5.39 thf(fact_6690_uminus__set__def,axiom,
% 5.06/5.39 ( uminus6221592323253981072nt_int
% 5.06/5.39 = ( ^ [A5: set_Pr958786334691620121nt_int] :
% 5.06/5.39 ( collec213857154873943460nt_int
% 5.06/5.39 @ ( uminus7117520113953359693_int_o
% 5.06/5.39 @ ^ [X2: product_prod_int_int] : ( member5262025264175285858nt_int @ X2 @ A5 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % uminus_set_def
% 5.06/5.39 thf(fact_6691_uminus__set__def,axiom,
% 5.06/5.39 ( uminus8566677241136511917omplex
% 5.06/5.39 = ( ^ [A5: set_complex] :
% 5.06/5.39 ( collect_complex
% 5.06/5.39 @ ( uminus1680532995456772888plex_o
% 5.06/5.39 @ ^ [X2: complex] : ( member_complex @ X2 @ A5 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % uminus_set_def
% 5.06/5.39 thf(fact_6692_uminus__set__def,axiom,
% 5.06/5.39 ( uminus613421341184616069et_nat
% 5.06/5.39 = ( ^ [A5: set_set_nat] :
% 5.06/5.39 ( collect_set_nat
% 5.06/5.39 @ ( uminus6401447641752708672_nat_o
% 5.06/5.39 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A5 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % uminus_set_def
% 5.06/5.39 thf(fact_6693_uminus__set__def,axiom,
% 5.06/5.39 ( uminus5710092332889474511et_nat
% 5.06/5.39 = ( ^ [A5: set_nat] :
% 5.06/5.39 ( collect_nat
% 5.06/5.39 @ ( uminus_uminus_nat_o
% 5.06/5.39 @ ^ [X2: nat] : ( member_nat @ X2 @ A5 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % uminus_set_def
% 5.06/5.39 thf(fact_6694_uminus__set__def,axiom,
% 5.06/5.39 ( uminus1532241313380277803et_int
% 5.06/5.39 = ( ^ [A5: set_int] :
% 5.06/5.39 ( collect_int
% 5.06/5.39 @ ( uminus_uminus_int_o
% 5.06/5.39 @ ^ [X2: int] : ( member_int @ X2 @ A5 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % uminus_set_def
% 5.06/5.39 thf(fact_6695_abs__ge__self,axiom,
% 5.06/5.39 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_self
% 5.06/5.39 thf(fact_6696_abs__ge__self,axiom,
% 5.06/5.39 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_self
% 5.06/5.39 thf(fact_6697_abs__ge__self,axiom,
% 5.06/5.39 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_self
% 5.06/5.39 thf(fact_6698_abs__ge__self,axiom,
% 5.06/5.39 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_self
% 5.06/5.39 thf(fact_6699_abs__le__D1,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.06/5.39 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_D1
% 5.06/5.39 thf(fact_6700_abs__le__D1,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_D1
% 5.06/5.39 thf(fact_6701_abs__le__D1,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.06/5.39 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_D1
% 5.06/5.39 thf(fact_6702_abs__le__D1,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.06/5.39 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_D1
% 5.06/5.39 thf(fact_6703_abs__eq__0__iff,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( ( abs_abs_Code_integer @ A )
% 5.06/5.39 = zero_z3403309356797280102nteger )
% 5.06/5.39 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_0_iff
% 5.06/5.39 thf(fact_6704_abs__eq__0__iff,axiom,
% 5.06/5.39 ! [A: complex] :
% 5.06/5.39 ( ( ( abs_abs_complex @ A )
% 5.06/5.39 = zero_zero_complex )
% 5.06/5.39 = ( A = zero_zero_complex ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_0_iff
% 5.06/5.39 thf(fact_6705_abs__eq__0__iff,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( ( abs_abs_real @ A )
% 5.06/5.39 = zero_zero_real )
% 5.06/5.39 = ( A = zero_zero_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_0_iff
% 5.06/5.39 thf(fact_6706_abs__eq__0__iff,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( ( abs_abs_rat @ A )
% 5.06/5.39 = zero_zero_rat )
% 5.06/5.39 = ( A = zero_zero_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_0_iff
% 5.06/5.39 thf(fact_6707_abs__eq__0__iff,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( ( abs_abs_int @ A )
% 5.06/5.39 = zero_zero_int )
% 5.06/5.39 = ( A = zero_zero_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_0_iff
% 5.06/5.39 thf(fact_6708_abs__mult,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.06/5.39 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult
% 5.06/5.39 thf(fact_6709_abs__mult,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.06/5.39 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult
% 5.06/5.39 thf(fact_6710_abs__mult,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.06/5.39 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult
% 5.06/5.39 thf(fact_6711_abs__mult,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.06/5.39 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult
% 5.06/5.39 thf(fact_6712_abs__one,axiom,
% 5.06/5.39 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.06/5.39 = one_one_Code_integer ) ).
% 5.06/5.39
% 5.06/5.39 % abs_one
% 5.06/5.39 thf(fact_6713_abs__one,axiom,
% 5.06/5.39 ( ( abs_abs_real @ one_one_real )
% 5.06/5.39 = one_one_real ) ).
% 5.06/5.39
% 5.06/5.39 % abs_one
% 5.06/5.39 thf(fact_6714_abs__one,axiom,
% 5.06/5.39 ( ( abs_abs_rat @ one_one_rat )
% 5.06/5.39 = one_one_rat ) ).
% 5.06/5.39
% 5.06/5.39 % abs_one
% 5.06/5.39 thf(fact_6715_abs__one,axiom,
% 5.06/5.39 ( ( abs_abs_int @ one_one_int )
% 5.06/5.39 = one_one_int ) ).
% 5.06/5.39
% 5.06/5.39 % abs_one
% 5.06/5.39 thf(fact_6716_abs__minus__commute,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.06/5.39 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus_commute
% 5.06/5.39 thf(fact_6717_abs__minus__commute,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.06/5.39 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus_commute
% 5.06/5.39 thf(fact_6718_abs__minus__commute,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.06/5.39 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus_commute
% 5.06/5.39 thf(fact_6719_abs__minus__commute,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.06/5.39 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus_commute
% 5.06/5.39 thf(fact_6720_abs__eq__iff,axiom,
% 5.06/5.39 ! [X: real,Y: real] :
% 5.06/5.39 ( ( ( abs_abs_real @ X )
% 5.06/5.39 = ( abs_abs_real @ Y ) )
% 5.06/5.39 = ( ( X = Y )
% 5.06/5.39 | ( X
% 5.06/5.39 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_iff
% 5.06/5.39 thf(fact_6721_abs__eq__iff,axiom,
% 5.06/5.39 ! [X: int,Y: int] :
% 5.06/5.39 ( ( ( abs_abs_int @ X )
% 5.06/5.39 = ( abs_abs_int @ Y ) )
% 5.06/5.39 = ( ( X = Y )
% 5.06/5.39 | ( X
% 5.06/5.39 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_iff
% 5.06/5.39 thf(fact_6722_abs__eq__iff,axiom,
% 5.06/5.39 ! [X: rat,Y: rat] :
% 5.06/5.39 ( ( ( abs_abs_rat @ X )
% 5.06/5.39 = ( abs_abs_rat @ Y ) )
% 5.06/5.39 = ( ( X = Y )
% 5.06/5.39 | ( X
% 5.06/5.39 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_iff
% 5.06/5.39 thf(fact_6723_abs__eq__iff,axiom,
% 5.06/5.39 ! [X: code_integer,Y: code_integer] :
% 5.06/5.39 ( ( ( abs_abs_Code_integer @ X )
% 5.06/5.39 = ( abs_abs_Code_integer @ Y ) )
% 5.06/5.39 = ( ( X = Y )
% 5.06/5.39 | ( X
% 5.06/5.39 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_iff
% 5.06/5.39 thf(fact_6724_power__abs,axiom,
% 5.06/5.39 ! [A: rat,N2: nat] :
% 5.06/5.39 ( ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) )
% 5.06/5.39 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_abs
% 5.06/5.39 thf(fact_6725_power__abs,axiom,
% 5.06/5.39 ! [A: code_integer,N2: nat] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.06/5.39 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_abs
% 5.06/5.39 thf(fact_6726_power__abs,axiom,
% 5.06/5.39 ! [A: real,N2: nat] :
% 5.06/5.39 ( ( abs_abs_real @ ( power_power_real @ A @ N2 ) )
% 5.06/5.39 = ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_abs
% 5.06/5.39 thf(fact_6727_power__abs,axiom,
% 5.06/5.39 ! [A: int,N2: nat] :
% 5.06/5.39 ( ( abs_abs_int @ ( power_power_int @ A @ N2 ) )
% 5.06/5.39 = ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_abs
% 5.06/5.39 thf(fact_6728_dvd__if__abs__eq,axiom,
% 5.06/5.39 ! [L2: real,K: real] :
% 5.06/5.39 ( ( ( abs_abs_real @ L2 )
% 5.06/5.39 = ( abs_abs_real @ K ) )
% 5.06/5.39 => ( dvd_dvd_real @ L2 @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_if_abs_eq
% 5.06/5.39 thf(fact_6729_dvd__if__abs__eq,axiom,
% 5.06/5.39 ! [L2: int,K: int] :
% 5.06/5.39 ( ( ( abs_abs_int @ L2 )
% 5.06/5.39 = ( abs_abs_int @ K ) )
% 5.06/5.39 => ( dvd_dvd_int @ L2 @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_if_abs_eq
% 5.06/5.39 thf(fact_6730_dvd__if__abs__eq,axiom,
% 5.06/5.39 ! [L2: rat,K: rat] :
% 5.06/5.39 ( ( ( abs_abs_rat @ L2 )
% 5.06/5.39 = ( abs_abs_rat @ K ) )
% 5.06/5.39 => ( dvd_dvd_rat @ L2 @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_if_abs_eq
% 5.06/5.39 thf(fact_6731_dvd__if__abs__eq,axiom,
% 5.06/5.39 ! [L2: code_integer,K: code_integer] :
% 5.06/5.39 ( ( ( abs_abs_Code_integer @ L2 )
% 5.06/5.39 = ( abs_abs_Code_integer @ K ) )
% 5.06/5.39 => ( dvd_dvd_Code_integer @ L2 @ K ) ) ).
% 5.06/5.39
% 5.06/5.39 % dvd_if_abs_eq
% 5.06/5.39 thf(fact_6732_mem__case__prodE,axiom,
% 5.06/5.39 ! [Z: complex,C: code_integer > $o > set_complex,P4: produc6271795597528267376eger_o] :
% 5.06/5.39 ( ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P4 ) )
% 5.06/5.39 => ~ ! [X3: code_integer,Y5: $o] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( produc6677183202524767010eger_o @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( member_complex @ Z @ ( C @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodE
% 5.06/5.39 thf(fact_6733_mem__case__prodE,axiom,
% 5.06/5.39 ! [Z: real,C: code_integer > $o > set_real,P4: produc6271795597528267376eger_o] :
% 5.06/5.39 ( ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P4 ) )
% 5.06/5.39 => ~ ! [X3: code_integer,Y5: $o] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( produc6677183202524767010eger_o @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( member_real @ Z @ ( C @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodE
% 5.06/5.39 thf(fact_6734_mem__case__prodE,axiom,
% 5.06/5.39 ! [Z: nat,C: code_integer > $o > set_nat,P4: produc6271795597528267376eger_o] :
% 5.06/5.39 ( ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P4 ) )
% 5.06/5.39 => ~ ! [X3: code_integer,Y5: $o] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( produc6677183202524767010eger_o @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( member_nat @ Z @ ( C @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodE
% 5.06/5.39 thf(fact_6735_mem__case__prodE,axiom,
% 5.06/5.39 ! [Z: int,C: code_integer > $o > set_int,P4: produc6271795597528267376eger_o] :
% 5.06/5.39 ( ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P4 ) )
% 5.06/5.39 => ~ ! [X3: code_integer,Y5: $o] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( produc6677183202524767010eger_o @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( member_int @ Z @ ( C @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodE
% 5.06/5.39 thf(fact_6736_mem__case__prodE,axiom,
% 5.06/5.39 ! [Z: complex,C: num > num > set_complex,P4: product_prod_num_num] :
% 5.06/5.39 ( ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P4 ) )
% 5.06/5.39 => ~ ! [X3: num,Y5: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_num_num @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( member_complex @ Z @ ( C @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodE
% 5.06/5.39 thf(fact_6737_mem__case__prodE,axiom,
% 5.06/5.39 ! [Z: real,C: num > num > set_real,P4: product_prod_num_num] :
% 5.06/5.39 ( ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P4 ) )
% 5.06/5.39 => ~ ! [X3: num,Y5: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_num_num @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( member_real @ Z @ ( C @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodE
% 5.06/5.39 thf(fact_6738_mem__case__prodE,axiom,
% 5.06/5.39 ! [Z: nat,C: num > num > set_nat,P4: product_prod_num_num] :
% 5.06/5.39 ( ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P4 ) )
% 5.06/5.39 => ~ ! [X3: num,Y5: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_num_num @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( member_nat @ Z @ ( C @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodE
% 5.06/5.39 thf(fact_6739_mem__case__prodE,axiom,
% 5.06/5.39 ! [Z: int,C: num > num > set_int,P4: product_prod_num_num] :
% 5.06/5.39 ( ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P4 ) )
% 5.06/5.39 => ~ ! [X3: num,Y5: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_num_num @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( member_int @ Z @ ( C @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodE
% 5.06/5.39 thf(fact_6740_mem__case__prodE,axiom,
% 5.06/5.39 ! [Z: complex,C: nat > num > set_complex,P4: product_prod_nat_num] :
% 5.06/5.39 ( ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P4 ) )
% 5.06/5.39 => ~ ! [X3: nat,Y5: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_nat_num @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( member_complex @ Z @ ( C @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodE
% 5.06/5.39 thf(fact_6741_mem__case__prodE,axiom,
% 5.06/5.39 ! [Z: real,C: nat > num > set_real,P4: product_prod_nat_num] :
% 5.06/5.39 ( ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P4 ) )
% 5.06/5.39 => ~ ! [X3: nat,Y5: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_nat_num @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( member_real @ Z @ ( C @ X3 @ Y5 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mem_case_prodE
% 5.06/5.39 thf(fact_6742_verit__eq__simplify_I14_J,axiom,
% 5.06/5.39 ! [X22: num,X32: num] :
% 5.06/5.39 ( ( bit0 @ X22 )
% 5.06/5.39 != ( bit1 @ X32 ) ) ).
% 5.06/5.39
% 5.06/5.39 % verit_eq_simplify(14)
% 5.06/5.39 thf(fact_6743_verit__eq__simplify_I12_J,axiom,
% 5.06/5.39 ! [X32: num] :
% 5.06/5.39 ( one
% 5.06/5.39 != ( bit1 @ X32 ) ) ).
% 5.06/5.39
% 5.06/5.39 % verit_eq_simplify(12)
% 5.06/5.39 thf(fact_6744_case__prodD,axiom,
% 5.06/5.39 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.06/5.39 ( ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) )
% 5.06/5.39 => ( F @ A @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodD
% 5.06/5.39 thf(fact_6745_case__prodD,axiom,
% 5.06/5.39 ! [F: num > num > $o,A: num,B: num] :
% 5.06/5.39 ( ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) )
% 5.06/5.39 => ( F @ A @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodD
% 5.06/5.39 thf(fact_6746_case__prodD,axiom,
% 5.06/5.39 ! [F: nat > num > $o,A: nat,B: num] :
% 5.06/5.39 ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 5.06/5.39 => ( F @ A @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodD
% 5.06/5.39 thf(fact_6747_case__prodD,axiom,
% 5.06/5.39 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.06/5.39 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.06/5.39 => ( F @ A @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodD
% 5.06/5.39 thf(fact_6748_case__prodD,axiom,
% 5.06/5.39 ! [F: int > int > $o,A: int,B: int] :
% 5.06/5.39 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.06/5.39 => ( F @ A @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodD
% 5.06/5.39 thf(fact_6749_case__prodE,axiom,
% 5.06/5.39 ! [C: code_integer > $o > $o,P4: produc6271795597528267376eger_o] :
% 5.06/5.39 ( ( produc7828578312038201481er_o_o @ C @ P4 )
% 5.06/5.39 => ~ ! [X3: code_integer,Y5: $o] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( produc6677183202524767010eger_o @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( C @ X3 @ Y5 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodE
% 5.06/5.39 thf(fact_6750_case__prodE,axiom,
% 5.06/5.39 ! [C: num > num > $o,P4: product_prod_num_num] :
% 5.06/5.39 ( ( produc5703948589228662326_num_o @ C @ P4 )
% 5.06/5.39 => ~ ! [X3: num,Y5: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_num_num @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( C @ X3 @ Y5 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodE
% 5.06/5.39 thf(fact_6751_case__prodE,axiom,
% 5.06/5.39 ! [C: nat > num > $o,P4: product_prod_nat_num] :
% 5.06/5.39 ( ( produc4927758841916487424_num_o @ C @ P4 )
% 5.06/5.39 => ~ ! [X3: nat,Y5: num] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_nat_num @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( C @ X3 @ Y5 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodE
% 5.06/5.39 thf(fact_6752_case__prodE,axiom,
% 5.06/5.39 ! [C: nat > nat > $o,P4: product_prod_nat_nat] :
% 5.06/5.39 ( ( produc6081775807080527818_nat_o @ C @ P4 )
% 5.06/5.39 => ~ ! [X3: nat,Y5: nat] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_nat_nat @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( C @ X3 @ Y5 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodE
% 5.06/5.39 thf(fact_6753_case__prodE,axiom,
% 5.06/5.39 ! [C: int > int > $o,P4: product_prod_int_int] :
% 5.06/5.39 ( ( produc4947309494688390418_int_o @ C @ P4 )
% 5.06/5.39 => ~ ! [X3: int,Y5: int] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_int_int @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( C @ X3 @ Y5 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodE
% 5.06/5.39 thf(fact_6754_case__prodD_H,axiom,
% 5.06/5.39 ! [R: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.06/5.39 ( ( produc8739625826339149834_nat_o @ R @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.06/5.39 => ( R @ A @ B @ C ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodD'
% 5.06/5.39 thf(fact_6755_case__prodE_H,axiom,
% 5.06/5.39 ! [C: nat > nat > product_prod_nat_nat > $o,P4: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.06/5.39 ( ( produc8739625826339149834_nat_o @ C @ P4 @ Z )
% 5.06/5.39 => ~ ! [X3: nat,Y5: nat] :
% 5.06/5.39 ( ( P4
% 5.06/5.39 = ( product_Pair_nat_nat @ X3 @ Y5 ) )
% 5.06/5.39 => ~ ( C @ X3 @ Y5 @ Z ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % case_prodE'
% 5.06/5.39 thf(fact_6756_abs__ge__zero,axiom,
% 5.06/5.39 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_zero
% 5.06/5.39 thf(fact_6757_abs__ge__zero,axiom,
% 5.06/5.39 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_zero
% 5.06/5.39 thf(fact_6758_abs__ge__zero,axiom,
% 5.06/5.39 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_zero
% 5.06/5.39 thf(fact_6759_abs__ge__zero,axiom,
% 5.06/5.39 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_zero
% 5.06/5.39 thf(fact_6760_abs__of__pos,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.06/5.39 => ( ( abs_abs_Code_integer @ A )
% 5.06/5.39 = A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_pos
% 5.06/5.39 thf(fact_6761_abs__of__pos,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.39 => ( ( abs_abs_real @ A )
% 5.06/5.39 = A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_pos
% 5.06/5.39 thf(fact_6762_abs__of__pos,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.06/5.39 => ( ( abs_abs_rat @ A )
% 5.06/5.39 = A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_pos
% 5.06/5.39 thf(fact_6763_abs__of__pos,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.39 => ( ( abs_abs_int @ A )
% 5.06/5.39 = A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_pos
% 5.06/5.39 thf(fact_6764_abs__not__less__zero,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.06/5.39
% 5.06/5.39 % abs_not_less_zero
% 5.06/5.39 thf(fact_6765_abs__not__less__zero,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.06/5.39
% 5.06/5.39 % abs_not_less_zero
% 5.06/5.39 thf(fact_6766_abs__not__less__zero,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.06/5.39
% 5.06/5.39 % abs_not_less_zero
% 5.06/5.39 thf(fact_6767_abs__not__less__zero,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.06/5.39
% 5.06/5.39 % abs_not_less_zero
% 5.06/5.39 thf(fact_6768_abs__triangle__ineq,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq
% 5.06/5.39 thf(fact_6769_abs__triangle__ineq,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq
% 5.06/5.39 thf(fact_6770_abs__triangle__ineq,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq
% 5.06/5.39 thf(fact_6771_abs__triangle__ineq,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq
% 5.06/5.39 thf(fact_6772_abs__mult__less,axiom,
% 5.06/5.39 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.06/5.39 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.06/5.39 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.06/5.39 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_less
% 5.06/5.39 thf(fact_6773_abs__mult__less,axiom,
% 5.06/5.39 ! [A: real,C: real,B: real,D: real] :
% 5.06/5.39 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.06/5.39 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.06/5.39 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_less
% 5.06/5.39 thf(fact_6774_abs__mult__less,axiom,
% 5.06/5.39 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.06/5.39 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.06/5.39 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.06/5.39 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_less
% 5.06/5.39 thf(fact_6775_abs__mult__less,axiom,
% 5.06/5.39 ! [A: int,C: int,B: int,D: int] :
% 5.06/5.39 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.06/5.39 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.06/5.39 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_less
% 5.06/5.39 thf(fact_6776_abs__triangle__ineq2__sym,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq2_sym
% 5.06/5.39 thf(fact_6777_abs__triangle__ineq2__sym,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq2_sym
% 5.06/5.39 thf(fact_6778_abs__triangle__ineq2__sym,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq2_sym
% 5.06/5.39 thf(fact_6779_abs__triangle__ineq2__sym,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq2_sym
% 5.06/5.39 thf(fact_6780_abs__triangle__ineq3,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq3
% 5.06/5.39 thf(fact_6781_abs__triangle__ineq3,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq3
% 5.06/5.39 thf(fact_6782_abs__triangle__ineq3,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq3
% 5.06/5.39 thf(fact_6783_abs__triangle__ineq3,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq3
% 5.06/5.39 thf(fact_6784_abs__triangle__ineq2,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq2
% 5.06/5.39 thf(fact_6785_abs__triangle__ineq2,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq2
% 5.06/5.39 thf(fact_6786_abs__triangle__ineq2,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq2
% 5.06/5.39 thf(fact_6787_abs__triangle__ineq2,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq2
% 5.06/5.39 thf(fact_6788_nonzero__abs__divide,axiom,
% 5.06/5.39 ! [B: real,A: real] :
% 5.06/5.39 ( ( B != zero_zero_real )
% 5.06/5.39 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.39 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % nonzero_abs_divide
% 5.06/5.39 thf(fact_6789_nonzero__abs__divide,axiom,
% 5.06/5.39 ! [B: rat,A: rat] :
% 5.06/5.39 ( ( B != zero_zero_rat )
% 5.06/5.39 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.06/5.39 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % nonzero_abs_divide
% 5.06/5.39 thf(fact_6790_abs__ge__minus__self,axiom,
% 5.06/5.39 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_minus_self
% 5.06/5.39 thf(fact_6791_abs__ge__minus__self,axiom,
% 5.06/5.39 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_minus_self
% 5.06/5.39 thf(fact_6792_abs__ge__minus__self,axiom,
% 5.06/5.39 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_minus_self
% 5.06/5.39 thf(fact_6793_abs__ge__minus__self,axiom,
% 5.06/5.39 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ge_minus_self
% 5.06/5.39 thf(fact_6794_abs__le__iff,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.06/5.39 = ( ( ord_less_eq_real @ A @ B )
% 5.06/5.39 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_iff
% 5.06/5.39 thf(fact_6795_abs__le__iff,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.06/5.39 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.06/5.39 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_iff
% 5.06/5.39 thf(fact_6796_abs__le__iff,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.06/5.39 = ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.39 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_iff
% 5.06/5.39 thf(fact_6797_abs__le__iff,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.06/5.39 = ( ( ord_less_eq_int @ A @ B )
% 5.06/5.39 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_iff
% 5.06/5.39 thf(fact_6798_abs__le__D2,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.06/5.39 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_D2
% 5.06/5.39 thf(fact_6799_abs__le__D2,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_D2
% 5.06/5.39 thf(fact_6800_abs__le__D2,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.06/5.39 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_D2
% 5.06/5.39 thf(fact_6801_abs__le__D2,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.06/5.39 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_D2
% 5.06/5.39 thf(fact_6802_abs__leI,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.39 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.06/5.39 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_leI
% 5.06/5.39 thf(fact_6803_abs__leI,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.06/5.39 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_leI
% 5.06/5.39 thf(fact_6804_abs__leI,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ A @ B )
% 5.06/5.39 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.06/5.39 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_leI
% 5.06/5.39 thf(fact_6805_abs__leI,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ A @ B )
% 5.06/5.39 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.06/5.39 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_leI
% 5.06/5.39 thf(fact_6806_abs__less__iff,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.06/5.39 = ( ( ord_less_real @ A @ B )
% 5.06/5.39 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_less_iff
% 5.06/5.39 thf(fact_6807_abs__less__iff,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.06/5.39 = ( ( ord_less_int @ A @ B )
% 5.06/5.39 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_less_iff
% 5.06/5.39 thf(fact_6808_abs__less__iff,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.06/5.39 = ( ( ord_less_rat @ A @ B )
% 5.06/5.39 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_less_iff
% 5.06/5.39 thf(fact_6809_abs__less__iff,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.06/5.39 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.06/5.39 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_less_iff
% 5.06/5.39 thf(fact_6810_sum__cong__Suc,axiom,
% 5.06/5.39 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.06/5.39 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.06/5.39 => ( ! [X3: nat] :
% 5.06/5.39 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.06/5.39 => ( ( F @ ( suc @ X3 ) )
% 5.06/5.39 = ( G @ ( suc @ X3 ) ) ) )
% 5.06/5.39 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.06/5.39 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_cong_Suc
% 5.06/5.39 thf(fact_6811_sum__cong__Suc,axiom,
% 5.06/5.39 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.06/5.39 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.06/5.39 => ( ! [X3: nat] :
% 5.06/5.39 ( ( member_nat @ ( suc @ X3 ) @ A2 )
% 5.06/5.39 => ( ( F @ ( suc @ X3 ) )
% 5.06/5.39 = ( G @ ( suc @ X3 ) ) ) )
% 5.06/5.39 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 5.06/5.39 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_cong_Suc
% 5.06/5.39 thf(fact_6812_abs__real__def,axiom,
% 5.06/5.39 ( abs_abs_real
% 5.06/5.39 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_real_def
% 5.06/5.39 thf(fact_6813_num_Oexhaust,axiom,
% 5.06/5.39 ! [Y: num] :
% 5.06/5.39 ( ( Y != one )
% 5.06/5.39 => ( ! [X23: num] :
% 5.06/5.39 ( Y
% 5.06/5.39 != ( bit0 @ X23 ) )
% 5.06/5.39 => ~ ! [X33: num] :
% 5.06/5.39 ( Y
% 5.06/5.39 != ( bit1 @ X33 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % num.exhaust
% 5.06/5.39 thf(fact_6814_xor__num_Ocases,axiom,
% 5.06/5.39 ! [X: product_prod_num_num] :
% 5.06/5.39 ( ( X
% 5.06/5.39 != ( product_Pair_num_num @ one @ one ) )
% 5.06/5.39 => ( ! [N3: num] :
% 5.06/5.39 ( X
% 5.06/5.39 != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 5.06/5.39 => ( ! [N3: num] :
% 5.06/5.39 ( X
% 5.06/5.39 != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 5.06/5.39 => ( ! [M2: num] :
% 5.06/5.39 ( X
% 5.06/5.39 != ( product_Pair_num_num @ ( bit0 @ M2 ) @ one ) )
% 5.06/5.39 => ( ! [M2: num,N3: num] :
% 5.06/5.39 ( X
% 5.06/5.39 != ( product_Pair_num_num @ ( bit0 @ M2 ) @ ( bit0 @ N3 ) ) )
% 5.06/5.39 => ( ! [M2: num,N3: num] :
% 5.06/5.39 ( X
% 5.06/5.39 != ( product_Pair_num_num @ ( bit0 @ M2 ) @ ( bit1 @ N3 ) ) )
% 5.06/5.39 => ( ! [M2: num] :
% 5.06/5.39 ( X
% 5.06/5.39 != ( product_Pair_num_num @ ( bit1 @ M2 ) @ one ) )
% 5.06/5.39 => ( ! [M2: num,N3: num] :
% 5.06/5.39 ( X
% 5.06/5.39 != ( product_Pair_num_num @ ( bit1 @ M2 ) @ ( bit0 @ N3 ) ) )
% 5.06/5.39 => ~ ! [M2: num,N3: num] :
% 5.06/5.39 ( X
% 5.06/5.39 != ( product_Pair_num_num @ ( bit1 @ M2 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % xor_num.cases
% 5.06/5.39 thf(fact_6815_sin__bound__lemma,axiom,
% 5.06/5.39 ! [X: real,Y: real,U: real,V: real] :
% 5.06/5.39 ( ( X = Y )
% 5.06/5.39 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.06/5.39 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sin_bound_lemma
% 5.06/5.39 thf(fact_6816_sum__subtractf__nat,axiom,
% 5.06/5.39 ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 5.06/5.39 ( ! [X3: complex] :
% 5.06/5.39 ( ( member_complex @ X3 @ A2 )
% 5.06/5.39 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.06/5.39 => ( ( groups5693394587270226106ex_nat
% 5.06/5.39 @ ^ [X2: complex] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_subtractf_nat
% 5.06/5.39 thf(fact_6817_sum__subtractf__nat,axiom,
% 5.06/5.39 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.06/5.39 ( ! [X3: real] :
% 5.06/5.39 ( ( member_real @ X3 @ A2 )
% 5.06/5.39 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.06/5.39 => ( ( groups1935376822645274424al_nat
% 5.06/5.39 @ ^ [X2: real] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_subtractf_nat
% 5.06/5.39 thf(fact_6818_sum__subtractf__nat,axiom,
% 5.06/5.39 ! [A2: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 5.06/5.39 ( ! [X3: set_nat] :
% 5.06/5.39 ( ( member_set_nat @ X3 @ A2 )
% 5.06/5.39 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.06/5.39 => ( ( groups8294997508430121362at_nat
% 5.06/5.39 @ ^ [X2: set_nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( groups8294997508430121362at_nat @ G @ A2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_subtractf_nat
% 5.06/5.39 thf(fact_6819_sum__subtractf__nat,axiom,
% 5.06/5.39 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.06/5.39 ( ! [X3: int] :
% 5.06/5.39 ( ( member_int @ X3 @ A2 )
% 5.06/5.39 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.06/5.39 => ( ( groups4541462559716669496nt_nat
% 5.06/5.39 @ ^ [X2: int] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_subtractf_nat
% 5.06/5.39 thf(fact_6820_sum__subtractf__nat,axiom,
% 5.06/5.39 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.06/5.39 ( ! [X3: nat] :
% 5.06/5.39 ( ( member_nat @ X3 @ A2 )
% 5.06/5.39 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.06/5.39 => ( ( groups3542108847815614940at_nat
% 5.06/5.39 @ ^ [X2: nat] : ( minus_minus_nat @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.39 @ A2 )
% 5.06/5.39 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_subtractf_nat
% 5.06/5.39 thf(fact_6821_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.06/5.39 ! [G: nat > nat,M: nat,N2: nat] :
% 5.06/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( groups3542108847815614940at_nat
% 5.06/5.39 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.shift_bounds_cl_Suc_ivl
% 5.06/5.39 thf(fact_6822_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.06/5.39 ! [G: nat > real,M: nat,N2: nat] :
% 5.06/5.39 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.shift_bounds_cl_Suc_ivl
% 5.06/5.39 thf(fact_6823_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.06/5.39 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.06/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.06/5.39 = ( groups3542108847815614940at_nat
% 5.06/5.39 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.shift_bounds_cl_nat_ivl
% 5.06/5.39 thf(fact_6824_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.06/5.39 ! [G: nat > real,M: nat,K: nat,N2: nat] :
% 5.06/5.39 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.06/5.39 = ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.shift_bounds_cl_nat_ivl
% 5.06/5.39 thf(fact_6825_dense__eq0__I,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ! [E2: real] :
% 5.06/5.39 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.06/5.39 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 5.06/5.39 => ( X = zero_zero_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % dense_eq0_I
% 5.06/5.39 thf(fact_6826_dense__eq0__I,axiom,
% 5.06/5.39 ! [X: rat] :
% 5.06/5.39 ( ! [E2: rat] :
% 5.06/5.39 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.06/5.39 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 5.06/5.39 => ( X = zero_zero_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % dense_eq0_I
% 5.06/5.39 thf(fact_6827_abs__eq__mult,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.06/5.39 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.06/5.39 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.06/5.39 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.06/5.39 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.06/5.39 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_mult
% 5.06/5.39 thf(fact_6828_abs__eq__mult,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.39 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.06/5.39 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.39 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.06/5.39 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.06/5.39 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_mult
% 5.06/5.39 thf(fact_6829_abs__eq__mult,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.39 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.06/5.39 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.39 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.06/5.39 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.06/5.39 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_mult
% 5.06/5.39 thf(fact_6830_abs__eq__mult,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.39 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.06/5.39 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.39 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.06/5.39 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.06/5.39 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_mult
% 5.06/5.39 thf(fact_6831_abs__mult__pos,axiom,
% 5.06/5.39 ! [X: code_integer,Y: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.06/5.39 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 5.06/5.39 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_pos
% 5.06/5.39 thf(fact_6832_abs__mult__pos,axiom,
% 5.06/5.39 ! [X: real,Y: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.39 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 5.06/5.39 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_pos
% 5.06/5.39 thf(fact_6833_abs__mult__pos,axiom,
% 5.06/5.39 ! [X: rat,Y: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.06/5.39 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 5.06/5.39 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_pos
% 5.06/5.39 thf(fact_6834_abs__mult__pos,axiom,
% 5.06/5.39 ! [X: int,Y: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.39 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 5.06/5.39 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_mult_pos
% 5.06/5.39 thf(fact_6835_abs__minus__le__zero,axiom,
% 5.06/5.39 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus_le_zero
% 5.06/5.39 thf(fact_6836_abs__minus__le__zero,axiom,
% 5.06/5.39 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus_le_zero
% 5.06/5.39 thf(fact_6837_abs__minus__le__zero,axiom,
% 5.06/5.39 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus_le_zero
% 5.06/5.39 thf(fact_6838_abs__minus__le__zero,axiom,
% 5.06/5.39 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.06/5.39
% 5.06/5.39 % abs_minus_le_zero
% 5.06/5.39 thf(fact_6839_eq__abs__iff_H,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( A
% 5.06/5.39 = ( abs_abs_real @ B ) )
% 5.06/5.39 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.39 & ( ( B = A )
% 5.06/5.39 | ( B
% 5.06/5.39 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % eq_abs_iff'
% 5.06/5.39 thf(fact_6840_eq__abs__iff_H,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( A
% 5.06/5.39 = ( abs_abs_Code_integer @ B ) )
% 5.06/5.39 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.06/5.39 & ( ( B = A )
% 5.06/5.39 | ( B
% 5.06/5.39 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % eq_abs_iff'
% 5.06/5.39 thf(fact_6841_eq__abs__iff_H,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( A
% 5.06/5.39 = ( abs_abs_rat @ B ) )
% 5.06/5.39 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.06/5.39 & ( ( B = A )
% 5.06/5.39 | ( B
% 5.06/5.39 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % eq_abs_iff'
% 5.06/5.39 thf(fact_6842_eq__abs__iff_H,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( A
% 5.06/5.39 = ( abs_abs_int @ B ) )
% 5.06/5.39 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.06/5.39 & ( ( B = A )
% 5.06/5.39 | ( B
% 5.06/5.39 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % eq_abs_iff'
% 5.06/5.39 thf(fact_6843_abs__eq__iff_H,axiom,
% 5.06/5.39 ! [A: real,B: real] :
% 5.06/5.39 ( ( ( abs_abs_real @ A )
% 5.06/5.39 = B )
% 5.06/5.39 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.06/5.39 & ( ( A = B )
% 5.06/5.39 | ( A
% 5.06/5.39 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_iff'
% 5.06/5.39 thf(fact_6844_abs__eq__iff_H,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( ( abs_abs_Code_integer @ A )
% 5.06/5.39 = B )
% 5.06/5.39 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.06/5.39 & ( ( A = B )
% 5.06/5.39 | ( A
% 5.06/5.39 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_iff'
% 5.06/5.39 thf(fact_6845_abs__eq__iff_H,axiom,
% 5.06/5.39 ! [A: rat,B: rat] :
% 5.06/5.39 ( ( ( abs_abs_rat @ A )
% 5.06/5.39 = B )
% 5.06/5.39 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.06/5.39 & ( ( A = B )
% 5.06/5.39 | ( A
% 5.06/5.39 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_iff'
% 5.06/5.39 thf(fact_6846_abs__eq__iff_H,axiom,
% 5.06/5.39 ! [A: int,B: int] :
% 5.06/5.39 ( ( ( abs_abs_int @ A )
% 5.06/5.39 = B )
% 5.06/5.39 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.39 & ( ( A = B )
% 5.06/5.39 | ( A
% 5.06/5.39 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_eq_iff'
% 5.06/5.39 thf(fact_6847_abs__div__pos,axiom,
% 5.06/5.39 ! [Y: real,X: real] :
% 5.06/5.39 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.39 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 5.06/5.39 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_div_pos
% 5.06/5.39 thf(fact_6848_abs__div__pos,axiom,
% 5.06/5.39 ! [Y: rat,X: rat] :
% 5.06/5.39 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.06/5.39 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 5.06/5.39 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_div_pos
% 5.06/5.39 thf(fact_6849_zero__le__power__abs,axiom,
% 5.06/5.39 ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_le_power_abs
% 5.06/5.39 thf(fact_6850_zero__le__power__abs,axiom,
% 5.06/5.39 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_le_power_abs
% 5.06/5.39 thf(fact_6851_zero__le__power__abs,axiom,
% 5.06/5.39 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_le_power_abs
% 5.06/5.39 thf(fact_6852_zero__le__power__abs,axiom,
% 5.06/5.39 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_le_power_abs
% 5.06/5.39 thf(fact_6853_abs__if__raw,axiom,
% 5.06/5.39 ( abs_abs_real
% 5.06/5.39 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_if_raw
% 5.06/5.39 thf(fact_6854_abs__if__raw,axiom,
% 5.06/5.39 ( abs_abs_int
% 5.06/5.39 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_if_raw
% 5.06/5.39 thf(fact_6855_abs__if__raw,axiom,
% 5.06/5.39 ( abs_abs_rat
% 5.06/5.39 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_if_raw
% 5.06/5.39 thf(fact_6856_abs__if__raw,axiom,
% 5.06/5.39 ( abs_abs_Code_integer
% 5.06/5.39 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_if_raw
% 5.06/5.39 thf(fact_6857_abs__of__neg,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( ord_less_real @ A @ zero_zero_real )
% 5.06/5.39 => ( ( abs_abs_real @ A )
% 5.06/5.39 = ( uminus_uminus_real @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_neg
% 5.06/5.39 thf(fact_6858_abs__of__neg,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( ord_less_int @ A @ zero_zero_int )
% 5.06/5.39 => ( ( abs_abs_int @ A )
% 5.06/5.39 = ( uminus_uminus_int @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_neg
% 5.06/5.39 thf(fact_6859_abs__of__neg,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.06/5.39 => ( ( abs_abs_rat @ A )
% 5.06/5.39 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_neg
% 5.06/5.39 thf(fact_6860_abs__of__neg,axiom,
% 5.06/5.39 ! [A: code_integer] :
% 5.06/5.39 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.06/5.39 => ( ( abs_abs_Code_integer @ A )
% 5.06/5.39 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_neg
% 5.06/5.39 thf(fact_6861_abs__if,axiom,
% 5.06/5.39 ( abs_abs_real
% 5.06/5.39 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_if
% 5.06/5.39 thf(fact_6862_abs__if,axiom,
% 5.06/5.39 ( abs_abs_int
% 5.06/5.39 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_if
% 5.06/5.39 thf(fact_6863_abs__if,axiom,
% 5.06/5.39 ( abs_abs_rat
% 5.06/5.39 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_if
% 5.06/5.39 thf(fact_6864_abs__if,axiom,
% 5.06/5.39 ( abs_abs_Code_integer
% 5.06/5.39 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_if
% 5.06/5.39 thf(fact_6865_abs__diff__triangle__ineq,axiom,
% 5.06/5.39 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_triangle_ineq
% 5.06/5.39 thf(fact_6866_abs__diff__triangle__ineq,axiom,
% 5.06/5.39 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_triangle_ineq
% 5.06/5.39 thf(fact_6867_abs__diff__triangle__ineq,axiom,
% 5.06/5.39 ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_triangle_ineq
% 5.06/5.39 thf(fact_6868_abs__diff__triangle__ineq,axiom,
% 5.06/5.39 ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_triangle_ineq
% 5.06/5.39 thf(fact_6869_abs__triangle__ineq4,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq4
% 5.06/5.39 thf(fact_6870_abs__triangle__ineq4,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq4
% 5.06/5.39 thf(fact_6871_abs__triangle__ineq4,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq4
% 5.06/5.39 thf(fact_6872_abs__triangle__ineq4,axiom,
% 5.06/5.39 ! [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 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_triangle_ineq4
% 5.06/5.39 thf(fact_6873_abs__diff__le__iff,axiom,
% 5.06/5.39 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 5.06/5.39 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 5.06/5.39 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_le_iff
% 5.06/5.39 thf(fact_6874_abs__diff__le__iff,axiom,
% 5.06/5.39 ! [X: real,A: real,R2: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 5.06/5.39 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 5.06/5.39 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_le_iff
% 5.06/5.39 thf(fact_6875_abs__diff__le__iff,axiom,
% 5.06/5.39 ! [X: rat,A: rat,R2: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 5.06/5.39 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 5.06/5.39 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_le_iff
% 5.06/5.39 thf(fact_6876_abs__diff__le__iff,axiom,
% 5.06/5.39 ! [X: int,A: int,R2: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 5.06/5.39 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 5.06/5.39 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_le_iff
% 5.06/5.39 thf(fact_6877_abs__diff__less__iff,axiom,
% 5.06/5.39 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 5.06/5.39 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 5.06/5.39 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 5.06/5.39 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_less_iff
% 5.06/5.39 thf(fact_6878_abs__diff__less__iff,axiom,
% 5.06/5.39 ! [X: real,A: real,R2: real] :
% 5.06/5.39 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 5.06/5.39 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 5.06/5.39 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_less_iff
% 5.06/5.39 thf(fact_6879_abs__diff__less__iff,axiom,
% 5.06/5.39 ! [X: rat,A: rat,R2: rat] :
% 5.06/5.39 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 5.06/5.39 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 5.06/5.39 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_less_iff
% 5.06/5.39 thf(fact_6880_abs__diff__less__iff,axiom,
% 5.06/5.39 ! [X: int,A: int,R2: int] :
% 5.06/5.39 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 5.06/5.39 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 5.06/5.39 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_diff_less_iff
% 5.06/5.39 thf(fact_6881_sum__eq__Suc0__iff,axiom,
% 5.06/5.39 ! [A2: set_int,F: int > nat] :
% 5.06/5.39 ( ( finite_finite_int @ A2 )
% 5.06/5.39 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.06/5.39 = ( suc @ zero_zero_nat ) )
% 5.06/5.39 = ( ? [X2: int] :
% 5.06/5.39 ( ( member_int @ X2 @ A2 )
% 5.06/5.39 & ( ( F @ X2 )
% 5.06/5.39 = ( suc @ zero_zero_nat ) )
% 5.06/5.39 & ! [Y2: int] :
% 5.06/5.39 ( ( member_int @ Y2 @ A2 )
% 5.06/5.39 => ( ( X2 != Y2 )
% 5.06/5.39 => ( ( F @ Y2 )
% 5.06/5.39 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_eq_Suc0_iff
% 5.06/5.39 thf(fact_6882_sum__eq__Suc0__iff,axiom,
% 5.06/5.39 ! [A2: set_complex,F: complex > nat] :
% 5.06/5.39 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.39 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.06/5.39 = ( suc @ zero_zero_nat ) )
% 5.06/5.39 = ( ? [X2: complex] :
% 5.06/5.39 ( ( member_complex @ X2 @ A2 )
% 5.06/5.39 & ( ( F @ X2 )
% 5.06/5.39 = ( suc @ zero_zero_nat ) )
% 5.06/5.39 & ! [Y2: complex] :
% 5.06/5.39 ( ( member_complex @ Y2 @ A2 )
% 5.06/5.39 => ( ( X2 != Y2 )
% 5.06/5.39 => ( ( F @ Y2 )
% 5.06/5.39 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_eq_Suc0_iff
% 5.06/5.39 thf(fact_6883_sum__eq__Suc0__iff,axiom,
% 5.06/5.39 ! [A2: set_nat,F: nat > nat] :
% 5.06/5.39 ( ( finite_finite_nat @ A2 )
% 5.06/5.39 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.06/5.39 = ( suc @ zero_zero_nat ) )
% 5.06/5.39 = ( ? [X2: nat] :
% 5.06/5.39 ( ( member_nat @ X2 @ A2 )
% 5.06/5.39 & ( ( F @ X2 )
% 5.06/5.39 = ( suc @ zero_zero_nat ) )
% 5.06/5.39 & ! [Y2: nat] :
% 5.06/5.39 ( ( member_nat @ Y2 @ A2 )
% 5.06/5.39 => ( ( X2 != Y2 )
% 5.06/5.39 => ( ( F @ Y2 )
% 5.06/5.39 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_eq_Suc0_iff
% 5.06/5.39 thf(fact_6884_sum__SucD,axiom,
% 5.06/5.39 ! [F: nat > nat,A2: set_nat,N2: nat] :
% 5.06/5.39 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.06/5.39 = ( suc @ N2 ) )
% 5.06/5.39 => ? [X3: nat] :
% 5.06/5.39 ( ( member_nat @ X3 @ A2 )
% 5.06/5.39 & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_SucD
% 5.06/5.39 thf(fact_6885_sum__eq__1__iff,axiom,
% 5.06/5.39 ! [A2: set_int,F: int > nat] :
% 5.06/5.39 ( ( finite_finite_int @ A2 )
% 5.06/5.39 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.06/5.39 = one_one_nat )
% 5.06/5.39 = ( ? [X2: int] :
% 5.06/5.39 ( ( member_int @ X2 @ A2 )
% 5.06/5.39 & ( ( F @ X2 )
% 5.06/5.39 = one_one_nat )
% 5.06/5.39 & ! [Y2: int] :
% 5.06/5.39 ( ( member_int @ Y2 @ A2 )
% 5.06/5.39 => ( ( X2 != Y2 )
% 5.06/5.39 => ( ( F @ Y2 )
% 5.06/5.39 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_eq_1_iff
% 5.06/5.39 thf(fact_6886_sum__eq__1__iff,axiom,
% 5.06/5.39 ! [A2: set_complex,F: complex > nat] :
% 5.06/5.39 ( ( finite3207457112153483333omplex @ A2 )
% 5.06/5.39 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.06/5.39 = one_one_nat )
% 5.06/5.39 = ( ? [X2: complex] :
% 5.06/5.39 ( ( member_complex @ X2 @ A2 )
% 5.06/5.39 & ( ( F @ X2 )
% 5.06/5.39 = one_one_nat )
% 5.06/5.39 & ! [Y2: complex] :
% 5.06/5.39 ( ( member_complex @ Y2 @ A2 )
% 5.06/5.39 => ( ( X2 != Y2 )
% 5.06/5.39 => ( ( F @ Y2 )
% 5.06/5.39 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_eq_1_iff
% 5.06/5.39 thf(fact_6887_sum__eq__1__iff,axiom,
% 5.06/5.39 ! [A2: set_nat,F: nat > nat] :
% 5.06/5.39 ( ( finite_finite_nat @ A2 )
% 5.06/5.39 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.06/5.39 = one_one_nat )
% 5.06/5.39 = ( ? [X2: nat] :
% 5.06/5.39 ( ( member_nat @ X2 @ A2 )
% 5.06/5.39 & ( ( F @ X2 )
% 5.06/5.39 = one_one_nat )
% 5.06/5.39 & ! [Y2: nat] :
% 5.06/5.39 ( ( member_nat @ Y2 @ A2 )
% 5.06/5.39 => ( ( X2 != Y2 )
% 5.06/5.39 => ( ( F @ Y2 )
% 5.06/5.39 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_eq_1_iff
% 5.06/5.39 thf(fact_6888_numeral__Bit1,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_Bit1
% 5.06/5.39 thf(fact_6889_numeral__Bit1,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_Bit1
% 5.06/5.39 thf(fact_6890_numeral__Bit1,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_Bit1
% 5.06/5.39 thf(fact_6891_numeral__Bit1,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_Bit1
% 5.06/5.39 thf(fact_6892_numeral__Bit1,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_Bit1
% 5.06/5.39 thf(fact_6893_eval__nat__numeral_I3_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % eval_nat_numeral(3)
% 5.06/5.39 thf(fact_6894_cong__exp__iff__simps_I13_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num,N2: num] :
% 5.06/5.39 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.39 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.06/5.39 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(13)
% 5.06/5.39 thf(fact_6895_cong__exp__iff__simps_I13_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num,N2: num] :
% 5.06/5.39 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.39 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.06/5.39 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(13)
% 5.06/5.39 thf(fact_6896_cong__exp__iff__simps_I13_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num,N2: num] :
% 5.06/5.39 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.39 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.06/5.39 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(13)
% 5.06/5.39 thf(fact_6897_cong__exp__iff__simps_I12_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num,N2: num] :
% 5.06/5.39 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(12)
% 5.06/5.39 thf(fact_6898_cong__exp__iff__simps_I12_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num,N2: num] :
% 5.06/5.39 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(12)
% 5.06/5.39 thf(fact_6899_cong__exp__iff__simps_I12_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num,N2: num] :
% 5.06/5.39 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(12)
% 5.06/5.39 thf(fact_6900_cong__exp__iff__simps_I10_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num,N2: num] :
% 5.06/5.39 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(10)
% 5.06/5.39 thf(fact_6901_cong__exp__iff__simps_I10_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num,N2: num] :
% 5.06/5.39 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(10)
% 5.06/5.39 thf(fact_6902_cong__exp__iff__simps_I10_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num,N2: num] :
% 5.06/5.39 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(10)
% 5.06/5.39 thf(fact_6903_power__minus__Bit1,axiom,
% 5.06/5.39 ! [X: real,K: num] :
% 5.06/5.39 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.06/5.39 = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_minus_Bit1
% 5.06/5.39 thf(fact_6904_power__minus__Bit1,axiom,
% 5.06/5.39 ! [X: int,K: num] :
% 5.06/5.39 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.06/5.39 = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_minus_Bit1
% 5.06/5.39 thf(fact_6905_power__minus__Bit1,axiom,
% 5.06/5.39 ! [X: complex,K: num] :
% 5.06/5.39 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.06/5.39 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_minus_Bit1
% 5.06/5.39 thf(fact_6906_power__minus__Bit1,axiom,
% 5.06/5.39 ! [X: rat,K: num] :
% 5.06/5.39 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.06/5.39 = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_minus_Bit1
% 5.06/5.39 thf(fact_6907_power__minus__Bit1,axiom,
% 5.06/5.39 ! [X: code_integer,K: num] :
% 5.06/5.39 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.06/5.39 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_minus_Bit1
% 5.06/5.39 thf(fact_6908_lemma__interval__lt,axiom,
% 5.06/5.39 ! [A: real,X: real,B: real] :
% 5.06/5.39 ( ( ord_less_real @ A @ X )
% 5.06/5.39 => ( ( ord_less_real @ X @ B )
% 5.06/5.39 => ? [D4: real] :
% 5.06/5.39 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.06/5.39 & ! [Y3: real] :
% 5.06/5.39 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D4 )
% 5.06/5.39 => ( ( ord_less_real @ A @ Y3 )
% 5.06/5.39 & ( ord_less_real @ Y3 @ B ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % lemma_interval_lt
% 5.06/5.39 thf(fact_6909_sum__power__add,axiom,
% 5.06/5.39 ! [X: complex,M: nat,I6: set_nat] :
% 5.06/5.39 ( ( groups2073611262835488442omplex
% 5.06/5.39 @ ^ [I5: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I6 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_power_add
% 5.06/5.39 thf(fact_6910_sum__power__add,axiom,
% 5.06/5.39 ! [X: rat,M: nat,I6: set_nat] :
% 5.06/5.39 ( ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [I5: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I6 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_power_add
% 5.06/5.39 thf(fact_6911_sum__power__add,axiom,
% 5.06/5.39 ! [X: int,M: nat,I6: set_nat] :
% 5.06/5.39 ( ( groups3539618377306564664at_int
% 5.06/5.39 @ ^ [I5: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I6 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_power_add
% 5.06/5.39 thf(fact_6912_sum__power__add,axiom,
% 5.06/5.39 ! [X: real,M: nat,I6: set_nat] :
% 5.06/5.39 ( ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I6 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_power_add
% 5.06/5.39 thf(fact_6913_sum_OatLeastAtMost__rev,axiom,
% 5.06/5.39 ! [G: nat > nat,N2: nat,M: nat] :
% 5.06/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.06/5.39 = ( groups3542108847815614940at_nat
% 5.06/5.39 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.atLeastAtMost_rev
% 5.06/5.39 thf(fact_6914_sum_OatLeastAtMost__rev,axiom,
% 5.06/5.39 ! [G: nat > real,N2: nat,M: nat] :
% 5.06/5.39 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.06/5.39 = ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.atLeastAtMost_rev
% 5.06/5.39 thf(fact_6915_numeral__code_I3_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_code(3)
% 5.06/5.39 thf(fact_6916_numeral__code_I3_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_code(3)
% 5.06/5.39 thf(fact_6917_numeral__code_I3_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_code(3)
% 5.06/5.39 thf(fact_6918_numeral__code_I3_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_code(3)
% 5.06/5.39 thf(fact_6919_numeral__code_I3_J,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.06/5.39 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_code(3)
% 5.06/5.39 thf(fact_6920_power__numeral__odd,axiom,
% 5.06/5.39 ! [Z: complex,W: num] :
% 5.06/5.39 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.06/5.39 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_numeral_odd
% 5.06/5.39 thf(fact_6921_power__numeral__odd,axiom,
% 5.06/5.39 ! [Z: real,W: num] :
% 5.06/5.39 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.06/5.39 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_numeral_odd
% 5.06/5.39 thf(fact_6922_power__numeral__odd,axiom,
% 5.06/5.39 ! [Z: rat,W: num] :
% 5.06/5.39 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.06/5.39 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_numeral_odd
% 5.06/5.39 thf(fact_6923_power__numeral__odd,axiom,
% 5.06/5.39 ! [Z: nat,W: num] :
% 5.06/5.39 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.06/5.39 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_numeral_odd
% 5.06/5.39 thf(fact_6924_power__numeral__odd,axiom,
% 5.06/5.39 ! [Z: int,W: num] :
% 5.06/5.39 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.06/5.39 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_numeral_odd
% 5.06/5.39 thf(fact_6925_sum__nth__roots,axiom,
% 5.06/5.39 ! [N2: nat,C: complex] :
% 5.06/5.39 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.06/5.39 => ( ( groups7754918857620584856omplex
% 5.06/5.39 @ ^ [X2: complex] : X2
% 5.06/5.39 @ ( collect_complex
% 5.06/5.39 @ ^ [Z2: complex] :
% 5.06/5.39 ( ( power_power_complex @ Z2 @ N2 )
% 5.06/5.39 = C ) ) )
% 5.06/5.39 = zero_zero_complex ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_nth_roots
% 5.06/5.39 thf(fact_6926_sum__roots__unity,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.06/5.39 => ( ( groups7754918857620584856omplex
% 5.06/5.39 @ ^ [X2: complex] : X2
% 5.06/5.39 @ ( collect_complex
% 5.06/5.39 @ ^ [Z2: complex] :
% 5.06/5.39 ( ( power_power_complex @ Z2 @ N2 )
% 5.06/5.39 = one_one_complex ) ) )
% 5.06/5.39 = zero_zero_complex ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_roots_unity
% 5.06/5.39 thf(fact_6927_abs__add__one__gt__zero,axiom,
% 5.06/5.39 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_add_one_gt_zero
% 5.06/5.39 thf(fact_6928_abs__add__one__gt__zero,axiom,
% 5.06/5.39 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_add_one_gt_zero
% 5.06/5.39 thf(fact_6929_abs__add__one__gt__zero,axiom,
% 5.06/5.39 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_add_one_gt_zero
% 5.06/5.39 thf(fact_6930_abs__add__one__gt__zero,axiom,
% 5.06/5.39 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_add_one_gt_zero
% 5.06/5.39 thf(fact_6931_sum__diff__nat,axiom,
% 5.06/5.39 ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 5.06/5.39 ( ( finite3207457112153483333omplex @ B3 )
% 5.06/5.39 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.06/5.39 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.06/5.39 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_diff_nat
% 5.06/5.39 thf(fact_6932_sum__diff__nat,axiom,
% 5.06/5.39 ! [B3: set_int,A2: set_int,F: int > nat] :
% 5.06/5.39 ( ( finite_finite_int @ B3 )
% 5.06/5.39 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.06/5.39 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.06/5.39 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_diff_nat
% 5.06/5.39 thf(fact_6933_sum__diff__nat,axiom,
% 5.06/5.39 ! [B3: set_nat,A2: set_nat,F: nat > nat] :
% 5.06/5.39 ( ( finite_finite_nat @ B3 )
% 5.06/5.39 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.06/5.39 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.06/5.39 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B3 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_diff_nat
% 5.06/5.39 thf(fact_6934_sum__shift__lb__Suc0__0,axiom,
% 5.06/5.39 ! [F: nat > complex,K: nat] :
% 5.06/5.39 ( ( ( F @ zero_zero_nat )
% 5.06/5.39 = zero_zero_complex )
% 5.06/5.39 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.06/5.39 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_shift_lb_Suc0_0
% 5.06/5.39 thf(fact_6935_sum__shift__lb__Suc0__0,axiom,
% 5.06/5.39 ! [F: nat > rat,K: nat] :
% 5.06/5.39 ( ( ( F @ zero_zero_nat )
% 5.06/5.39 = zero_zero_rat )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.06/5.39 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_shift_lb_Suc0_0
% 5.06/5.39 thf(fact_6936_sum__shift__lb__Suc0__0,axiom,
% 5.06/5.39 ! [F: nat > int,K: nat] :
% 5.06/5.39 ( ( ( F @ zero_zero_nat )
% 5.06/5.39 = zero_zero_int )
% 5.06/5.39 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.06/5.39 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_shift_lb_Suc0_0
% 5.06/5.39 thf(fact_6937_sum__shift__lb__Suc0__0,axiom,
% 5.06/5.39 ! [F: nat > nat,K: nat] :
% 5.06/5.39 ( ( ( F @ zero_zero_nat )
% 5.06/5.39 = zero_zero_nat )
% 5.06/5.39 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.06/5.39 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_shift_lb_Suc0_0
% 5.06/5.39 thf(fact_6938_sum__shift__lb__Suc0__0,axiom,
% 5.06/5.39 ! [F: nat > real,K: nat] :
% 5.06/5.39 ( ( ( F @ zero_zero_nat )
% 5.06/5.39 = zero_zero_real )
% 5.06/5.39 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.06/5.39 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_shift_lb_Suc0_0
% 5.06/5.39 thf(fact_6939_sum_OatLeast0__atMost__Suc,axiom,
% 5.06/5.39 ! [G: nat > rat,N2: nat] :
% 5.06/5.39 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.atLeast0_atMost_Suc
% 5.06/5.39 thf(fact_6940_sum_OatLeast0__atMost__Suc,axiom,
% 5.06/5.39 ! [G: nat > int,N2: nat] :
% 5.06/5.39 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.atLeast0_atMost_Suc
% 5.06/5.39 thf(fact_6941_sum_OatLeast0__atMost__Suc,axiom,
% 5.06/5.39 ! [G: nat > nat,N2: nat] :
% 5.06/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.atLeast0_atMost_Suc
% 5.06/5.39 thf(fact_6942_sum_OatLeast0__atMost__Suc,axiom,
% 5.06/5.39 ! [G: nat > real,N2: nat] :
% 5.06/5.39 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.atLeast0_atMost_Suc
% 5.06/5.39 thf(fact_6943_sum_OatLeast__Suc__atMost,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > rat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.atLeast_Suc_atMost
% 5.06/5.39 thf(fact_6944_sum_OatLeast__Suc__atMost,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > int] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.atLeast_Suc_atMost
% 5.06/5.39 thf(fact_6945_sum_OatLeast__Suc__atMost,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > nat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.atLeast_Suc_atMost
% 5.06/5.39 thf(fact_6946_sum_OatLeast__Suc__atMost,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > real] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.atLeast_Suc_atMost
% 5.06/5.39 thf(fact_6947_sum_Onat__ivl__Suc_H,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > rat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.nat_ivl_Suc'
% 5.06/5.39 thf(fact_6948_sum_Onat__ivl__Suc_H,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > int] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.06/5.39 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.nat_ivl_Suc'
% 5.06/5.39 thf(fact_6949_sum_Onat__ivl__Suc_H,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > nat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.06/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.nat_ivl_Suc'
% 5.06/5.39 thf(fact_6950_sum_Onat__ivl__Suc_H,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > real] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.06/5.39 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_real @ ( G @ ( suc @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.nat_ivl_Suc'
% 5.06/5.39 thf(fact_6951_numeral__Bit1__div__2,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_Bit1_div_2
% 5.06/5.39 thf(fact_6952_numeral__Bit1__div__2,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.39 = ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_Bit1_div_2
% 5.06/5.39 thf(fact_6953_odd__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % odd_numeral
% 5.06/5.39 thf(fact_6954_odd__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % odd_numeral
% 5.06/5.39 thf(fact_6955_odd__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % odd_numeral
% 5.06/5.39 thf(fact_6956_cong__exp__iff__simps_I3_J,axiom,
% 5.06/5.39 ! [N2: num,Q2: num] :
% 5.06/5.39 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 != zero_zero_nat ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(3)
% 5.06/5.39 thf(fact_6957_cong__exp__iff__simps_I3_J,axiom,
% 5.06/5.39 ! [N2: num,Q2: num] :
% 5.06/5.39 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 != zero_zero_int ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(3)
% 5.06/5.39 thf(fact_6958_cong__exp__iff__simps_I3_J,axiom,
% 5.06/5.39 ! [N2: num,Q2: num] :
% 5.06/5.39 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 != zero_z3403309356797280102nteger ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(3)
% 5.06/5.39 thf(fact_6959_power3__eq__cube,axiom,
% 5.06/5.39 ! [A: complex] :
% 5.06/5.39 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.06/5.39 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % power3_eq_cube
% 5.06/5.39 thf(fact_6960_power3__eq__cube,axiom,
% 5.06/5.39 ! [A: real] :
% 5.06/5.39 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.06/5.39 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % power3_eq_cube
% 5.06/5.39 thf(fact_6961_power3__eq__cube,axiom,
% 5.06/5.39 ! [A: rat] :
% 5.06/5.39 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.06/5.39 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % power3_eq_cube
% 5.06/5.39 thf(fact_6962_power3__eq__cube,axiom,
% 5.06/5.39 ! [A: nat] :
% 5.06/5.39 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.06/5.39 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % power3_eq_cube
% 5.06/5.39 thf(fact_6963_power3__eq__cube,axiom,
% 5.06/5.39 ! [A: int] :
% 5.06/5.39 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.06/5.39 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.06/5.39
% 5.06/5.39 % power3_eq_cube
% 5.06/5.39 thf(fact_6964_numeral__3__eq__3,axiom,
% 5.06/5.39 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.06/5.39 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % numeral_3_eq_3
% 5.06/5.39 thf(fact_6965_Suc3__eq__add__3,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % Suc3_eq_add_3
% 5.06/5.39 thf(fact_6966_lemma__interval,axiom,
% 5.06/5.39 ! [A: real,X: real,B: real] :
% 5.06/5.39 ( ( ord_less_real @ A @ X )
% 5.06/5.39 => ( ( ord_less_real @ X @ B )
% 5.06/5.39 => ? [D4: real] :
% 5.06/5.39 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.06/5.39 & ! [Y3: real] :
% 5.06/5.39 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D4 )
% 5.06/5.39 => ( ( ord_less_eq_real @ A @ Y3 )
% 5.06/5.39 & ( ord_less_eq_real @ Y3 @ B ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % lemma_interval
% 5.06/5.39 thf(fact_6967_sum_OSuc__reindex__ivl,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > rat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_rat @ ( G @ M )
% 5.06/5.39 @ ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.Suc_reindex_ivl
% 5.06/5.39 thf(fact_6968_sum_OSuc__reindex__ivl,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > int] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_int @ ( G @ M )
% 5.06/5.39 @ ( groups3539618377306564664at_int
% 5.06/5.39 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.Suc_reindex_ivl
% 5.06/5.39 thf(fact_6969_sum_OSuc__reindex__ivl,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > nat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_nat @ ( G @ M )
% 5.06/5.39 @ ( groups3542108847815614940at_nat
% 5.06/5.39 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.Suc_reindex_ivl
% 5.06/5.39 thf(fact_6970_sum_OSuc__reindex__ivl,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > real] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.06/5.39 = ( plus_plus_real @ ( G @ M )
% 5.06/5.39 @ ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.Suc_reindex_ivl
% 5.06/5.39 thf(fact_6971_sum__Suc__diff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,F: nat > rat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_Suc_diff
% 5.06/5.39 thf(fact_6972_sum__Suc__diff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,F: nat > int] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.06/5.39 => ( ( groups3539618377306564664at_int
% 5.06/5.39 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_Suc_diff
% 5.06/5.39 thf(fact_6973_sum__Suc__diff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,F: nat > real] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.06/5.39 => ( ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_Suc_diff
% 5.06/5.39 thf(fact_6974_mod__exhaust__less__4,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = zero_zero_nat )
% 5.06/5.39 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = one_one_nat )
% 5.06/5.39 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mod_exhaust_less_4
% 5.06/5.39 thf(fact_6975_abs__le__square__iff,axiom,
% 5.06/5.39 ! [X: code_integer,Y: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 5.06/5.39 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_square_iff
% 5.06/5.39 thf(fact_6976_abs__le__square__iff,axiom,
% 5.06/5.39 ! [X: real,Y: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 5.06/5.39 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_square_iff
% 5.06/5.39 thf(fact_6977_abs__le__square__iff,axiom,
% 5.06/5.39 ! [X: rat,Y: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 5.06/5.39 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_square_iff
% 5.06/5.39 thf(fact_6978_abs__le__square__iff,axiom,
% 5.06/5.39 ! [X: int,Y: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 5.06/5.39 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_le_square_iff
% 5.06/5.39 thf(fact_6979_abs__square__eq__1,axiom,
% 5.06/5.39 ! [X: code_integer] :
% 5.06/5.39 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 = one_one_Code_integer )
% 5.06/5.39 = ( ( abs_abs_Code_integer @ X )
% 5.06/5.39 = one_one_Code_integer ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_eq_1
% 5.06/5.39 thf(fact_6980_abs__square__eq__1,axiom,
% 5.06/5.39 ! [X: rat] :
% 5.06/5.39 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 = one_one_rat )
% 5.06/5.39 = ( ( abs_abs_rat @ X )
% 5.06/5.39 = one_one_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_eq_1
% 5.06/5.39 thf(fact_6981_abs__square__eq__1,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 = one_one_real )
% 5.06/5.39 = ( ( abs_abs_real @ X )
% 5.06/5.39 = one_one_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_eq_1
% 5.06/5.39 thf(fact_6982_abs__square__eq__1,axiom,
% 5.06/5.39 ! [X: int] :
% 5.06/5.39 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 = one_one_int )
% 5.06/5.39 = ( ( abs_abs_int @ X )
% 5.06/5.39 = one_one_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_eq_1
% 5.06/5.39 thf(fact_6983_num_Osize_I6_J,axiom,
% 5.06/5.39 ! [X32: num] :
% 5.06/5.39 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.06/5.39 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % num.size(6)
% 5.06/5.39 thf(fact_6984_power__even__abs,axiom,
% 5.06/5.39 ! [N2: nat,A: rat] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.39 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 )
% 5.06/5.39 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_even_abs
% 5.06/5.39 thf(fact_6985_power__even__abs,axiom,
% 5.06/5.39 ! [N2: nat,A: code_integer] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.39 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 )
% 5.06/5.39 = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_even_abs
% 5.06/5.39 thf(fact_6986_power__even__abs,axiom,
% 5.06/5.39 ! [N2: nat,A: real] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.39 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N2 )
% 5.06/5.39 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_even_abs
% 5.06/5.39 thf(fact_6987_power__even__abs,axiom,
% 5.06/5.39 ! [N2: nat,A: int] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.39 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N2 )
% 5.06/5.39 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_even_abs
% 5.06/5.39 thf(fact_6988_sum_Oub__add__nat,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > rat,P4: nat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 5.06/5.39 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.ub_add_nat
% 5.06/5.39 thf(fact_6989_sum_Oub__add__nat,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > int,P4: nat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.06/5.39 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 5.06/5.39 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.ub_add_nat
% 5.06/5.39 thf(fact_6990_sum_Oub__add__nat,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > nat,P4: nat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.06/5.39 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 5.06/5.39 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.ub_add_nat
% 5.06/5.39 thf(fact_6991_sum_Oub__add__nat,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,G: nat > real,P4: nat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.06/5.39 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P4 ) ) )
% 5.06/5.39 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P4 ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.ub_add_nat
% 5.06/5.39 thf(fact_6992_cong__exp__iff__simps_I11_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num] :
% 5.06/5.39 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.39 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.06/5.39 = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(11)
% 5.06/5.39 thf(fact_6993_cong__exp__iff__simps_I11_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num] :
% 5.06/5.39 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.39 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.06/5.39 = zero_zero_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(11)
% 5.06/5.39 thf(fact_6994_cong__exp__iff__simps_I11_J,axiom,
% 5.06/5.39 ! [M: num,Q2: num] :
% 5.06/5.39 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.39 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.06/5.39 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(11)
% 5.06/5.39 thf(fact_6995_cong__exp__iff__simps_I7_J,axiom,
% 5.06/5.39 ! [Q2: num,N2: num] :
% 5.06/5.39 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.39 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.06/5.39 = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(7)
% 5.06/5.39 thf(fact_6996_cong__exp__iff__simps_I7_J,axiom,
% 5.06/5.39 ! [Q2: num,N2: num] :
% 5.06/5.39 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.39 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) )
% 5.06/5.39 = zero_zero_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(7)
% 5.06/5.39 thf(fact_6997_cong__exp__iff__simps_I7_J,axiom,
% 5.06/5.39 ! [Q2: num,N2: num] :
% 5.06/5.39 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.06/5.39 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.06/5.39 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.06/5.39 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.39
% 5.06/5.39 % cong_exp_iff_simps(7)
% 5.06/5.39 thf(fact_6998_Suc__div__eq__add3__div,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 5.06/5.39 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % Suc_div_eq_add3_div
% 5.06/5.39 thf(fact_6999_Suc__mod__eq__add3__mod,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 5.06/5.39 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % Suc_mod_eq_add3_mod
% 5.06/5.39 thf(fact_7000_divmod__int__def,axiom,
% 5.06/5.39 ( unique5052692396658037445od_int
% 5.06/5.39 = ( ^ [M6: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_int_def
% 5.06/5.39 thf(fact_7001_Divides_Oadjust__div__def,axiom,
% 5.06/5.39 ( adjust_div
% 5.06/5.39 = ( produc8211389475949308722nt_int
% 5.06/5.39 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Divides.adjust_div_def
% 5.06/5.39 thf(fact_7002_abs__sqrt__wlog,axiom,
% 5.06/5.39 ! [P: code_integer > code_integer > $o,X: code_integer] :
% 5.06/5.39 ( ! [X3: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 5.06/5.39 => ( P @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.39 => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_sqrt_wlog
% 5.06/5.39 thf(fact_7003_abs__sqrt__wlog,axiom,
% 5.06/5.39 ! [P: real > real > $o,X: real] :
% 5.06/5.39 ( ! [X3: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.06/5.39 => ( P @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.39 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_sqrt_wlog
% 5.06/5.39 thf(fact_7004_abs__sqrt__wlog,axiom,
% 5.06/5.39 ! [P: rat > rat > $o,X: rat] :
% 5.06/5.39 ( ! [X3: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 5.06/5.39 => ( P @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.39 => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_sqrt_wlog
% 5.06/5.39 thf(fact_7005_abs__sqrt__wlog,axiom,
% 5.06/5.39 ! [P: int > int > $o,X: int] :
% 5.06/5.39 ( ! [X3: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.06/5.39 => ( P @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.39 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_sqrt_wlog
% 5.06/5.39 thf(fact_7006_power2__le__iff__abs__le,axiom,
% 5.06/5.39 ! [Y: code_integer,X: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.06/5.39 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power2_le_iff_abs_le
% 5.06/5.39 thf(fact_7007_power2__le__iff__abs__le,axiom,
% 5.06/5.39 ! [Y: real,X: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.39 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power2_le_iff_abs_le
% 5.06/5.39 thf(fact_7008_power2__le__iff__abs__le,axiom,
% 5.06/5.39 ! [Y: rat,X: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.06/5.39 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power2_le_iff_abs_le
% 5.06/5.39 thf(fact_7009_power2__le__iff__abs__le,axiom,
% 5.06/5.39 ! [Y: int,X: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.39 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power2_le_iff_abs_le
% 5.06/5.39 thf(fact_7010_abs__square__le__1,axiom,
% 5.06/5.39 ! [X: code_integer] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.06/5.39 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_le_1
% 5.06/5.39 thf(fact_7011_abs__square__le__1,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.06/5.39 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_le_1
% 5.06/5.39 thf(fact_7012_abs__square__le__1,axiom,
% 5.06/5.39 ! [X: rat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.06/5.39 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_le_1
% 5.06/5.39 thf(fact_7013_abs__square__le__1,axiom,
% 5.06/5.39 ! [X: int] :
% 5.06/5.39 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.06/5.39 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_le_1
% 5.06/5.39 thf(fact_7014_abs__square__less__1,axiom,
% 5.06/5.39 ! [X: code_integer] :
% 5.06/5.39 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.06/5.39 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_less_1
% 5.06/5.39 thf(fact_7015_abs__square__less__1,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.06/5.39 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_less_1
% 5.06/5.39 thf(fact_7016_abs__square__less__1,axiom,
% 5.06/5.39 ! [X: rat] :
% 5.06/5.39 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.06/5.39 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_less_1
% 5.06/5.39 thf(fact_7017_abs__square__less__1,axiom,
% 5.06/5.39 ! [X: int] :
% 5.06/5.39 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.06/5.39 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_square_less_1
% 5.06/5.39 thf(fact_7018_divmod__def,axiom,
% 5.06/5.39 ( unique5052692396658037445od_int
% 5.06/5.39 = ( ^ [M6: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_def
% 5.06/5.39 thf(fact_7019_divmod__def,axiom,
% 5.06/5.39 ( unique5055182867167087721od_nat
% 5.06/5.39 = ( ^ [M6: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_def
% 5.06/5.39 thf(fact_7020_divmod__def,axiom,
% 5.06/5.39 ( unique3479559517661332726nteger
% 5.06/5.39 = ( ^ [M6: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_def
% 5.06/5.39 thf(fact_7021_divmod_H__nat__def,axiom,
% 5.06/5.39 ( unique5055182867167087721od_nat
% 5.06/5.39 = ( ^ [M6: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod'_nat_def
% 5.06/5.39 thf(fact_7022_power__mono__even,axiom,
% 5.06/5.39 ! [N2: nat,A: code_integer,B: code_integer] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.39 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_mono_even
% 5.06/5.39 thf(fact_7023_power__mono__even,axiom,
% 5.06/5.39 ! [N2: nat,A: real,B: real] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.39 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.06/5.39 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_mono_even
% 5.06/5.39 thf(fact_7024_power__mono__even,axiom,
% 5.06/5.39 ! [N2: nat,A: rat,B: rat] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.39 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.06/5.39 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_mono_even
% 5.06/5.39 thf(fact_7025_power__mono__even,axiom,
% 5.06/5.39 ! [N2: nat,A: int,B: int] :
% 5.06/5.39 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.39 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.06/5.39 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % power_mono_even
% 5.06/5.39 thf(fact_7026_convex__sum__bound__le,axiom,
% 5.06/5.39 ! [I6: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.06/5.39 ( ! [I3: complex] :
% 5.06/5.39 ( ( member_complex @ I3 @ I6 )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.06/5.39 => ( ( ( groups6621422865394947399nteger @ X @ I6 )
% 5.06/5.39 = one_one_Code_integer )
% 5.06/5.39 => ( ! [I3: complex] :
% 5.06/5.39 ( ( member_complex @ I3 @ I6 )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.06/5.39 => ( ord_le3102999989581377725nteger
% 5.06/5.39 @ ( abs_abs_Code_integer
% 5.06/5.39 @ ( minus_8373710615458151222nteger
% 5.06/5.39 @ ( groups6621422865394947399nteger
% 5.06/5.39 @ ^ [I5: complex] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 @ B ) )
% 5.06/5.39 @ Delta ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % convex_sum_bound_le
% 5.06/5.39 thf(fact_7027_convex__sum__bound__le,axiom,
% 5.06/5.39 ! [I6: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.06/5.39 ( ! [I3: real] :
% 5.06/5.39 ( ( member_real @ I3 @ I6 )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.06/5.39 => ( ( ( groups7713935264441627589nteger @ X @ I6 )
% 5.06/5.39 = one_one_Code_integer )
% 5.06/5.39 => ( ! [I3: real] :
% 5.06/5.39 ( ( member_real @ I3 @ I6 )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.06/5.39 => ( ord_le3102999989581377725nteger
% 5.06/5.39 @ ( abs_abs_Code_integer
% 5.06/5.39 @ ( minus_8373710615458151222nteger
% 5.06/5.39 @ ( groups7713935264441627589nteger
% 5.06/5.39 @ ^ [I5: real] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 @ B ) )
% 5.06/5.39 @ Delta ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % convex_sum_bound_le
% 5.06/5.39 thf(fact_7028_convex__sum__bound__le,axiom,
% 5.06/5.39 ! [I6: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.06/5.39 ( ! [I3: nat] :
% 5.06/5.39 ( ( member_nat @ I3 @ I6 )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.06/5.39 => ( ( ( groups7501900531339628137nteger @ X @ I6 )
% 5.06/5.39 = one_one_Code_integer )
% 5.06/5.39 => ( ! [I3: nat] :
% 5.06/5.39 ( ( member_nat @ I3 @ I6 )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.06/5.39 => ( ord_le3102999989581377725nteger
% 5.06/5.39 @ ( abs_abs_Code_integer
% 5.06/5.39 @ ( minus_8373710615458151222nteger
% 5.06/5.39 @ ( groups7501900531339628137nteger
% 5.06/5.39 @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 @ B ) )
% 5.06/5.39 @ Delta ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % convex_sum_bound_le
% 5.06/5.39 thf(fact_7029_convex__sum__bound__le,axiom,
% 5.06/5.39 ! [I6: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.06/5.39 ( ! [I3: int] :
% 5.06/5.39 ( ( member_int @ I3 @ I6 )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.06/5.39 => ( ( ( groups7873554091576472773nteger @ X @ I6 )
% 5.06/5.39 = one_one_Code_integer )
% 5.06/5.39 => ( ! [I3: int] :
% 5.06/5.39 ( ( member_int @ I3 @ I6 )
% 5.06/5.39 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.06/5.39 => ( ord_le3102999989581377725nteger
% 5.06/5.39 @ ( abs_abs_Code_integer
% 5.06/5.39 @ ( minus_8373710615458151222nteger
% 5.06/5.39 @ ( groups7873554091576472773nteger
% 5.06/5.39 @ ^ [I5: int] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 @ B ) )
% 5.06/5.39 @ Delta ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % convex_sum_bound_le
% 5.06/5.39 thf(fact_7030_convex__sum__bound__le,axiom,
% 5.06/5.39 ! [I6: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 5.06/5.39 ( ! [I3: complex] :
% 5.06/5.39 ( ( member_complex @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.06/5.39 => ( ( ( groups5808333547571424918x_real @ X @ I6 )
% 5.06/5.39 = one_one_real )
% 5.06/5.39 => ( ! [I3: complex] :
% 5.06/5.39 ( ( member_complex @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.06/5.39 => ( ord_less_eq_real
% 5.06/5.39 @ ( abs_abs_real
% 5.06/5.39 @ ( minus_minus_real
% 5.06/5.39 @ ( groups5808333547571424918x_real
% 5.06/5.39 @ ^ [I5: complex] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 @ B ) )
% 5.06/5.39 @ Delta ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % convex_sum_bound_le
% 5.06/5.39 thf(fact_7031_convex__sum__bound__le,axiom,
% 5.06/5.39 ! [I6: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 5.06/5.39 ( ! [I3: real] :
% 5.06/5.39 ( ( member_real @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.06/5.39 => ( ( ( groups8097168146408367636l_real @ X @ I6 )
% 5.06/5.39 = one_one_real )
% 5.06/5.39 => ( ! [I3: real] :
% 5.06/5.39 ( ( member_real @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.06/5.39 => ( ord_less_eq_real
% 5.06/5.39 @ ( abs_abs_real
% 5.06/5.39 @ ( minus_minus_real
% 5.06/5.39 @ ( groups8097168146408367636l_real
% 5.06/5.39 @ ^ [I5: real] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 @ B ) )
% 5.06/5.39 @ Delta ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % convex_sum_bound_le
% 5.06/5.39 thf(fact_7032_convex__sum__bound__le,axiom,
% 5.06/5.39 ! [I6: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 5.06/5.39 ( ! [I3: int] :
% 5.06/5.39 ( ( member_int @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 5.06/5.39 => ( ( ( groups8778361861064173332t_real @ X @ I6 )
% 5.06/5.39 = one_one_real )
% 5.06/5.39 => ( ! [I3: int] :
% 5.06/5.39 ( ( member_int @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.06/5.39 => ( ord_less_eq_real
% 5.06/5.39 @ ( abs_abs_real
% 5.06/5.39 @ ( minus_minus_real
% 5.06/5.39 @ ( groups8778361861064173332t_real
% 5.06/5.39 @ ^ [I5: int] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 @ B ) )
% 5.06/5.39 @ Delta ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % convex_sum_bound_le
% 5.06/5.39 thf(fact_7033_convex__sum__bound__le,axiom,
% 5.06/5.39 ! [I6: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 5.06/5.39 ( ! [I3: complex] :
% 5.06/5.39 ( ( member_complex @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.06/5.39 => ( ( ( groups5058264527183730370ex_rat @ X @ I6 )
% 5.06/5.39 = one_one_rat )
% 5.06/5.39 => ( ! [I3: complex] :
% 5.06/5.39 ( ( member_complex @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.06/5.39 => ( ord_less_eq_rat
% 5.06/5.39 @ ( abs_abs_rat
% 5.06/5.39 @ ( minus_minus_rat
% 5.06/5.39 @ ( groups5058264527183730370ex_rat
% 5.06/5.39 @ ^ [I5: complex] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 @ B ) )
% 5.06/5.39 @ Delta ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % convex_sum_bound_le
% 5.06/5.39 thf(fact_7034_convex__sum__bound__le,axiom,
% 5.06/5.39 ! [I6: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.06/5.39 ( ! [I3: real] :
% 5.06/5.39 ( ( member_real @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.06/5.39 => ( ( ( groups1300246762558778688al_rat @ X @ I6 )
% 5.06/5.39 = one_one_rat )
% 5.06/5.39 => ( ! [I3: real] :
% 5.06/5.39 ( ( member_real @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.06/5.39 => ( ord_less_eq_rat
% 5.06/5.39 @ ( abs_abs_rat
% 5.06/5.39 @ ( minus_minus_rat
% 5.06/5.39 @ ( groups1300246762558778688al_rat
% 5.06/5.39 @ ^ [I5: real] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 @ B ) )
% 5.06/5.39 @ Delta ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % convex_sum_bound_le
% 5.06/5.39 thf(fact_7035_convex__sum__bound__le,axiom,
% 5.06/5.39 ! [I6: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.06/5.39 ( ! [I3: nat] :
% 5.06/5.39 ( ( member_nat @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.06/5.39 => ( ( ( groups2906978787729119204at_rat @ X @ I6 )
% 5.06/5.39 = one_one_rat )
% 5.06/5.39 => ( ! [I3: nat] :
% 5.06/5.39 ( ( member_nat @ I3 @ I6 )
% 5.06/5.39 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.06/5.39 => ( ord_less_eq_rat
% 5.06/5.39 @ ( abs_abs_rat
% 5.06/5.39 @ ( minus_minus_rat
% 5.06/5.39 @ ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.06/5.39 @ I6 )
% 5.06/5.39 @ B ) )
% 5.06/5.39 @ Delta ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % convex_sum_bound_le
% 5.06/5.39 thf(fact_7036_sum__natinterval__diff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,F: nat > complex] :
% 5.06/5.39 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups2073611262835488442omplex
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.06/5.39 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups2073611262835488442omplex
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = zero_zero_complex ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_natinterval_diff
% 5.06/5.39 thf(fact_7037_sum__natinterval__diff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,F: nat > rat] :
% 5.06/5.39 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.06/5.39 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = zero_zero_rat ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_natinterval_diff
% 5.06/5.39 thf(fact_7038_sum__natinterval__diff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,F: nat > int] :
% 5.06/5.39 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups3539618377306564664at_int
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.06/5.39 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups3539618377306564664at_int
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = zero_zero_int ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_natinterval_diff
% 5.06/5.39 thf(fact_7039_sum__natinterval__diff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,F: nat > real] :
% 5.06/5.39 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.06/5.39 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = zero_zero_real ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_natinterval_diff
% 5.06/5.39 thf(fact_7040_sum__telescope_H_H,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,F: nat > rat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.06/5.39 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_telescope''
% 5.06/5.39 thf(fact_7041_sum__telescope_H_H,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,F: nat > int] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups3539618377306564664at_int
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.06/5.39 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_telescope''
% 5.06/5.39 thf(fact_7042_sum__telescope_H_H,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,F: nat > real] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.06/5.39 = ( minus_minus_real @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_telescope''
% 5.06/5.39 thf(fact_7043_divmod__nat__def,axiom,
% 5.06/5.39 ( divmod_nat
% 5.06/5.39 = ( ^ [M6: nat,N: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N ) @ ( modulo_modulo_nat @ M6 @ N ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_nat_def
% 5.06/5.39 thf(fact_7044_mask__eq__sum__exp,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 5.06/5.39 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.39 @ ( collect_nat
% 5.06/5.39 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mask_eq_sum_exp
% 5.06/5.39 thf(fact_7045_mask__eq__sum__exp,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 5.06/5.39 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 @ ( collect_nat
% 5.06/5.39 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mask_eq_sum_exp
% 5.06/5.39 thf(fact_7046_sum__gp__multiplied,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,X: complex] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.06/5.39 = ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_gp_multiplied
% 5.06/5.39 thf(fact_7047_sum__gp__multiplied,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,X: rat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.06/5.39 = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_gp_multiplied
% 5.06/5.39 thf(fact_7048_sum__gp__multiplied,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,X: int] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.06/5.39 = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_gp_multiplied
% 5.06/5.39 thf(fact_7049_sum__gp__multiplied,axiom,
% 5.06/5.39 ! [M: nat,N2: nat,X: real] :
% 5.06/5.39 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.39 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.06/5.39 = ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_gp_multiplied
% 5.06/5.39 thf(fact_7050_sum_Oin__pairs,axiom,
% 5.06/5.39 ! [G: nat > rat,M: nat,N2: nat] :
% 5.06/5.39 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.39 = ( groups2906978787729119204at_rat
% 5.06/5.39 @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.in_pairs
% 5.06/5.39 thf(fact_7051_sum_Oin__pairs,axiom,
% 5.06/5.39 ! [G: nat > int,M: nat,N2: nat] :
% 5.06/5.39 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.39 = ( groups3539618377306564664at_int
% 5.06/5.39 @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.in_pairs
% 5.06/5.39 thf(fact_7052_sum_Oin__pairs,axiom,
% 5.06/5.39 ! [G: nat > nat,M: nat,N2: nat] :
% 5.06/5.39 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.39 = ( groups3542108847815614940at_nat
% 5.06/5.39 @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.in_pairs
% 5.06/5.39 thf(fact_7053_sum_Oin__pairs,axiom,
% 5.06/5.39 ! [G: nat > real,M: nat,N2: nat] :
% 5.06/5.39 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.39 = ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum.in_pairs
% 5.06/5.39 thf(fact_7054_eq__diff__eq_H,axiom,
% 5.06/5.39 ! [X: real,Y: real,Z: real] :
% 5.06/5.39 ( ( X
% 5.06/5.39 = ( minus_minus_real @ Y @ Z ) )
% 5.06/5.39 = ( Y
% 5.06/5.39 = ( plus_plus_real @ X @ Z ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % eq_diff_eq'
% 5.06/5.39 thf(fact_7055_mask__eq__sum__exp__nat,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 5.06/5.39 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.39 @ ( collect_nat
% 5.06/5.39 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % mask_eq_sum_exp_nat
% 5.06/5.39 thf(fact_7056_gauss__sum__nat,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( groups3542108847815614940at_nat
% 5.06/5.39 @ ^ [X2: nat] : X2
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.39 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % gauss_sum_nat
% 5.06/5.39 thf(fact_7057_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.39 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.39 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.06/5.39 thf(fact_7058_arith__series__nat,axiom,
% 5.06/5.39 ! [A: nat,D: nat,N2: nat] :
% 5.06/5.39 ( ( groups3542108847815614940at_nat
% 5.06/5.39 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I5 @ D ) )
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.39 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % arith_series_nat
% 5.06/5.39 thf(fact_7059_Sum__Icc__nat,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( groups3542108847815614940at_nat
% 5.06/5.39 @ ^ [X2: nat] : X2
% 5.06/5.39 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Sum_Icc_nat
% 5.06/5.39 thf(fact_7060_odd__mod__4__div__2,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.06/5.39 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.06/5.39 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % odd_mod_4_div_2
% 5.06/5.39 thf(fact_7061_divmod__divmod__step,axiom,
% 5.06/5.39 ( unique5055182867167087721od_nat
% 5.06/5.39 = ( ^ [M6: num,N: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_divmod_step
% 5.06/5.39 thf(fact_7062_divmod__divmod__step,axiom,
% 5.06/5.39 ( unique5052692396658037445od_int
% 5.06/5.39 = ( ^ [M6: num,N: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_divmod_step
% 5.06/5.39 thf(fact_7063_divmod__divmod__step,axiom,
% 5.06/5.39 ( unique3479559517661332726nteger
% 5.06/5.39 = ( ^ [M6: num,N: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % divmod_divmod_step
% 5.06/5.39 thf(fact_7064_signed__take__bit__numeral__minus__bit1,axiom,
% 5.06/5.39 ! [L2: num,K: num] :
% 5.06/5.39 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.06/5.39 = ( 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 ) ) ).
% 5.06/5.39
% 5.06/5.39 % signed_take_bit_numeral_minus_bit1
% 5.06/5.39 thf(fact_7065_dbl__dec__simps_I4_J,axiom,
% 5.06/5.39 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.39 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_dec_simps(4)
% 5.06/5.39 thf(fact_7066_dbl__dec__simps_I4_J,axiom,
% 5.06/5.39 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.39 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_dec_simps(4)
% 5.06/5.39 thf(fact_7067_dbl__dec__simps_I4_J,axiom,
% 5.06/5.39 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.39 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_dec_simps(4)
% 5.06/5.39 thf(fact_7068_dbl__dec__simps_I4_J,axiom,
% 5.06/5.39 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.39 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_dec_simps(4)
% 5.06/5.39 thf(fact_7069_dbl__dec__simps_I4_J,axiom,
% 5.06/5.39 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.39 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_dec_simps(4)
% 5.06/5.39 thf(fact_7070_signed__take__bit__numeral__bit1,axiom,
% 5.06/5.39 ! [L2: num,K: num] :
% 5.06/5.39 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.06/5.39 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % signed_take_bit_numeral_bit1
% 5.06/5.39 thf(fact_7071_arctan__double,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.39 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 5.06/5.39 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % arctan_double
% 5.06/5.39 thf(fact_7072_dbl__inc__simps_I3_J,axiom,
% 5.06/5.39 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.06/5.39 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(3)
% 5.06/5.39 thf(fact_7073_dbl__inc__simps_I3_J,axiom,
% 5.06/5.39 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.06/5.39 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(3)
% 5.06/5.39 thf(fact_7074_dbl__inc__simps_I3_J,axiom,
% 5.06/5.39 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.06/5.39 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(3)
% 5.06/5.39 thf(fact_7075_dbl__inc__simps_I3_J,axiom,
% 5.06/5.39 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.06/5.39 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(3)
% 5.06/5.39 thf(fact_7076_sum__gp,axiom,
% 5.06/5.39 ! [N2: nat,M: nat,X: complex] :
% 5.06/5.39 ( ( ( ord_less_nat @ N2 @ M )
% 5.06/5.39 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = zero_zero_complex ) )
% 5.06/5.39 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.06/5.39 => ( ( ( X = one_one_complex )
% 5.06/5.39 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.06/5.39 & ( ( X != one_one_complex )
% 5.06/5.39 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_gp
% 5.06/5.39 thf(fact_7077_sum__gp,axiom,
% 5.06/5.39 ! [N2: nat,M: nat,X: rat] :
% 5.06/5.39 ( ( ( ord_less_nat @ N2 @ M )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = zero_zero_rat ) )
% 5.06/5.39 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.06/5.39 => ( ( ( X = one_one_rat )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.06/5.39 & ( ( X != one_one_rat )
% 5.06/5.39 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_gp
% 5.06/5.39 thf(fact_7078_sum__gp,axiom,
% 5.06/5.39 ! [N2: nat,M: nat,X: real] :
% 5.06/5.39 ( ( ( ord_less_nat @ N2 @ M )
% 5.06/5.39 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = zero_zero_real ) )
% 5.06/5.39 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.06/5.39 => ( ( ( X = one_one_real )
% 5.06/5.39 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.06/5.39 & ( ( X != one_one_real )
% 5.06/5.39 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.39 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % sum_gp
% 5.06/5.39 thf(fact_7079_of__nat__eq__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ( semiri1314217659103216013at_int @ M )
% 5.06/5.39 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.39 = ( M = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_iff
% 5.06/5.39 thf(fact_7080_of__nat__eq__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ( semiri5074537144036343181t_real @ M )
% 5.06/5.39 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.39 = ( M = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_iff
% 5.06/5.39 thf(fact_7081_of__nat__eq__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.06/5.39 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.06/5.39 = ( M = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_iff
% 5.06/5.39 thf(fact_7082_of__nat__eq__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ( semiri4939895301339042750nteger @ M )
% 5.06/5.39 = ( semiri4939895301339042750nteger @ N2 ) )
% 5.06/5.39 = ( M = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_iff
% 5.06/5.39 thf(fact_7083_split__part,axiom,
% 5.06/5.39 ! [P: $o,Q: int > int > $o] :
% 5.06/5.39 ( ( produc4947309494688390418_int_o
% 5.06/5.39 @ ^ [A4: int,B4: int] :
% 5.06/5.39 ( P
% 5.06/5.39 & ( Q @ A4 @ B4 ) ) )
% 5.06/5.39 = ( ^ [Ab: product_prod_int_int] :
% 5.06/5.39 ( P
% 5.06/5.39 & ( produc4947309494688390418_int_o @ Q @ Ab ) ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % split_part
% 5.06/5.39 thf(fact_7084_int__eq__iff__numeral,axiom,
% 5.06/5.39 ! [M: nat,V: num] :
% 5.06/5.39 ( ( ( semiri1314217659103216013at_int @ M )
% 5.06/5.39 = ( numeral_numeral_int @ V ) )
% 5.06/5.39 = ( M
% 5.06/5.39 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % int_eq_iff_numeral
% 5.06/5.39 thf(fact_7085_abs__of__nat,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.06/5.39 = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nat
% 5.06/5.39 thf(fact_7086_abs__of__nat,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.39 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nat
% 5.06/5.39 thf(fact_7087_abs__of__nat,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.39 = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nat
% 5.06/5.39 thf(fact_7088_abs__of__nat,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.06/5.39 = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % abs_of_nat
% 5.06/5.39 thf(fact_7089_negative__zle,axiom,
% 5.06/5.39 ! [N2: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.06/5.39
% 5.06/5.39 % negative_zle
% 5.06/5.39 thf(fact_7090_dbl__dec__simps_I3_J,axiom,
% 5.06/5.39 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.06/5.39 = one_one_complex ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_dec_simps(3)
% 5.06/5.39 thf(fact_7091_dbl__dec__simps_I3_J,axiom,
% 5.06/5.39 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.06/5.39 = one_one_real ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_dec_simps(3)
% 5.06/5.39 thf(fact_7092_dbl__dec__simps_I3_J,axiom,
% 5.06/5.39 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.06/5.39 = one_one_rat ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_dec_simps(3)
% 5.06/5.39 thf(fact_7093_dbl__dec__simps_I3_J,axiom,
% 5.06/5.39 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.06/5.39 = one_one_int ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_dec_simps(3)
% 5.06/5.39 thf(fact_7094_of__nat__eq__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ( semiri8010041392384452111omplex @ M )
% 5.06/5.39 = zero_zero_complex )
% 5.06/5.39 = ( M = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_0_iff
% 5.06/5.39 thf(fact_7095_of__nat__eq__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ( semiri681578069525770553at_rat @ M )
% 5.06/5.39 = zero_zero_rat )
% 5.06/5.39 = ( M = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_0_iff
% 5.06/5.39 thf(fact_7096_of__nat__eq__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ( semiri1314217659103216013at_int @ M )
% 5.06/5.39 = zero_zero_int )
% 5.06/5.39 = ( M = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_0_iff
% 5.06/5.39 thf(fact_7097_of__nat__eq__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ( semiri5074537144036343181t_real @ M )
% 5.06/5.39 = zero_zero_real )
% 5.06/5.39 = ( M = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_0_iff
% 5.06/5.39 thf(fact_7098_of__nat__eq__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.06/5.39 = zero_zero_nat )
% 5.06/5.39 = ( M = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_0_iff
% 5.06/5.39 thf(fact_7099_of__nat__eq__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ( semiri4939895301339042750nteger @ M )
% 5.06/5.39 = zero_z3403309356797280102nteger )
% 5.06/5.39 = ( M = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_0_iff
% 5.06/5.39 thf(fact_7100_of__nat__0__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( zero_zero_complex
% 5.06/5.39 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.06/5.39 = ( zero_zero_nat = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0_eq_iff
% 5.06/5.39 thf(fact_7101_of__nat__0__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( zero_zero_rat
% 5.06/5.39 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.06/5.39 = ( zero_zero_nat = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0_eq_iff
% 5.06/5.39 thf(fact_7102_of__nat__0__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( zero_zero_int
% 5.06/5.39 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.39 = ( zero_zero_nat = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0_eq_iff
% 5.06/5.39 thf(fact_7103_of__nat__0__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( zero_zero_real
% 5.06/5.39 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.39 = ( zero_zero_nat = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0_eq_iff
% 5.06/5.39 thf(fact_7104_of__nat__0__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( zero_zero_nat
% 5.06/5.39 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.06/5.39 = ( zero_zero_nat = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0_eq_iff
% 5.06/5.39 thf(fact_7105_of__nat__0__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( zero_z3403309356797280102nteger
% 5.06/5.39 = ( semiri4939895301339042750nteger @ N2 ) )
% 5.06/5.39 = ( zero_zero_nat = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0_eq_iff
% 5.06/5.39 thf(fact_7106_of__nat__0,axiom,
% 5.06/5.39 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.06/5.39 = zero_zero_complex ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0
% 5.06/5.39 thf(fact_7107_of__nat__0,axiom,
% 5.06/5.39 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.06/5.39 = zero_zero_rat ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0
% 5.06/5.39 thf(fact_7108_of__nat__0,axiom,
% 5.06/5.39 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.06/5.39 = zero_zero_int ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0
% 5.06/5.39 thf(fact_7109_of__nat__0,axiom,
% 5.06/5.39 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.06/5.39 = zero_zero_real ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0
% 5.06/5.39 thf(fact_7110_of__nat__0,axiom,
% 5.06/5.39 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.06/5.39 = zero_zero_nat ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0
% 5.06/5.39 thf(fact_7111_of__nat__0,axiom,
% 5.06/5.39 ( ( semiri4939895301339042750nteger @ zero_zero_nat )
% 5.06/5.39 = zero_z3403309356797280102nteger ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_0
% 5.06/5.39 thf(fact_7112_of__nat__less__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.06/5.39 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_less_iff
% 5.06/5.39 thf(fact_7113_of__nat__less__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.39 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_less_iff
% 5.06/5.39 thf(fact_7114_of__nat__less__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.39 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_less_iff
% 5.06/5.39 thf(fact_7115_of__nat__less__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.06/5.39 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_less_iff
% 5.06/5.39 thf(fact_7116_of__nat__less__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.06/5.39 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_less_iff
% 5.06/5.39 thf(fact_7117_of__nat__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N2 ) )
% 5.06/5.39 = ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_numeral
% 5.06/5.39 thf(fact_7118_of__nat__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N2 ) )
% 5.06/5.39 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_numeral
% 5.06/5.39 thf(fact_7119_of__nat__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 5.06/5.39 = ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_numeral
% 5.06/5.39 thf(fact_7120_of__nat__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N2 ) )
% 5.06/5.39 = ( numeral_numeral_real @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_numeral
% 5.06/5.39 thf(fact_7121_of__nat__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.06/5.39 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_numeral
% 5.06/5.39 thf(fact_7122_of__nat__numeral,axiom,
% 5.06/5.39 ! [N2: num] :
% 5.06/5.39 ( ( semiri4939895301339042750nteger @ ( numeral_numeral_nat @ N2 ) )
% 5.06/5.39 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_numeral
% 5.06/5.39 thf(fact_7123_of__nat__le__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.39 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_le_iff
% 5.06/5.39 thf(fact_7124_of__nat__le__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.06/5.39 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_le_iff
% 5.06/5.39 thf(fact_7125_of__nat__le__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.06/5.39 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_le_iff
% 5.06/5.39 thf(fact_7126_of__nat__le__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.06/5.39 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_le_iff
% 5.06/5.39 thf(fact_7127_of__nat__le__iff,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.39 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_le_iff
% 5.06/5.39 thf(fact_7128_of__nat__add,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.39 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_add
% 5.06/5.39 thf(fact_7129_of__nat__add,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.39 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_add
% 5.06/5.39 thf(fact_7130_of__nat__add,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.39 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_add
% 5.06/5.39 thf(fact_7131_of__nat__add,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.39 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_add
% 5.06/5.39 thf(fact_7132_of__nat__add,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.39 = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_add
% 5.06/5.39 thf(fact_7133_of__nat__mult,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N2 ) )
% 5.06/5.39 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_mult
% 5.06/5.39 thf(fact_7134_of__nat__mult,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 5.06/5.39 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_mult
% 5.06/5.39 thf(fact_7135_of__nat__mult,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N2 ) )
% 5.06/5.39 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_mult
% 5.06/5.39 thf(fact_7136_of__nat__mult,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 5.06/5.39 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_mult
% 5.06/5.39 thf(fact_7137_of__nat__mult,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N2 ) )
% 5.06/5.39 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_mult
% 5.06/5.39 thf(fact_7138_of__nat__1,axiom,
% 5.06/5.39 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.06/5.39 = one_one_complex ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1
% 5.06/5.39 thf(fact_7139_of__nat__1,axiom,
% 5.06/5.39 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.06/5.39 = one_one_rat ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1
% 5.06/5.39 thf(fact_7140_of__nat__1,axiom,
% 5.06/5.39 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.06/5.39 = one_one_int ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1
% 5.06/5.39 thf(fact_7141_of__nat__1,axiom,
% 5.06/5.39 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.06/5.39 = one_one_real ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1
% 5.06/5.39 thf(fact_7142_of__nat__1,axiom,
% 5.06/5.39 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.06/5.39 = one_one_nat ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1
% 5.06/5.39 thf(fact_7143_of__nat__1,axiom,
% 5.06/5.39 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 5.06/5.39 = one_one_Code_integer ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1
% 5.06/5.39 thf(fact_7144_of__nat__1__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( one_one_complex
% 5.06/5.39 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1_eq_iff
% 5.06/5.39 thf(fact_7145_of__nat__1__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( one_one_rat
% 5.06/5.39 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1_eq_iff
% 5.06/5.39 thf(fact_7146_of__nat__1__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( one_one_int
% 5.06/5.39 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1_eq_iff
% 5.06/5.39 thf(fact_7147_of__nat__1__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( one_one_real
% 5.06/5.39 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1_eq_iff
% 5.06/5.39 thf(fact_7148_of__nat__1__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( one_one_nat
% 5.06/5.39 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1_eq_iff
% 5.06/5.39 thf(fact_7149_of__nat__1__eq__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( one_one_Code_integer
% 5.06/5.39 = ( semiri4939895301339042750nteger @ N2 ) )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_1_eq_iff
% 5.06/5.39 thf(fact_7150_of__nat__eq__1__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( ( semiri8010041392384452111omplex @ N2 )
% 5.06/5.39 = one_one_complex )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_1_iff
% 5.06/5.39 thf(fact_7151_of__nat__eq__1__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( ( semiri681578069525770553at_rat @ N2 )
% 5.06/5.39 = one_one_rat )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_1_iff
% 5.06/5.39 thf(fact_7152_of__nat__eq__1__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( ( semiri1314217659103216013at_int @ N2 )
% 5.06/5.39 = one_one_int )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_1_iff
% 5.06/5.39 thf(fact_7153_of__nat__eq__1__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( ( semiri5074537144036343181t_real @ N2 )
% 5.06/5.39 = one_one_real )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_1_iff
% 5.06/5.39 thf(fact_7154_of__nat__eq__1__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 5.06/5.39 = one_one_nat )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_1_iff
% 5.06/5.39 thf(fact_7155_of__nat__eq__1__iff,axiom,
% 5.06/5.39 ! [N2: nat] :
% 5.06/5.39 ( ( ( semiri4939895301339042750nteger @ N2 )
% 5.06/5.39 = one_one_Code_integer )
% 5.06/5.39 = ( N2 = one_one_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_1_iff
% 5.06/5.39 thf(fact_7156_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.39 ! [X: nat,B: nat,W: nat] :
% 5.06/5.39 ( ( ( semiri8010041392384452111omplex @ X )
% 5.06/5.39 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.06/5.39 = ( X
% 5.06/5.39 = ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_power_eq_of_nat_cancel_iff
% 5.06/5.39 thf(fact_7157_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.39 ! [X: nat,B: nat,W: nat] :
% 5.06/5.39 ( ( ( semiri1314217659103216013at_int @ X )
% 5.06/5.39 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.06/5.39 = ( X
% 5.06/5.39 = ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_power_eq_of_nat_cancel_iff
% 5.06/5.39 thf(fact_7158_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.39 ! [X: nat,B: nat,W: nat] :
% 5.06/5.39 ( ( ( semiri5074537144036343181t_real @ X )
% 5.06/5.39 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.06/5.39 = ( X
% 5.06/5.39 = ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_power_eq_of_nat_cancel_iff
% 5.06/5.39 thf(fact_7159_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.39 ! [X: nat,B: nat,W: nat] :
% 5.06/5.39 ( ( ( semiri1316708129612266289at_nat @ X )
% 5.06/5.39 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.06/5.39 = ( X
% 5.06/5.39 = ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_power_eq_of_nat_cancel_iff
% 5.06/5.39 thf(fact_7160_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.39 ! [X: nat,B: nat,W: nat] :
% 5.06/5.39 ( ( ( semiri4939895301339042750nteger @ X )
% 5.06/5.39 = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 5.06/5.39 = ( X
% 5.06/5.39 = ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_power_eq_of_nat_cancel_iff
% 5.06/5.39 thf(fact_7161_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.06/5.39 ! [B: nat,W: nat,X: nat] :
% 5.06/5.39 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.06/5.39 = ( semiri8010041392384452111omplex @ X ) )
% 5.06/5.39 = ( ( power_power_nat @ B @ W )
% 5.06/5.39 = X ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_of_nat_power_cancel_iff
% 5.06/5.39 thf(fact_7162_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.06/5.39 ! [B: nat,W: nat,X: nat] :
% 5.06/5.39 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.06/5.39 = ( semiri1314217659103216013at_int @ X ) )
% 5.06/5.39 = ( ( power_power_nat @ B @ W )
% 5.06/5.39 = X ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_of_nat_power_cancel_iff
% 5.06/5.39 thf(fact_7163_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.06/5.39 ! [B: nat,W: nat,X: nat] :
% 5.06/5.39 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.06/5.39 = ( semiri5074537144036343181t_real @ X ) )
% 5.06/5.39 = ( ( power_power_nat @ B @ W )
% 5.06/5.39 = X ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_of_nat_power_cancel_iff
% 5.06/5.39 thf(fact_7164_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.06/5.39 ! [B: nat,W: nat,X: nat] :
% 5.06/5.39 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.06/5.39 = ( semiri1316708129612266289at_nat @ X ) )
% 5.06/5.39 = ( ( power_power_nat @ B @ W )
% 5.06/5.39 = X ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_of_nat_power_cancel_iff
% 5.06/5.39 thf(fact_7165_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.06/5.39 ! [B: nat,W: nat,X: nat] :
% 5.06/5.39 ( ( ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W )
% 5.06/5.39 = ( semiri4939895301339042750nteger @ X ) )
% 5.06/5.39 = ( ( power_power_nat @ B @ W )
% 5.06/5.39 = X ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_eq_of_nat_power_cancel_iff
% 5.06/5.39 thf(fact_7166_of__nat__power,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N2 ) )
% 5.06/5.39 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_power
% 5.06/5.39 thf(fact_7167_of__nat__power,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N2 ) )
% 5.06/5.39 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_power
% 5.06/5.39 thf(fact_7168_of__nat__power,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N2 ) )
% 5.06/5.39 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_power
% 5.06/5.39 thf(fact_7169_of__nat__power,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N2 ) )
% 5.06/5.39 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_power
% 5.06/5.39 thf(fact_7170_of__nat__power,axiom,
% 5.06/5.39 ! [M: nat,N2: nat] :
% 5.06/5.39 ( ( semiri4939895301339042750nteger @ ( power_power_nat @ M @ N2 ) )
% 5.06/5.39 = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ M ) @ N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_power
% 5.06/5.39 thf(fact_7171_negative__zless,axiom,
% 5.06/5.39 ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.06/5.39
% 5.06/5.39 % negative_zless
% 5.06/5.39 thf(fact_7172_pred__numeral__simps_I1_J,axiom,
% 5.06/5.39 ( ( pred_numeral @ one )
% 5.06/5.39 = zero_zero_nat ) ).
% 5.06/5.39
% 5.06/5.39 % pred_numeral_simps(1)
% 5.06/5.39 thf(fact_7173_Suc__eq__numeral,axiom,
% 5.06/5.39 ! [N2: nat,K: num] :
% 5.06/5.39 ( ( ( suc @ N2 )
% 5.06/5.39 = ( numeral_numeral_nat @ K ) )
% 5.06/5.39 = ( N2
% 5.06/5.39 = ( pred_numeral @ K ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % Suc_eq_numeral
% 5.06/5.39 thf(fact_7174_eq__numeral__Suc,axiom,
% 5.06/5.39 ! [K: num,N2: nat] :
% 5.06/5.39 ( ( ( numeral_numeral_nat @ K )
% 5.06/5.39 = ( suc @ N2 ) )
% 5.06/5.39 = ( ( pred_numeral @ K )
% 5.06/5.39 = N2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % eq_numeral_Suc
% 5.06/5.39 thf(fact_7175_zero__le__arctan__iff,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 5.06/5.39 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.06/5.39
% 5.06/5.39 % zero_le_arctan_iff
% 5.06/5.39 thf(fact_7176_arctan__le__zero__iff,axiom,
% 5.06/5.39 ! [X: real] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 5.06/5.39 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % arctan_le_zero_iff
% 5.06/5.39 thf(fact_7177_dbl__inc__simps_I2_J,axiom,
% 5.06/5.39 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.06/5.39 = one_one_complex ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(2)
% 5.06/5.39 thf(fact_7178_dbl__inc__simps_I2_J,axiom,
% 5.06/5.39 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.06/5.39 = one_one_real ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(2)
% 5.06/5.39 thf(fact_7179_dbl__inc__simps_I2_J,axiom,
% 5.06/5.39 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.06/5.39 = one_one_rat ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(2)
% 5.06/5.39 thf(fact_7180_dbl__inc__simps_I2_J,axiom,
% 5.06/5.39 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.06/5.39 = one_one_int ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(2)
% 5.06/5.39 thf(fact_7181_of__nat__of__bool,axiom,
% 5.06/5.39 ! [P: $o] :
% 5.06/5.39 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.06/5.39 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_of_bool
% 5.06/5.39 thf(fact_7182_of__nat__of__bool,axiom,
% 5.06/5.39 ! [P: $o] :
% 5.06/5.39 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.06/5.39 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_of_bool
% 5.06/5.39 thf(fact_7183_of__nat__of__bool,axiom,
% 5.06/5.39 ! [P: $o] :
% 5.06/5.39 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.06/5.39 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_of_bool
% 5.06/5.39 thf(fact_7184_of__nat__of__bool,axiom,
% 5.06/5.39 ! [P: $o] :
% 5.06/5.39 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.06/5.39 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_of_bool
% 5.06/5.39 thf(fact_7185_dbl__inc__simps_I4_J,axiom,
% 5.06/5.39 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.39 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(4)
% 5.06/5.39 thf(fact_7186_dbl__inc__simps_I4_J,axiom,
% 5.06/5.39 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.39 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(4)
% 5.06/5.39 thf(fact_7187_dbl__inc__simps_I4_J,axiom,
% 5.06/5.39 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.06/5.39 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(4)
% 5.06/5.39 thf(fact_7188_dbl__inc__simps_I4_J,axiom,
% 5.06/5.39 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.06/5.39 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(4)
% 5.06/5.39 thf(fact_7189_dbl__inc__simps_I4_J,axiom,
% 5.06/5.39 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.06/5.39 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(4)
% 5.06/5.39 thf(fact_7190_dbl__inc__simps_I5_J,axiom,
% 5.06/5.39 ! [K: num] :
% 5.06/5.39 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.06/5.39 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(5)
% 5.06/5.39 thf(fact_7191_dbl__inc__simps_I5_J,axiom,
% 5.06/5.39 ! [K: num] :
% 5.06/5.39 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.06/5.39 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(5)
% 5.06/5.39 thf(fact_7192_dbl__inc__simps_I5_J,axiom,
% 5.06/5.39 ! [K: num] :
% 5.06/5.39 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.06/5.39 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(5)
% 5.06/5.39 thf(fact_7193_dbl__inc__simps_I5_J,axiom,
% 5.06/5.39 ! [K: num] :
% 5.06/5.39 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.06/5.39 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.06/5.39
% 5.06/5.39 % dbl_inc_simps(5)
% 5.06/5.39 thf(fact_7194_of__nat__sum,axiom,
% 5.06/5.39 ! [F: int > nat,A2: set_int] :
% 5.06/5.39 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.06/5.39 = ( groups4538972089207619220nt_int
% 5.06/5.39 @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_sum
% 5.06/5.39 thf(fact_7195_of__nat__sum,axiom,
% 5.06/5.39 ! [F: complex > nat,A2: set_complex] :
% 5.06/5.39 ( ( semiri8010041392384452111omplex @ ( groups5693394587270226106ex_nat @ F @ A2 ) )
% 5.06/5.39 = ( groups7754918857620584856omplex
% 5.06/5.39 @ ^ [X2: complex] : ( semiri8010041392384452111omplex @ ( F @ X2 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_sum
% 5.06/5.39 thf(fact_7196_of__nat__sum,axiom,
% 5.06/5.39 ! [F: nat > nat,A2: set_nat] :
% 5.06/5.39 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.06/5.39 = ( groups3539618377306564664at_int
% 5.06/5.39 @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_sum
% 5.06/5.39 thf(fact_7197_of__nat__sum,axiom,
% 5.06/5.39 ! [F: nat > nat,A2: set_nat] :
% 5.06/5.39 ( ( semiri4939895301339042750nteger @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.06/5.39 = ( groups7501900531339628137nteger
% 5.06/5.39 @ ^ [X2: nat] : ( semiri4939895301339042750nteger @ ( F @ X2 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_sum
% 5.06/5.39 thf(fact_7198_of__nat__sum,axiom,
% 5.06/5.39 ! [F: nat > nat,A2: set_nat] :
% 5.06/5.39 ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.06/5.39 = ( groups3542108847815614940at_nat
% 5.06/5.39 @ ^ [X2: nat] : ( semiri1316708129612266289at_nat @ ( F @ X2 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_sum
% 5.06/5.39 thf(fact_7199_of__nat__sum,axiom,
% 5.06/5.39 ! [F: nat > nat,A2: set_nat] :
% 5.06/5.39 ( ( semiri5074537144036343181t_real @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.06/5.39 = ( groups6591440286371151544t_real
% 5.06/5.39 @ ^ [X2: nat] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 5.06/5.39 @ A2 ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_sum
% 5.06/5.39 thf(fact_7200_of__nat__le__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.06/5.39 = ( M = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_le_0_iff
% 5.06/5.39 thf(fact_7201_of__nat__le__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger )
% 5.06/5.39 = ( M = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_le_0_iff
% 5.06/5.39 thf(fact_7202_of__nat__le__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.06/5.39 = ( M = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_le_0_iff
% 5.06/5.39 thf(fact_7203_of__nat__le__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.06/5.39 = ( M = zero_zero_nat ) ) ).
% 5.06/5.39
% 5.06/5.39 % of_nat_le_0_iff
% 5.06/5.39 thf(fact_7204_of__nat__le__0__iff,axiom,
% 5.06/5.39 ! [M: nat] :
% 5.06/5.39 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.06/5.40 = ( M = zero_zero_nat ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_0_iff
% 5.06/5.40 thf(fact_7205_of__nat__Suc,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.06/5.40 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_Suc
% 5.06/5.40 thf(fact_7206_of__nat__Suc,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.06/5.40 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_Suc
% 5.06/5.40 thf(fact_7207_of__nat__Suc,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.06/5.40 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_Suc
% 5.06/5.40 thf(fact_7208_of__nat__Suc,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.06/5.40 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_Suc
% 5.06/5.40 thf(fact_7209_of__nat__Suc,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.06/5.40 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_Suc
% 5.06/5.40 thf(fact_7210_of__nat__Suc,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 5.06/5.40 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_Suc
% 5.06/5.40 thf(fact_7211_numeral__less__real__of__nat__iff,axiom,
% 5.06/5.40 ! [W: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_less_real_of_nat_iff
% 5.06/5.40 thf(fact_7212_real__of__nat__less__numeral__iff,axiom,
% 5.06/5.40 ! [N2: nat,W: num] :
% 5.06/5.40 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( numeral_numeral_real @ W ) )
% 5.06/5.40 = ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_less_numeral_iff
% 5.06/5.40 thf(fact_7213_numeral__le__real__of__nat__iff,axiom,
% 5.06/5.40 ! [N2: num,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ M ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_le_real_of_nat_iff
% 5.06/5.40 thf(fact_7214_less__Suc__numeral,axiom,
% 5.06/5.40 ! [N2: nat,K: num] :
% 5.06/5.40 ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.06/5.40 = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % less_Suc_numeral
% 5.06/5.40 thf(fact_7215_less__numeral__Suc,axiom,
% 5.06/5.40 ! [K: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % less_numeral_Suc
% 5.06/5.40 thf(fact_7216_pred__numeral__simps_I3_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.06/5.40 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_numeral_simps(3)
% 5.06/5.40 thf(fact_7217_le__Suc__numeral,axiom,
% 5.06/5.40 ! [N2: nat,K: num] :
% 5.06/5.40 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.06/5.40 = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % le_Suc_numeral
% 5.06/5.40 thf(fact_7218_le__numeral__Suc,axiom,
% 5.06/5.40 ! [K: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % le_numeral_Suc
% 5.06/5.40 thf(fact_7219_diff__numeral__Suc,axiom,
% 5.06/5.40 ! [K: num,N2: nat] :
% 5.06/5.40 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.06/5.40 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % diff_numeral_Suc
% 5.06/5.40 thf(fact_7220_diff__Suc__numeral,axiom,
% 5.06/5.40 ! [N2: nat,K: num] :
% 5.06/5.40 ( ( minus_minus_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.06/5.40 = ( minus_minus_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % diff_Suc_numeral
% 5.06/5.40 thf(fact_7221_max__numeral__Suc,axiom,
% 5.06/5.40 ! [K: num,N2: nat] :
% 5.06/5.40 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.06/5.40 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % max_numeral_Suc
% 5.06/5.40 thf(fact_7222_max__Suc__numeral,axiom,
% 5.06/5.40 ! [N2: nat,K: num] :
% 5.06/5.40 ( ( ord_max_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.06/5.40 = ( suc @ ( ord_max_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % max_Suc_numeral
% 5.06/5.40 thf(fact_7223_dbl__dec__simps_I2_J,axiom,
% 5.06/5.40 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.06/5.40 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_simps(2)
% 5.06/5.40 thf(fact_7224_dbl__dec__simps_I2_J,axiom,
% 5.06/5.40 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.06/5.40 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_simps(2)
% 5.06/5.40 thf(fact_7225_dbl__dec__simps_I2_J,axiom,
% 5.06/5.40 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.06/5.40 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_simps(2)
% 5.06/5.40 thf(fact_7226_dbl__dec__simps_I2_J,axiom,
% 5.06/5.40 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.06/5.40 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_simps(2)
% 5.06/5.40 thf(fact_7227_dbl__dec__simps_I2_J,axiom,
% 5.06/5.40 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.06/5.40 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_simps(2)
% 5.06/5.40 thf(fact_7228_of__nat__0__less__iff,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_0_less_iff
% 5.06/5.40 thf(fact_7229_of__nat__0__less__iff,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_0_less_iff
% 5.06/5.40 thf(fact_7230_of__nat__0__less__iff,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_0_less_iff
% 5.06/5.40 thf(fact_7231_of__nat__0__less__iff,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_0_less_iff
% 5.06/5.40 thf(fact_7232_of__nat__0__less__iff,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_0_less_iff
% 5.06/5.40 thf(fact_7233_dbl__dec__simps_I1_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.06/5.40 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_simps(1)
% 5.06/5.40 thf(fact_7234_dbl__dec__simps_I1_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.06/5.40 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_simps(1)
% 5.06/5.40 thf(fact_7235_dbl__dec__simps_I1_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.06/5.40 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_simps(1)
% 5.06/5.40 thf(fact_7236_dbl__dec__simps_I1_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.06/5.40 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_simps(1)
% 5.06/5.40 thf(fact_7237_dbl__dec__simps_I1_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.06/5.40 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_simps(1)
% 5.06/5.40 thf(fact_7238_dbl__inc__simps_I1_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.06/5.40 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_inc_simps(1)
% 5.06/5.40 thf(fact_7239_dbl__inc__simps_I1_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.06/5.40 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_inc_simps(1)
% 5.06/5.40 thf(fact_7240_dbl__inc__simps_I1_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.06/5.40 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_inc_simps(1)
% 5.06/5.40 thf(fact_7241_dbl__inc__simps_I1_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.06/5.40 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_inc_simps(1)
% 5.06/5.40 thf(fact_7242_dbl__inc__simps_I1_J,axiom,
% 5.06/5.40 ! [K: num] :
% 5.06/5.40 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.06/5.40 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_inc_simps(1)
% 5.06/5.40 thf(fact_7243_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,B: nat,W: nat] :
% 5.06/5.40 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.06/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_power_less_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7244_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,B: nat,W: nat] :
% 5.06/5.40 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.06/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_power_less_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7245_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,B: nat,W: nat] :
% 5.06/5.40 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.06/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_power_less_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7246_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,B: nat,W: nat] :
% 5.06/5.40 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.06/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_power_less_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7247_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,B: nat,W: nat] :
% 5.06/5.40 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 5.06/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_power_less_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7248_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.06/5.40 ! [B: nat,W: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.06/5.40 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_of_nat_power_cancel_iff
% 5.06/5.40 thf(fact_7249_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.06/5.40 ! [B: nat,W: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.06/5.40 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_of_nat_power_cancel_iff
% 5.06/5.40 thf(fact_7250_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.06/5.40 ! [B: nat,W: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.06/5.40 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_of_nat_power_cancel_iff
% 5.06/5.40 thf(fact_7251_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.06/5.40 ! [B: nat,W: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.06/5.40 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_of_nat_power_cancel_iff
% 5.06/5.40 thf(fact_7252_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.06/5.40 ! [B: nat,W: nat,X: nat] :
% 5.06/5.40 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.06/5.40 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_of_nat_power_cancel_iff
% 5.06/5.40 thf(fact_7253_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [Y: nat,X: num,N2: nat] :
% 5.06/5.40 ( ( ( semiri8010041392384452111omplex @ Y )
% 5.06/5.40 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 ) )
% 5.06/5.40 = ( Y
% 5.06/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7254_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [Y: nat,X: num,N2: nat] :
% 5.06/5.40 ( ( ( semiri681578069525770553at_rat @ Y )
% 5.06/5.40 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 5.06/5.40 = ( Y
% 5.06/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7255_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [Y: nat,X: num,N2: nat] :
% 5.06/5.40 ( ( ( semiri1314217659103216013at_int @ Y )
% 5.06/5.40 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.06/5.40 = ( Y
% 5.06/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7256_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [Y: nat,X: num,N2: nat] :
% 5.06/5.40 ( ( ( semiri5074537144036343181t_real @ Y )
% 5.06/5.40 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 ) )
% 5.06/5.40 = ( Y
% 5.06/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7257_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [Y: nat,X: num,N2: nat] :
% 5.06/5.40 ( ( ( semiri1316708129612266289at_nat @ Y )
% 5.06/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.06/5.40 = ( Y
% 5.06/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7258_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [Y: nat,X: num,N2: nat] :
% 5.06/5.40 ( ( ( semiri4939895301339042750nteger @ Y )
% 5.06/5.40 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 ) )
% 5.06/5.40 = ( Y
% 5.06/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7259_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: num,N2: nat,Y: nat] :
% 5.06/5.40 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N2 )
% 5.06/5.40 = ( semiri8010041392384452111omplex @ Y ) )
% 5.06/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.06/5.40 = Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7260_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: num,N2: nat,Y: nat] :
% 5.06/5.40 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 )
% 5.06/5.40 = ( semiri681578069525770553at_rat @ Y ) )
% 5.06/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.06/5.40 = Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7261_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: num,N2: nat,Y: nat] :
% 5.06/5.40 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.06/5.40 = ( semiri1314217659103216013at_int @ Y ) )
% 5.06/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.06/5.40 = Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7262_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: num,N2: nat,Y: nat] :
% 5.06/5.40 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N2 )
% 5.06/5.40 = ( semiri5074537144036343181t_real @ Y ) )
% 5.06/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.06/5.40 = Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7263_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: num,N2: nat,Y: nat] :
% 5.06/5.40 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.06/5.40 = ( semiri1316708129612266289at_nat @ Y ) )
% 5.06/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.06/5.40 = Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7264_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: num,N2: nat,Y: nat] :
% 5.06/5.40 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 )
% 5.06/5.40 = ( semiri4939895301339042750nteger @ Y ) )
% 5.06/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.06/5.40 = Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7265_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,B: nat,W: nat] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_power_le_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7266_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,B: nat,W: nat] :
% 5.06/5.40 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_power_le_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7267_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,B: nat,W: nat] :
% 5.06/5.40 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_power_le_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7268_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,B: nat,W: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_power_le_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7269_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,B: nat,W: nat] :
% 5.06/5.40 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_power_le_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7270_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.06/5.40 ! [B: nat,W: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_of_nat_power_cancel_iff
% 5.06/5.40 thf(fact_7271_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.06/5.40 ! [B: nat,W: nat,X: nat] :
% 5.06/5.40 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_of_nat_power_cancel_iff
% 5.06/5.40 thf(fact_7272_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.06/5.40 ! [B: nat,W: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_of_nat_power_cancel_iff
% 5.06/5.40 thf(fact_7273_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.06/5.40 ! [B: nat,W: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_of_nat_power_cancel_iff
% 5.06/5.40 thf(fact_7274_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.06/5.40 ! [B: nat,W: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_of_nat_power_cancel_iff
% 5.06/5.40 thf(fact_7275_of__nat__zero__less__power__iff,axiom,
% 5.06/5.40 ! [X: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N2 ) )
% 5.06/5.40 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.06/5.40 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_zero_less_power_iff
% 5.06/5.40 thf(fact_7276_of__nat__zero__less__power__iff,axiom,
% 5.06/5.40 ! [X: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N2 ) )
% 5.06/5.40 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.06/5.40 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_zero_less_power_iff
% 5.06/5.40 thf(fact_7277_of__nat__zero__less__power__iff,axiom,
% 5.06/5.40 ! [X: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N2 ) )
% 5.06/5.40 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.06/5.40 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_zero_less_power_iff
% 5.06/5.40 thf(fact_7278_of__nat__zero__less__power__iff,axiom,
% 5.06/5.40 ! [X: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N2 ) )
% 5.06/5.40 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.06/5.40 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_zero_less_power_iff
% 5.06/5.40 thf(fact_7279_of__nat__zero__less__power__iff,axiom,
% 5.06/5.40 ! [X: nat,N2: nat] :
% 5.06/5.40 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X ) @ N2 ) )
% 5.06/5.40 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.06/5.40 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_zero_less_power_iff
% 5.06/5.40 thf(fact_7280_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,I2: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7281_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,I2: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7282_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,I2: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7283_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,I2: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7284_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,I2: num,N2: nat] :
% 5.06/5.40 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7285_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [I2: num,N2: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.06/5.40 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_less_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7286_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [I2: num,N2: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.06/5.40 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_less_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7287_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [I2: num,N2: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.06/5.40 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_less_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7288_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [I2: num,N2: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.06/5.40 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_less_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7289_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [I2: num,N2: nat,X: nat] :
% 5.06/5.40 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.06/5.40 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_less_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7290_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,I2: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7291_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,I2: num,N2: nat] :
% 5.06/5.40 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7292_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,I2: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7293_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,I2: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7294_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.06/5.40 ! [X: nat,I2: num,N2: nat] :
% 5.06/5.40 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_le_numeral_power_cancel_iff
% 5.06/5.40 thf(fact_7295_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [I2: num,N2: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_le_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7296_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [I2: num,N2: nat,X: nat] :
% 5.06/5.40 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_le_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7297_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [I2: num,N2: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_le_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7298_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [I2: num,N2: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_le_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7299_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.06/5.40 ! [I2: num,N2: nat,X: nat] :
% 5.06/5.40 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.06/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_power_le_of_nat_cancel_iff
% 5.06/5.40 thf(fact_7300_even__of__nat,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.40 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % even_of_nat
% 5.06/5.40 thf(fact_7301_even__of__nat,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.06/5.40 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % even_of_nat
% 5.06/5.40 thf(fact_7302_even__of__nat,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.06/5.40 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % even_of_nat
% 5.06/5.40 thf(fact_7303_signed__take__bit__numeral__bit0,axiom,
% 5.06/5.40 ! [L2: num,K: num] :
% 5.06/5.40 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.06/5.40 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % signed_take_bit_numeral_bit0
% 5.06/5.40 thf(fact_7304_signed__take__bit__numeral__minus__bit0,axiom,
% 5.06/5.40 ! [L2: num,K: num] :
% 5.06/5.40 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.06/5.40 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % signed_take_bit_numeral_minus_bit0
% 5.06/5.40 thf(fact_7305_Collect__case__prod__mono,axiom,
% 5.06/5.40 ! [A2: int > int > $o,B3: int > int > $o] :
% 5.06/5.40 ( ( ord_le6741204236512500942_int_o @ A2 @ B3 )
% 5.06/5.40 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A2 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B3 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % Collect_case_prod_mono
% 5.06/5.40 thf(fact_7306_prod_Odisc__eq__case,axiom,
% 5.06/5.40 ! [Prod: product_prod_int_int] :
% 5.06/5.40 ( produc4947309494688390418_int_o
% 5.06/5.40 @ ^ [Uu3: int,Uv3: int] : $true
% 5.06/5.40 @ Prod ) ).
% 5.06/5.40
% 5.06/5.40 % prod.disc_eq_case
% 5.06/5.40 thf(fact_7307_mult__of__nat__commute,axiom,
% 5.06/5.40 ! [X: nat,Y: rat] :
% 5.06/5.40 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 5.06/5.40 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % mult_of_nat_commute
% 5.06/5.40 thf(fact_7308_mult__of__nat__commute,axiom,
% 5.06/5.40 ! [X: nat,Y: int] :
% 5.06/5.40 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 5.06/5.40 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % mult_of_nat_commute
% 5.06/5.40 thf(fact_7309_mult__of__nat__commute,axiom,
% 5.06/5.40 ! [X: nat,Y: real] :
% 5.06/5.40 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 5.06/5.40 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % mult_of_nat_commute
% 5.06/5.40 thf(fact_7310_mult__of__nat__commute,axiom,
% 5.06/5.40 ! [X: nat,Y: nat] :
% 5.06/5.40 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 5.06/5.40 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % mult_of_nat_commute
% 5.06/5.40 thf(fact_7311_mult__of__nat__commute,axiom,
% 5.06/5.40 ! [X: nat,Y: code_integer] :
% 5.06/5.40 ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X ) @ Y )
% 5.06/5.40 = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % mult_of_nat_commute
% 5.06/5.40 thf(fact_7312_arctan__monotone_H,axiom,
% 5.06/5.40 ! [X: real,Y: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.40 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % arctan_monotone'
% 5.06/5.40 thf(fact_7313_arctan__le__iff,axiom,
% 5.06/5.40 ! [X: real,Y: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.06/5.40 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % arctan_le_iff
% 5.06/5.40 thf(fact_7314_int__diff__cases,axiom,
% 5.06/5.40 ! [Z: int] :
% 5.06/5.40 ~ ! [M2: nat,N3: nat] :
% 5.06/5.40 ( Z
% 5.06/5.40 != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_diff_cases
% 5.06/5.40 thf(fact_7315_of__nat__0__le__iff,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_0_le_iff
% 5.06/5.40 thf(fact_7316_of__nat__0__le__iff,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_0_le_iff
% 5.06/5.40 thf(fact_7317_of__nat__0__le__iff,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_0_le_iff
% 5.06/5.40 thf(fact_7318_of__nat__0__le__iff,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_0_le_iff
% 5.06/5.40 thf(fact_7319_of__nat__0__le__iff,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_0_le_iff
% 5.06/5.40 thf(fact_7320_of__nat__less__0__iff,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_0_iff
% 5.06/5.40 thf(fact_7321_of__nat__less__0__iff,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_0_iff
% 5.06/5.40 thf(fact_7322_of__nat__less__0__iff,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_0_iff
% 5.06/5.40 thf(fact_7323_of__nat__less__0__iff,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_0_iff
% 5.06/5.40 thf(fact_7324_of__nat__less__0__iff,axiom,
% 5.06/5.40 ! [M: nat] :
% 5.06/5.40 ~ ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_0_iff
% 5.06/5.40 thf(fact_7325_of__nat__neq__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( semiri8010041392384452111omplex @ ( suc @ N2 ) )
% 5.06/5.40 != zero_zero_complex ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_neq_0
% 5.06/5.40 thf(fact_7326_of__nat__neq__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( semiri681578069525770553at_rat @ ( suc @ N2 ) )
% 5.06/5.40 != zero_zero_rat ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_neq_0
% 5.06/5.40 thf(fact_7327_of__nat__neq__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.06/5.40 != zero_zero_int ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_neq_0
% 5.06/5.40 thf(fact_7328_of__nat__neq__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( semiri5074537144036343181t_real @ ( suc @ N2 ) )
% 5.06/5.40 != zero_zero_real ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_neq_0
% 5.06/5.40 thf(fact_7329_of__nat__neq__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 5.06/5.40 != zero_zero_nat ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_neq_0
% 5.06/5.40 thf(fact_7330_of__nat__neq__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( semiri4939895301339042750nteger @ ( suc @ N2 ) )
% 5.06/5.40 != zero_z3403309356797280102nteger ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_neq_0
% 5.06/5.40 thf(fact_7331_div__mult2__eq_H,axiom,
% 5.06/5.40 ! [A: int,M: nat,N2: nat] :
% 5.06/5.40 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.06/5.40 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % div_mult2_eq'
% 5.06/5.40 thf(fact_7332_div__mult2__eq_H,axiom,
% 5.06/5.40 ! [A: nat,M: nat,N2: nat] :
% 5.06/5.40 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.06/5.40 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % div_mult2_eq'
% 5.06/5.40 thf(fact_7333_div__mult2__eq_H,axiom,
% 5.06/5.40 ! [A: code_integer,M: nat,N2: nat] :
% 5.06/5.40 ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 5.06/5.40 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % div_mult2_eq'
% 5.06/5.40 thf(fact_7334_less__imp__of__nat__less,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ M @ N2 )
% 5.06/5.40 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % less_imp_of_nat_less
% 5.06/5.40 thf(fact_7335_less__imp__of__nat__less,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ M @ N2 )
% 5.06/5.40 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % less_imp_of_nat_less
% 5.06/5.40 thf(fact_7336_less__imp__of__nat__less,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ M @ N2 )
% 5.06/5.40 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % less_imp_of_nat_less
% 5.06/5.40 thf(fact_7337_less__imp__of__nat__less,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ M @ N2 )
% 5.06/5.40 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % less_imp_of_nat_less
% 5.06/5.40 thf(fact_7338_less__imp__of__nat__less,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ M @ N2 )
% 5.06/5.40 => ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % less_imp_of_nat_less
% 5.06/5.40 thf(fact_7339_of__nat__less__imp__less,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.06/5.40 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_imp_less
% 5.06/5.40 thf(fact_7340_of__nat__less__imp__less,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.40 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_imp_less
% 5.06/5.40 thf(fact_7341_of__nat__less__imp__less,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.40 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_imp_less
% 5.06/5.40 thf(fact_7342_of__nat__less__imp__less,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.06/5.40 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_imp_less
% 5.06/5.40 thf(fact_7343_of__nat__less__imp__less,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.06/5.40 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_imp_less
% 5.06/5.40 thf(fact_7344_of__nat__mono,axiom,
% 5.06/5.40 ! [I2: nat,J: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ I2 @ J )
% 5.06/5.40 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_mono
% 5.06/5.40 thf(fact_7345_of__nat__mono,axiom,
% 5.06/5.40 ! [I2: nat,J: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ I2 @ J )
% 5.06/5.40 => ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ I2 ) @ ( semiri4939895301339042750nteger @ J ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_mono
% 5.06/5.40 thf(fact_7346_of__nat__mono,axiom,
% 5.06/5.40 ! [I2: nat,J: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ I2 @ J )
% 5.06/5.40 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_mono
% 5.06/5.40 thf(fact_7347_of__nat__mono,axiom,
% 5.06/5.40 ! [I2: nat,J: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ I2 @ J )
% 5.06/5.40 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_mono
% 5.06/5.40 thf(fact_7348_of__nat__mono,axiom,
% 5.06/5.40 ! [I2: nat,J: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ I2 @ J )
% 5.06/5.40 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_mono
% 5.06/5.40 thf(fact_7349_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) )
% 5.06/5.40 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.06/5.40 thf(fact_7350_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N2 ) )
% 5.06/5.40 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.06/5.40 thf(fact_7351_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( semiri4939895301339042750nteger @ ( divide_divide_nat @ M @ N2 ) )
% 5.06/5.40 = ( divide6298287555418463151nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.06/5.40 thf(fact_7352_of__nat__dvd__iff,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.40 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_dvd_iff
% 5.06/5.40 thf(fact_7353_of__nat__dvd__iff,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.06/5.40 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_dvd_iff
% 5.06/5.40 thf(fact_7354_of__nat__dvd__iff,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.06/5.40 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_dvd_iff
% 5.06/5.40 thf(fact_7355_int__ops_I3_J,axiom,
% 5.06/5.40 ! [N2: num] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 5.06/5.40 = ( numeral_numeral_int @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_ops(3)
% 5.06/5.40 thf(fact_7356_abs__zmult__eq__1,axiom,
% 5.06/5.40 ! [M: int,N2: int] :
% 5.06/5.40 ( ( ( abs_abs_int @ ( times_times_int @ M @ N2 ) )
% 5.06/5.40 = one_one_int )
% 5.06/5.40 => ( ( abs_abs_int @ M )
% 5.06/5.40 = one_one_int ) ) ).
% 5.06/5.40
% 5.06/5.40 % abs_zmult_eq_1
% 5.06/5.40 thf(fact_7357_int__cases,axiom,
% 5.06/5.40 ! [Z: int] :
% 5.06/5.40 ( ! [N3: nat] :
% 5.06/5.40 ( Z
% 5.06/5.40 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.06/5.40 => ~ ! [N3: nat] :
% 5.06/5.40 ( Z
% 5.06/5.40 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_cases
% 5.06/5.40 thf(fact_7358_int__of__nat__induct,axiom,
% 5.06/5.40 ! [P: int > $o,Z: int] :
% 5.06/5.40 ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 5.06/5.40 => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 5.06/5.40 => ( P @ Z ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_of_nat_induct
% 5.06/5.40 thf(fact_7359_nat__int__comparison_I2_J,axiom,
% 5.06/5.40 ( ord_less_nat
% 5.06/5.40 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat_int_comparison(2)
% 5.06/5.40 thf(fact_7360_zle__int,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.40 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % zle_int
% 5.06/5.40 thf(fact_7361_nat__int__comparison_I3_J,axiom,
% 5.06/5.40 ( ord_less_eq_nat
% 5.06/5.40 = ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat_int_comparison(3)
% 5.06/5.40 thf(fact_7362_nonneg__int__cases,axiom,
% 5.06/5.40 ! [K: int] :
% 5.06/5.40 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.40 => ~ ! [N3: nat] :
% 5.06/5.40 ( K
% 5.06/5.40 != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nonneg_int_cases
% 5.06/5.40 thf(fact_7363_zero__le__imp__eq__int,axiom,
% 5.06/5.40 ! [K: int] :
% 5.06/5.40 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.40 => ? [N3: nat] :
% 5.06/5.40 ( K
% 5.06/5.40 = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % zero_le_imp_eq_int
% 5.06/5.40 thf(fact_7364_of__nat__mod,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.06/5.40 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_mod
% 5.06/5.40 thf(fact_7365_of__nat__mod,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.06/5.40 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_mod
% 5.06/5.40 thf(fact_7366_of__nat__mod,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.06/5.40 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_mod
% 5.06/5.40 thf(fact_7367_int__ops_I5_J,axiom,
% 5.06/5.40 ! [A: nat,B: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.06/5.40 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_ops(5)
% 5.06/5.40 thf(fact_7368_int__plus,axiom,
% 5.06/5.40 ! [N2: nat,M: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M ) )
% 5.06/5.40 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_plus
% 5.06/5.40 thf(fact_7369_zadd__int__left,axiom,
% 5.06/5.40 ! [M: nat,N2: nat,Z: int] :
% 5.06/5.40 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z ) )
% 5.06/5.40 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) ) @ Z ) ) ).
% 5.06/5.40
% 5.06/5.40 % zadd_int_left
% 5.06/5.40 thf(fact_7370_int__ops_I7_J,axiom,
% 5.06/5.40 ! [A: nat,B: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.06/5.40 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_ops(7)
% 5.06/5.40 thf(fact_7371_int__ops_I2_J,axiom,
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.06/5.40 = one_one_int ) ).
% 5.06/5.40
% 5.06/5.40 % int_ops(2)
% 5.06/5.40 thf(fact_7372_zle__iff__zadd,axiom,
% 5.06/5.40 ( ord_less_eq_int
% 5.06/5.40 = ( ^ [W3: int,Z2: int] :
% 5.06/5.40 ? [N: nat] :
% 5.06/5.40 ( Z2
% 5.06/5.40 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % zle_iff_zadd
% 5.06/5.40 thf(fact_7373_zdiv__int,axiom,
% 5.06/5.40 ! [A: nat,B: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.06/5.40 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % zdiv_int
% 5.06/5.40 thf(fact_7374_int__sum,axiom,
% 5.06/5.40 ! [F: int > nat,A2: set_int] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A2 ) )
% 5.06/5.40 = ( groups4538972089207619220nt_int
% 5.06/5.40 @ ^ [X2: int] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.06/5.40 @ A2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_sum
% 5.06/5.40 thf(fact_7375_int__sum,axiom,
% 5.06/5.40 ! [F: nat > nat,A2: set_nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.06/5.40 = ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [X2: nat] : ( semiri1314217659103216013at_int @ ( F @ X2 ) )
% 5.06/5.40 @ A2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_sum
% 5.06/5.40 thf(fact_7376_numeral__eq__Suc,axiom,
% 5.06/5.40 ( numeral_numeral_nat
% 5.06/5.40 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % numeral_eq_Suc
% 5.06/5.40 thf(fact_7377_of__nat__max,axiom,
% 5.06/5.40 ! [X: nat,Y: nat] :
% 5.06/5.40 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y ) )
% 5.06/5.40 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_max
% 5.06/5.40 thf(fact_7378_of__nat__max,axiom,
% 5.06/5.40 ! [X: nat,Y: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 5.06/5.40 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_max
% 5.06/5.40 thf(fact_7379_of__nat__max,axiom,
% 5.06/5.40 ! [X: nat,Y: nat] :
% 5.06/5.40 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 5.06/5.40 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_max
% 5.06/5.40 thf(fact_7380_of__nat__max,axiom,
% 5.06/5.40 ! [X: nat,Y: nat] :
% 5.06/5.40 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 5.06/5.40 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_max
% 5.06/5.40 thf(fact_7381_of__nat__max,axiom,
% 5.06/5.40 ! [X: nat,Y: nat] :
% 5.06/5.40 ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X @ Y ) )
% 5.06/5.40 = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X ) @ ( semiri4939895301339042750nteger @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_max
% 5.06/5.40 thf(fact_7382_nat__less__as__int,axiom,
% 5.06/5.40 ( ord_less_nat
% 5.06/5.40 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat_less_as_int
% 5.06/5.40 thf(fact_7383_nat__leq__as__int,axiom,
% 5.06/5.40 ( ord_less_eq_nat
% 5.06/5.40 = ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat_leq_as_int
% 5.06/5.40 thf(fact_7384_of__nat__diff,axiom,
% 5.06/5.40 ! [N2: nat,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.40 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.40 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_diff
% 5.06/5.40 thf(fact_7385_of__nat__diff,axiom,
% 5.06/5.40 ! [N2: nat,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.40 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.40 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_diff
% 5.06/5.40 thf(fact_7386_of__nat__diff,axiom,
% 5.06/5.40 ! [N2: nat,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.40 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.40 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_diff
% 5.06/5.40 thf(fact_7387_of__nat__diff,axiom,
% 5.06/5.40 ! [N2: nat,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.40 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.40 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_diff
% 5.06/5.40 thf(fact_7388_of__nat__diff,axiom,
% 5.06/5.40 ! [N2: nat,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.40 => ( ( semiri4939895301339042750nteger @ ( minus_minus_nat @ M @ N2 ) )
% 5.06/5.40 = ( minus_8373710615458151222nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_diff
% 5.06/5.40 thf(fact_7389_reals__Archimedean3,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.40 => ! [Y3: real] :
% 5.06/5.40 ? [N3: nat] : ( ord_less_real @ Y3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % reals_Archimedean3
% 5.06/5.40 thf(fact_7390_int__cases4,axiom,
% 5.06/5.40 ! [M: int] :
% 5.06/5.40 ( ! [N3: nat] :
% 5.06/5.40 ( M
% 5.06/5.40 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.06/5.40 => ~ ! [N3: nat] :
% 5.06/5.40 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.06/5.40 => ( M
% 5.06/5.40 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_cases4
% 5.06/5.40 thf(fact_7391_real__of__nat__div4,axiom,
% 5.06/5.40 ! [N2: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_div4
% 5.06/5.40 thf(fact_7392_dvd__imp__le__int,axiom,
% 5.06/5.40 ! [I2: int,D: int] :
% 5.06/5.40 ( ( I2 != zero_zero_int )
% 5.06/5.40 => ( ( dvd_dvd_int @ D @ I2 )
% 5.06/5.40 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dvd_imp_le_int
% 5.06/5.40 thf(fact_7393_int__ops_I4_J,axiom,
% 5.06/5.40 ! [A: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.06/5.40 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_ops(4)
% 5.06/5.40 thf(fact_7394_int__Suc,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.06/5.40 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_Suc
% 5.06/5.40 thf(fact_7395_zless__iff__Suc__zadd,axiom,
% 5.06/5.40 ( ord_less_int
% 5.06/5.40 = ( ^ [W3: int,Z2: int] :
% 5.06/5.40 ? [N: nat] :
% 5.06/5.40 ( Z2
% 5.06/5.40 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % zless_iff_Suc_zadd
% 5.06/5.40 thf(fact_7396_int__zle__neg,axiom,
% 5.06/5.40 ! [N2: nat,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.06/5.40 = ( ( N2 = zero_zero_nat )
% 5.06/5.40 & ( M = zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_zle_neg
% 5.06/5.40 thf(fact_7397_abs__mod__less,axiom,
% 5.06/5.40 ! [L2: int,K: int] :
% 5.06/5.40 ( ( L2 != zero_zero_int )
% 5.06/5.40 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % abs_mod_less
% 5.06/5.40 thf(fact_7398_real__of__nat__div,axiom,
% 5.06/5.40 ! [D: nat,N2: nat] :
% 5.06/5.40 ( ( dvd_dvd_nat @ D @ N2 )
% 5.06/5.40 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ D ) )
% 5.06/5.40 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_div
% 5.06/5.40 thf(fact_7399_negative__zle__0,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ zero_zero_int ) ).
% 5.06/5.40
% 5.06/5.40 % negative_zle_0
% 5.06/5.40 thf(fact_7400_nonpos__int__cases,axiom,
% 5.06/5.40 ! [K: int] :
% 5.06/5.40 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.06/5.40 => ~ ! [N3: nat] :
% 5.06/5.40 ( K
% 5.06/5.40 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nonpos_int_cases
% 5.06/5.40 thf(fact_7401_pred__numeral__def,axiom,
% 5.06/5.40 ( pred_numeral
% 5.06/5.40 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_numeral_def
% 5.06/5.40 thf(fact_7402_mod__mult2__eq_H,axiom,
% 5.06/5.40 ! [A: int,M: nat,N2: nat] :
% 5.06/5.40 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % mod_mult2_eq'
% 5.06/5.40 thf(fact_7403_mod__mult2__eq_H,axiom,
% 5.06/5.40 ! [A: nat,M: nat,N2: nat] :
% 5.06/5.40 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % mod_mult2_eq'
% 5.06/5.40 thf(fact_7404_mod__mult2__eq_H,axiom,
% 5.06/5.40 ! [A: code_integer,M: nat,N2: nat] :
% 5.06/5.40 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 5.06/5.40 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % mod_mult2_eq'
% 5.06/5.40 thf(fact_7405_field__char__0__class_Oof__nat__div,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N2 ) )
% 5.06/5.40 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % field_char_0_class.of_nat_div
% 5.06/5.40 thf(fact_7406_field__char__0__class_Oof__nat__div,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N2 ) )
% 5.06/5.40 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % field_char_0_class.of_nat_div
% 5.06/5.40 thf(fact_7407_field__char__0__class_Oof__nat__div,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N2 ) )
% 5.06/5.40 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % field_char_0_class.of_nat_div
% 5.06/5.40 thf(fact_7408_zero__less__imp__eq__int,axiom,
% 5.06/5.40 ! [K: int] :
% 5.06/5.40 ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.40 => ? [N3: nat] :
% 5.06/5.40 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.06/5.40 & ( K
% 5.06/5.40 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % zero_less_imp_eq_int
% 5.06/5.40 thf(fact_7409_pos__int__cases,axiom,
% 5.06/5.40 ! [K: int] :
% 5.06/5.40 ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.40 => ~ ! [N3: nat] :
% 5.06/5.40 ( ( K
% 5.06/5.40 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.06/5.40 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % pos_int_cases
% 5.06/5.40 thf(fact_7410_int__cases3,axiom,
% 5.06/5.40 ! [K: int] :
% 5.06/5.40 ( ( K != zero_zero_int )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ( K
% 5.06/5.40 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.06/5.40 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.06/5.40 => ~ ! [N3: nat] :
% 5.06/5.40 ( ( K
% 5.06/5.40 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.06/5.40 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_cases3
% 5.06/5.40 thf(fact_7411_nat__less__real__le,axiom,
% 5.06/5.40 ( ord_less_nat
% 5.06/5.40 = ( ^ [N: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat_less_real_le
% 5.06/5.40 thf(fact_7412_nat__le__real__less,axiom,
% 5.06/5.40 ( ord_less_eq_nat
% 5.06/5.40 = ( ^ [N: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat_le_real_less
% 5.06/5.40 thf(fact_7413_zmult__zless__mono2__lemma,axiom,
% 5.06/5.40 ! [I2: int,J: int,K: nat] :
% 5.06/5.40 ( ( ord_less_int @ I2 @ J )
% 5.06/5.40 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.40 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % zmult_zless_mono2_lemma
% 5.06/5.40 thf(fact_7414_zdvd__mult__cancel1,axiom,
% 5.06/5.40 ! [M: int,N2: int] :
% 5.06/5.40 ( ( M != zero_zero_int )
% 5.06/5.40 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N2 ) @ M )
% 5.06/5.40 = ( ( abs_abs_int @ N2 )
% 5.06/5.40 = one_one_int ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % zdvd_mult_cancel1
% 5.06/5.40 thf(fact_7415_not__zle__0__negative,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % not_zle_0_negative
% 5.06/5.40 thf(fact_7416_negative__zless__0,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 5.06/5.40
% 5.06/5.40 % negative_zless_0
% 5.06/5.40 thf(fact_7417_negD,axiom,
% 5.06/5.40 ! [X: int] :
% 5.06/5.40 ( ( ord_less_int @ X @ zero_zero_int )
% 5.06/5.40 => ? [N3: nat] :
% 5.06/5.40 ( X
% 5.06/5.40 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % negD
% 5.06/5.40 thf(fact_7418_dbl__inc__def,axiom,
% 5.06/5.40 ( neg_nu8557863876264182079omplex
% 5.06/5.40 = ( ^ [X2: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_inc_def
% 5.06/5.40 thf(fact_7419_dbl__inc__def,axiom,
% 5.06/5.40 ( neg_nu8295874005876285629c_real
% 5.06/5.40 = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_inc_def
% 5.06/5.40 thf(fact_7420_dbl__inc__def,axiom,
% 5.06/5.40 ( neg_nu5219082963157363817nc_rat
% 5.06/5.40 = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_inc_def
% 5.06/5.40 thf(fact_7421_dbl__inc__def,axiom,
% 5.06/5.40 ( neg_nu5851722552734809277nc_int
% 5.06/5.40 = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_inc_def
% 5.06/5.40 thf(fact_7422_int__ops_I6_J,axiom,
% 5.06/5.40 ! [A: nat,B: nat] :
% 5.06/5.40 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.06/5.40 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.06/5.40 = zero_zero_int ) )
% 5.06/5.40 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.06/5.40 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.06/5.40 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % int_ops(6)
% 5.06/5.40 thf(fact_7423_real__of__nat__div__aux,axiom,
% 5.06/5.40 ! [X: nat,D: nat] :
% 5.06/5.40 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.06/5.40 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_div_aux
% 5.06/5.40 thf(fact_7424_of__nat__less__two__power,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_two_power
% 5.06/5.40 thf(fact_7425_of__nat__less__two__power,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_two_power
% 5.06/5.40 thf(fact_7426_of__nat__less__two__power,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_two_power
% 5.06/5.40 thf(fact_7427_of__nat__less__two__power,axiom,
% 5.06/5.40 ! [N2: nat] : ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_less_two_power
% 5.06/5.40 thf(fact_7428_inverse__of__nat__le,axiom,
% 5.06/5.40 ! [N2: nat,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.40 => ( ( N2 != zero_zero_nat )
% 5.06/5.40 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % inverse_of_nat_le
% 5.06/5.40 thf(fact_7429_inverse__of__nat__le,axiom,
% 5.06/5.40 ! [N2: nat,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.40 => ( ( N2 != zero_zero_nat )
% 5.06/5.40 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % inverse_of_nat_le
% 5.06/5.40 thf(fact_7430_even__abs__add__iff,axiom,
% 5.06/5.40 ! [K: int,L2: int] :
% 5.06/5.40 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 5.06/5.40 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % even_abs_add_iff
% 5.06/5.40 thf(fact_7431_even__add__abs__iff,axiom,
% 5.06/5.40 ! [K: int,L2: int] :
% 5.06/5.40 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 5.06/5.40 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % even_add_abs_iff
% 5.06/5.40 thf(fact_7432_real__archimedian__rdiv__eq__0,axiom,
% 5.06/5.40 ! [X: real,C: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.06/5.40 => ( ! [M2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 5.06/5.40 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ X ) @ C ) )
% 5.06/5.40 => ( X = zero_zero_real ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_archimedian_rdiv_eq_0
% 5.06/5.40 thf(fact_7433_neg__int__cases,axiom,
% 5.06/5.40 ! [K: int] :
% 5.06/5.40 ( ( ord_less_int @ K @ zero_zero_int )
% 5.06/5.40 => ~ ! [N3: nat] :
% 5.06/5.40 ( ( K
% 5.06/5.40 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.06/5.40 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % neg_int_cases
% 5.06/5.40 thf(fact_7434_zdiff__int__split,axiom,
% 5.06/5.40 ! [P: int > $o,X: nat,Y: nat] :
% 5.06/5.40 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 5.06/5.40 = ( ( ( ord_less_eq_nat @ Y @ X )
% 5.06/5.40 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.06/5.40 & ( ( ord_less_nat @ X @ Y )
% 5.06/5.40 => ( P @ zero_zero_int ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % zdiff_int_split
% 5.06/5.40 thf(fact_7435_real__of__nat__div2,axiom,
% 5.06/5.40 ! [N2: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_div2
% 5.06/5.40 thf(fact_7436_real__of__nat__div3,axiom,
% 5.06/5.40 ! [N2: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X ) ) ) @ one_one_real ) ).
% 5.06/5.40
% 5.06/5.40 % real_of_nat_div3
% 5.06/5.40 thf(fact_7437_ln__realpow,axiom,
% 5.06/5.40 ! [X: real,N2: nat] :
% 5.06/5.40 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.40 => ( ( ln_ln_real @ ( power_power_real @ X @ N2 ) )
% 5.06/5.40 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % ln_realpow
% 5.06/5.40 thf(fact_7438_nat__intermed__int__val,axiom,
% 5.06/5.40 ! [M: nat,N2: nat,F: nat > int,K: int] :
% 5.06/5.40 ( ! [I3: nat] :
% 5.06/5.40 ( ( ( ord_less_eq_nat @ M @ I3 )
% 5.06/5.40 & ( ord_less_nat @ I3 @ N2 ) )
% 5.06/5.40 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.06/5.40 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.40 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.06/5.40 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.06/5.40 => ? [I3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ M @ I3 )
% 5.06/5.40 & ( ord_less_eq_nat @ I3 @ N2 )
% 5.06/5.40 & ( ( F @ I3 )
% 5.06/5.40 = K ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat_intermed_int_val
% 5.06/5.40 thf(fact_7439_dbl__dec__def,axiom,
% 5.06/5.40 ( neg_nu6511756317524482435omplex
% 5.06/5.40 = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_def
% 5.06/5.40 thf(fact_7440_dbl__dec__def,axiom,
% 5.06/5.40 ( neg_nu6075765906172075777c_real
% 5.06/5.40 = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_def
% 5.06/5.40 thf(fact_7441_dbl__dec__def,axiom,
% 5.06/5.40 ( neg_nu3179335615603231917ec_rat
% 5.06/5.40 = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_def
% 5.06/5.40 thf(fact_7442_dbl__dec__def,axiom,
% 5.06/5.40 ( neg_nu3811975205180677377ec_int
% 5.06/5.40 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % dbl_dec_def
% 5.06/5.40 thf(fact_7443_decr__lemma,axiom,
% 5.06/5.40 ! [D: int,X: int,Z: int] :
% 5.06/5.40 ( ( ord_less_int @ zero_zero_int @ D )
% 5.06/5.40 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.06/5.40
% 5.06/5.40 % decr_lemma
% 5.06/5.40 thf(fact_7444_incr__lemma,axiom,
% 5.06/5.40 ! [D: int,Z: int,X: int] :
% 5.06/5.40 ( ( ord_less_int @ zero_zero_int @ D )
% 5.06/5.40 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % incr_lemma
% 5.06/5.40 thf(fact_7445_linear__plus__1__le__power,axiom,
% 5.06/5.40 ! [X: real,N2: nat] :
% 5.06/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.40 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % linear_plus_1_le_power
% 5.06/5.40 thf(fact_7446_Bernoulli__inequality,axiom,
% 5.06/5.40 ! [X: real,N2: nat] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.40 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % Bernoulli_inequality
% 5.06/5.40 thf(fact_7447_nat__ivt__aux,axiom,
% 5.06/5.40 ! [N2: nat,F: nat > int,K: int] :
% 5.06/5.40 ( ! [I3: nat] :
% 5.06/5.40 ( ( ord_less_nat @ I3 @ N2 )
% 5.06/5.40 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.06/5.40 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.06/5.40 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.06/5.40 => ? [I3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ I3 @ N2 )
% 5.06/5.40 & ( ( F @ I3 )
% 5.06/5.40 = K ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat_ivt_aux
% 5.06/5.40 thf(fact_7448_nat0__intermed__int__val,axiom,
% 5.06/5.40 ! [N2: nat,F: nat > int,K: int] :
% 5.06/5.40 ( ! [I3: nat] :
% 5.06/5.40 ( ( ord_less_nat @ I3 @ N2 )
% 5.06/5.40 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.06/5.40 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.06/5.40 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.06/5.40 => ? [I3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ I3 @ N2 )
% 5.06/5.40 & ( ( F @ I3 )
% 5.06/5.40 = K ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat0_intermed_int_val
% 5.06/5.40 thf(fact_7449_double__arith__series,axiom,
% 5.06/5.40 ! [A: complex,D: complex,N2: nat] :
% 5.06/5.40 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.06/5.40 @ ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [I5: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I5 ) @ D ) )
% 5.06/5.40 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_arith_series
% 5.06/5.40 thf(fact_7450_double__arith__series,axiom,
% 5.06/5.40 ! [A: rat,D: rat,N2: nat] :
% 5.06/5.40 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.06/5.40 @ ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I5 ) @ D ) )
% 5.06/5.40 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_arith_series
% 5.06/5.40 thf(fact_7451_double__arith__series,axiom,
% 5.06/5.40 ! [A: int,D: int,N2: nat] :
% 5.06/5.40 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.06/5.40 @ ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 5.06/5.40 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_arith_series
% 5.06/5.40 thf(fact_7452_double__arith__series,axiom,
% 5.06/5.40 ! [A: code_integer,D: code_integer,N2: nat] :
% 5.06/5.40 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.06/5.40 @ ( groups7501900531339628137nteger
% 5.06/5.40 @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I5 ) @ D ) )
% 5.06/5.40 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_arith_series
% 5.06/5.40 thf(fact_7453_double__arith__series,axiom,
% 5.06/5.40 ! [A: nat,D: nat,N2: nat] :
% 5.06/5.40 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.06/5.40 @ ( groups3542108847815614940at_nat
% 5.06/5.40 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 5.06/5.40 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_arith_series
% 5.06/5.40 thf(fact_7454_double__arith__series,axiom,
% 5.06/5.40 ! [A: real,D: real,N2: nat] :
% 5.06/5.40 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.06/5.40 @ ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I5 ) @ D ) )
% 5.06/5.40 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_arith_series
% 5.06/5.40 thf(fact_7455_double__gauss__sum,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum
% 5.06/5.40 thf(fact_7456_double__gauss__sum,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum
% 5.06/5.40 thf(fact_7457_double__gauss__sum,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum
% 5.06/5.40 thf(fact_7458_double__gauss__sum,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum
% 5.06/5.40 thf(fact_7459_double__gauss__sum,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum
% 5.06/5.40 thf(fact_7460_double__gauss__sum,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.40 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum
% 5.06/5.40 thf(fact_7461_arctan__add,axiom,
% 5.06/5.40 ! [X: real,Y: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.40 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.06/5.40 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.06/5.40 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % arctan_add
% 5.06/5.40 thf(fact_7462_arith__series,axiom,
% 5.06/5.40 ! [A: int,D: int,N2: nat] :
% 5.06/5.40 ( ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 5.06/5.40 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.40 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % arith_series
% 5.06/5.40 thf(fact_7463_arith__series,axiom,
% 5.06/5.40 ! [A: code_integer,D: code_integer,N2: nat] :
% 5.06/5.40 ( ( groups7501900531339628137nteger
% 5.06/5.40 @ ^ [I5: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I5 ) @ D ) )
% 5.06/5.40 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.40 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % arith_series
% 5.06/5.40 thf(fact_7464_arith__series,axiom,
% 5.06/5.40 ! [A: nat,D: nat,N2: nat] :
% 5.06/5.40 ( ( groups3542108847815614940at_nat
% 5.06/5.40 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 5.06/5.40 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.40 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % arith_series
% 5.06/5.40 thf(fact_7465_gauss__sum,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.40 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % gauss_sum
% 5.06/5.40 thf(fact_7466_gauss__sum,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.40 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % gauss_sum
% 5.06/5.40 thf(fact_7467_gauss__sum,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.40 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % gauss_sum
% 5.06/5.40 thf(fact_7468_double__gauss__sum__from__Suc__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.06/5.40 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum_from_Suc_0
% 5.06/5.40 thf(fact_7469_double__gauss__sum__from__Suc__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.06/5.40 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum_from_Suc_0
% 5.06/5.40 thf(fact_7470_double__gauss__sum__from__Suc__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.06/5.40 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum_from_Suc_0
% 5.06/5.40 thf(fact_7471_double__gauss__sum__from__Suc__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.06/5.40 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum_from_Suc_0
% 5.06/5.40 thf(fact_7472_double__gauss__sum__from__Suc__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.06/5.40 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum_from_Suc_0
% 5.06/5.40 thf(fact_7473_double__gauss__sum__from__Suc__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.06/5.40 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % double_gauss_sum_from_Suc_0
% 5.06/5.40 thf(fact_7474_Bernoulli__inequality__even,axiom,
% 5.06/5.40 ! [N2: nat,X: real] :
% 5.06/5.40 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.40 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % Bernoulli_inequality_even
% 5.06/5.40 thf(fact_7475_sum__gp__offset,axiom,
% 5.06/5.40 ! [X: complex,M: nat,N2: nat] :
% 5.06/5.40 ( ( ( X = one_one_complex )
% 5.06/5.40 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) )
% 5.06/5.40 & ( ( X != one_one_complex )
% 5.06/5.40 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.06/5.40 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_gp_offset
% 5.06/5.40 thf(fact_7476_sum__gp__offset,axiom,
% 5.06/5.40 ! [X: rat,M: nat,N2: nat] :
% 5.06/5.40 ( ( ( X = one_one_rat )
% 5.06/5.40 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 5.06/5.40 & ( ( X != one_one_rat )
% 5.06/5.40 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.06/5.40 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_gp_offset
% 5.06/5.40 thf(fact_7477_sum__gp__offset,axiom,
% 5.06/5.40 ! [X: real,M: nat,N2: nat] :
% 5.06/5.40 ( ( ( X = one_one_real )
% 5.06/5.40 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) )
% 5.06/5.40 & ( ( X != one_one_real )
% 5.06/5.40 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.06/5.40 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_gp_offset
% 5.06/5.40 thf(fact_7478_gauss__sum__from__Suc__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.06/5.40 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % gauss_sum_from_Suc_0
% 5.06/5.40 thf(fact_7479_gauss__sum__from__Suc__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.06/5.40 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % gauss_sum_from_Suc_0
% 5.06/5.40 thf(fact_7480_gauss__sum__from__Suc__0,axiom,
% 5.06/5.40 ! [N2: nat] :
% 5.06/5.40 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.06/5.40 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % gauss_sum_from_Suc_0
% 5.06/5.40 thf(fact_7481_of__nat__code__if,axiom,
% 5.06/5.40 ( semiri8010041392384452111omplex
% 5.06/5.40 = ( ^ [N: nat] :
% 5.06/5.40 ( if_complex @ ( N = zero_zero_nat ) @ zero_zero_complex
% 5.06/5.40 @ ( produc1917071388513777916omplex
% 5.06/5.40 @ ^ [M6: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ one_one_complex ) )
% 5.06/5.40 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_code_if
% 5.06/5.40 thf(fact_7482_of__nat__code__if,axiom,
% 5.06/5.40 ( semiri681578069525770553at_rat
% 5.06/5.40 = ( ^ [N: nat] :
% 5.06/5.40 ( if_rat @ ( N = zero_zero_nat ) @ zero_zero_rat
% 5.06/5.40 @ ( produc6207742614233964070at_rat
% 5.06/5.40 @ ^ [M6: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ one_one_rat ) )
% 5.06/5.40 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_code_if
% 5.06/5.40 thf(fact_7483_of__nat__code__if,axiom,
% 5.06/5.40 ( semiri1314217659103216013at_int
% 5.06/5.40 = ( ^ [N: nat] :
% 5.06/5.40 ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int
% 5.06/5.40 @ ( produc6840382203811409530at_int
% 5.06/5.40 @ ^ [M6: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ one_one_int ) )
% 5.06/5.40 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_code_if
% 5.06/5.40 thf(fact_7484_of__nat__code__if,axiom,
% 5.06/5.40 ( semiri5074537144036343181t_real
% 5.06/5.40 = ( ^ [N: nat] :
% 5.06/5.40 ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 5.06/5.40 @ ( produc1703576794950452218t_real
% 5.06/5.40 @ ^ [M6: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ one_one_real ) )
% 5.06/5.40 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_code_if
% 5.06/5.40 thf(fact_7485_of__nat__code__if,axiom,
% 5.06/5.40 ( semiri1316708129612266289at_nat
% 5.06/5.40 = ( ^ [N: nat] :
% 5.06/5.40 ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 5.06/5.40 @ ( produc6842872674320459806at_nat
% 5.06/5.40 @ ^ [M6: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ one_one_nat ) )
% 5.06/5.40 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_code_if
% 5.06/5.40 thf(fact_7486_of__nat__code__if,axiom,
% 5.06/5.40 ( semiri4939895301339042750nteger
% 5.06/5.40 = ( ^ [N: nat] :
% 5.06/5.40 ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger
% 5.06/5.40 @ ( produc1830744345554046123nteger
% 5.06/5.40 @ ^ [M6: nat,Q4: nat] : ( if_Code_integer @ ( Q4 = zero_zero_nat ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ M6 ) ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ M6 ) ) @ one_one_Code_integer ) )
% 5.06/5.40 @ ( divmod_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % of_nat_code_if
% 5.06/5.40 thf(fact_7487_nat__approx__posE,axiom,
% 5.06/5.40 ! [E: rat] :
% 5.06/5.40 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.06/5.40 => ~ ! [N3: nat] :
% 5.06/5.40 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat_approx_posE
% 5.06/5.40 thf(fact_7488_nat__approx__posE,axiom,
% 5.06/5.40 ! [E: real] :
% 5.06/5.40 ( ( ord_less_real @ zero_zero_real @ E )
% 5.06/5.40 => ~ ! [N3: nat] :
% 5.06/5.40 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.06/5.40
% 5.06/5.40 % nat_approx_posE
% 5.06/5.40 thf(fact_7489_monoseq__arctan__series,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.40 => ( topolo6980174941875973593q_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % monoseq_arctan_series
% 5.06/5.40 thf(fact_7490_lemma__termdiff3,axiom,
% 5.06/5.40 ! [H2: real,Z: real,K5: real,N2: nat] :
% 5.06/5.40 ( ( H2 != zero_zero_real )
% 5.06/5.40 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.06/5.40 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lemma_termdiff3
% 5.06/5.40 thf(fact_7491_lemma__termdiff3,axiom,
% 5.06/5.40 ! [H2: complex,Z: complex,K5: real,N2: nat] :
% 5.06/5.40 ( ( H2 != zero_zero_complex )
% 5.06/5.40 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.06/5.40 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lemma_termdiff3
% 5.06/5.40 thf(fact_7492_ex__less__of__nat__mult,axiom,
% 5.06/5.40 ! [X: rat,Y: rat] :
% 5.06/5.40 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.06/5.40 => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % ex_less_of_nat_mult
% 5.06/5.40 thf(fact_7493_ex__less__of__nat__mult,axiom,
% 5.06/5.40 ! [X: real,Y: real] :
% 5.06/5.40 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.40 => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % ex_less_of_nat_mult
% 5.06/5.40 thf(fact_7494_ln__series,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.40 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.40 => ( ( ln_ln_real @ X )
% 5.06/5.40 = ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % ln_series
% 5.06/5.40 thf(fact_7495_powser__zero,axiom,
% 5.06/5.40 ! [F: nat > complex] :
% 5.06/5.40 ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) )
% 5.06/5.40 = ( F @ zero_zero_nat ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_zero
% 5.06/5.40 thf(fact_7496_powser__zero,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) )
% 5.06/5.40 = ( F @ zero_zero_nat ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_zero
% 5.06/5.40 thf(fact_7497_complex__mod__minus__le__complex__mod,axiom,
% 5.06/5.40 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % complex_mod_minus_le_complex_mod
% 5.06/5.40 thf(fact_7498_complex__mod__triangle__ineq2,axiom,
% 5.06/5.40 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.06/5.40
% 5.06/5.40 % complex_mod_triangle_ineq2
% 5.06/5.40 thf(fact_7499_monoseq__realpow,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.40 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.40 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % monoseq_realpow
% 5.06/5.40 thf(fact_7500_real__arch__simple,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_arch_simple
% 5.06/5.40 thf(fact_7501_real__arch__simple,axiom,
% 5.06/5.40 ! [X: rat] :
% 5.06/5.40 ? [N3: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_arch_simple
% 5.06/5.40 thf(fact_7502_reals__Archimedean2,axiom,
% 5.06/5.40 ! [X: rat] :
% 5.06/5.40 ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % reals_Archimedean2
% 5.06/5.40 thf(fact_7503_reals__Archimedean2,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % reals_Archimedean2
% 5.06/5.40 thf(fact_7504_exists__least__lemma,axiom,
% 5.06/5.40 ! [P: nat > $o] :
% 5.06/5.40 ( ~ ( P @ zero_zero_nat )
% 5.06/5.40 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.06/5.40 => ? [N3: nat] :
% 5.06/5.40 ( ~ ( P @ N3 )
% 5.06/5.40 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % exists_least_lemma
% 5.06/5.40 thf(fact_7505_arctan__series,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.40 => ( ( arctan @ X )
% 5.06/5.40 = ( suminf_real
% 5.06/5.40 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % arctan_series
% 5.06/5.40 thf(fact_7506_norm__divide__numeral,axiom,
% 5.06/5.40 ! [A: real,W: num] :
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.06/5.40 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_divide_numeral
% 5.06/5.40 thf(fact_7507_norm__divide__numeral,axiom,
% 5.06/5.40 ! [A: complex,W: num] :
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.40 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_divide_numeral
% 5.06/5.40 thf(fact_7508_norm__mult__numeral1,axiom,
% 5.06/5.40 ! [W: num,A: real] :
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.06/5.40 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_mult_numeral1
% 5.06/5.40 thf(fact_7509_norm__mult__numeral1,axiom,
% 5.06/5.40 ! [W: num,A: complex] :
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.06/5.40 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_mult_numeral1
% 5.06/5.40 thf(fact_7510_norm__mult__numeral2,axiom,
% 5.06/5.40 ! [A: real,W: num] :
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.06/5.40 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_mult_numeral2
% 5.06/5.40 thf(fact_7511_norm__mult__numeral2,axiom,
% 5.06/5.40 ! [A: complex,W: num] :
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.40 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_mult_numeral2
% 5.06/5.40 thf(fact_7512_norm__neg__numeral,axiom,
% 5.06/5.40 ! [W: num] :
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.06/5.40 = ( numeral_numeral_real @ W ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_neg_numeral
% 5.06/5.40 thf(fact_7513_norm__neg__numeral,axiom,
% 5.06/5.40 ! [W: num] :
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.40 = ( numeral_numeral_real @ W ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_neg_numeral
% 5.06/5.40 thf(fact_7514_norm__le__zero__iff,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 5.06/5.40 = ( X = zero_zero_real ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_le_zero_iff
% 5.06/5.40 thf(fact_7515_norm__le__zero__iff,axiom,
% 5.06/5.40 ! [X: complex] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 5.06/5.40 = ( X = zero_zero_complex ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_le_zero_iff
% 5.06/5.40 thf(fact_7516_suminf__geometric,axiom,
% 5.06/5.40 ! [C: real] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.06/5.40 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.06/5.40 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_geometric
% 5.06/5.40 thf(fact_7517_suminf__geometric,axiom,
% 5.06/5.40 ! [C: complex] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.06/5.40 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.06/5.40 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_geometric
% 5.06/5.40 thf(fact_7518_suminf__zero,axiom,
% 5.06/5.40 ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : zero_zero_complex )
% 5.06/5.40 = zero_zero_complex ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_zero
% 5.06/5.40 thf(fact_7519_suminf__zero,axiom,
% 5.06/5.40 ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : zero_zero_real )
% 5.06/5.40 = zero_zero_real ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_zero
% 5.06/5.40 thf(fact_7520_suminf__zero,axiom,
% 5.06/5.40 ( ( suminf_nat
% 5.06/5.40 @ ^ [N: nat] : zero_zero_nat )
% 5.06/5.40 = zero_zero_nat ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_zero
% 5.06/5.40 thf(fact_7521_suminf__zero,axiom,
% 5.06/5.40 ( ( suminf_int
% 5.06/5.40 @ ^ [N: nat] : zero_zero_int )
% 5.06/5.40 = zero_zero_int ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_zero
% 5.06/5.40 thf(fact_7522_norm__one,axiom,
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.06/5.40 = one_one_real ) ).
% 5.06/5.40
% 5.06/5.40 % norm_one
% 5.06/5.40 thf(fact_7523_norm__one,axiom,
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.06/5.40 = one_one_real ) ).
% 5.06/5.40
% 5.06/5.40 % norm_one
% 5.06/5.40 thf(fact_7524_norm__numeral,axiom,
% 5.06/5.40 ! [W: num] :
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.06/5.40 = ( numeral_numeral_real @ W ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_numeral
% 5.06/5.40 thf(fact_7525_norm__numeral,axiom,
% 5.06/5.40 ! [W: num] :
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.40 = ( numeral_numeral_real @ W ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_numeral
% 5.06/5.40 thf(fact_7526_norm__minus__commute,axiom,
% 5.06/5.40 ! [A: real,B: real] :
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) )
% 5.06/5.40 = ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_minus_commute
% 5.06/5.40 thf(fact_7527_norm__minus__commute,axiom,
% 5.06/5.40 ! [A: complex,B: complex] :
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 5.06/5.40 = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_minus_commute
% 5.06/5.40 thf(fact_7528_norm__ge__zero,axiom,
% 5.06/5.40 ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_ge_zero
% 5.06/5.40 thf(fact_7529_norm__mult,axiom,
% 5.06/5.40 ! [X: real,Y: real] :
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) )
% 5.06/5.40 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_mult
% 5.06/5.40 thf(fact_7530_norm__mult,axiom,
% 5.06/5.40 ! [X: complex,Y: complex] :
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) )
% 5.06/5.40 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_mult
% 5.06/5.40 thf(fact_7531_norm__divide,axiom,
% 5.06/5.40 ! [A: real,B: real] :
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.40 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_divide
% 5.06/5.40 thf(fact_7532_norm__divide,axiom,
% 5.06/5.40 ! [A: complex,B: complex] :
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.06/5.40 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_divide
% 5.06/5.40 thf(fact_7533_sum__norm__le,axiom,
% 5.06/5.40 ! [S3: set_real,F: real > complex,G: real > real] :
% 5.06/5.40 ( ! [X3: real] :
% 5.06/5.40 ( ( member_real @ X3 @ S3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S3 ) ) @ ( groups8097168146408367636l_real @ G @ S3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_norm_le
% 5.06/5.40 thf(fact_7534_sum__norm__le,axiom,
% 5.06/5.40 ! [S3: set_set_nat,F: set_nat > complex,G: set_nat > real] :
% 5.06/5.40 ( ! [X3: set_nat] :
% 5.06/5.40 ( ( member_set_nat @ X3 @ S3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F @ S3 ) ) @ ( groups5107569545109728110t_real @ G @ S3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_norm_le
% 5.06/5.40 thf(fact_7535_sum__norm__le,axiom,
% 5.06/5.40 ! [S3: set_int,F: int > complex,G: int > real] :
% 5.06/5.40 ( ! [X3: int] :
% 5.06/5.40 ( ( member_int @ X3 @ S3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S3 ) ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_norm_le
% 5.06/5.40 thf(fact_7536_sum__norm__le,axiom,
% 5.06/5.40 ! [S3: set_nat,F: nat > complex,G: nat > real] :
% 5.06/5.40 ( ! [X3: nat] :
% 5.06/5.40 ( ( member_nat @ X3 @ S3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S3 ) ) @ ( groups6591440286371151544t_real @ G @ S3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_norm_le
% 5.06/5.40 thf(fact_7537_sum__norm__le,axiom,
% 5.06/5.40 ! [S3: set_complex,F: complex > complex,G: complex > real] :
% 5.06/5.40 ( ! [X3: complex] :
% 5.06/5.40 ( ( member_complex @ X3 @ S3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S3 ) ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_norm_le
% 5.06/5.40 thf(fact_7538_sum__norm__le,axiom,
% 5.06/5.40 ! [S3: set_nat,F: nat > real,G: nat > real] :
% 5.06/5.40 ( ! [X3: nat] :
% 5.06/5.40 ( ( member_nat @ X3 @ S3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X3 ) ) @ ( G @ X3 ) ) )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S3 ) ) @ ( groups6591440286371151544t_real @ G @ S3 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_norm_le
% 5.06/5.40 thf(fact_7539_norm__power,axiom,
% 5.06/5.40 ! [X: real,N2: nat] :
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N2 ) )
% 5.06/5.40 = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_power
% 5.06/5.40 thf(fact_7540_norm__power,axiom,
% 5.06/5.40 ! [X: complex,N2: nat] :
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N2 ) )
% 5.06/5.40 = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_power
% 5.06/5.40 thf(fact_7541_norm__sum,axiom,
% 5.06/5.40 ! [F: nat > complex,A2: set_nat] :
% 5.06/5.40 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 5.06/5.40 @ ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( real_V1022390504157884413omplex @ ( F @ I5 ) )
% 5.06/5.40 @ A2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_sum
% 5.06/5.40 thf(fact_7542_norm__sum,axiom,
% 5.06/5.40 ! [F: complex > complex,A2: set_complex] :
% 5.06/5.40 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.06/5.40 @ ( groups5808333547571424918x_real
% 5.06/5.40 @ ^ [I5: complex] : ( real_V1022390504157884413omplex @ ( F @ I5 ) )
% 5.06/5.40 @ A2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_sum
% 5.06/5.40 thf(fact_7543_norm__sum,axiom,
% 5.06/5.40 ! [F: nat > real,A2: set_nat] :
% 5.06/5.40 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.06/5.40 @ ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( real_V7735802525324610683m_real @ ( F @ I5 ) )
% 5.06/5.40 @ A2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_sum
% 5.06/5.40 thf(fact_7544_norm__uminus__minus,axiom,
% 5.06/5.40 ! [X: real,Y: real] :
% 5.06/5.40 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y ) )
% 5.06/5.40 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_uminus_minus
% 5.06/5.40 thf(fact_7545_norm__uminus__minus,axiom,
% 5.06/5.40 ! [X: complex,Y: complex] :
% 5.06/5.40 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y ) )
% 5.06/5.40 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_uminus_minus
% 5.06/5.40 thf(fact_7546_nonzero__norm__divide,axiom,
% 5.06/5.40 ! [B: real,A: real] :
% 5.06/5.40 ( ( B != zero_zero_real )
% 5.06/5.40 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.40 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nonzero_norm_divide
% 5.06/5.40 thf(fact_7547_nonzero__norm__divide,axiom,
% 5.06/5.40 ! [B: complex,A: complex] :
% 5.06/5.40 ( ( B != zero_zero_complex )
% 5.06/5.40 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.06/5.40 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % nonzero_norm_divide
% 5.06/5.40 thf(fact_7548_power__eq__imp__eq__norm,axiom,
% 5.06/5.40 ! [W: real,N2: nat,Z: real] :
% 5.06/5.40 ( ( ( power_power_real @ W @ N2 )
% 5.06/5.40 = ( power_power_real @ Z @ N2 ) )
% 5.06/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.40 => ( ( real_V7735802525324610683m_real @ W )
% 5.06/5.40 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_eq_imp_eq_norm
% 5.06/5.40 thf(fact_7549_power__eq__imp__eq__norm,axiom,
% 5.06/5.40 ! [W: complex,N2: nat,Z: complex] :
% 5.06/5.40 ( ( ( power_power_complex @ W @ N2 )
% 5.06/5.40 = ( power_power_complex @ Z @ N2 ) )
% 5.06/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.40 => ( ( real_V1022390504157884413omplex @ W )
% 5.06/5.40 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_eq_imp_eq_norm
% 5.06/5.40 thf(fact_7550_norm__mult__less,axiom,
% 5.06/5.40 ! [X: real,R2: real,Y: real,S2: real] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 5.06/5.40 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S2 )
% 5.06/5.40 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_mult_less
% 5.06/5.40 thf(fact_7551_norm__mult__less,axiom,
% 5.06/5.40 ! [X: complex,R2: real,Y: complex,S2: real] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 5.06/5.40 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S2 )
% 5.06/5.40 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_mult_less
% 5.06/5.40 thf(fact_7552_norm__mult__ineq,axiom,
% 5.06/5.40 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_mult_ineq
% 5.06/5.40 thf(fact_7553_norm__mult__ineq,axiom,
% 5.06/5.40 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_mult_ineq
% 5.06/5.40 thf(fact_7554_norm__triangle__lt,axiom,
% 5.06/5.40 ! [X: real,Y: real,E: real] :
% 5.06/5.40 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.06/5.40 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_lt
% 5.06/5.40 thf(fact_7555_norm__triangle__lt,axiom,
% 5.06/5.40 ! [X: complex,Y: complex,E: real] :
% 5.06/5.40 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.06/5.40 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_lt
% 5.06/5.40 thf(fact_7556_norm__add__less,axiom,
% 5.06/5.40 ! [X: real,R2: real,Y: real,S2: real] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 5.06/5.40 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S2 )
% 5.06/5.40 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_add_less
% 5.06/5.40 thf(fact_7557_norm__add__less,axiom,
% 5.06/5.40 ! [X: complex,R2: real,Y: complex,S2: real] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 5.06/5.40 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S2 )
% 5.06/5.40 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_add_less
% 5.06/5.40 thf(fact_7558_norm__power__ineq,axiom,
% 5.06/5.40 ! [X: real,N2: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N2 ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_power_ineq
% 5.06/5.40 thf(fact_7559_norm__power__ineq,axiom,
% 5.06/5.40 ! [X: complex,N2: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_power_ineq
% 5.06/5.40 thf(fact_7560_norm__triangle__mono,axiom,
% 5.06/5.40 ! [A: real,R2: real,B: real,S2: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 5.06/5.40 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S2 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_mono
% 5.06/5.40 thf(fact_7561_norm__triangle__mono,axiom,
% 5.06/5.40 ! [A: complex,R2: real,B: complex,S2: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 5.06/5.40 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S2 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_mono
% 5.06/5.40 thf(fact_7562_norm__triangle__ineq,axiom,
% 5.06/5.40 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_ineq
% 5.06/5.40 thf(fact_7563_norm__triangle__ineq,axiom,
% 5.06/5.40 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_ineq
% 5.06/5.40 thf(fact_7564_norm__triangle__le,axiom,
% 5.06/5.40 ! [X: real,Y: real,E: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_le
% 5.06/5.40 thf(fact_7565_norm__triangle__le,axiom,
% 5.06/5.40 ! [X: complex,Y: complex,E: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_le
% 5.06/5.40 thf(fact_7566_norm__add__leD,axiom,
% 5.06/5.40 ! [A: real,B: real,C: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_add_leD
% 5.06/5.40 thf(fact_7567_norm__add__leD,axiom,
% 5.06/5.40 ! [A: complex,B: complex,C: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_add_leD
% 5.06/5.40 thf(fact_7568_norm__diff__triangle__less,axiom,
% 5.06/5.40 ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 5.06/5.40 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.06/5.40 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_diff_triangle_less
% 5.06/5.40 thf(fact_7569_norm__diff__triangle__less,axiom,
% 5.06/5.40 ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 5.06/5.40 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.06/5.40 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_diff_triangle_less
% 5.06/5.40 thf(fact_7570_norm__triangle__sub,axiom,
% 5.06/5.40 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_sub
% 5.06/5.40 thf(fact_7571_norm__triangle__sub,axiom,
% 5.06/5.40 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_sub
% 5.06/5.40 thf(fact_7572_norm__triangle__ineq4,axiom,
% 5.06/5.40 ! [A: real,B: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_ineq4
% 5.06/5.40 thf(fact_7573_norm__triangle__ineq4,axiom,
% 5.06/5.40 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_ineq4
% 5.06/5.40 thf(fact_7574_norm__diff__triangle__le,axiom,
% 5.06/5.40 ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 5.06/5.40 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_diff_triangle_le
% 5.06/5.40 thf(fact_7575_norm__diff__triangle__le,axiom,
% 5.06/5.40 ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 5.06/5.40 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_diff_triangle_le
% 5.06/5.40 thf(fact_7576_norm__triangle__le__diff,axiom,
% 5.06/5.40 ! [X: real,Y: real,E: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_le_diff
% 5.06/5.40 thf(fact_7577_norm__triangle__le__diff,axiom,
% 5.06/5.40 ! [X: complex,Y: complex,E: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_le_diff
% 5.06/5.40 thf(fact_7578_norm__diff__ineq,axiom,
% 5.06/5.40 ! [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 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_diff_ineq
% 5.06/5.40 thf(fact_7579_norm__diff__ineq,axiom,
% 5.06/5.40 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_diff_ineq
% 5.06/5.40 thf(fact_7580_norm__triangle__ineq2,axiom,
% 5.06/5.40 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_ineq2
% 5.06/5.40 thf(fact_7581_norm__triangle__ineq2,axiom,
% 5.06/5.40 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_ineq2
% 5.06/5.40 thf(fact_7582_suminf__finite,axiom,
% 5.06/5.40 ! [N4: set_nat,F: nat > complex] :
% 5.06/5.40 ( ( finite_finite_nat @ N4 )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ~ ( member_nat @ N3 @ N4 )
% 5.06/5.40 => ( ( F @ N3 )
% 5.06/5.40 = zero_zero_complex ) )
% 5.06/5.40 => ( ( suminf_complex @ F )
% 5.06/5.40 = ( groups2073611262835488442omplex @ F @ N4 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_finite
% 5.06/5.40 thf(fact_7583_suminf__finite,axiom,
% 5.06/5.40 ! [N4: set_nat,F: nat > int] :
% 5.06/5.40 ( ( finite_finite_nat @ N4 )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ~ ( member_nat @ N3 @ N4 )
% 5.06/5.40 => ( ( F @ N3 )
% 5.06/5.40 = zero_zero_int ) )
% 5.06/5.40 => ( ( suminf_int @ F )
% 5.06/5.40 = ( groups3539618377306564664at_int @ F @ N4 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_finite
% 5.06/5.40 thf(fact_7584_suminf__finite,axiom,
% 5.06/5.40 ! [N4: set_nat,F: nat > nat] :
% 5.06/5.40 ( ( finite_finite_nat @ N4 )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ~ ( member_nat @ N3 @ N4 )
% 5.06/5.40 => ( ( F @ N3 )
% 5.06/5.40 = zero_zero_nat ) )
% 5.06/5.40 => ( ( suminf_nat @ F )
% 5.06/5.40 = ( groups3542108847815614940at_nat @ F @ N4 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_finite
% 5.06/5.40 thf(fact_7585_suminf__finite,axiom,
% 5.06/5.40 ! [N4: set_nat,F: nat > real] :
% 5.06/5.40 ( ( finite_finite_nat @ N4 )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ~ ( member_nat @ N3 @ N4 )
% 5.06/5.40 => ( ( F @ N3 )
% 5.06/5.40 = zero_zero_real ) )
% 5.06/5.40 => ( ( suminf_real @ F )
% 5.06/5.40 = ( groups6591440286371151544t_real @ F @ N4 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_finite
% 5.06/5.40 thf(fact_7586_power__eq__1__iff,axiom,
% 5.06/5.40 ! [W: real,N2: nat] :
% 5.06/5.40 ( ( ( power_power_real @ W @ N2 )
% 5.06/5.40 = one_one_real )
% 5.06/5.40 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.06/5.40 = one_one_real )
% 5.06/5.40 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_eq_1_iff
% 5.06/5.40 thf(fact_7587_power__eq__1__iff,axiom,
% 5.06/5.40 ! [W: complex,N2: nat] :
% 5.06/5.40 ( ( ( power_power_complex @ W @ N2 )
% 5.06/5.40 = one_one_complex )
% 5.06/5.40 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.06/5.40 = one_one_real )
% 5.06/5.40 | ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_eq_1_iff
% 5.06/5.40 thf(fact_7588_norm__diff__triangle__ineq,axiom,
% 5.06/5.40 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_diff_triangle_ineq
% 5.06/5.40 thf(fact_7589_norm__diff__triangle__ineq,axiom,
% 5.06/5.40 ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_diff_triangle_ineq
% 5.06/5.40 thf(fact_7590_norm__triangle__ineq3,axiom,
% 5.06/5.40 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_ineq3
% 5.06/5.40 thf(fact_7591_norm__triangle__ineq3,axiom,
% 5.06/5.40 ! [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 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_triangle_ineq3
% 5.06/5.40 thf(fact_7592_square__norm__one,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.40 = one_one_real )
% 5.06/5.40 => ( ( real_V7735802525324610683m_real @ X )
% 5.06/5.40 = one_one_real ) ) ).
% 5.06/5.40
% 5.06/5.40 % square_norm_one
% 5.06/5.40 thf(fact_7593_square__norm__one,axiom,
% 5.06/5.40 ! [X: complex] :
% 5.06/5.40 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.40 = one_one_complex )
% 5.06/5.40 => ( ( real_V1022390504157884413omplex @ X )
% 5.06/5.40 = one_one_real ) ) ).
% 5.06/5.40
% 5.06/5.40 % square_norm_one
% 5.06/5.40 thf(fact_7594_norm__power__diff,axiom,
% 5.06/5.40 ! [Z: real,W: real,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.06/5.40 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.06/5.40 => ( 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 ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_power_diff
% 5.06/5.40 thf(fact_7595_norm__power__diff,axiom,
% 5.06/5.40 ! [Z: complex,W: complex,M: nat] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.06/5.40 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.06/5.40 => ( 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 ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % norm_power_diff
% 5.06/5.40 thf(fact_7596_pi__series,axiom,
% 5.06/5.40 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.06/5.40 = ( suminf_real
% 5.06/5.40 @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % pi_series
% 5.06/5.40 thf(fact_7597_lemma__termdiff2,axiom,
% 5.06/5.40 ! [H2: complex,Z: complex,N2: nat] :
% 5.06/5.40 ( ( H2 != zero_zero_complex )
% 5.06/5.40 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.06/5.40 = ( times_times_complex @ H2
% 5.06/5.40 @ ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [P5: nat] :
% 5.06/5.40 ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q4 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lemma_termdiff2
% 5.06/5.40 thf(fact_7598_lemma__termdiff2,axiom,
% 5.06/5.40 ! [H2: rat,Z: rat,N2: nat] :
% 5.06/5.40 ( ( H2 != zero_zero_rat )
% 5.06/5.40 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N2 ) @ ( power_power_rat @ Z @ N2 ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.06/5.40 = ( times_times_rat @ H2
% 5.06/5.40 @ ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [P5: nat] :
% 5.06/5.40 ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [Q4: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q4 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lemma_termdiff2
% 5.06/5.40 thf(fact_7599_lemma__termdiff2,axiom,
% 5.06/5.40 ! [H2: real,Z: real,N2: nat] :
% 5.06/5.40 ( ( H2 != zero_zero_real )
% 5.06/5.40 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.06/5.40 = ( times_times_real @ H2
% 5.06/5.40 @ ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [P5: nat] :
% 5.06/5.40 ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q4 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lemma_termdiff2
% 5.06/5.40 thf(fact_7600_summable__arctan__series,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_arctan_series
% 5.06/5.40 thf(fact_7601_pred__subset__eq2,axiom,
% 5.06/5.40 ! [R: set_Pr448751882837621926eger_o,S3: set_Pr448751882837621926eger_o] :
% 5.06/5.40 ( ( ord_le2162486998276636481er_o_o
% 5.06/5.40 @ ^ [X2: code_integer,Y2: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X2 @ Y2 ) @ R )
% 5.06/5.40 @ ^ [X2: code_integer,Y2: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X2 @ Y2 ) @ S3 ) )
% 5.06/5.40 = ( ord_le8980329558974975238eger_o @ R @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_subset_eq2
% 5.06/5.40 thf(fact_7602_pred__subset__eq2,axiom,
% 5.06/5.40 ! [R: set_Pr8218934625190621173um_num,S3: set_Pr8218934625190621173um_num] :
% 5.06/5.40 ( ( ord_le6124364862034508274_num_o
% 5.06/5.40 @ ^ [X2: num,Y2: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X2 @ Y2 ) @ R )
% 5.06/5.40 @ ^ [X2: num,Y2: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X2 @ Y2 ) @ S3 ) )
% 5.06/5.40 = ( ord_le880128212290418581um_num @ R @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_subset_eq2
% 5.06/5.40 thf(fact_7603_pred__subset__eq2,axiom,
% 5.06/5.40 ! [R: set_Pr6200539531224447659at_num,S3: set_Pr6200539531224447659at_num] :
% 5.06/5.40 ( ( ord_le3404735783095501756_num_o
% 5.06/5.40 @ ^ [X2: nat,Y2: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Y2 ) @ R )
% 5.06/5.40 @ ^ [X2: nat,Y2: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Y2 ) @ S3 ) )
% 5.06/5.40 = ( ord_le8085105155179020875at_num @ R @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_subset_eq2
% 5.06/5.40 thf(fact_7604_pred__subset__eq2,axiom,
% 5.06/5.40 ! [R: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 5.06/5.40 ( ( ord_le2646555220125990790_nat_o
% 5.06/5.40 @ ^ [X2: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ R )
% 5.06/5.40 @ ^ [X2: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ S3 ) )
% 5.06/5.40 = ( ord_le3146513528884898305at_nat @ R @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_subset_eq2
% 5.06/5.40 thf(fact_7605_pred__subset__eq2,axiom,
% 5.06/5.40 ! [R: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 5.06/5.40 ( ( ord_le6741204236512500942_int_o
% 5.06/5.40 @ ^ [X2: int,Y2: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y2 ) @ R )
% 5.06/5.40 @ ^ [X2: int,Y2: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y2 ) @ S3 ) )
% 5.06/5.40 = ( ord_le2843351958646193337nt_int @ R @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_subset_eq2
% 5.06/5.40 thf(fact_7606_infinite__int__iff__unbounded__le,axiom,
% 5.06/5.40 ! [S3: set_int] :
% 5.06/5.40 ( ( ~ ( finite_finite_int @ S3 ) )
% 5.06/5.40 = ( ! [M6: int] :
% 5.06/5.40 ? [N: int] :
% 5.06/5.40 ( ( ord_less_eq_int @ M6 @ ( abs_abs_int @ N ) )
% 5.06/5.40 & ( member_int @ N @ S3 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % infinite_int_iff_unbounded_le
% 5.06/5.40 thf(fact_7607_accp__subset,axiom,
% 5.06/5.40 ! [R1: product_prod_num_num > product_prod_num_num > $o,R22: product_prod_num_num > product_prod_num_num > $o] :
% 5.06/5.40 ( ( ord_le2556027599737686990_num_o @ R1 @ R22 )
% 5.06/5.40 => ( ord_le2239182809043710856_num_o @ ( accp_P3113834385874906142um_num @ R22 ) @ ( accp_P3113834385874906142um_num @ R1 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % accp_subset
% 5.06/5.40 thf(fact_7608_accp__subset,axiom,
% 5.06/5.40 ! [R1: product_prod_nat_nat > product_prod_nat_nat > $o,R22: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.06/5.40 ( ( ord_le5604493270027003598_nat_o @ R1 @ R22 )
% 5.06/5.40 => ( ord_le704812498762024988_nat_o @ ( accp_P4275260045618599050at_nat @ R22 ) @ ( accp_P4275260045618599050at_nat @ R1 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % accp_subset
% 5.06/5.40 thf(fact_7609_accp__subset,axiom,
% 5.06/5.40 ! [R1: product_prod_int_int > product_prod_int_int > $o,R22: product_prod_int_int > product_prod_int_int > $o] :
% 5.06/5.40 ( ( ord_le1598226405681992910_int_o @ R1 @ R22 )
% 5.06/5.40 => ( ord_le8369615600986905444_int_o @ ( accp_P1096762738010456898nt_int @ R22 ) @ ( accp_P1096762738010456898nt_int @ R1 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % accp_subset
% 5.06/5.40 thf(fact_7610_accp__subset,axiom,
% 5.06/5.40 ! [R1: list_nat > list_nat > $o,R22: list_nat > list_nat > $o] :
% 5.06/5.40 ( ( ord_le6558929396352911974_nat_o @ R1 @ R22 )
% 5.06/5.40 => ( ord_le1520216061033275535_nat_o @ ( accp_list_nat @ R22 ) @ ( accp_list_nat @ R1 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % accp_subset
% 5.06/5.40 thf(fact_7611_accp__subset,axiom,
% 5.06/5.40 ! [R1: nat > nat > $o,R22: nat > nat > $o] :
% 5.06/5.40 ( ( ord_le2646555220125990790_nat_o @ R1 @ R22 )
% 5.06/5.40 => ( ord_less_eq_nat_o @ ( accp_nat @ R22 ) @ ( accp_nat @ R1 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % accp_subset
% 5.06/5.40 thf(fact_7612_lessThan__iff,axiom,
% 5.06/5.40 ! [I2: set_nat,K: set_nat] :
% 5.06/5.40 ( ( member_set_nat @ I2 @ ( set_or890127255671739683et_nat @ K ) )
% 5.06/5.40 = ( ord_less_set_nat @ I2 @ K ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_iff
% 5.06/5.40 thf(fact_7613_lessThan__iff,axiom,
% 5.06/5.40 ! [I2: rat,K: rat] :
% 5.06/5.40 ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K ) )
% 5.06/5.40 = ( ord_less_rat @ I2 @ K ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_iff
% 5.06/5.40 thf(fact_7614_lessThan__iff,axiom,
% 5.06/5.40 ! [I2: num,K: num] :
% 5.06/5.40 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 5.06/5.40 = ( ord_less_num @ I2 @ K ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_iff
% 5.06/5.40 thf(fact_7615_lessThan__iff,axiom,
% 5.06/5.40 ! [I2: nat,K: nat] :
% 5.06/5.40 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 5.06/5.40 = ( ord_less_nat @ I2 @ K ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_iff
% 5.06/5.40 thf(fact_7616_lessThan__iff,axiom,
% 5.06/5.40 ! [I2: int,K: int] :
% 5.06/5.40 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 5.06/5.40 = ( ord_less_int @ I2 @ K ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_iff
% 5.06/5.40 thf(fact_7617_lessThan__iff,axiom,
% 5.06/5.40 ! [I2: real,K: real] :
% 5.06/5.40 ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K ) )
% 5.06/5.40 = ( ord_less_real @ I2 @ K ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_iff
% 5.06/5.40 thf(fact_7618_lessThan__iff,axiom,
% 5.06/5.40 ! [I2: $o,K: $o] :
% 5.06/5.40 ( ( member_o @ I2 @ ( set_ord_lessThan_o @ K ) )
% 5.06/5.40 = ( ord_less_o @ I2 @ K ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_iff
% 5.06/5.40 thf(fact_7619_summable__single,axiom,
% 5.06/5.40 ! [I2: nat,F: nat > complex] :
% 5.06/5.40 ( summable_complex
% 5.06/5.40 @ ^ [R5: nat] : ( if_complex @ ( R5 = I2 ) @ ( F @ R5 ) @ zero_zero_complex ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_single
% 5.06/5.40 thf(fact_7620_summable__single,axiom,
% 5.06/5.40 ! [I2: nat,F: nat > real] :
% 5.06/5.40 ( summable_real
% 5.06/5.40 @ ^ [R5: nat] : ( if_real @ ( R5 = I2 ) @ ( F @ R5 ) @ zero_zero_real ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_single
% 5.06/5.40 thf(fact_7621_summable__single,axiom,
% 5.06/5.40 ! [I2: nat,F: nat > nat] :
% 5.06/5.40 ( summable_nat
% 5.06/5.40 @ ^ [R5: nat] : ( if_nat @ ( R5 = I2 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_single
% 5.06/5.40 thf(fact_7622_summable__single,axiom,
% 5.06/5.40 ! [I2: nat,F: nat > int] :
% 5.06/5.40 ( summable_int
% 5.06/5.40 @ ^ [R5: nat] : ( if_int @ ( R5 = I2 ) @ ( F @ R5 ) @ zero_zero_int ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_single
% 5.06/5.40 thf(fact_7623_summable__zero,axiom,
% 5.06/5.40 ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : zero_zero_complex ) ).
% 5.06/5.40
% 5.06/5.40 % summable_zero
% 5.06/5.40 thf(fact_7624_summable__zero,axiom,
% 5.06/5.40 ( summable_real
% 5.06/5.40 @ ^ [N: nat] : zero_zero_real ) ).
% 5.06/5.40
% 5.06/5.40 % summable_zero
% 5.06/5.40 thf(fact_7625_summable__zero,axiom,
% 5.06/5.40 ( summable_nat
% 5.06/5.40 @ ^ [N: nat] : zero_zero_nat ) ).
% 5.06/5.40
% 5.06/5.40 % summable_zero
% 5.06/5.40 thf(fact_7626_summable__zero,axiom,
% 5.06/5.40 ( summable_int
% 5.06/5.40 @ ^ [N: nat] : zero_zero_int ) ).
% 5.06/5.40
% 5.06/5.40 % summable_zero
% 5.06/5.40 thf(fact_7627_summable__iff__shift,axiom,
% 5.06/5.40 ! [F: nat > real,K: nat] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.06/5.40 = ( summable_real @ F ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_iff_shift
% 5.06/5.40 thf(fact_7628_summable__iff__shift,axiom,
% 5.06/5.40 ! [F: nat > complex,K: nat] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.06/5.40 = ( summable_complex @ F ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_iff_shift
% 5.06/5.40 thf(fact_7629_lessThan__subset__iff,axiom,
% 5.06/5.40 ! [X: rat,Y: rat] :
% 5.06/5.40 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 5.06/5.40 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_subset_iff
% 5.06/5.40 thf(fact_7630_lessThan__subset__iff,axiom,
% 5.06/5.40 ! [X: num,Y: num] :
% 5.06/5.40 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 5.06/5.40 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_subset_iff
% 5.06/5.40 thf(fact_7631_lessThan__subset__iff,axiom,
% 5.06/5.40 ! [X: nat,Y: nat] :
% 5.06/5.40 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 5.06/5.40 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_subset_iff
% 5.06/5.40 thf(fact_7632_lessThan__subset__iff,axiom,
% 5.06/5.40 ! [X: int,Y: int] :
% 5.06/5.40 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 5.06/5.40 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_subset_iff
% 5.06/5.40 thf(fact_7633_lessThan__subset__iff,axiom,
% 5.06/5.40 ! [X: real,Y: real] :
% 5.06/5.40 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y ) )
% 5.06/5.40 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_subset_iff
% 5.06/5.40 thf(fact_7634_lessThan__subset__iff,axiom,
% 5.06/5.40 ! [X: $o,Y: $o] :
% 5.06/5.40 ( ( ord_less_eq_set_o @ ( set_ord_lessThan_o @ X ) @ ( set_ord_lessThan_o @ Y ) )
% 5.06/5.40 = ( ord_less_eq_o @ X @ Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_subset_iff
% 5.06/5.40 thf(fact_7635_summable__cmult__iff,axiom,
% 5.06/5.40 ! [C: complex,F: nat > complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 5.06/5.40 = ( ( C = zero_zero_complex )
% 5.06/5.40 | ( summable_complex @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_cmult_iff
% 5.06/5.40 thf(fact_7636_summable__cmult__iff,axiom,
% 5.06/5.40 ! [C: real,F: nat > real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 5.06/5.40 = ( ( C = zero_zero_real )
% 5.06/5.40 | ( summable_real @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_cmult_iff
% 5.06/5.40 thf(fact_7637_summable__divide__iff,axiom,
% 5.06/5.40 ! [F: nat > complex,C: complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 5.06/5.40 = ( ( C = zero_zero_complex )
% 5.06/5.40 | ( summable_complex @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_divide_iff
% 5.06/5.40 thf(fact_7638_summable__divide__iff,axiom,
% 5.06/5.40 ! [F: nat > real,C: real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 5.06/5.40 = ( ( C = zero_zero_real )
% 5.06/5.40 | ( summable_real @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_divide_iff
% 5.06/5.40 thf(fact_7639_summable__If__finite,axiom,
% 5.06/5.40 ! [P: nat > $o,F: nat > complex] :
% 5.06/5.40 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [R5: nat] : ( if_complex @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_complex ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_If_finite
% 5.06/5.40 thf(fact_7640_summable__If__finite,axiom,
% 5.06/5.40 ! [P: nat > $o,F: nat > real] :
% 5.06/5.40 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_If_finite
% 5.06/5.40 thf(fact_7641_summable__If__finite,axiom,
% 5.06/5.40 ! [P: nat > $o,F: nat > nat] :
% 5.06/5.40 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.40 => ( summable_nat
% 5.06/5.40 @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_If_finite
% 5.06/5.40 thf(fact_7642_summable__If__finite,axiom,
% 5.06/5.40 ! [P: nat > $o,F: nat > int] :
% 5.06/5.40 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.40 => ( summable_int
% 5.06/5.40 @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_If_finite
% 5.06/5.40 thf(fact_7643_summable__If__finite__set,axiom,
% 5.06/5.40 ! [A2: set_nat,F: nat > complex] :
% 5.06/5.40 ( ( finite_finite_nat @ A2 )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [R5: nat] : ( if_complex @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_complex ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_If_finite_set
% 5.06/5.40 thf(fact_7644_summable__If__finite__set,axiom,
% 5.06/5.40 ! [A2: set_nat,F: nat > real] :
% 5.06/5.40 ( ( finite_finite_nat @ A2 )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_real ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_If_finite_set
% 5.06/5.40 thf(fact_7645_summable__If__finite__set,axiom,
% 5.06/5.40 ! [A2: set_nat,F: nat > nat] :
% 5.06/5.40 ( ( finite_finite_nat @ A2 )
% 5.06/5.40 => ( summable_nat
% 5.06/5.40 @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_If_finite_set
% 5.06/5.40 thf(fact_7646_summable__If__finite__set,axiom,
% 5.06/5.40 ! [A2: set_nat,F: nat > int] :
% 5.06/5.40 ( ( finite_finite_nat @ A2 )
% 5.06/5.40 => ( summable_int
% 5.06/5.40 @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_int ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_If_finite_set
% 5.06/5.40 thf(fact_7647_sum_OlessThan__Suc,axiom,
% 5.06/5.40 ! [G: nat > rat,N2: nat] :
% 5.06/5.40 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.lessThan_Suc
% 5.06/5.40 thf(fact_7648_sum_OlessThan__Suc,axiom,
% 5.06/5.40 ! [G: nat > int,N2: nat] :
% 5.06/5.40 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.lessThan_Suc
% 5.06/5.40 thf(fact_7649_sum_OlessThan__Suc,axiom,
% 5.06/5.40 ! [G: nat > nat,N2: nat] :
% 5.06/5.40 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.lessThan_Suc
% 5.06/5.40 thf(fact_7650_sum_OlessThan__Suc,axiom,
% 5.06/5.40 ! [G: nat > real,N2: nat] :
% 5.06/5.40 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.lessThan_Suc
% 5.06/5.40 thf(fact_7651_summable__geometric__iff,axiom,
% 5.06/5.40 ! [C: real] :
% 5.06/5.40 ( ( summable_real @ ( power_power_real @ C ) )
% 5.06/5.40 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_geometric_iff
% 5.06/5.40 thf(fact_7652_summable__geometric__iff,axiom,
% 5.06/5.40 ! [C: complex] :
% 5.06/5.40 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.06/5.40 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_geometric_iff
% 5.06/5.40 thf(fact_7653_summable__norm__cancel,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) )
% 5.06/5.40 => ( summable_real @ F ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_norm_cancel
% 5.06/5.40 thf(fact_7654_summable__norm__cancel,axiom,
% 5.06/5.40 ! [F: nat > complex] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) )
% 5.06/5.40 => ( summable_complex @ F ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_norm_cancel
% 5.06/5.40 thf(fact_7655_summable__comparison__test,axiom,
% 5.06/5.40 ! [F: nat > real,G: nat > real] :
% 5.06/5.40 ( ? [N7: nat] :
% 5.06/5.40 ! [N3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.06/5.40 => ( ( summable_real @ G )
% 5.06/5.40 => ( summable_real @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_comparison_test
% 5.06/5.40 thf(fact_7656_summable__comparison__test,axiom,
% 5.06/5.40 ! [F: nat > complex,G: nat > real] :
% 5.06/5.40 ( ? [N7: nat] :
% 5.06/5.40 ! [N3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.06/5.40 => ( ( summable_real @ G )
% 5.06/5.40 => ( summable_complex @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_comparison_test
% 5.06/5.40 thf(fact_7657_summable__comparison__test_H,axiom,
% 5.06/5.40 ! [G: nat > real,N4: nat,F: nat > real] :
% 5.06/5.40 ( ( summable_real @ G )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.06/5.40 => ( summable_real @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_comparison_test'
% 5.06/5.40 thf(fact_7658_summable__comparison__test_H,axiom,
% 5.06/5.40 ! [G: nat > real,N4: nat,F: nat > complex] :
% 5.06/5.40 ( ( summable_real @ G )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.06/5.40 => ( summable_complex @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_comparison_test'
% 5.06/5.40 thf(fact_7659_summable__const__iff,axiom,
% 5.06/5.40 ! [C: complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [Uu3: nat] : C )
% 5.06/5.40 = ( C = zero_zero_complex ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_const_iff
% 5.06/5.40 thf(fact_7660_summable__const__iff,axiom,
% 5.06/5.40 ! [C: real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [Uu3: nat] : C )
% 5.06/5.40 = ( C = zero_zero_real ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_const_iff
% 5.06/5.40 thf(fact_7661_summable__mult2,axiom,
% 5.06/5.40 ! [F: nat > complex,C: complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_mult2
% 5.06/5.40 thf(fact_7662_summable__mult2,axiom,
% 5.06/5.40 ! [F: nat > real,C: real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_mult2
% 5.06/5.40 thf(fact_7663_summable__mult,axiom,
% 5.06/5.40 ! [F: nat > complex,C: complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_mult
% 5.06/5.40 thf(fact_7664_summable__mult,axiom,
% 5.06/5.40 ! [F: nat > real,C: real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_mult
% 5.06/5.40 thf(fact_7665_summable__add,axiom,
% 5.06/5.40 ! [F: nat > complex,G: nat > complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( summable_complex @ G )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( plus_plus_complex @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_add
% 5.06/5.40 thf(fact_7666_summable__add,axiom,
% 5.06/5.40 ! [F: nat > real,G: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( summable_real @ G )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_add
% 5.06/5.40 thf(fact_7667_summable__add,axiom,
% 5.06/5.40 ! [F: nat > nat,G: nat > nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ( summable_nat @ G )
% 5.06/5.40 => ( summable_nat
% 5.06/5.40 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_add
% 5.06/5.40 thf(fact_7668_summable__add,axiom,
% 5.06/5.40 ! [F: nat > int,G: nat > int] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ( summable_int @ G )
% 5.06/5.40 => ( summable_int
% 5.06/5.40 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_add
% 5.06/5.40 thf(fact_7669_summable__diff,axiom,
% 5.06/5.40 ! [F: nat > complex,G: nat > complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( summable_complex @ G )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( minus_minus_complex @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_diff
% 5.06/5.40 thf(fact_7670_summable__diff,axiom,
% 5.06/5.40 ! [F: nat > real,G: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( summable_real @ G )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_diff
% 5.06/5.40 thf(fact_7671_summable__divide,axiom,
% 5.06/5.40 ! [F: nat > complex,C: complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_divide
% 5.06/5.40 thf(fact_7672_summable__divide,axiom,
% 5.06/5.40 ! [F: nat > real,C: real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_divide
% 5.06/5.40 thf(fact_7673_summable__Suc__iff,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 5.06/5.40 = ( summable_real @ F ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_Suc_iff
% 5.06/5.40 thf(fact_7674_summable__Suc__iff,axiom,
% 5.06/5.40 ! [F: nat > complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 5.06/5.40 = ( summable_complex @ F ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_Suc_iff
% 5.06/5.40 thf(fact_7675_summable__minus,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( uminus_uminus_real @ ( F @ N ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_minus
% 5.06/5.40 thf(fact_7676_summable__minus,axiom,
% 5.06/5.40 ! [F: nat > complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( uminus1482373934393186551omplex @ ( F @ N ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_minus
% 5.06/5.40 thf(fact_7677_summable__minus__iff,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( uminus_uminus_real @ ( F @ N ) ) )
% 5.06/5.40 = ( summable_real @ F ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_minus_iff
% 5.06/5.40 thf(fact_7678_summable__minus__iff,axiom,
% 5.06/5.40 ! [F: nat > complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( uminus1482373934393186551omplex @ ( F @ N ) ) )
% 5.06/5.40 = ( summable_complex @ F ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_minus_iff
% 5.06/5.40 thf(fact_7679_summable__sum,axiom,
% 5.06/5.40 ! [I6: set_complex,F: complex > nat > real] :
% 5.06/5.40 ( ! [I3: complex] :
% 5.06/5.40 ( ( member_complex @ I3 @ I6 )
% 5.06/5.40 => ( summable_real @ ( F @ I3 ) ) )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups5808333547571424918x_real
% 5.06/5.40 @ ^ [I5: complex] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_sum
% 5.06/5.40 thf(fact_7680_summable__sum,axiom,
% 5.06/5.40 ! [I6: set_real,F: real > nat > real] :
% 5.06/5.40 ( ! [I3: real] :
% 5.06/5.40 ( ( member_real @ I3 @ I6 )
% 5.06/5.40 => ( summable_real @ ( F @ I3 ) ) )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups8097168146408367636l_real
% 5.06/5.40 @ ^ [I5: real] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_sum
% 5.06/5.40 thf(fact_7681_summable__sum,axiom,
% 5.06/5.40 ! [I6: set_int,F: int > nat > real] :
% 5.06/5.40 ( ! [I3: int] :
% 5.06/5.40 ( ( member_int @ I3 @ I6 )
% 5.06/5.40 => ( summable_real @ ( F @ I3 ) ) )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups8778361861064173332t_real
% 5.06/5.40 @ ^ [I5: int] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_sum
% 5.06/5.40 thf(fact_7682_summable__sum,axiom,
% 5.06/5.40 ! [I6: set_real,F: real > nat > complex] :
% 5.06/5.40 ( ! [I3: real] :
% 5.06/5.40 ( ( member_real @ I3 @ I6 )
% 5.06/5.40 => ( summable_complex @ ( F @ I3 ) ) )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups5754745047067104278omplex
% 5.06/5.40 @ ^ [I5: real] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_sum
% 5.06/5.40 thf(fact_7683_summable__sum,axiom,
% 5.06/5.40 ! [I6: set_nat,F: nat > nat > complex] :
% 5.06/5.40 ( ! [I3: nat] :
% 5.06/5.40 ( ( member_nat @ I3 @ I6 )
% 5.06/5.40 => ( summable_complex @ ( F @ I3 ) ) )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [I5: nat] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_sum
% 5.06/5.40 thf(fact_7684_summable__sum,axiom,
% 5.06/5.40 ! [I6: set_int,F: int > nat > complex] :
% 5.06/5.40 ( ! [I3: int] :
% 5.06/5.40 ( ( member_int @ I3 @ I6 )
% 5.06/5.40 => ( summable_complex @ ( F @ I3 ) ) )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups3049146728041665814omplex
% 5.06/5.40 @ ^ [I5: int] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_sum
% 5.06/5.40 thf(fact_7685_summable__sum,axiom,
% 5.06/5.40 ! [I6: set_int,F: int > nat > int] :
% 5.06/5.40 ( ! [I3: int] :
% 5.06/5.40 ( ( member_int @ I3 @ I6 )
% 5.06/5.40 => ( summable_int @ ( F @ I3 ) ) )
% 5.06/5.40 => ( summable_int
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups4538972089207619220nt_int
% 5.06/5.40 @ ^ [I5: int] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_sum
% 5.06/5.40 thf(fact_7686_summable__sum,axiom,
% 5.06/5.40 ! [I6: set_complex,F: complex > nat > complex] :
% 5.06/5.40 ( ! [I3: complex] :
% 5.06/5.40 ( ( member_complex @ I3 @ I6 )
% 5.06/5.40 => ( summable_complex @ ( F @ I3 ) ) )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups7754918857620584856omplex
% 5.06/5.40 @ ^ [I5: complex] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_sum
% 5.06/5.40 thf(fact_7687_summable__sum,axiom,
% 5.06/5.40 ! [I6: set_nat,F: nat > nat > nat] :
% 5.06/5.40 ( ! [I3: nat] :
% 5.06/5.40 ( ( member_nat @ I3 @ I6 )
% 5.06/5.40 => ( summable_nat @ ( F @ I3 ) ) )
% 5.06/5.40 => ( summable_nat
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups3542108847815614940at_nat
% 5.06/5.40 @ ^ [I5: nat] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_sum
% 5.06/5.40 thf(fact_7688_summable__sum,axiom,
% 5.06/5.40 ! [I6: set_nat,F: nat > nat > real] :
% 5.06/5.40 ( ! [I3: nat] :
% 5.06/5.40 ( ( member_nat @ I3 @ I6 )
% 5.06/5.40 => ( summable_real @ ( F @ I3 ) ) )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_sum
% 5.06/5.40 thf(fact_7689_summable__ignore__initial__segment,axiom,
% 5.06/5.40 ! [F: nat > real,K: nat] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_ignore_initial_segment
% 5.06/5.40 thf(fact_7690_summable__ignore__initial__segment,axiom,
% 5.06/5.40 ! [F: nat > complex,K: nat] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_ignore_initial_segment
% 5.06/5.40 thf(fact_7691_suminf__le__const,axiom,
% 5.06/5.40 ! [F: nat > int,X: int] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.06/5.40 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_le_const
% 5.06/5.40 thf(fact_7692_suminf__le__const,axiom,
% 5.06/5.40 ! [F: nat > nat,X: nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.06/5.40 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_le_const
% 5.06/5.40 thf(fact_7693_suminf__le__const,axiom,
% 5.06/5.40 ! [F: nat > real,X: real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.06/5.40 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_le_const
% 5.06/5.40 thf(fact_7694_summable__rabs__cancel,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) )
% 5.06/5.40 => ( summable_real @ F ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_rabs_cancel
% 5.06/5.40 thf(fact_7695_lessThan__def,axiom,
% 5.06/5.40 ( set_or890127255671739683et_nat
% 5.06/5.40 = ( ^ [U2: set_nat] :
% 5.06/5.40 ( collect_set_nat
% 5.06/5.40 @ ^ [X2: set_nat] : ( ord_less_set_nat @ X2 @ U2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_def
% 5.06/5.40 thf(fact_7696_lessThan__def,axiom,
% 5.06/5.40 ( set_ord_lessThan_rat
% 5.06/5.40 = ( ^ [U2: rat] :
% 5.06/5.40 ( collect_rat
% 5.06/5.40 @ ^ [X2: rat] : ( ord_less_rat @ X2 @ U2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_def
% 5.06/5.40 thf(fact_7697_lessThan__def,axiom,
% 5.06/5.40 ( set_ord_lessThan_num
% 5.06/5.40 = ( ^ [U2: num] :
% 5.06/5.40 ( collect_num
% 5.06/5.40 @ ^ [X2: num] : ( ord_less_num @ X2 @ U2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_def
% 5.06/5.40 thf(fact_7698_lessThan__def,axiom,
% 5.06/5.40 ( set_ord_lessThan_nat
% 5.06/5.40 = ( ^ [U2: nat] :
% 5.06/5.40 ( collect_nat
% 5.06/5.40 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ U2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_def
% 5.06/5.40 thf(fact_7699_lessThan__def,axiom,
% 5.06/5.40 ( set_ord_lessThan_int
% 5.06/5.40 = ( ^ [U2: int] :
% 5.06/5.40 ( collect_int
% 5.06/5.40 @ ^ [X2: int] : ( ord_less_int @ X2 @ U2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_def
% 5.06/5.40 thf(fact_7700_lessThan__def,axiom,
% 5.06/5.40 ( set_or5984915006950818249n_real
% 5.06/5.40 = ( ^ [U2: real] :
% 5.06/5.40 ( collect_real
% 5.06/5.40 @ ^ [X2: real] : ( ord_less_real @ X2 @ U2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_def
% 5.06/5.40 thf(fact_7701_lessThan__def,axiom,
% 5.06/5.40 ( set_ord_lessThan_o
% 5.06/5.40 = ( ^ [U2: $o] :
% 5.06/5.40 ( collect_o
% 5.06/5.40 @ ^ [X2: $o] : ( ord_less_o @ X2 @ U2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_def
% 5.06/5.40 thf(fact_7702_summableI__nonneg__bounded,axiom,
% 5.06/5.40 ! [F: nat > int,X: int] :
% 5.06/5.40 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.06/5.40 => ( summable_int @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summableI_nonneg_bounded
% 5.06/5.40 thf(fact_7703_summableI__nonneg__bounded,axiom,
% 5.06/5.40 ! [F: nat > nat,X: nat] :
% 5.06/5.40 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.06/5.40 => ( summable_nat @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summableI_nonneg_bounded
% 5.06/5.40 thf(fact_7704_summableI__nonneg__bounded,axiom,
% 5.06/5.40 ! [F: nat > real,X: real] :
% 5.06/5.40 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X )
% 5.06/5.40 => ( summable_real @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summableI_nonneg_bounded
% 5.06/5.40 thf(fact_7705_finite__nat__iff__bounded,axiom,
% 5.06/5.40 ( finite_finite_nat
% 5.06/5.40 = ( ^ [S5: set_nat] :
% 5.06/5.40 ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % finite_nat_iff_bounded
% 5.06/5.40 thf(fact_7706_finite__nat__bounded,axiom,
% 5.06/5.40 ! [S3: set_nat] :
% 5.06/5.40 ( ( finite_finite_nat @ S3 )
% 5.06/5.40 => ? [K2: nat] : ( ord_less_eq_set_nat @ S3 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % finite_nat_bounded
% 5.06/5.40 thf(fact_7707_powser__insidea,axiom,
% 5.06/5.40 ! [F: nat > real,X: real,Z: real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X @ N ) ) )
% 5.06/5.40 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_insidea
% 5.06/5.40 thf(fact_7708_powser__insidea,axiom,
% 5.06/5.40 ! [F: nat > complex,X: complex,Z: complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X @ N ) ) )
% 5.06/5.40 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_insidea
% 5.06/5.40 thf(fact_7709_suminf__le,axiom,
% 5.06/5.40 ! [F: nat > real,G: nat > real] :
% 5.06/5.40 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.06/5.40 => ( ( summable_real @ F )
% 5.06/5.40 => ( ( summable_real @ G )
% 5.06/5.40 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_le
% 5.06/5.40 thf(fact_7710_suminf__le,axiom,
% 5.06/5.40 ! [F: nat > nat,G: nat > nat] :
% 5.06/5.40 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.06/5.40 => ( ( summable_nat @ F )
% 5.06/5.40 => ( ( summable_nat @ G )
% 5.06/5.40 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_le
% 5.06/5.40 thf(fact_7711_suminf__le,axiom,
% 5.06/5.40 ! [F: nat > int,G: nat > int] :
% 5.06/5.40 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.06/5.40 => ( ( summable_int @ F )
% 5.06/5.40 => ( ( summable_int @ G )
% 5.06/5.40 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_le
% 5.06/5.40 thf(fact_7712_suminf__split__initial__segment,axiom,
% 5.06/5.40 ! [F: nat > complex,K: nat] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( suminf_complex @ F )
% 5.06/5.40 = ( plus_plus_complex
% 5.06/5.40 @ ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.06/5.40 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_split_initial_segment
% 5.06/5.40 thf(fact_7713_suminf__split__initial__segment,axiom,
% 5.06/5.40 ! [F: nat > real,K: nat] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( suminf_real @ F )
% 5.06/5.40 = ( plus_plus_real
% 5.06/5.40 @ ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.06/5.40 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_split_initial_segment
% 5.06/5.40 thf(fact_7714_suminf__minus__initial__segment,axiom,
% 5.06/5.40 ! [F: nat > complex,K: nat] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.06/5.40 = ( minus_minus_complex @ ( suminf_complex @ F ) @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_minus_initial_segment
% 5.06/5.40 thf(fact_7715_suminf__minus__initial__segment,axiom,
% 5.06/5.40 ! [F: nat > real,K: nat] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.06/5.40 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_minus_initial_segment
% 5.06/5.40 thf(fact_7716_lessThan__strict__subset__iff,axiom,
% 5.06/5.40 ! [M: rat,N2: rat] :
% 5.06/5.40 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N2 ) )
% 5.06/5.40 = ( ord_less_rat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_strict_subset_iff
% 5.06/5.40 thf(fact_7717_lessThan__strict__subset__iff,axiom,
% 5.06/5.40 ! [M: num,N2: num] :
% 5.06/5.40 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 5.06/5.40 = ( ord_less_num @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_strict_subset_iff
% 5.06/5.40 thf(fact_7718_lessThan__strict__subset__iff,axiom,
% 5.06/5.40 ! [M: nat,N2: nat] :
% 5.06/5.40 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_strict_subset_iff
% 5.06/5.40 thf(fact_7719_lessThan__strict__subset__iff,axiom,
% 5.06/5.40 ! [M: int,N2: int] :
% 5.06/5.40 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 5.06/5.40 = ( ord_less_int @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_strict_subset_iff
% 5.06/5.40 thf(fact_7720_lessThan__strict__subset__iff,axiom,
% 5.06/5.40 ! [M: real,N2: real] :
% 5.06/5.40 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N2 ) )
% 5.06/5.40 = ( ord_less_real @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_strict_subset_iff
% 5.06/5.40 thf(fact_7721_lessThan__strict__subset__iff,axiom,
% 5.06/5.40 ! [M: $o,N2: $o] :
% 5.06/5.40 ( ( ord_less_set_o @ ( set_ord_lessThan_o @ M ) @ ( set_ord_lessThan_o @ N2 ) )
% 5.06/5.40 = ( ord_less_o @ M @ N2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % lessThan_strict_subset_iff
% 5.06/5.40 thf(fact_7722_summable__mult__D,axiom,
% 5.06/5.40 ! [C: complex,F: nat > complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 5.06/5.40 => ( ( C != zero_zero_complex )
% 5.06/5.40 => ( summable_complex @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_mult_D
% 5.06/5.40 thf(fact_7723_summable__mult__D,axiom,
% 5.06/5.40 ! [C: real,F: nat > real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 5.06/5.40 => ( ( C != zero_zero_real )
% 5.06/5.40 => ( summable_real @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_mult_D
% 5.06/5.40 thf(fact_7724_summable__zero__power,axiom,
% 5.06/5.40 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.06/5.40
% 5.06/5.40 % summable_zero_power
% 5.06/5.40 thf(fact_7725_summable__zero__power,axiom,
% 5.06/5.40 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.06/5.40
% 5.06/5.40 % summable_zero_power
% 5.06/5.40 thf(fact_7726_summable__zero__power,axiom,
% 5.06/5.40 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.06/5.40
% 5.06/5.40 % summable_zero_power
% 5.06/5.40 thf(fact_7727_pi__ge__zero,axiom,
% 5.06/5.40 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.06/5.40
% 5.06/5.40 % pi_ge_zero
% 5.06/5.40 thf(fact_7728_sum__less__suminf,axiom,
% 5.06/5.40 ! [F: nat > int,N2: nat] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ! [M2: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M2 )
% 5.06/5.40 => ( ord_less_int @ zero_zero_int @ ( F @ M2 ) ) )
% 5.06/5.40 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_less_suminf
% 5.06/5.40 thf(fact_7729_sum__less__suminf,axiom,
% 5.06/5.40 ! [F: nat > nat,N2: nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ! [M2: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M2 )
% 5.06/5.40 => ( ord_less_nat @ zero_zero_nat @ ( F @ M2 ) ) )
% 5.06/5.40 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_less_suminf
% 5.06/5.40 thf(fact_7730_sum__less__suminf,axiom,
% 5.06/5.40 ! [F: nat > real,N2: nat] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ! [M2: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M2 )
% 5.06/5.40 => ( ord_less_real @ zero_zero_real @ ( F @ M2 ) ) )
% 5.06/5.40 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_less_suminf
% 5.06/5.40 thf(fact_7731_suminf__mult2,axiom,
% 5.06/5.40 ! [F: nat > complex,C: complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( times_times_complex @ ( suminf_complex @ F ) @ C )
% 5.06/5.40 = ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_mult2
% 5.06/5.40 thf(fact_7732_suminf__mult2,axiom,
% 5.06/5.40 ! [F: nat > real,C: real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 5.06/5.40 = ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_mult2
% 5.06/5.40 thf(fact_7733_suminf__mult,axiom,
% 5.06/5.40 ! [F: nat > complex,C: complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) ) )
% 5.06/5.40 = ( times_times_complex @ C @ ( suminf_complex @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_mult
% 5.06/5.40 thf(fact_7734_suminf__mult,axiom,
% 5.06/5.40 ! [F: nat > real,C: real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) ) )
% 5.06/5.40 = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_mult
% 5.06/5.40 thf(fact_7735_suminf__add,axiom,
% 5.06/5.40 ! [F: nat > complex,G: nat > complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( summable_complex @ G )
% 5.06/5.40 => ( ( plus_plus_complex @ ( suminf_complex @ F ) @ ( suminf_complex @ G ) )
% 5.06/5.40 = ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( plus_plus_complex @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_add
% 5.06/5.40 thf(fact_7736_suminf__add,axiom,
% 5.06/5.40 ! [F: nat > real,G: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( summable_real @ G )
% 5.06/5.40 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.06/5.40 = ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_add
% 5.06/5.40 thf(fact_7737_suminf__add,axiom,
% 5.06/5.40 ! [F: nat > nat,G: nat > nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ( summable_nat @ G )
% 5.06/5.40 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.06/5.40 = ( suminf_nat
% 5.06/5.40 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_add
% 5.06/5.40 thf(fact_7738_suminf__add,axiom,
% 5.06/5.40 ! [F: nat > int,G: nat > int] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ( summable_int @ G )
% 5.06/5.40 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.06/5.40 = ( suminf_int
% 5.06/5.40 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_add
% 5.06/5.40 thf(fact_7739_suminf__diff,axiom,
% 5.06/5.40 ! [F: nat > complex,G: nat > complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( summable_complex @ G )
% 5.06/5.40 => ( ( minus_minus_complex @ ( suminf_complex @ F ) @ ( suminf_complex @ G ) )
% 5.06/5.40 = ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( minus_minus_complex @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_diff
% 5.06/5.40 thf(fact_7740_suminf__diff,axiom,
% 5.06/5.40 ! [F: nat > real,G: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( summable_real @ G )
% 5.06/5.40 => ( ( minus_minus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.06/5.40 = ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_diff
% 5.06/5.40 thf(fact_7741_suminf__divide,axiom,
% 5.06/5.40 ! [F: nat > complex,C: complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 5.06/5.40 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_divide
% 5.06/5.40 thf(fact_7742_suminf__divide,axiom,
% 5.06/5.40 ! [F: nat > real,C: real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 5.06/5.40 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_divide
% 5.06/5.40 thf(fact_7743_suminf__minus,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( uminus_uminus_real @ ( F @ N ) ) )
% 5.06/5.40 = ( uminus_uminus_real @ ( suminf_real @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_minus
% 5.06/5.40 thf(fact_7744_suminf__minus,axiom,
% 5.06/5.40 ! [F: nat > complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( uminus1482373934393186551omplex @ ( F @ N ) ) )
% 5.06/5.40 = ( uminus1482373934393186551omplex @ ( suminf_complex @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_minus
% 5.06/5.40 thf(fact_7745_suminf__sum,axiom,
% 5.06/5.40 ! [I6: set_complex,F: complex > nat > real] :
% 5.06/5.40 ( ! [I3: complex] :
% 5.06/5.40 ( ( member_complex @ I3 @ I6 )
% 5.06/5.40 => ( summable_real @ ( F @ I3 ) ) )
% 5.06/5.40 => ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups5808333547571424918x_real
% 5.06/5.40 @ ^ [I5: complex] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) )
% 5.06/5.40 = ( groups5808333547571424918x_real
% 5.06/5.40 @ ^ [I5: complex] : ( suminf_real @ ( F @ I5 ) )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_sum
% 5.06/5.40 thf(fact_7746_suminf__sum,axiom,
% 5.06/5.40 ! [I6: set_real,F: real > nat > real] :
% 5.06/5.40 ( ! [I3: real] :
% 5.06/5.40 ( ( member_real @ I3 @ I6 )
% 5.06/5.40 => ( summable_real @ ( F @ I3 ) ) )
% 5.06/5.40 => ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups8097168146408367636l_real
% 5.06/5.40 @ ^ [I5: real] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) )
% 5.06/5.40 = ( groups8097168146408367636l_real
% 5.06/5.40 @ ^ [I5: real] : ( suminf_real @ ( F @ I5 ) )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_sum
% 5.06/5.40 thf(fact_7747_suminf__sum,axiom,
% 5.06/5.40 ! [I6: set_int,F: int > nat > real] :
% 5.06/5.40 ( ! [I3: int] :
% 5.06/5.40 ( ( member_int @ I3 @ I6 )
% 5.06/5.40 => ( summable_real @ ( F @ I3 ) ) )
% 5.06/5.40 => ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups8778361861064173332t_real
% 5.06/5.40 @ ^ [I5: int] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) )
% 5.06/5.40 = ( groups8778361861064173332t_real
% 5.06/5.40 @ ^ [I5: int] : ( suminf_real @ ( F @ I5 ) )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_sum
% 5.06/5.40 thf(fact_7748_suminf__sum,axiom,
% 5.06/5.40 ! [I6: set_real,F: real > nat > complex] :
% 5.06/5.40 ( ! [I3: real] :
% 5.06/5.40 ( ( member_real @ I3 @ I6 )
% 5.06/5.40 => ( summable_complex @ ( F @ I3 ) ) )
% 5.06/5.40 => ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups5754745047067104278omplex
% 5.06/5.40 @ ^ [I5: real] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) )
% 5.06/5.40 = ( groups5754745047067104278omplex
% 5.06/5.40 @ ^ [I5: real] : ( suminf_complex @ ( F @ I5 ) )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_sum
% 5.06/5.40 thf(fact_7749_suminf__sum,axiom,
% 5.06/5.40 ! [I6: set_nat,F: nat > nat > complex] :
% 5.06/5.40 ( ! [I3: nat] :
% 5.06/5.40 ( ( member_nat @ I3 @ I6 )
% 5.06/5.40 => ( summable_complex @ ( F @ I3 ) ) )
% 5.06/5.40 => ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [I5: nat] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) )
% 5.06/5.40 = ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [I5: nat] : ( suminf_complex @ ( F @ I5 ) )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_sum
% 5.06/5.40 thf(fact_7750_suminf__sum,axiom,
% 5.06/5.40 ! [I6: set_int,F: int > nat > complex] :
% 5.06/5.40 ( ! [I3: int] :
% 5.06/5.40 ( ( member_int @ I3 @ I6 )
% 5.06/5.40 => ( summable_complex @ ( F @ I3 ) ) )
% 5.06/5.40 => ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups3049146728041665814omplex
% 5.06/5.40 @ ^ [I5: int] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) )
% 5.06/5.40 = ( groups3049146728041665814omplex
% 5.06/5.40 @ ^ [I5: int] : ( suminf_complex @ ( F @ I5 ) )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_sum
% 5.06/5.40 thf(fact_7751_suminf__sum,axiom,
% 5.06/5.40 ! [I6: set_int,F: int > nat > int] :
% 5.06/5.40 ( ! [I3: int] :
% 5.06/5.40 ( ( member_int @ I3 @ I6 )
% 5.06/5.40 => ( summable_int @ ( F @ I3 ) ) )
% 5.06/5.40 => ( ( suminf_int
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups4538972089207619220nt_int
% 5.06/5.40 @ ^ [I5: int] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) )
% 5.06/5.40 = ( groups4538972089207619220nt_int
% 5.06/5.40 @ ^ [I5: int] : ( suminf_int @ ( F @ I5 ) )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_sum
% 5.06/5.40 thf(fact_7752_suminf__sum,axiom,
% 5.06/5.40 ! [I6: set_complex,F: complex > nat > complex] :
% 5.06/5.40 ( ! [I3: complex] :
% 5.06/5.40 ( ( member_complex @ I3 @ I6 )
% 5.06/5.40 => ( summable_complex @ ( F @ I3 ) ) )
% 5.06/5.40 => ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups7754918857620584856omplex
% 5.06/5.40 @ ^ [I5: complex] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) )
% 5.06/5.40 = ( groups7754918857620584856omplex
% 5.06/5.40 @ ^ [I5: complex] : ( suminf_complex @ ( F @ I5 ) )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_sum
% 5.06/5.40 thf(fact_7753_suminf__sum,axiom,
% 5.06/5.40 ! [I6: set_nat,F: nat > nat > nat] :
% 5.06/5.40 ( ! [I3: nat] :
% 5.06/5.40 ( ( member_nat @ I3 @ I6 )
% 5.06/5.40 => ( summable_nat @ ( F @ I3 ) ) )
% 5.06/5.40 => ( ( suminf_nat
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups3542108847815614940at_nat
% 5.06/5.40 @ ^ [I5: nat] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) )
% 5.06/5.40 = ( groups3542108847815614940at_nat
% 5.06/5.40 @ ^ [I5: nat] : ( suminf_nat @ ( F @ I5 ) )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_sum
% 5.06/5.40 thf(fact_7754_suminf__sum,axiom,
% 5.06/5.40 ! [I6: set_nat,F: nat > nat > real] :
% 5.06/5.40 ( ! [I3: nat] :
% 5.06/5.40 ( ( member_nat @ I3 @ I6 )
% 5.06/5.40 => ( summable_real @ ( F @ I3 ) ) )
% 5.06/5.40 => ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] :
% 5.06/5.40 ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( F @ I5 @ N )
% 5.06/5.40 @ I6 ) )
% 5.06/5.40 = ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( suminf_real @ ( F @ I5 ) )
% 5.06/5.40 @ I6 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_sum
% 5.06/5.40 thf(fact_7755_sum__less__suminf2,axiom,
% 5.06/5.40 ! [F: nat > int,N2: nat,I2: nat] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ! [M2: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M2 )
% 5.06/5.40 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M2 ) ) )
% 5.06/5.40 => ( ( ord_less_eq_nat @ N2 @ I2 )
% 5.06/5.40 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.06/5.40 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_less_suminf2
% 5.06/5.40 thf(fact_7756_sum__less__suminf2,axiom,
% 5.06/5.40 ! [F: nat > nat,N2: nat,I2: nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ! [M2: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M2 )
% 5.06/5.40 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M2 ) ) )
% 5.06/5.40 => ( ( ord_less_eq_nat @ N2 @ I2 )
% 5.06/5.40 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.06/5.40 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_less_suminf2
% 5.06/5.40 thf(fact_7757_sum__less__suminf2,axiom,
% 5.06/5.40 ! [F: nat > real,N2: nat,I2: nat] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ! [M2: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N2 @ M2 )
% 5.06/5.40 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M2 ) ) )
% 5.06/5.40 => ( ( ord_less_eq_nat @ N2 @ I2 )
% 5.06/5.40 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.06/5.40 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_less_suminf2
% 5.06/5.40 thf(fact_7758_suminf__eq__zero__iff,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.06/5.40 => ( ( ( suminf_real @ F )
% 5.06/5.40 = zero_zero_real )
% 5.06/5.40 = ( ! [N: nat] :
% 5.06/5.40 ( ( F @ N )
% 5.06/5.40 = zero_zero_real ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_eq_zero_iff
% 5.06/5.40 thf(fact_7759_suminf__eq__zero__iff,axiom,
% 5.06/5.40 ! [F: nat > nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.06/5.40 => ( ( ( suminf_nat @ F )
% 5.06/5.40 = zero_zero_nat )
% 5.06/5.40 = ( ! [N: nat] :
% 5.06/5.40 ( ( F @ N )
% 5.06/5.40 = zero_zero_nat ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_eq_zero_iff
% 5.06/5.40 thf(fact_7760_suminf__eq__zero__iff,axiom,
% 5.06/5.40 ! [F: nat > int] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.06/5.40 => ( ( ( suminf_int @ F )
% 5.06/5.40 = zero_zero_int )
% 5.06/5.40 = ( ! [N: nat] :
% 5.06/5.40 ( ( F @ N )
% 5.06/5.40 = zero_zero_int ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_eq_zero_iff
% 5.06/5.40 thf(fact_7761_suminf__nonneg,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.06/5.40 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_nonneg
% 5.06/5.40 thf(fact_7762_suminf__nonneg,axiom,
% 5.06/5.40 ! [F: nat > nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.06/5.40 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_nonneg
% 5.06/5.40 thf(fact_7763_suminf__nonneg,axiom,
% 5.06/5.40 ! [F: nat > int] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.06/5.40 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_nonneg
% 5.06/5.40 thf(fact_7764_suminf__pos,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 5.06/5.40 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_pos
% 5.06/5.40 thf(fact_7765_suminf__pos,axiom,
% 5.06/5.40 ! [F: nat > nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.06/5.40 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_pos
% 5.06/5.40 thf(fact_7766_suminf__pos,axiom,
% 5.06/5.40 ! [F: nat > int] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 5.06/5.40 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_pos
% 5.06/5.40 thf(fact_7767_summable__0__powser,axiom,
% 5.06/5.40 ! [F: nat > complex] :
% 5.06/5.40 ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_0_powser
% 5.06/5.40 thf(fact_7768_summable__0__powser,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_0_powser
% 5.06/5.40 thf(fact_7769_summable__zero__power_H,axiom,
% 5.06/5.40 ! [F: nat > complex] :
% 5.06/5.40 ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_zero_power'
% 5.06/5.40 thf(fact_7770_summable__zero__power_H,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_zero_power'
% 5.06/5.40 thf(fact_7771_summable__zero__power_H,axiom,
% 5.06/5.40 ! [F: nat > int] :
% 5.06/5.40 ( summable_int
% 5.06/5.40 @ ^ [N: nat] : ( times_times_int @ ( F @ N ) @ ( power_power_int @ zero_zero_int @ N ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_zero_power'
% 5.06/5.40 thf(fact_7772_powser__split__head_I3_J,axiom,
% 5.06/5.40 ! [F: nat > complex,Z: complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_split_head(3)
% 5.06/5.40 thf(fact_7773_powser__split__head_I3_J,axiom,
% 5.06/5.40 ! [F: nat > real,Z: real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_split_head(3)
% 5.06/5.40 thf(fact_7774_summable__powser__split__head,axiom,
% 5.06/5.40 ! [F: nat > complex,Z: complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.06/5.40 = ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_powser_split_head
% 5.06/5.40 thf(fact_7775_summable__powser__split__head,axiom,
% 5.06/5.40 ! [F: nat > real,Z: real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.06/5.40 = ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_powser_split_head
% 5.06/5.40 thf(fact_7776_summable__powser__ignore__initial__segment,axiom,
% 5.06/5.40 ! [F: nat > complex,M: nat,Z: complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.06/5.40 = ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_powser_ignore_initial_segment
% 5.06/5.40 thf(fact_7777_summable__powser__ignore__initial__segment,axiom,
% 5.06/5.40 ! [F: nat > real,M: nat,Z: real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.06/5.40 = ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_powser_ignore_initial_segment
% 5.06/5.40 thf(fact_7778_summable__norm__comparison__test,axiom,
% 5.06/5.40 ! [F: nat > complex,G: nat > real] :
% 5.06/5.40 ( ? [N7: nat] :
% 5.06/5.40 ! [N3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.06/5.40 => ( ( summable_real @ G )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_norm_comparison_test
% 5.06/5.40 thf(fact_7779_summable__rabs__comparison__test,axiom,
% 5.06/5.40 ! [F: nat > real,G: nat > real] :
% 5.06/5.40 ( ? [N7: nat] :
% 5.06/5.40 ! [N3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.06/5.40 => ( ( summable_real @ G )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_rabs_comparison_test
% 5.06/5.40 thf(fact_7780_sum_Onat__diff__reindex,axiom,
% 5.06/5.40 ! [G: nat > nat,N2: nat] :
% 5.06/5.40 ( ( groups3542108847815614940at_nat
% 5.06/5.40 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.nat_diff_reindex
% 5.06/5.40 thf(fact_7781_sum_Onat__diff__reindex,axiom,
% 5.06/5.40 ! [G: nat > real,N2: nat] :
% 5.06/5.40 ( ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.nat_diff_reindex
% 5.06/5.40 thf(fact_7782_summable__rabs,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) )
% 5.06/5.40 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.06/5.40 @ ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_rabs
% 5.06/5.40 thf(fact_7783_sum__diff__distrib,axiom,
% 5.06/5.40 ! [Q: int > nat,P: int > nat,N2: int] :
% 5.06/5.40 ( ! [X3: int] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.06/5.40 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N2 ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N2 ) ) )
% 5.06/5.40 = ( groups4541462559716669496nt_nat
% 5.06/5.40 @ ^ [X2: int] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.06/5.40 @ ( set_ord_lessThan_int @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_diff_distrib
% 5.06/5.40 thf(fact_7784_sum__diff__distrib,axiom,
% 5.06/5.40 ! [Q: real > nat,P: real > nat,N2: real] :
% 5.06/5.40 ( ! [X3: real] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.06/5.40 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N2 ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N2 ) ) )
% 5.06/5.40 = ( groups1935376822645274424al_nat
% 5.06/5.40 @ ^ [X2: real] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.06/5.40 @ ( set_or5984915006950818249n_real @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_diff_distrib
% 5.06/5.40 thf(fact_7785_sum__diff__distrib,axiom,
% 5.06/5.40 ! [Q: $o > nat,P: $o > nat,N2: $o] :
% 5.06/5.40 ( ! [X3: $o] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.06/5.40 => ( ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ P @ ( set_ord_lessThan_o @ N2 ) ) @ ( groups8507830703676809646_o_nat @ Q @ ( set_ord_lessThan_o @ N2 ) ) )
% 5.06/5.40 = ( groups8507830703676809646_o_nat
% 5.06/5.40 @ ^ [X2: $o] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.06/5.40 @ ( set_ord_lessThan_o @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_diff_distrib
% 5.06/5.40 thf(fact_7786_sum__diff__distrib,axiom,
% 5.06/5.40 ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 5.06/5.40 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.06/5.40 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.06/5.40 = ( groups3542108847815614940at_nat
% 5.06/5.40 @ ^ [X2: nat] : ( minus_minus_nat @ ( P @ X2 ) @ ( Q @ X2 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_diff_distrib
% 5.06/5.40 thf(fact_7787_suminf__pos2,axiom,
% 5.06/5.40 ! [F: nat > real,I2: nat] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.06/5.40 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.06/5.40 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_pos2
% 5.06/5.40 thf(fact_7788_suminf__pos2,axiom,
% 5.06/5.40 ! [F: nat > nat,I2: nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.06/5.40 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.06/5.40 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_pos2
% 5.06/5.40 thf(fact_7789_suminf__pos2,axiom,
% 5.06/5.40 ! [F: nat > int,I2: nat] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.06/5.40 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.06/5.40 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_pos2
% 5.06/5.40 thf(fact_7790_suminf__pos__iff,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.06/5.40 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.06/5.40 = ( ? [I5: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I5 ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_pos_iff
% 5.06/5.40 thf(fact_7791_suminf__pos__iff,axiom,
% 5.06/5.40 ! [F: nat > nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.06/5.40 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.06/5.40 = ( ? [I5: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I5 ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_pos_iff
% 5.06/5.40 thf(fact_7792_suminf__pos__iff,axiom,
% 5.06/5.40 ! [F: nat > int] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.06/5.40 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.06/5.40 = ( ? [I5: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I5 ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_pos_iff
% 5.06/5.40 thf(fact_7793_powser__inside,axiom,
% 5.06/5.40 ! [F: nat > real,X: real,Z: real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X @ N ) ) )
% 5.06/5.40 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X ) )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_inside
% 5.06/5.40 thf(fact_7794_powser__inside,axiom,
% 5.06/5.40 ! [F: nat > complex,X: complex,Z: complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X @ N ) ) )
% 5.06/5.40 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X ) )
% 5.06/5.40 => ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_inside
% 5.06/5.40 thf(fact_7795_complete__algebra__summable__geometric,axiom,
% 5.06/5.40 ! [X: real] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ one_one_real )
% 5.06/5.40 => ( summable_real @ ( power_power_real @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % complete_algebra_summable_geometric
% 5.06/5.40 thf(fact_7796_complete__algebra__summable__geometric,axiom,
% 5.06/5.40 ! [X: complex] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ one_one_real )
% 5.06/5.40 => ( summable_complex @ ( power_power_complex @ X ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % complete_algebra_summable_geometric
% 5.06/5.40 thf(fact_7797_summable__geometric,axiom,
% 5.06/5.40 ! [C: real] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.06/5.40 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_geometric
% 5.06/5.40 thf(fact_7798_summable__geometric,axiom,
% 5.06/5.40 ! [C: complex] :
% 5.06/5.40 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.06/5.40 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_geometric
% 5.06/5.40 thf(fact_7799_suminf__split__head,axiom,
% 5.06/5.40 ! [F: nat > complex] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 5.06/5.40 = ( minus_minus_complex @ ( suminf_complex @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_split_head
% 5.06/5.40 thf(fact_7800_suminf__split__head,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 5.06/5.40 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_split_head
% 5.06/5.40 thf(fact_7801_pi__less__4,axiom,
% 5.06/5.40 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % pi_less_4
% 5.06/5.40 thf(fact_7802_pi__ge__two,axiom,
% 5.06/5.40 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.06/5.40
% 5.06/5.40 % pi_ge_two
% 5.06/5.40 thf(fact_7803_pi__half__neq__two,axiom,
% 5.06/5.40 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.40 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % pi_half_neq_two
% 5.06/5.40 thf(fact_7804_sum__pos__lt__pair,axiom,
% 5.06/5.40 ! [F: nat > real,K: nat] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ! [D4: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D4 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D4 ) @ one_one_nat ) ) ) ) )
% 5.06/5.40 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_pos_lt_pair
% 5.06/5.40 thf(fact_7805_sum_OlessThan__Suc__shift,axiom,
% 5.06/5.40 ! [G: nat > rat,N2: nat] :
% 5.06/5.40 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.06/5.40 @ ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.lessThan_Suc_shift
% 5.06/5.40 thf(fact_7806_sum_OlessThan__Suc__shift,axiom,
% 5.06/5.40 ! [G: nat > int,N2: nat] :
% 5.06/5.40 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.06/5.40 @ ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.lessThan_Suc_shift
% 5.06/5.40 thf(fact_7807_sum_OlessThan__Suc__shift,axiom,
% 5.06/5.40 ! [G: nat > nat,N2: nat] :
% 5.06/5.40 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.06/5.40 @ ( groups3542108847815614940at_nat
% 5.06/5.40 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.lessThan_Suc_shift
% 5.06/5.40 thf(fact_7808_sum_OlessThan__Suc__shift,axiom,
% 5.06/5.40 ! [G: nat > real,N2: nat] :
% 5.06/5.40 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.06/5.40 @ ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.lessThan_Suc_shift
% 5.06/5.40 thf(fact_7809_sum__lessThan__telescope_H,axiom,
% 5.06/5.40 ! [F: nat > rat,M: nat] :
% 5.06/5.40 ( ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [N: nat] : ( minus_minus_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) )
% 5.06/5.40 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_lessThan_telescope'
% 5.06/5.40 thf(fact_7810_sum__lessThan__telescope_H,axiom,
% 5.06/5.40 ! [F: nat > int,M: nat] :
% 5.06/5.40 ( ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [N: nat] : ( minus_minus_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) )
% 5.06/5.40 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_lessThan_telescope'
% 5.06/5.40 thf(fact_7811_sum__lessThan__telescope_H,axiom,
% 5.06/5.40 ! [F: nat > real,M: nat] :
% 5.06/5.40 ( ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) )
% 5.06/5.40 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_lessThan_telescope'
% 5.06/5.40 thf(fact_7812_sum__lessThan__telescope,axiom,
% 5.06/5.40 ! [F: nat > rat,M: nat] :
% 5.06/5.40 ( ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [N: nat] : ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) )
% 5.06/5.40 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_lessThan_telescope
% 5.06/5.40 thf(fact_7813_sum__lessThan__telescope,axiom,
% 5.06/5.40 ! [F: nat > int,M: nat] :
% 5.06/5.40 ( ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [N: nat] : ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) )
% 5.06/5.40 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_lessThan_telescope
% 5.06/5.40 thf(fact_7814_sum__lessThan__telescope,axiom,
% 5.06/5.40 ! [F: nat > real,M: nat] :
% 5.06/5.40 ( ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [N: nat] : ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) )
% 5.06/5.40 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_lessThan_telescope
% 5.06/5.40 thf(fact_7815_sumr__diff__mult__const2,axiom,
% 5.06/5.40 ! [F: nat > rat,N2: nat,R2: rat] :
% 5.06/5.40 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ R2 ) )
% 5.06/5.40 = ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ I5 ) @ R2 )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sumr_diff_mult_const2
% 5.06/5.40 thf(fact_7816_sumr__diff__mult__const2,axiom,
% 5.06/5.40 ! [F: nat > int,N2: nat,R2: int] :
% 5.06/5.40 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ R2 ) )
% 5.06/5.40 = ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ R2 )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sumr_diff_mult_const2
% 5.06/5.40 thf(fact_7817_sumr__diff__mult__const2,axiom,
% 5.06/5.40 ! [F: nat > code_integer,N2: nat,R2: code_integer] :
% 5.06/5.40 ( ( minus_8373710615458151222nteger @ ( groups7501900531339628137nteger @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ R2 ) )
% 5.06/5.40 = ( groups7501900531339628137nteger
% 5.06/5.40 @ ^ [I5: nat] : ( minus_8373710615458151222nteger @ ( F @ I5 ) @ R2 )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sumr_diff_mult_const2
% 5.06/5.40 thf(fact_7818_sumr__diff__mult__const2,axiom,
% 5.06/5.40 ! [F: nat > real,N2: nat,R2: real] :
% 5.06/5.40 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ R2 ) )
% 5.06/5.40 = ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ R2 )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sumr_diff_mult_const2
% 5.06/5.40 thf(fact_7819_summable__norm,axiom,
% 5.06/5.40 ! [F: nat > real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 5.06/5.40 @ ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_norm
% 5.06/5.40 thf(fact_7820_summable__norm,axiom,
% 5.06/5.40 ! [F: nat > complex] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 5.06/5.40 @ ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_norm
% 5.06/5.40 thf(fact_7821_sum_OatLeast1__atMost__eq,axiom,
% 5.06/5.40 ! [G: nat > nat,N2: nat] :
% 5.06/5.40 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.06/5.40 = ( groups3542108847815614940at_nat
% 5.06/5.40 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.atLeast1_atMost_eq
% 5.06/5.40 thf(fact_7822_sum_OatLeast1__atMost__eq,axiom,
% 5.06/5.40 ! [G: nat > real,N2: nat] :
% 5.06/5.40 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.06/5.40 = ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum.atLeast1_atMost_eq
% 5.06/5.40 thf(fact_7823_sum__le__suminf,axiom,
% 5.06/5.40 ! [F: nat > int,I6: set_nat] :
% 5.06/5.40 ( ( summable_int @ F )
% 5.06/5.40 => ( ( finite_finite_nat @ I6 )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 5.06/5.40 => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 5.06/5.40 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I6 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_le_suminf
% 5.06/5.40 thf(fact_7824_sum__le__suminf,axiom,
% 5.06/5.40 ! [F: nat > nat,I6: set_nat] :
% 5.06/5.40 ( ( summable_nat @ F )
% 5.06/5.40 => ( ( finite_finite_nat @ I6 )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 5.06/5.40 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 5.06/5.40 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I6 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_le_suminf
% 5.06/5.40 thf(fact_7825_sum__le__suminf,axiom,
% 5.06/5.40 ! [F: nat > real,I6: set_nat] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( finite_finite_nat @ I6 )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I6 ) )
% 5.06/5.40 => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 5.06/5.40 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I6 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_le_suminf
% 5.06/5.40 thf(fact_7826_pred__equals__eq2,axiom,
% 5.06/5.40 ! [R: set_Pr448751882837621926eger_o,S3: set_Pr448751882837621926eger_o] :
% 5.06/5.40 ( ( ( ^ [X2: code_integer,Y2: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X2 @ Y2 ) @ R ) )
% 5.06/5.40 = ( ^ [X2: code_integer,Y2: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X2 @ Y2 ) @ S3 ) ) )
% 5.06/5.40 = ( R = S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_equals_eq2
% 5.06/5.40 thf(fact_7827_pred__equals__eq2,axiom,
% 5.06/5.40 ! [R: set_Pr8218934625190621173um_num,S3: set_Pr8218934625190621173um_num] :
% 5.06/5.40 ( ( ( ^ [X2: num,Y2: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X2 @ Y2 ) @ R ) )
% 5.06/5.40 = ( ^ [X2: num,Y2: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X2 @ Y2 ) @ S3 ) ) )
% 5.06/5.40 = ( R = S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_equals_eq2
% 5.06/5.40 thf(fact_7828_pred__equals__eq2,axiom,
% 5.06/5.40 ! [R: set_Pr6200539531224447659at_num,S3: set_Pr6200539531224447659at_num] :
% 5.06/5.40 ( ( ( ^ [X2: nat,Y2: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Y2 ) @ R ) )
% 5.06/5.40 = ( ^ [X2: nat,Y2: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Y2 ) @ S3 ) ) )
% 5.06/5.40 = ( R = S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_equals_eq2
% 5.06/5.40 thf(fact_7829_pred__equals__eq2,axiom,
% 5.06/5.40 ! [R: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 5.06/5.40 ( ( ( ^ [X2: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ R ) )
% 5.06/5.40 = ( ^ [X2: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ S3 ) ) )
% 5.06/5.40 = ( R = S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_equals_eq2
% 5.06/5.40 thf(fact_7830_pred__equals__eq2,axiom,
% 5.06/5.40 ! [R: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 5.06/5.40 ( ( ( ^ [X2: int,Y2: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y2 ) @ R ) )
% 5.06/5.40 = ( ^ [X2: int,Y2: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y2 ) @ S3 ) ) )
% 5.06/5.40 = ( R = S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_equals_eq2
% 5.06/5.40 thf(fact_7831_bot__empty__eq2,axiom,
% 5.06/5.40 ( bot_bo4731626569425807221er_o_o
% 5.06/5.40 = ( ^ [X2: code_integer,Y2: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X2 @ Y2 ) @ bot_bo5379713665208646970eger_o ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % bot_empty_eq2
% 5.06/5.40 thf(fact_7832_bot__empty__eq2,axiom,
% 5.06/5.40 ( bot_bot_num_num_o
% 5.06/5.40 = ( ^ [X2: num,Y2: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X2 @ Y2 ) @ bot_bo9056780473022590049um_num ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % bot_empty_eq2
% 5.06/5.40 thf(fact_7833_bot__empty__eq2,axiom,
% 5.06/5.40 ( bot_bot_nat_num_o
% 5.06/5.40 = ( ^ [X2: nat,Y2: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X2 @ Y2 ) @ bot_bo7038385379056416535at_num ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % bot_empty_eq2
% 5.06/5.40 thf(fact_7834_bot__empty__eq2,axiom,
% 5.06/5.40 ( bot_bot_nat_nat_o
% 5.06/5.40 = ( ^ [X2: nat,Y2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % bot_empty_eq2
% 5.06/5.40 thf(fact_7835_bot__empty__eq2,axiom,
% 5.06/5.40 ( bot_bot_int_int_o
% 5.06/5.40 = ( ^ [X2: int,Y2: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y2 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % bot_empty_eq2
% 5.06/5.40 thf(fact_7836_pi__half__neq__zero,axiom,
% 5.06/5.40 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.40 != zero_zero_real ) ).
% 5.06/5.40
% 5.06/5.40 % pi_half_neq_zero
% 5.06/5.40 thf(fact_7837_pi__half__less__two,axiom,
% 5.06/5.40 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.06/5.40
% 5.06/5.40 % pi_half_less_two
% 5.06/5.40 thf(fact_7838_pi__half__le__two,axiom,
% 5.06/5.40 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.06/5.40
% 5.06/5.40 % pi_half_le_two
% 5.06/5.40 thf(fact_7839_power__diff__1__eq,axiom,
% 5.06/5.40 ! [X: complex,N2: nat] :
% 5.06/5.40 ( ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ one_one_complex )
% 5.06/5.40 = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_diff_1_eq
% 5.06/5.40 thf(fact_7840_power__diff__1__eq,axiom,
% 5.06/5.40 ! [X: rat,N2: nat] :
% 5.06/5.40 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat )
% 5.06/5.40 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_diff_1_eq
% 5.06/5.40 thf(fact_7841_power__diff__1__eq,axiom,
% 5.06/5.40 ! [X: int,N2: nat] :
% 5.06/5.40 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ one_one_int )
% 5.06/5.40 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_diff_1_eq
% 5.06/5.40 thf(fact_7842_power__diff__1__eq,axiom,
% 5.06/5.40 ! [X: real,N2: nat] :
% 5.06/5.40 ( ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ one_one_real )
% 5.06/5.40 = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_diff_1_eq
% 5.06/5.40 thf(fact_7843_one__diff__power__eq,axiom,
% 5.06/5.40 ! [X: complex,N2: nat] :
% 5.06/5.40 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) )
% 5.06/5.40 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % one_diff_power_eq
% 5.06/5.40 thf(fact_7844_one__diff__power__eq,axiom,
% 5.06/5.40 ! [X: rat,N2: nat] :
% 5.06/5.40 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 5.06/5.40 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % one_diff_power_eq
% 5.06/5.40 thf(fact_7845_one__diff__power__eq,axiom,
% 5.06/5.40 ! [X: int,N2: nat] :
% 5.06/5.40 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 5.06/5.40 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % one_diff_power_eq
% 5.06/5.40 thf(fact_7846_one__diff__power__eq,axiom,
% 5.06/5.40 ! [X: real,N2: nat] :
% 5.06/5.40 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) )
% 5.06/5.40 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % one_diff_power_eq
% 5.06/5.40 thf(fact_7847_geometric__sum,axiom,
% 5.06/5.40 ! [X: complex,N2: nat] :
% 5.06/5.40 ( ( X != one_one_complex )
% 5.06/5.40 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % geometric_sum
% 5.06/5.40 thf(fact_7848_geometric__sum,axiom,
% 5.06/5.40 ! [X: rat,N2: nat] :
% 5.06/5.40 ( ( X != one_one_rat )
% 5.06/5.40 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % geometric_sum
% 5.06/5.40 thf(fact_7849_geometric__sum,axiom,
% 5.06/5.40 ! [X: real,N2: nat] :
% 5.06/5.40 ( ( X != one_one_real )
% 5.06/5.40 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % geometric_sum
% 5.06/5.40 thf(fact_7850_powser__split__head_I1_J,axiom,
% 5.06/5.40 ! [F: nat > complex,Z: complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.06/5.40 => ( ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.06/5.40 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.06/5.40 @ ( times_times_complex
% 5.06/5.40 @ ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.06/5.40 @ Z ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_split_head(1)
% 5.06/5.40 thf(fact_7851_powser__split__head_I1_J,axiom,
% 5.06/5.40 ! [F: nat > real,Z: real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.06/5.40 => ( ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.06/5.40 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.06/5.40 @ ( times_times_real
% 5.06/5.40 @ ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.06/5.40 @ Z ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_split_head(1)
% 5.06/5.40 thf(fact_7852_powser__split__head_I2_J,axiom,
% 5.06/5.40 ! [F: nat > complex,Z: complex] :
% 5.06/5.40 ( ( summable_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.06/5.40 => ( ( times_times_complex
% 5.06/5.40 @ ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.06/5.40 @ Z )
% 5.06/5.40 = ( minus_minus_complex
% 5.06/5.40 @ ( suminf_complex
% 5.06/5.40 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.06/5.40 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_split_head(2)
% 5.06/5.40 thf(fact_7853_powser__split__head_I2_J,axiom,
% 5.06/5.40 ! [F: nat > real,Z: real] :
% 5.06/5.40 ( ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.06/5.40 => ( ( times_times_real
% 5.06/5.40 @ ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.06/5.40 @ Z )
% 5.06/5.40 = ( minus_minus_real
% 5.06/5.40 @ ( suminf_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.06/5.40 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % powser_split_head(2)
% 5.06/5.40 thf(fact_7854_summable__partial__sum__bound,axiom,
% 5.06/5.40 ! [F: nat > complex,E: real] :
% 5.06/5.40 ( ( summable_complex @ F )
% 5.06/5.40 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.06/5.40 => ~ ! [N8: nat] :
% 5.06/5.40 ~ ! [M3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N8 @ M3 )
% 5.06/5.40 => ! [N9: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M3 @ N9 ) ) ) @ E ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_partial_sum_bound
% 5.06/5.40 thf(fact_7855_summable__partial__sum__bound,axiom,
% 5.06/5.40 ! [F: nat > real,E: real] :
% 5.06/5.40 ( ( summable_real @ F )
% 5.06/5.40 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.06/5.40 => ~ ! [N8: nat] :
% 5.06/5.40 ~ ! [M3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N8 @ M3 )
% 5.06/5.40 => ! [N9: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M3 @ N9 ) ) ) @ E ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_partial_sum_bound
% 5.06/5.40 thf(fact_7856_suminf__exist__split,axiom,
% 5.06/5.40 ! [R2: real,F: nat > real] :
% 5.06/5.40 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.06/5.40 => ( ( summable_real @ F )
% 5.06/5.40 => ? [N8: nat] :
% 5.06/5.40 ! [N9: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N8 @ N9 )
% 5.06/5.40 => ( ord_less_real
% 5.06/5.40 @ ( real_V7735802525324610683m_real
% 5.06/5.40 @ ( suminf_real
% 5.06/5.40 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N9 ) ) ) )
% 5.06/5.40 @ R2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_exist_split
% 5.06/5.40 thf(fact_7857_suminf__exist__split,axiom,
% 5.06/5.40 ! [R2: real,F: nat > complex] :
% 5.06/5.40 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.06/5.40 => ( ( summable_complex @ F )
% 5.06/5.40 => ? [N8: nat] :
% 5.06/5.40 ! [N9: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N8 @ N9 )
% 5.06/5.40 => ( ord_less_real
% 5.06/5.40 @ ( real_V1022390504157884413omplex
% 5.06/5.40 @ ( suminf_complex
% 5.06/5.40 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N9 ) ) ) )
% 5.06/5.40 @ R2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % suminf_exist_split
% 5.06/5.40 thf(fact_7858_summable__power__series,axiom,
% 5.06/5.40 ! [F: nat > real,Z: real] :
% 5.06/5.40 ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 5.06/5.40 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.06/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.06/5.40 => ( ( ord_less_real @ Z @ one_one_real )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [I5: nat] : ( times_times_real @ ( F @ I5 ) @ ( power_power_real @ Z @ I5 ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_power_series
% 5.06/5.40 thf(fact_7859_Abel__lemma,axiom,
% 5.06/5.40 ! [R2: real,R0: real,A: nat > complex,M7: real] :
% 5.06/5.40 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.06/5.40 => ( ( ord_less_real @ R2 @ R0 )
% 5.06/5.40 => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 5.06/5.40 => ( summable_real
% 5.06/5.40 @ ^ [N: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N ) ) @ ( power_power_real @ R2 @ N ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % Abel_lemma
% 5.06/5.40 thf(fact_7860_sum__gp__strict,axiom,
% 5.06/5.40 ! [X: complex,N2: nat] :
% 5.06/5.40 ( ( ( X = one_one_complex )
% 5.06/5.40 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.06/5.40 & ( ( X != one_one_complex )
% 5.06/5.40 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_gp_strict
% 5.06/5.40 thf(fact_7861_sum__gp__strict,axiom,
% 5.06/5.40 ! [X: rat,N2: nat] :
% 5.06/5.40 ( ( ( X = one_one_rat )
% 5.06/5.40 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( semiri681578069525770553at_rat @ N2 ) ) )
% 5.06/5.40 & ( ( X != one_one_rat )
% 5.06/5.40 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_gp_strict
% 5.06/5.40 thf(fact_7862_sum__gp__strict,axiom,
% 5.06/5.40 ! [X: real,N2: nat] :
% 5.06/5.40 ( ( ( X = one_one_real )
% 5.06/5.40 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.06/5.40 & ( ( X != one_one_real )
% 5.06/5.40 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_gp_strict
% 5.06/5.40 thf(fact_7863_lemma__termdiff1,axiom,
% 5.06/5.40 ! [Z: complex,H2: complex,M: nat] :
% 5.06/5.40 ( ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [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 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) )
% 5.06/5.40 = ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [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 ) ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lemma_termdiff1
% 5.06/5.40 thf(fact_7864_lemma__termdiff1,axiom,
% 5.06/5.40 ! [Z: rat,H2: rat,M: nat] :
% 5.06/5.40 ( ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [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 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) )
% 5.06/5.40 = ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [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 ) ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lemma_termdiff1
% 5.06/5.40 thf(fact_7865_lemma__termdiff1,axiom,
% 5.06/5.40 ! [Z: int,H2: int,M: nat] :
% 5.06/5.40 ( ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [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 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) )
% 5.06/5.40 = ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [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 ) ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lemma_termdiff1
% 5.06/5.40 thf(fact_7866_lemma__termdiff1,axiom,
% 5.06/5.40 ! [Z: real,H2: real,M: nat] :
% 5.06/5.40 ( ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [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 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) )
% 5.06/5.40 = ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [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 ) ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % lemma_termdiff1
% 5.06/5.40 thf(fact_7867_pi__half__gt__zero,axiom,
% 5.06/5.40 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % pi_half_gt_zero
% 5.06/5.40 thf(fact_7868_power__diff__sumr2,axiom,
% 5.06/5.40 ! [X: complex,N2: nat,Y: complex] :
% 5.06/5.40 ( ( minus_minus_complex @ ( power_power_complex @ X @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 5.06/5.40 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.06/5.40 @ ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_complex @ X @ I5 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_diff_sumr2
% 5.06/5.40 thf(fact_7869_power__diff__sumr2,axiom,
% 5.06/5.40 ! [X: rat,N2: nat,Y: rat] :
% 5.06/5.40 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 5.06/5.40 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.06/5.40 @ ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [I5: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_rat @ X @ I5 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_diff_sumr2
% 5.06/5.40 thf(fact_7870_power__diff__sumr2,axiom,
% 5.06/5.40 ! [X: int,N2: nat,Y: int] :
% 5.06/5.40 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.06/5.40 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.06/5.40 @ ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_int @ X @ I5 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_diff_sumr2
% 5.06/5.40 thf(fact_7871_power__diff__sumr2,axiom,
% 5.06/5.40 ! [X: real,N2: nat,Y: real] :
% 5.06/5.40 ( ( minus_minus_real @ ( power_power_real @ X @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 5.06/5.40 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.06/5.40 @ ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_real @ X @ I5 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % power_diff_sumr2
% 5.06/5.40 thf(fact_7872_diff__power__eq__sum,axiom,
% 5.06/5.40 ! [X: complex,N2: nat,Y: complex] :
% 5.06/5.40 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) @ ( power_power_complex @ Y @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.06/5.40 @ ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X @ P5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % diff_power_eq_sum
% 5.06/5.40 thf(fact_7873_diff__power__eq__sum,axiom,
% 5.06/5.40 ! [X: rat,N2: nat,Y: rat] :
% 5.06/5.40 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.06/5.40 @ ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X @ P5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % diff_power_eq_sum
% 5.06/5.40 thf(fact_7874_diff__power__eq__sum,axiom,
% 5.06/5.40 ! [X: int,N2: nat,Y: int] :
% 5.06/5.40 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.06/5.40 @ ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X @ P5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % diff_power_eq_sum
% 5.06/5.40 thf(fact_7875_diff__power__eq__sum,axiom,
% 5.06/5.40 ! [X: real,N2: nat,Y: real] :
% 5.06/5.40 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N2 ) ) @ ( power_power_real @ Y @ ( suc @ N2 ) ) )
% 5.06/5.40 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.06/5.40 @ ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X @ P5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % diff_power_eq_sum
% 5.06/5.40 thf(fact_7876_pi__half__ge__zero,axiom,
% 5.06/5.40 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % pi_half_ge_zero
% 5.06/5.40 thf(fact_7877_m2pi__less__pi,axiom,
% 5.06/5.40 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.06/5.40
% 5.06/5.40 % m2pi_less_pi
% 5.06/5.40 thf(fact_7878_summable__ratio__test,axiom,
% 5.06/5.40 ! [C: real,N4: nat,F: nat > real] :
% 5.06/5.40 ( ( ord_less_real @ C @ one_one_real )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 5.06/5.40 => ( summable_real @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_ratio_test
% 5.06/5.40 thf(fact_7879_summable__ratio__test,axiom,
% 5.06/5.40 ! [C: real,N4: nat,F: nat > complex] :
% 5.06/5.40 ( ( ord_less_real @ C @ one_one_real )
% 5.06/5.40 => ( ! [N3: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.06/5.40 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 5.06/5.40 => ( summable_complex @ F ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % summable_ratio_test
% 5.06/5.40 thf(fact_7880_arctan__ubound,axiom,
% 5.06/5.40 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % arctan_ubound
% 5.06/5.40 thf(fact_7881_arctan__one,axiom,
% 5.06/5.40 ( ( arctan @ one_one_real )
% 5.06/5.40 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % arctan_one
% 5.06/5.40 thf(fact_7882_real__sum__nat__ivl__bounded2,axiom,
% 5.06/5.40 ! [N2: nat,F: nat > code_integer,K5: code_integer,K: nat] :
% 5.06/5.40 ( ! [P7: nat] :
% 5.06/5.40 ( ( ord_less_nat @ P7 @ N2 )
% 5.06/5.40 => ( ord_le3102999989581377725nteger @ ( F @ P7 ) @ K5 ) )
% 5.06/5.40 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ K5 )
% 5.06/5.40 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ K5 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_sum_nat_ivl_bounded2
% 5.06/5.40 thf(fact_7883_real__sum__nat__ivl__bounded2,axiom,
% 5.06/5.40 ! [N2: nat,F: nat > rat,K5: rat,K: nat] :
% 5.06/5.40 ( ! [P7: nat] :
% 5.06/5.40 ( ( ord_less_nat @ P7 @ N2 )
% 5.06/5.40 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.06/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.06/5.40 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ K5 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_sum_nat_ivl_bounded2
% 5.06/5.40 thf(fact_7884_real__sum__nat__ivl__bounded2,axiom,
% 5.06/5.40 ! [N2: nat,F: nat > int,K5: int,K: nat] :
% 5.06/5.40 ( ! [P7: nat] :
% 5.06/5.40 ( ( ord_less_nat @ P7 @ N2 )
% 5.06/5.40 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.06/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.06/5.40 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ K5 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_sum_nat_ivl_bounded2
% 5.06/5.40 thf(fact_7885_real__sum__nat__ivl__bounded2,axiom,
% 5.06/5.40 ! [N2: nat,F: nat > nat,K5: nat,K: nat] :
% 5.06/5.40 ( ! [P7: nat] :
% 5.06/5.40 ( ( ord_less_nat @ P7 @ N2 )
% 5.06/5.40 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.06/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.06/5.40 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ K5 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_sum_nat_ivl_bounded2
% 5.06/5.40 thf(fact_7886_real__sum__nat__ivl__bounded2,axiom,
% 5.06/5.40 ! [N2: nat,F: nat > real,K5: real,K: nat] :
% 5.06/5.40 ( ! [P7: nat] :
% 5.06/5.40 ( ( ord_less_nat @ P7 @ N2 )
% 5.06/5.40 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.06/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.06/5.40 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ K5 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % real_sum_nat_ivl_bounded2
% 5.06/5.40 thf(fact_7887_one__diff__power__eq_H,axiom,
% 5.06/5.40 ! [X: complex,N2: nat] :
% 5.06/5.40 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N2 ) )
% 5.06/5.40 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 5.06/5.40 @ ( groups2073611262835488442omplex
% 5.06/5.40 @ ^ [I5: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % one_diff_power_eq'
% 5.06/5.40 thf(fact_7888_one__diff__power__eq_H,axiom,
% 5.06/5.40 ! [X: rat,N2: nat] :
% 5.06/5.40 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 5.06/5.40 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 5.06/5.40 @ ( groups2906978787729119204at_rat
% 5.06/5.40 @ ^ [I5: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % one_diff_power_eq'
% 5.06/5.40 thf(fact_7889_one__diff__power__eq_H,axiom,
% 5.06/5.40 ! [X: int,N2: nat] :
% 5.06/5.40 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 5.06/5.40 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 5.06/5.40 @ ( groups3539618377306564664at_int
% 5.06/5.40 @ ^ [I5: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % one_diff_power_eq'
% 5.06/5.40 thf(fact_7890_one__diff__power__eq_H,axiom,
% 5.06/5.40 ! [X: real,N2: nat] :
% 5.06/5.40 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N2 ) )
% 5.06/5.40 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 5.06/5.40 @ ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % one_diff_power_eq'
% 5.06/5.40 thf(fact_7891_subrelI,axiom,
% 5.06/5.40 ! [R2: set_Pr448751882837621926eger_o,S2: set_Pr448751882837621926eger_o] :
% 5.06/5.40 ( ! [X3: code_integer,Y5: $o] :
% 5.06/5.40 ( ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X3 @ Y5 ) @ R2 )
% 5.06/5.40 => ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X3 @ Y5 ) @ S2 ) )
% 5.06/5.40 => ( ord_le8980329558974975238eger_o @ R2 @ S2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % subrelI
% 5.06/5.40 thf(fact_7892_subrelI,axiom,
% 5.06/5.40 ! [R2: set_Pr8218934625190621173um_num,S2: set_Pr8218934625190621173um_num] :
% 5.06/5.40 ( ! [X3: num,Y5: num] :
% 5.06/5.40 ( ( member7279096912039735102um_num @ ( product_Pair_num_num @ X3 @ Y5 ) @ R2 )
% 5.06/5.40 => ( member7279096912039735102um_num @ ( product_Pair_num_num @ X3 @ Y5 ) @ S2 ) )
% 5.06/5.40 => ( ord_le880128212290418581um_num @ R2 @ S2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % subrelI
% 5.06/5.40 thf(fact_7893_subrelI,axiom,
% 5.06/5.40 ! [R2: set_Pr6200539531224447659at_num,S2: set_Pr6200539531224447659at_num] :
% 5.06/5.40 ( ! [X3: nat,Y5: num] :
% 5.06/5.40 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X3 @ Y5 ) @ R2 )
% 5.06/5.40 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X3 @ Y5 ) @ S2 ) )
% 5.06/5.40 => ( ord_le8085105155179020875at_num @ R2 @ S2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % subrelI
% 5.06/5.40 thf(fact_7894_subrelI,axiom,
% 5.06/5.40 ! [R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 5.06/5.40 ( ! [X3: nat,Y5: nat] :
% 5.06/5.40 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y5 ) @ R2 )
% 5.06/5.40 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y5 ) @ S2 ) )
% 5.06/5.40 => ( ord_le3146513528884898305at_nat @ R2 @ S2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % subrelI
% 5.06/5.40 thf(fact_7895_subrelI,axiom,
% 5.06/5.40 ! [R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 5.06/5.40 ( ! [X3: int,Y5: int] :
% 5.06/5.40 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y5 ) @ R2 )
% 5.06/5.40 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y5 ) @ S2 ) )
% 5.06/5.40 => ( ord_le2843351958646193337nt_int @ R2 @ S2 ) ) ).
% 5.06/5.40
% 5.06/5.40 % subrelI
% 5.06/5.40 thf(fact_7896_minus__pi__half__less__zero,axiom,
% 5.06/5.40 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.06/5.40
% 5.06/5.40 % minus_pi_half_less_zero
% 5.06/5.40 thf(fact_7897_arctan__bounded,axiom,
% 5.06/5.40 ! [Y: real] :
% 5.06/5.40 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.06/5.40 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % arctan_bounded
% 5.06/5.40 thf(fact_7898_arctan__lbound,axiom,
% 5.06/5.40 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 5.06/5.40
% 5.06/5.40 % arctan_lbound
% 5.06/5.40 thf(fact_7899_infinite__nat__iff__unbounded,axiom,
% 5.06/5.40 ! [S3: set_nat] :
% 5.06/5.40 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.06/5.40 = ( ! [M6: nat] :
% 5.06/5.40 ? [N: nat] :
% 5.06/5.40 ( ( ord_less_nat @ M6 @ N )
% 5.06/5.40 & ( member_nat @ N @ S3 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % infinite_nat_iff_unbounded
% 5.06/5.40 thf(fact_7900_unbounded__k__infinite,axiom,
% 5.06/5.40 ! [K: nat,S3: set_nat] :
% 5.06/5.40 ( ! [M2: nat] :
% 5.06/5.40 ( ( ord_less_nat @ K @ M2 )
% 5.06/5.40 => ? [N9: nat] :
% 5.06/5.40 ( ( ord_less_nat @ M2 @ N9 )
% 5.06/5.40 & ( member_nat @ N9 @ S3 ) ) )
% 5.06/5.40 => ~ ( finite_finite_nat @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % unbounded_k_infinite
% 5.06/5.40 thf(fact_7901_infinite__nat__iff__unbounded__le,axiom,
% 5.06/5.40 ! [S3: set_nat] :
% 5.06/5.40 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.06/5.40 = ( ! [M6: nat] :
% 5.06/5.40 ? [N: nat] :
% 5.06/5.40 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.40 & ( member_nat @ N @ S3 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % infinite_nat_iff_unbounded_le
% 5.06/5.40 thf(fact_7902_accp__subset__induct,axiom,
% 5.06/5.40 ! [D3: product_prod_num_num > $o,R: product_prod_num_num > product_prod_num_num > $o,X: product_prod_num_num,P: product_prod_num_num > $o] :
% 5.06/5.40 ( ( ord_le2239182809043710856_num_o @ D3 @ ( accp_P3113834385874906142um_num @ R ) )
% 5.06/5.40 => ( ! [X3: product_prod_num_num,Z4: product_prod_num_num] :
% 5.06/5.40 ( ( D3 @ X3 )
% 5.06/5.40 => ( ( R @ Z4 @ X3 )
% 5.06/5.40 => ( D3 @ Z4 ) ) )
% 5.06/5.40 => ( ( D3 @ X )
% 5.06/5.40 => ( ! [X3: product_prod_num_num] :
% 5.06/5.40 ( ( D3 @ X3 )
% 5.06/5.40 => ( ! [Z5: product_prod_num_num] :
% 5.06/5.40 ( ( R @ Z5 @ X3 )
% 5.06/5.40 => ( P @ Z5 ) )
% 5.06/5.40 => ( P @ X3 ) ) )
% 5.06/5.40 => ( P @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % accp_subset_induct
% 5.06/5.40 thf(fact_7903_accp__subset__induct,axiom,
% 5.06/5.40 ! [D3: product_prod_nat_nat > $o,R: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.06/5.40 ( ( ord_le704812498762024988_nat_o @ D3 @ ( accp_P4275260045618599050at_nat @ R ) )
% 5.06/5.40 => ( ! [X3: product_prod_nat_nat,Z4: product_prod_nat_nat] :
% 5.06/5.40 ( ( D3 @ X3 )
% 5.06/5.40 => ( ( R @ Z4 @ X3 )
% 5.06/5.40 => ( D3 @ Z4 ) ) )
% 5.06/5.40 => ( ( D3 @ X )
% 5.06/5.40 => ( ! [X3: product_prod_nat_nat] :
% 5.06/5.40 ( ( D3 @ X3 )
% 5.06/5.40 => ( ! [Z5: product_prod_nat_nat] :
% 5.06/5.40 ( ( R @ Z5 @ X3 )
% 5.06/5.40 => ( P @ Z5 ) )
% 5.06/5.40 => ( P @ X3 ) ) )
% 5.06/5.40 => ( P @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % accp_subset_induct
% 5.06/5.40 thf(fact_7904_accp__subset__induct,axiom,
% 5.06/5.40 ! [D3: product_prod_int_int > $o,R: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.06/5.40 ( ( ord_le8369615600986905444_int_o @ D3 @ ( accp_P1096762738010456898nt_int @ R ) )
% 5.06/5.40 => ( ! [X3: product_prod_int_int,Z4: product_prod_int_int] :
% 5.06/5.40 ( ( D3 @ X3 )
% 5.06/5.40 => ( ( R @ Z4 @ X3 )
% 5.06/5.40 => ( D3 @ Z4 ) ) )
% 5.06/5.40 => ( ( D3 @ X )
% 5.06/5.40 => ( ! [X3: product_prod_int_int] :
% 5.06/5.40 ( ( D3 @ X3 )
% 5.06/5.40 => ( ! [Z5: product_prod_int_int] :
% 5.06/5.40 ( ( R @ Z5 @ X3 )
% 5.06/5.40 => ( P @ Z5 ) )
% 5.06/5.40 => ( P @ X3 ) ) )
% 5.06/5.40 => ( P @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % accp_subset_induct
% 5.06/5.40 thf(fact_7905_accp__subset__induct,axiom,
% 5.06/5.40 ! [D3: list_nat > $o,R: list_nat > list_nat > $o,X: list_nat,P: list_nat > $o] :
% 5.06/5.40 ( ( ord_le1520216061033275535_nat_o @ D3 @ ( accp_list_nat @ R ) )
% 5.06/5.40 => ( ! [X3: list_nat,Z4: list_nat] :
% 5.06/5.40 ( ( D3 @ X3 )
% 5.06/5.40 => ( ( R @ Z4 @ X3 )
% 5.06/5.40 => ( D3 @ Z4 ) ) )
% 5.06/5.40 => ( ( D3 @ X )
% 5.06/5.40 => ( ! [X3: list_nat] :
% 5.06/5.40 ( ( D3 @ X3 )
% 5.06/5.40 => ( ! [Z5: list_nat] :
% 5.06/5.40 ( ( R @ Z5 @ X3 )
% 5.06/5.40 => ( P @ Z5 ) )
% 5.06/5.40 => ( P @ X3 ) ) )
% 5.06/5.40 => ( P @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % accp_subset_induct
% 5.06/5.40 thf(fact_7906_accp__subset__induct,axiom,
% 5.06/5.40 ! [D3: nat > $o,R: nat > nat > $o,X: nat,P: nat > $o] :
% 5.06/5.40 ( ( ord_less_eq_nat_o @ D3 @ ( accp_nat @ R ) )
% 5.06/5.40 => ( ! [X3: nat,Z4: nat] :
% 5.06/5.40 ( ( D3 @ X3 )
% 5.06/5.40 => ( ( R @ Z4 @ X3 )
% 5.06/5.40 => ( D3 @ Z4 ) ) )
% 5.06/5.40 => ( ( D3 @ X )
% 5.06/5.40 => ( ! [X3: nat] :
% 5.06/5.40 ( ( D3 @ X3 )
% 5.06/5.40 => ( ! [Z5: nat] :
% 5.06/5.40 ( ( R @ Z5 @ X3 )
% 5.06/5.40 => ( P @ Z5 ) )
% 5.06/5.40 => ( P @ X3 ) ) )
% 5.06/5.40 => ( P @ X ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % accp_subset_induct
% 5.06/5.40 thf(fact_7907_sum__split__even__odd,axiom,
% 5.06/5.40 ! [F: nat > real,G: nat > real,N2: nat] :
% 5.06/5.40 ( ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( F @ I5 ) @ ( G @ I5 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.40 = ( plus_plus_real
% 5.06/5.40 @ ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.40 @ ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ one_one_nat ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_split_even_odd
% 5.06/5.40 thf(fact_7908_pred__subset__eq,axiom,
% 5.06/5.40 ! [R: set_complex,S3: set_complex] :
% 5.06/5.40 ( ( ord_le4573692005234683329plex_o
% 5.06/5.40 @ ^ [X2: complex] : ( member_complex @ X2 @ R )
% 5.06/5.40 @ ^ [X2: complex] : ( member_complex @ X2 @ S3 ) )
% 5.06/5.40 = ( ord_le211207098394363844omplex @ R @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_subset_eq
% 5.06/5.40 thf(fact_7909_pred__subset__eq,axiom,
% 5.06/5.40 ! [R: set_real,S3: set_real] :
% 5.06/5.40 ( ( ord_less_eq_real_o
% 5.06/5.40 @ ^ [X2: real] : ( member_real @ X2 @ R )
% 5.06/5.40 @ ^ [X2: real] : ( member_real @ X2 @ S3 ) )
% 5.06/5.40 = ( ord_less_eq_set_real @ R @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_subset_eq
% 5.06/5.40 thf(fact_7910_pred__subset__eq,axiom,
% 5.06/5.40 ! [R: set_set_nat,S3: set_set_nat] :
% 5.06/5.40 ( ( ord_le3964352015994296041_nat_o
% 5.06/5.40 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ R )
% 5.06/5.40 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ S3 ) )
% 5.06/5.40 = ( ord_le6893508408891458716et_nat @ R @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_subset_eq
% 5.06/5.40 thf(fact_7911_pred__subset__eq,axiom,
% 5.06/5.40 ! [R: set_nat,S3: set_nat] :
% 5.06/5.40 ( ( ord_less_eq_nat_o
% 5.06/5.40 @ ^ [X2: nat] : ( member_nat @ X2 @ R )
% 5.06/5.40 @ ^ [X2: nat] : ( member_nat @ X2 @ S3 ) )
% 5.06/5.40 = ( ord_less_eq_set_nat @ R @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_subset_eq
% 5.06/5.40 thf(fact_7912_pred__subset__eq,axiom,
% 5.06/5.40 ! [R: set_int,S3: set_int] :
% 5.06/5.40 ( ( ord_less_eq_int_o
% 5.06/5.40 @ ^ [X2: int] : ( member_int @ X2 @ R )
% 5.06/5.40 @ ^ [X2: int] : ( member_int @ X2 @ S3 ) )
% 5.06/5.40 = ( ord_less_eq_set_int @ R @ S3 ) ) ).
% 5.06/5.40
% 5.06/5.40 % pred_subset_eq
% 5.06/5.40 thf(fact_7913_machin__Euler,axiom,
% 5.06/5.40 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.06/5.40 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % machin_Euler
% 5.06/5.40 thf(fact_7914_machin,axiom,
% 5.06/5.40 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.06/5.40 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % machin
% 5.06/5.40 thf(fact_7915_vebt__maxt_Opelims,axiom,
% 5.06/5.40 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.06/5.40 ( ( ( vEBT_vebt_maxt @ X )
% 5.06/5.40 = Y )
% 5.06/5.40 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 5.06/5.40 => ( ! [A3: $o,B2: $o] :
% 5.06/5.40 ( ( X
% 5.06/5.40 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.40 => ( ( ( B2
% 5.06/5.40 => ( Y
% 5.06/5.40 = ( some_nat @ one_one_nat ) ) )
% 5.06/5.40 & ( ~ B2
% 5.06/5.40 => ( ( A3
% 5.06/5.40 => ( Y
% 5.06/5.40 = ( some_nat @ zero_zero_nat ) ) )
% 5.06/5.40 & ( ~ A3
% 5.06/5.40 => ( Y = none_nat ) ) ) ) )
% 5.06/5.40 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.06/5.40 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.40 ( ( X
% 5.06/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.06/5.40 => ( ( Y = none_nat )
% 5.06/5.40 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.06/5.40 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.06/5.40 ( ( X
% 5.06/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.06/5.40 => ( ( Y
% 5.06/5.40 = ( some_nat @ Ma2 ) )
% 5.06/5.40 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % vebt_maxt.pelims
% 5.06/5.40 thf(fact_7916_vebt__mint_Opelims,axiom,
% 5.06/5.40 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.06/5.40 ( ( ( vEBT_vebt_mint @ X )
% 5.06/5.40 = Y )
% 5.06/5.40 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 5.06/5.40 => ( ! [A3: $o,B2: $o] :
% 5.06/5.40 ( ( X
% 5.06/5.40 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.06/5.40 => ( ( ( A3
% 5.06/5.40 => ( Y
% 5.06/5.40 = ( some_nat @ zero_zero_nat ) ) )
% 5.06/5.40 & ( ~ A3
% 5.06/5.40 => ( ( B2
% 5.06/5.40 => ( Y
% 5.06/5.40 = ( some_nat @ one_one_nat ) ) )
% 5.06/5.40 & ( ~ B2
% 5.06/5.40 => ( Y = none_nat ) ) ) ) )
% 5.06/5.40 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.06/5.40 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.06/5.40 ( ( X
% 5.06/5.40 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.06/5.40 => ( ( Y = none_nat )
% 5.06/5.40 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.06/5.40 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.06/5.40 ( ( X
% 5.06/5.40 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.06/5.40 => ( ( Y
% 5.06/5.40 = ( some_nat @ Mi2 ) )
% 5.06/5.40 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % vebt_mint.pelims
% 5.06/5.40 thf(fact_7917_sum__bounds__lt__plus1,axiom,
% 5.06/5.40 ! [F: nat > nat,Mm: nat] :
% 5.06/5.40 ( ( groups3542108847815614940at_nat
% 5.06/5.40 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.06/5.40 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_bounds_lt_plus1
% 5.06/5.40 thf(fact_7918_sum__bounds__lt__plus1,axiom,
% 5.06/5.40 ! [F: nat > real,Mm: nat] :
% 5.06/5.40 ( ( groups6591440286371151544t_real
% 5.06/5.40 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.06/5.40 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.06/5.40 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % sum_bounds_lt_plus1
% 5.06/5.40 thf(fact_7919_fold__atLeastAtMost__nat_Opinduct,axiom,
% 5.06/5.40 ! [A0: nat > num > num,A12: nat,A23: nat,A32: num,P: ( nat > num > num ) > nat > nat > num > $o] :
% 5.06/5.40 ( ( accp_P4916641582247091100at_num @ set_fo256927282339908995el_num @ ( produc851828971589881931at_num @ A0 @ ( produc1195630363706982562at_num @ A12 @ ( product_Pair_nat_num @ A23 @ A32 ) ) ) )
% 5.06/5.40 => ( ! [F2: nat > num > num,A3: nat,B2: nat,Acc: num] :
% 5.06/5.40 ( ( accp_P4916641582247091100at_num @ set_fo256927282339908995el_num @ ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A3 @ ( product_Pair_nat_num @ B2 @ Acc ) ) ) )
% 5.06/5.40 => ( ( ~ ( ord_less_nat @ B2 @ A3 )
% 5.06/5.40 => ( P @ F2 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B2 @ ( F2 @ A3 @ Acc ) ) )
% 5.06/5.40 => ( P @ F2 @ A3 @ B2 @ Acc ) ) )
% 5.06/5.40 => ( P @ A0 @ A12 @ A23 @ A32 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % fold_atLeastAtMost_nat.pinduct
% 5.06/5.40 thf(fact_7920_fold__atLeastAtMost__nat_Opinduct,axiom,
% 5.06/5.40 ! [A0: nat > nat > nat,A12: nat,A23: nat,A32: nat,P: ( nat > nat > nat ) > nat > nat > nat > $o] :
% 5.06/5.40 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ A0 @ ( produc487386426758144856at_nat @ A12 @ ( product_Pair_nat_nat @ A23 @ A32 ) ) ) )
% 5.06/5.40 => ( ! [F2: nat > nat > nat,A3: nat,B2: nat,Acc: nat] :
% 5.06/5.40 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A3 @ ( product_Pair_nat_nat @ B2 @ Acc ) ) ) )
% 5.06/5.40 => ( ( ~ ( ord_less_nat @ B2 @ A3 )
% 5.06/5.40 => ( P @ F2 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B2 @ ( F2 @ A3 @ Acc ) ) )
% 5.06/5.40 => ( P @ F2 @ A3 @ B2 @ Acc ) ) )
% 5.06/5.40 => ( P @ A0 @ A12 @ A23 @ A32 ) ) ) ).
% 5.06/5.40
% 5.06/5.40 % fold_atLeastAtMost_nat.pinduct
% 5.06/5.40 thf(fact_7921_VEBT__internal_Ooption__shift_Opelims,axiom,
% 5.06/5.40 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 5.06/5.40 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb )
% 5.06/5.40 = Y )
% 5.06/5.40 => ( ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X @ ( produc488173922507101015at_nat @ Xa2 @ Xb ) ) )
% 5.06/5.40 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.06/5.41 => ( ( Y = none_P5556105721700978146at_nat )
% 5.06/5.41 => ~ ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Xb ) ) ) ) )
% 5.06/5.41 => ( ! [V2: product_prod_nat_nat] :
% 5.06/5.41 ( ( Xa2
% 5.06/5.41 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.06/5.41 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.06/5.41 => ( ( Y = none_P5556105721700978146at_nat )
% 5.06/5.41 => ~ ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) ) ) ) )
% 5.06/5.41 => ~ ! [A3: product_prod_nat_nat] :
% 5.06/5.41 ( ( Xa2
% 5.06/5.41 = ( some_P7363390416028606310at_nat @ A3 ) )
% 5.06/5.41 => ! [B2: product_prod_nat_nat] :
% 5.06/5.41 ( ( Xb
% 5.06/5.41 = ( some_P7363390416028606310at_nat @ B2 ) )
% 5.06/5.41 => ( ( Y
% 5.06/5.41 = ( some_P7363390416028606310at_nat @ ( X @ A3 @ B2 ) ) )
% 5.06/5.41 => ~ ( accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ ( produc2899441246263362727at_nat @ X @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % VEBT_internal.option_shift.pelims
% 5.06/5.41 thf(fact_7922_VEBT__internal_Ooption__shift_Opelims,axiom,
% 5.06/5.41 ! [X: num > num > num,Xa2: option_num,Xb: option_num,Y: option_num] :
% 5.06/5.41 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb )
% 5.06/5.41 = Y )
% 5.06/5.41 => ( ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X @ ( produc8585076106096196333on_num @ Xa2 @ Xb ) ) )
% 5.06/5.41 => ( ( ( Xa2 = none_num )
% 5.06/5.41 => ( ( Y = none_num )
% 5.06/5.41 => ~ ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X @ ( produc8585076106096196333on_num @ none_num @ Xb ) ) ) ) )
% 5.06/5.41 => ( ! [V2: num] :
% 5.06/5.41 ( ( Xa2
% 5.06/5.41 = ( some_num @ V2 ) )
% 5.06/5.41 => ( ( Xb = none_num )
% 5.06/5.41 => ( ( Y = none_num )
% 5.06/5.41 => ~ ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) ) ) ) )
% 5.06/5.41 => ~ ! [A3: num] :
% 5.06/5.41 ( ( Xa2
% 5.06/5.41 = ( some_num @ A3 ) )
% 5.06/5.41 => ! [B2: num] :
% 5.06/5.41 ( ( Xb
% 5.06/5.41 = ( some_num @ B2 ) )
% 5.06/5.41 => ( ( Y
% 5.06/5.41 = ( some_num @ ( X @ A3 @ B2 ) ) )
% 5.06/5.41 => ~ ( accp_P7605991808943153877on_num @ vEBT_V452583751252753300el_num @ ( produc5778274026573060048on_num @ X @ ( produc8585076106096196333on_num @ ( some_num @ A3 ) @ ( some_num @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % VEBT_internal.option_shift.pelims
% 5.06/5.41 thf(fact_7923_VEBT__internal_Ooption__shift_Opelims,axiom,
% 5.06/5.41 ! [X: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y: option_nat] :
% 5.06/5.41 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb )
% 5.06/5.41 = Y )
% 5.06/5.41 => ( ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X @ ( produc5098337634421038937on_nat @ Xa2 @ Xb ) ) )
% 5.06/5.41 => ( ( ( Xa2 = none_nat )
% 5.06/5.41 => ( ( Y = none_nat )
% 5.06/5.41 => ~ ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X @ ( produc5098337634421038937on_nat @ none_nat @ Xb ) ) ) ) )
% 5.06/5.41 => ( ! [V2: nat] :
% 5.06/5.41 ( ( Xa2
% 5.06/5.41 = ( some_nat @ V2 ) )
% 5.06/5.41 => ( ( Xb = none_nat )
% 5.06/5.41 => ( ( Y = none_nat )
% 5.06/5.41 => ~ ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) ) ) ) )
% 5.06/5.41 => ~ ! [A3: nat] :
% 5.06/5.41 ( ( Xa2
% 5.06/5.41 = ( some_nat @ A3 ) )
% 5.06/5.41 => ! [B2: nat] :
% 5.06/5.41 ( ( Xb
% 5.06/5.41 = ( some_nat @ B2 ) )
% 5.06/5.41 => ( ( Y
% 5.06/5.41 = ( some_nat @ ( X @ A3 @ B2 ) ) )
% 5.06/5.41 => ~ ( accp_P5496254298877145759on_nat @ vEBT_V3895251965096974666el_nat @ ( produc8929957630744042906on_nat @ X @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % VEBT_internal.option_shift.pelims
% 5.06/5.41 thf(fact_7924_sumr__cos__zero__one,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % sumr_cos_zero_one
% 5.06/5.41 thf(fact_7925_fold__atLeastAtMost__nat_Opelims,axiom,
% 5.06/5.41 ! [X: nat > num > num,Xa2: nat,Xb: nat,Xc: num,Y: num] :
% 5.06/5.41 ( ( ( set_fo8365102181078989356at_num @ X @ Xa2 @ Xb @ Xc )
% 5.06/5.41 = Y )
% 5.06/5.41 => ( ( accp_P4916641582247091100at_num @ set_fo256927282339908995el_num @ ( produc851828971589881931at_num @ X @ ( produc1195630363706982562at_num @ Xa2 @ ( product_Pair_nat_num @ Xb @ Xc ) ) ) )
% 5.06/5.41 => ~ ( ( ( ( ord_less_nat @ Xb @ Xa2 )
% 5.06/5.41 => ( Y = Xc ) )
% 5.06/5.41 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 5.06/5.41 => ( Y
% 5.06/5.41 = ( set_fo8365102181078989356at_num @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X @ Xa2 @ Xc ) ) ) ) )
% 5.06/5.41 => ~ ( accp_P4916641582247091100at_num @ set_fo256927282339908995el_num @ ( produc851828971589881931at_num @ X @ ( produc1195630363706982562at_num @ Xa2 @ ( product_Pair_nat_num @ Xb @ Xc ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fold_atLeastAtMost_nat.pelims
% 5.06/5.41 thf(fact_7926_fold__atLeastAtMost__nat_Opelims,axiom,
% 5.06/5.41 ! [X: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y: nat] :
% 5.06/5.41 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb @ Xc )
% 5.06/5.41 = Y )
% 5.06/5.41 => ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa2 @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) )
% 5.06/5.41 => ~ ( ( ( ( ord_less_nat @ Xb @ Xa2 )
% 5.06/5.41 => ( Y = Xc ) )
% 5.06/5.41 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 5.06/5.41 => ( Y
% 5.06/5.41 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X @ Xa2 @ Xc ) ) ) ) )
% 5.06/5.41 => ~ ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa2 @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fold_atLeastAtMost_nat.pelims
% 5.06/5.41 thf(fact_7927_fold__atLeastAtMost__nat_Opsimps,axiom,
% 5.06/5.41 ! [F: nat > num > num,A: nat,B: nat,Acc2: num] :
% 5.06/5.41 ( ( accp_P4916641582247091100at_num @ set_fo256927282339908995el_num @ ( produc851828971589881931at_num @ F @ ( produc1195630363706982562at_num @ A @ ( product_Pair_nat_num @ B @ Acc2 ) ) ) )
% 5.06/5.41 => ( ( ( ord_less_nat @ B @ A )
% 5.06/5.41 => ( ( set_fo8365102181078989356at_num @ F @ A @ B @ Acc2 )
% 5.06/5.41 = Acc2 ) )
% 5.06/5.41 & ( ~ ( ord_less_nat @ B @ A )
% 5.06/5.41 => ( ( set_fo8365102181078989356at_num @ F @ A @ B @ Acc2 )
% 5.06/5.41 = ( set_fo8365102181078989356at_num @ F @ ( plus_plus_nat @ A @ one_one_nat ) @ B @ ( F @ A @ Acc2 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fold_atLeastAtMost_nat.psimps
% 5.06/5.41 thf(fact_7928_fold__atLeastAtMost__nat_Opsimps,axiom,
% 5.06/5.41 ! [F: nat > nat > nat,A: nat,B: nat,Acc2: nat] :
% 5.06/5.41 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F @ ( produc487386426758144856at_nat @ A @ ( product_Pair_nat_nat @ B @ Acc2 ) ) ) )
% 5.06/5.41 => ( ( ( ord_less_nat @ B @ A )
% 5.06/5.41 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc2 )
% 5.06/5.41 = Acc2 ) )
% 5.06/5.41 & ( ~ ( ord_less_nat @ B @ A )
% 5.06/5.41 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc2 )
% 5.06/5.41 = ( set_fo2584398358068434914at_nat @ F @ ( plus_plus_nat @ A @ one_one_nat ) @ B @ ( F @ A @ Acc2 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fold_atLeastAtMost_nat.psimps
% 5.06/5.41 thf(fact_7929_sin__cos__npi,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_cos_npi
% 5.06/5.41 thf(fact_7930_cos__pi__eq__zero,axiom,
% 5.06/5.41 ! [M: nat] :
% 5.06/5.41 ( ( 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 ) ) ) )
% 5.06/5.41 = zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % cos_pi_eq_zero
% 5.06/5.41 thf(fact_7931_cos__zero,axiom,
% 5.06/5.41 ( ( cos_complex @ zero_zero_complex )
% 5.06/5.41 = one_one_complex ) ).
% 5.06/5.41
% 5.06/5.41 % cos_zero
% 5.06/5.41 thf(fact_7932_cos__zero,axiom,
% 5.06/5.41 ( ( cos_real @ zero_zero_real )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % cos_zero
% 5.06/5.41 thf(fact_7933_sin__pi__minus,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sin_real @ ( minus_minus_real @ pi @ X ) )
% 5.06/5.41 = ( sin_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_pi_minus
% 5.06/5.41 thf(fact_7934_cos__periodic__pi,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_periodic_pi
% 5.06/5.41 thf(fact_7935_cos__periodic__pi2,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_periodic_pi2
% 5.06/5.41 thf(fact_7936_sin__periodic__pi,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_periodic_pi
% 5.06/5.41 thf(fact_7937_sin__periodic__pi2,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_periodic_pi2
% 5.06/5.41 thf(fact_7938_cos__pi__minus,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( cos_real @ ( minus_minus_real @ pi @ X ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_pi_minus
% 5.06/5.41 thf(fact_7939_cos__minus__pi,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( cos_real @ ( minus_minus_real @ X @ pi ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_minus_pi
% 5.06/5.41 thf(fact_7940_sin__minus__pi,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sin_real @ ( minus_minus_real @ X @ pi ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_minus_pi
% 5.06/5.41 thf(fact_7941_sin__cos__squared__add3,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 5.06/5.41 = one_one_complex ) ).
% 5.06/5.41
% 5.06/5.41 % sin_cos_squared_add3
% 5.06/5.41 thf(fact_7942_sin__cos__squared__add3,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % sin_cos_squared_add3
% 5.06/5.41 thf(fact_7943_sin__npi,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.06/5.41 = zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % sin_npi
% 5.06/5.41 thf(fact_7944_sin__npi2,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.06/5.41 = zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % sin_npi2
% 5.06/5.41 thf(fact_7945_cos__pi__half,axiom,
% 5.06/5.41 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % cos_pi_half
% 5.06/5.41 thf(fact_7946_sin__two__pi,axiom,
% 5.06/5.41 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.06/5.41 = zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % sin_two_pi
% 5.06/5.41 thf(fact_7947_sin__pi__half,axiom,
% 5.06/5.41 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % sin_pi_half
% 5.06/5.41 thf(fact_7948_cos__two__pi,axiom,
% 5.06/5.41 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % cos_two_pi
% 5.06/5.41 thf(fact_7949_cos__periodic,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.06/5.41 = ( cos_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_periodic
% 5.06/5.41 thf(fact_7950_sin__periodic,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.06/5.41 = ( sin_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_periodic
% 5.06/5.41 thf(fact_7951_cos__2pi__minus,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.06/5.41 = ( cos_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_2pi_minus
% 5.06/5.41 thf(fact_7952_cos__npi2,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.06/5.41 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_npi2
% 5.06/5.41 thf(fact_7953_cos__npi,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.06/5.41 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_npi
% 5.06/5.41 thf(fact_7954_sin__cos__squared__add,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % sin_cos_squared_add
% 5.06/5.41 thf(fact_7955_sin__cos__squared__add,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = one_one_complex ) ).
% 5.06/5.41
% 5.06/5.41 % sin_cos_squared_add
% 5.06/5.41 thf(fact_7956_sin__cos__squared__add2,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % sin_cos_squared_add2
% 5.06/5.41 thf(fact_7957_sin__cos__squared__add2,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = one_one_complex ) ).
% 5.06/5.41
% 5.06/5.41 % sin_cos_squared_add2
% 5.06/5.41 thf(fact_7958_sin__2npi,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 5.06/5.41 = zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % sin_2npi
% 5.06/5.41 thf(fact_7959_cos__2npi,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % cos_2npi
% 5.06/5.41 thf(fact_7960_sin__2pi__minus,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_2pi_minus
% 5.06/5.41 thf(fact_7961_cos__3over2__pi,axiom,
% 5.06/5.41 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.06/5.41 = zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % cos_3over2_pi
% 5.06/5.41 thf(fact_7962_sin__3over2__pi,axiom,
% 5.06/5.41 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.06/5.41 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_3over2_pi
% 5.06/5.41 thf(fact_7963_sin__add,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( sin_real @ ( plus_plus_real @ X @ Y ) )
% 5.06/5.41 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_add
% 5.06/5.41 thf(fact_7964_cos__one__sin__zero,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( ( cos_complex @ X )
% 5.06/5.41 = one_one_complex )
% 5.06/5.41 => ( ( sin_complex @ X )
% 5.06/5.41 = zero_zero_complex ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_one_sin_zero
% 5.06/5.41 thf(fact_7965_cos__one__sin__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ( cos_real @ X )
% 5.06/5.41 = one_one_real )
% 5.06/5.41 => ( ( sin_real @ X )
% 5.06/5.41 = zero_zero_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_one_sin_zero
% 5.06/5.41 thf(fact_7966_polar__Ex,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ? [R3: real,A3: real] :
% 5.06/5.41 ( ( X
% 5.06/5.41 = ( times_times_real @ R3 @ ( cos_real @ A3 ) ) )
% 5.06/5.41 & ( Y
% 5.06/5.41 = ( times_times_real @ R3 @ ( sin_real @ A3 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % polar_Ex
% 5.06/5.41 thf(fact_7967_sin__diff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( sin_real @ ( minus_minus_real @ X @ Y ) )
% 5.06/5.41 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_diff
% 5.06/5.41 thf(fact_7968_cos__diff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 5.06/5.41 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_diff
% 5.06/5.41 thf(fact_7969_cos__add,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 5.06/5.41 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_add
% 5.06/5.41 thf(fact_7970_sin__double,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.06/5.41 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_double
% 5.06/5.41 thf(fact_7971_sin__double,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.06/5.41 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_double
% 5.06/5.41 thf(fact_7972_sincos__principal__value,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ? [Y5: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y5 )
% 5.06/5.41 & ( ord_less_eq_real @ Y5 @ pi )
% 5.06/5.41 & ( ( sin_real @ Y5 )
% 5.06/5.41 = ( sin_real @ X ) )
% 5.06/5.41 & ( ( cos_real @ Y5 )
% 5.06/5.41 = ( cos_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sincos_principal_value
% 5.06/5.41 thf(fact_7973_sin__x__le__x,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_x_le_x
% 5.06/5.41 thf(fact_7974_sin__le__one,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % sin_le_one
% 5.06/5.41 thf(fact_7975_cos__le__one,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % cos_le_one
% 5.06/5.41 thf(fact_7976_abs__sin__x__le__abs__x,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % abs_sin_x_le_abs_x
% 5.06/5.41 thf(fact_7977_sin__cos__le1,axiom,
% 5.06/5.41 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % sin_cos_le1
% 5.06/5.41 thf(fact_7978_cos__squared__eq,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_squared_eq
% 5.06/5.41 thf(fact_7979_cos__squared__eq,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_squared_eq
% 5.06/5.41 thf(fact_7980_sin__squared__eq,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_squared_eq
% 5.06/5.41 thf(fact_7981_sin__squared__eq,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_squared_eq
% 5.06/5.41 thf(fact_7982_sin__x__ge__neg__x,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_x_ge_neg_x
% 5.06/5.41 thf(fact_7983_sin__ge__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.06/5.41 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_ge_zero
% 5.06/5.41 thf(fact_7984_sin__ge__minus__one,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_ge_minus_one
% 5.06/5.41 thf(fact_7985_cos__inj__pi,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ pi )
% 5.06/5.41 => ( ( ( cos_real @ X )
% 5.06/5.41 = ( cos_real @ Y ) )
% 5.06/5.41 => ( X = Y ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_inj_pi
% 5.06/5.41 thf(fact_7986_cos__mono__le__eq,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ pi )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 5.06/5.41 = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_mono_le_eq
% 5.06/5.41 thf(fact_7987_cos__monotone__0__pi__le,axiom,
% 5.06/5.41 ! [Y: real,X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.06/5.41 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_monotone_0_pi_le
% 5.06/5.41 thf(fact_7988_cos__ge__minus__one,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_ge_minus_one
% 5.06/5.41 thf(fact_7989_abs__sin__le__one,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % abs_sin_le_one
% 5.06/5.41 thf(fact_7990_abs__cos__le__one,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % abs_cos_le_one
% 5.06/5.41 thf(fact_7991_cos__diff__cos,axiom,
% 5.06/5.41 ! [W: complex,Z: complex] :
% 5.06/5.41 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_diff_cos
% 5.06/5.41 thf(fact_7992_cos__diff__cos,axiom,
% 5.06/5.41 ! [W: real,Z: real] :
% 5.06/5.41 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_diff_cos
% 5.06/5.41 thf(fact_7993_sin__diff__sin,axiom,
% 5.06/5.41 ! [W: complex,Z: complex] :
% 5.06/5.41 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_diff_sin
% 5.06/5.41 thf(fact_7994_sin__diff__sin,axiom,
% 5.06/5.41 ! [W: real,Z: real] :
% 5.06/5.41 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_diff_sin
% 5.06/5.41 thf(fact_7995_sin__plus__sin,axiom,
% 5.06/5.41 ! [W: complex,Z: complex] :
% 5.06/5.41 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_plus_sin
% 5.06/5.41 thf(fact_7996_sin__plus__sin,axiom,
% 5.06/5.41 ! [W: real,Z: real] :
% 5.06/5.41 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_plus_sin
% 5.06/5.41 thf(fact_7997_cos__times__sin,axiom,
% 5.06/5.41 ! [W: complex,Z: complex] :
% 5.06/5.41 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_times_sin
% 5.06/5.41 thf(fact_7998_cos__times__sin,axiom,
% 5.06/5.41 ! [W: real,Z: real] :
% 5.06/5.41 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_times_sin
% 5.06/5.41 thf(fact_7999_sin__times__cos,axiom,
% 5.06/5.41 ! [W: complex,Z: complex] :
% 5.06/5.41 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_times_cos
% 5.06/5.41 thf(fact_8000_sin__times__cos,axiom,
% 5.06/5.41 ! [W: real,Z: real] :
% 5.06/5.41 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_times_cos
% 5.06/5.41 thf(fact_8001_sin__times__sin,axiom,
% 5.06/5.41 ! [W: complex,Z: complex] :
% 5.06/5.41 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_times_sin
% 5.06/5.41 thf(fact_8002_sin__times__sin,axiom,
% 5.06/5.41 ! [W: real,Z: real] :
% 5.06/5.41 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_times_sin
% 5.06/5.41 thf(fact_8003_cos__double,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.06/5.41 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_double
% 5.06/5.41 thf(fact_8004_cos__double,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.06/5.41 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_double
% 5.06/5.41 thf(fact_8005_cos__double__sin,axiom,
% 5.06/5.41 ! [W: complex] :
% 5.06/5.41 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.06/5.41 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_double_sin
% 5.06/5.41 thf(fact_8006_cos__double__sin,axiom,
% 5.06/5.41 ! [W: real] :
% 5.06/5.41 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.06/5.41 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_double_sin
% 5.06/5.41 thf(fact_8007_cos__two__neq__zero,axiom,
% 5.06/5.41 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.41 != zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % cos_two_neq_zero
% 5.06/5.41 thf(fact_8008_cos__mono__less__eq,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ pi )
% 5.06/5.41 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 5.06/5.41 = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_mono_less_eq
% 5.06/5.41 thf(fact_8009_cos__monotone__0__pi,axiom,
% 5.06/5.41 ! [Y: real,X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( ord_less_real @ Y @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.06/5.41 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_monotone_0_pi
% 5.06/5.41 thf(fact_8010_cos__monotone__minus__pi__0_H,axiom,
% 5.06/5.41 ! [Y: real,X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.41 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_monotone_minus_pi_0'
% 5.06/5.41 thf(fact_8011_sincos__total__pi,axiom,
% 5.06/5.41 ! [Y: real,X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = one_one_real )
% 5.06/5.41 => ? [T5: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.06/5.41 & ( ord_less_eq_real @ T5 @ pi )
% 5.06/5.41 & ( X
% 5.06/5.41 = ( cos_real @ T5 ) )
% 5.06/5.41 & ( Y
% 5.06/5.41 = ( sin_real @ T5 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sincos_total_pi
% 5.06/5.41 thf(fact_8012_sin__expansion__lemma,axiom,
% 5.06/5.41 ! [X: real,M: nat] :
% 5.06/5.41 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_expansion_lemma
% 5.06/5.41 thf(fact_8013_cos__expansion__lemma,axiom,
% 5.06/5.41 ! [X: real,M: nat] :
% 5.06/5.41 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_expansion_lemma
% 5.06/5.41 thf(fact_8014_sin__gt__zero__02,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.41 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_gt_zero_02
% 5.06/5.41 thf(fact_8015_cos__two__less__zero,axiom,
% 5.06/5.41 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.06/5.41
% 5.06/5.41 % cos_two_less_zero
% 5.06/5.41 thf(fact_8016_cos__two__le__zero,axiom,
% 5.06/5.41 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.06/5.41
% 5.06/5.41 % cos_two_le_zero
% 5.06/5.41 thf(fact_8017_cos__is__zero,axiom,
% 5.06/5.41 ? [X3: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.06/5.41 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.41 & ( ( cos_real @ X3 )
% 5.06/5.41 = zero_zero_real )
% 5.06/5.41 & ! [Y3: real] :
% 5.06/5.41 ( ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.06/5.41 & ( ord_less_eq_real @ Y3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.41 & ( ( cos_real @ Y3 )
% 5.06/5.41 = zero_zero_real ) )
% 5.06/5.41 => ( Y3 = X3 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_is_zero
% 5.06/5.41 thf(fact_8018_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.06/5.41 ( set_fo2584398358068434914at_nat
% 5.06/5.41 = ( ^ [F3: nat > nat > nat,A4: nat,B4: nat,Acc3: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A4 ) @ Acc3 @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B4 @ ( F3 @ A4 @ Acc3 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fold_atLeastAtMost_nat.simps
% 5.06/5.41 thf(fact_8019_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.06/5.41 ! [X: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y: nat] :
% 5.06/5.41 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb @ Xc )
% 5.06/5.41 = Y )
% 5.06/5.41 => ( ( ( ord_less_nat @ Xb @ Xa2 )
% 5.06/5.41 => ( Y = Xc ) )
% 5.06/5.41 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 5.06/5.41 => ( Y
% 5.06/5.41 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fold_atLeastAtMost_nat.elims
% 5.06/5.41 thf(fact_8020_cos__monotone__minus__pi__0,axiom,
% 5.06/5.41 ! [Y: real,X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.06/5.41 => ( ( ord_less_real @ Y @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.41 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_monotone_minus_pi_0
% 5.06/5.41 thf(fact_8021_cos__total,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ? [X3: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.06/5.41 & ( ord_less_eq_real @ X3 @ pi )
% 5.06/5.41 & ( ( cos_real @ X3 )
% 5.06/5.41 = Y )
% 5.06/5.41 & ! [Y3: real] :
% 5.06/5.41 ( ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.06/5.41 & ( ord_less_eq_real @ Y3 @ pi )
% 5.06/5.41 & ( ( cos_real @ Y3 )
% 5.06/5.41 = Y ) )
% 5.06/5.41 => ( Y3 = X3 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_total
% 5.06/5.41 thf(fact_8022_sincos__total__pi__half,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = one_one_real )
% 5.06/5.41 => ? [T5: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.06/5.41 & ( ord_less_eq_real @ T5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 & ( X
% 5.06/5.41 = ( cos_real @ T5 ) )
% 5.06/5.41 & ( Y
% 5.06/5.41 = ( sin_real @ T5 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sincos_total_pi_half
% 5.06/5.41 thf(fact_8023_sincos__total__2pi__le,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = one_one_real )
% 5.06/5.41 => ? [T5: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.06/5.41 & ( ord_less_eq_real @ T5 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.06/5.41 & ( X
% 5.06/5.41 = ( cos_real @ T5 ) )
% 5.06/5.41 & ( Y
% 5.06/5.41 = ( sin_real @ T5 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sincos_total_2pi_le
% 5.06/5.41 thf(fact_8024_sincos__total__2pi,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = one_one_real )
% 5.06/5.41 => ~ ! [T5: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.06/5.41 => ( ( ord_less_real @ T5 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.06/5.41 => ( ( X
% 5.06/5.41 = ( cos_real @ T5 ) )
% 5.06/5.41 => ( Y
% 5.06/5.41 != ( sin_real @ T5 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sincos_total_2pi
% 5.06/5.41 thf(fact_8025_sin__pi__divide__n__ge__0,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( N2 != zero_zero_nat )
% 5.06/5.41 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_pi_divide_n_ge_0
% 5.06/5.41 thf(fact_8026_cos__plus__cos,axiom,
% 5.06/5.41 ! [W: complex,Z: complex] :
% 5.06/5.41 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_plus_cos
% 5.06/5.41 thf(fact_8027_cos__plus__cos,axiom,
% 5.06/5.41 ! [W: real,Z: real] :
% 5.06/5.41 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_plus_cos
% 5.06/5.41 thf(fact_8028_cos__times__cos,axiom,
% 5.06/5.41 ! [W: complex,Z: complex] :
% 5.06/5.41 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_times_cos
% 5.06/5.41 thf(fact_8029_cos__times__cos,axiom,
% 5.06/5.41 ! [W: real,Z: real] :
% 5.06/5.41 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.06/5.41 = ( 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 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_times_cos
% 5.06/5.41 thf(fact_8030_sin__gt__zero2,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_gt_zero2
% 5.06/5.41 thf(fact_8031_sin__lt__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ pi @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.06/5.41 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_lt_zero
% 5.06/5.41 thf(fact_8032_cos__double__less__one,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.41 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_double_less_one
% 5.06/5.41 thf(fact_8033_sin__30,axiom,
% 5.06/5.41 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.06/5.41 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_30
% 5.06/5.41 thf(fact_8034_cos__gt__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_gt_zero
% 5.06/5.41 thf(fact_8035_sin__inj__pi,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ( sin_real @ X )
% 5.06/5.41 = ( sin_real @ Y ) )
% 5.06/5.41 => ( X = Y ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_inj_pi
% 5.06/5.41 thf(fact_8036_sin__mono__le__eq,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 5.06/5.41 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_mono_le_eq
% 5.06/5.41 thf(fact_8037_sin__monotone__2pi__le,axiom,
% 5.06/5.41 ! [Y: real,X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_monotone_2pi_le
% 5.06/5.41 thf(fact_8038_cos__60,axiom,
% 5.06/5.41 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.06/5.41 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_60
% 5.06/5.41 thf(fact_8039_sum__atLeastAtMost__code,axiom,
% 5.06/5.41 ! [F: nat > complex,A: nat,B: nat] :
% 5.06/5.41 ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.06/5.41 = ( set_fo1517530859248394432omplex
% 5.06/5.41 @ ^ [A4: nat] : ( plus_plus_complex @ ( F @ A4 ) )
% 5.06/5.41 @ A
% 5.06/5.41 @ B
% 5.06/5.41 @ zero_zero_complex ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_atLeastAtMost_code
% 5.06/5.41 thf(fact_8040_sum__atLeastAtMost__code,axiom,
% 5.06/5.41 ! [F: nat > rat,A: nat,B: nat] :
% 5.06/5.41 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.06/5.41 = ( set_fo1949268297981939178at_rat
% 5.06/5.41 @ ^ [A4: nat] : ( plus_plus_rat @ ( F @ A4 ) )
% 5.06/5.41 @ A
% 5.06/5.41 @ B
% 5.06/5.41 @ zero_zero_rat ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_atLeastAtMost_code
% 5.06/5.41 thf(fact_8041_sum__atLeastAtMost__code,axiom,
% 5.06/5.41 ! [F: nat > int,A: nat,B: nat] :
% 5.06/5.41 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.06/5.41 = ( set_fo2581907887559384638at_int
% 5.06/5.41 @ ^ [A4: nat] : ( plus_plus_int @ ( F @ A4 ) )
% 5.06/5.41 @ A
% 5.06/5.41 @ B
% 5.06/5.41 @ zero_zero_int ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_atLeastAtMost_code
% 5.06/5.41 thf(fact_8042_sum__atLeastAtMost__code,axiom,
% 5.06/5.41 ! [F: nat > nat,A: nat,B: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.06/5.41 = ( set_fo2584398358068434914at_nat
% 5.06/5.41 @ ^ [A4: nat] : ( plus_plus_nat @ ( F @ A4 ) )
% 5.06/5.41 @ A
% 5.06/5.41 @ B
% 5.06/5.41 @ zero_zero_nat ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_atLeastAtMost_code
% 5.06/5.41 thf(fact_8043_sum__atLeastAtMost__code,axiom,
% 5.06/5.41 ! [F: nat > real,A: nat,B: nat] :
% 5.06/5.41 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.06/5.41 = ( set_fo3111899725591712190t_real
% 5.06/5.41 @ ^ [A4: nat] : ( plus_plus_real @ ( F @ A4 ) )
% 5.06/5.41 @ A
% 5.06/5.41 @ B
% 5.06/5.41 @ zero_zero_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_atLeastAtMost_code
% 5.06/5.41 thf(fact_8044_cos__double__cos,axiom,
% 5.06/5.41 ! [W: complex] :
% 5.06/5.41 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.06/5.41 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_double_cos
% 5.06/5.41 thf(fact_8045_cos__double__cos,axiom,
% 5.06/5.41 ! [W: real] :
% 5.06/5.41 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.06/5.41 = ( 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 ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_double_cos
% 5.06/5.41 thf(fact_8046_cos__treble__cos,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 5.06/5.41 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_treble_cos
% 5.06/5.41 thf(fact_8047_cos__treble__cos,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 5.06/5.41 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_treble_cos
% 5.06/5.41 thf(fact_8048_sin__le__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ pi @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.06/5.41 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_le_zero
% 5.06/5.41 thf(fact_8049_sin__less__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.06/5.41 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_less_zero
% 5.06/5.41 thf(fact_8050_sin__mono__less__eq,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 5.06/5.41 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_mono_less_eq
% 5.06/5.41 thf(fact_8051_sin__monotone__2pi,axiom,
% 5.06/5.41 ! [Y: real,X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_real @ Y @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_monotone_2pi
% 5.06/5.41 thf(fact_8052_sin__total,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ? [X3: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.06/5.41 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 & ( ( sin_real @ X3 )
% 5.06/5.41 = Y )
% 5.06/5.41 & ! [Y3: real] :
% 5.06/5.41 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.06/5.41 & ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 & ( ( sin_real @ Y3 )
% 5.06/5.41 = Y ) )
% 5.06/5.41 => ( Y3 = X3 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_total
% 5.06/5.41 thf(fact_8053_cos__gt__zero__pi,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_gt_zero_pi
% 5.06/5.41 thf(fact_8054_cos__ge__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_ge_zero
% 5.06/5.41 thf(fact_8055_cos__one__2pi,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ( cos_real @ X )
% 5.06/5.41 = one_one_real )
% 5.06/5.41 = ( ? [X2: nat] :
% 5.06/5.41 ( X
% 5.06/5.41 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.06/5.41 | ? [X2: nat] :
% 5.06/5.41 ( X
% 5.06/5.41 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_one_2pi
% 5.06/5.41 thf(fact_8056_sin__pi__divide__n__gt__0,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.41 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_pi_divide_n_gt_0
% 5.06/5.41 thf(fact_8057_sin__zero__lemma,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ( sin_real @ X )
% 5.06/5.41 = zero_zero_real )
% 5.06/5.41 => ? [N3: nat] :
% 5.06/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.06/5.41 & ( X
% 5.06/5.41 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_zero_lemma
% 5.06/5.41 thf(fact_8058_sin__zero__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ( sin_real @ X )
% 5.06/5.41 = zero_zero_real )
% 5.06/5.41 = ( ? [N: nat] :
% 5.06/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.06/5.41 & ( X
% 5.06/5.41 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.41 | ? [N: nat] :
% 5.06/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.06/5.41 & ( X
% 5.06/5.41 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_zero_iff
% 5.06/5.41 thf(fact_8059_cos__zero__lemma,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ( cos_real @ X )
% 5.06/5.41 = zero_zero_real )
% 5.06/5.41 => ? [N3: nat] :
% 5.06/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.06/5.41 & ( X
% 5.06/5.41 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_zero_lemma
% 5.06/5.41 thf(fact_8060_cos__zero__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ( cos_real @ X )
% 5.06/5.41 = zero_zero_real )
% 5.06/5.41 = ( ? [N: nat] :
% 5.06/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.06/5.41 & ( X
% 5.06/5.41 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.41 | ? [N: nat] :
% 5.06/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.06/5.41 & ( X
% 5.06/5.41 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_zero_iff
% 5.06/5.41 thf(fact_8061_Maclaurin__cos__expansion2,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ? [T5: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ T5 )
% 5.06/5.41 & ( ord_less_real @ T5 @ X )
% 5.06/5.41 & ( ( cos_real @ X )
% 5.06/5.41 = ( plus_plus_real
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_cos_expansion2
% 5.06/5.41 thf(fact_8062_Maclaurin__minus__cos__expansion,axiom,
% 5.06/5.41 ! [N2: nat,X: real] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.06/5.41 => ? [T5: real] :
% 5.06/5.41 ( ( ord_less_real @ X @ T5 )
% 5.06/5.41 & ( ord_less_real @ T5 @ zero_zero_real )
% 5.06/5.41 & ( ( cos_real @ X )
% 5.06/5.41 = ( plus_plus_real
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_minus_cos_expansion
% 5.06/5.41 thf(fact_8063_Maclaurin__cos__expansion,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ? [T5: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X ) )
% 5.06/5.41 & ( ( cos_real @ X )
% 5.06/5.41 = ( plus_plus_real
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_cos_expansion
% 5.06/5.41 thf(fact_8064_tan__double,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( ( cos_complex @ X )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_double
% 5.06/5.41 thf(fact_8065_tan__double,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ( cos_real @ X )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.06/5.41 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_double
% 5.06/5.41 thf(fact_8066_in__measure,axiom,
% 5.06/5.41 ! [X: num,Y: num,F: num > nat] :
% 5.06/5.41 ( ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y ) @ ( measure_num @ F ) )
% 5.06/5.41 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % in_measure
% 5.06/5.41 thf(fact_8067_in__measure,axiom,
% 5.06/5.41 ! [X: nat,Y: nat,F: nat > nat] :
% 5.06/5.41 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measure_nat @ F ) )
% 5.06/5.41 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % in_measure
% 5.06/5.41 thf(fact_8068_in__measure,axiom,
% 5.06/5.41 ! [X: int,Y: int,F: int > nat] :
% 5.06/5.41 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measure_int @ F ) )
% 5.06/5.41 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % in_measure
% 5.06/5.41 thf(fact_8069_tan__periodic__pi,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 5.06/5.41 = ( tan_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_periodic_pi
% 5.06/5.41 thf(fact_8070_fact__0,axiom,
% 5.06/5.41 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.06/5.41 = one_one_complex ) ).
% 5.06/5.41
% 5.06/5.41 % fact_0
% 5.06/5.41 thf(fact_8071_fact__0,axiom,
% 5.06/5.41 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.06/5.41 = one_one_rat ) ).
% 5.06/5.41
% 5.06/5.41 % fact_0
% 5.06/5.41 thf(fact_8072_fact__0,axiom,
% 5.06/5.41 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.06/5.41 = one_one_int ) ).
% 5.06/5.41
% 5.06/5.41 % fact_0
% 5.06/5.41 thf(fact_8073_fact__0,axiom,
% 5.06/5.41 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % fact_0
% 5.06/5.41 thf(fact_8074_fact__0,axiom,
% 5.06/5.41 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.06/5.41 = one_one_nat ) ).
% 5.06/5.41
% 5.06/5.41 % fact_0
% 5.06/5.41 thf(fact_8075_fact__1,axiom,
% 5.06/5.41 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.06/5.41 = one_one_complex ) ).
% 5.06/5.41
% 5.06/5.41 % fact_1
% 5.06/5.41 thf(fact_8076_fact__1,axiom,
% 5.06/5.41 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.06/5.41 = one_one_rat ) ).
% 5.06/5.41
% 5.06/5.41 % fact_1
% 5.06/5.41 thf(fact_8077_fact__1,axiom,
% 5.06/5.41 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.06/5.41 = one_one_int ) ).
% 5.06/5.41
% 5.06/5.41 % fact_1
% 5.06/5.41 thf(fact_8078_fact__1,axiom,
% 5.06/5.41 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % fact_1
% 5.06/5.41 thf(fact_8079_fact__1,axiom,
% 5.06/5.41 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.06/5.41 = one_one_nat ) ).
% 5.06/5.41
% 5.06/5.41 % fact_1
% 5.06/5.41 thf(fact_8080_fact__Suc__0,axiom,
% 5.06/5.41 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.06/5.41 = one_one_complex ) ).
% 5.06/5.41
% 5.06/5.41 % fact_Suc_0
% 5.06/5.41 thf(fact_8081_fact__Suc__0,axiom,
% 5.06/5.41 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.06/5.41 = one_one_rat ) ).
% 5.06/5.41
% 5.06/5.41 % fact_Suc_0
% 5.06/5.41 thf(fact_8082_fact__Suc__0,axiom,
% 5.06/5.41 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.06/5.41 = one_one_int ) ).
% 5.06/5.41
% 5.06/5.41 % fact_Suc_0
% 5.06/5.41 thf(fact_8083_fact__Suc__0,axiom,
% 5.06/5.41 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % fact_Suc_0
% 5.06/5.41 thf(fact_8084_fact__Suc__0,axiom,
% 5.06/5.41 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.06/5.41 = one_one_nat ) ).
% 5.06/5.41
% 5.06/5.41 % fact_Suc_0
% 5.06/5.41 thf(fact_8085_fact__Suc,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( semiri773545260158071498ct_rat @ ( suc @ N2 ) )
% 5.06/5.41 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_Suc
% 5.06/5.41 thf(fact_8086_fact__Suc,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( semiri1406184849735516958ct_int @ ( suc @ N2 ) )
% 5.06/5.41 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_Suc
% 5.06/5.41 thf(fact_8087_fact__Suc,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( semiri3624122377584611663nteger @ ( suc @ N2 ) )
% 5.06/5.41 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N2 ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_Suc
% 5.06/5.41 thf(fact_8088_fact__Suc,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( semiri2265585572941072030t_real @ ( suc @ N2 ) )
% 5.06/5.41 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_Suc
% 5.06/5.41 thf(fact_8089_fact__Suc,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( semiri1408675320244567234ct_nat @ ( suc @ N2 ) )
% 5.06/5.41 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_Suc
% 5.06/5.41 thf(fact_8090_tan__npi,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.06/5.41 = zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % tan_npi
% 5.06/5.41 thf(fact_8091_tan__periodic__n,axiom,
% 5.06/5.41 ! [X: real,N2: num] :
% 5.06/5.41 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N2 ) @ pi ) ) )
% 5.06/5.41 = ( tan_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_periodic_n
% 5.06/5.41 thf(fact_8092_tan__periodic__nat,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) ) )
% 5.06/5.41 = ( tan_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_periodic_nat
% 5.06/5.41 thf(fact_8093_fact__2,axiom,
% 5.06/5.41 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_2
% 5.06/5.41 thf(fact_8094_fact__2,axiom,
% 5.06/5.41 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_2
% 5.06/5.41 thf(fact_8095_fact__2,axiom,
% 5.06/5.41 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_2
% 5.06/5.41 thf(fact_8096_fact__2,axiom,
% 5.06/5.41 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_2
% 5.06/5.41 thf(fact_8097_fact__2,axiom,
% 5.06/5.41 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_2
% 5.06/5.41 thf(fact_8098_tan__periodic,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.06/5.41 = ( tan_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_periodic
% 5.06/5.41 thf(fact_8099_fact__ge__zero,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_ge_zero
% 5.06/5.41 thf(fact_8100_fact__ge__zero,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_ge_zero
% 5.06/5.41 thf(fact_8101_fact__ge__zero,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_ge_zero
% 5.06/5.41 thf(fact_8102_fact__ge__zero,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_ge_zero
% 5.06/5.41 thf(fact_8103_fact__not__neg,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ zero_zero_rat ) ).
% 5.06/5.41
% 5.06/5.41 % fact_not_neg
% 5.06/5.41 thf(fact_8104_fact__not__neg,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N2 ) @ zero_zero_int ) ).
% 5.06/5.41
% 5.06/5.41 % fact_not_neg
% 5.06/5.41 thf(fact_8105_fact__not__neg,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N2 ) @ zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % fact_not_neg
% 5.06/5.41 thf(fact_8106_fact__not__neg,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ zero_zero_nat ) ).
% 5.06/5.41
% 5.06/5.41 % fact_not_neg
% 5.06/5.41 thf(fact_8107_fact__gt__zero,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_gt_zero
% 5.06/5.41 thf(fact_8108_fact__gt__zero,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_gt_zero
% 5.06/5.41 thf(fact_8109_fact__gt__zero,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_gt_zero
% 5.06/5.41 thf(fact_8110_fact__gt__zero,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_gt_zero
% 5.06/5.41 thf(fact_8111_fact__ge__1,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_ge_1
% 5.06/5.41 thf(fact_8112_fact__ge__1,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_ge_1
% 5.06/5.41 thf(fact_8113_fact__ge__1,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_ge_1
% 5.06/5.41 thf(fact_8114_fact__ge__1,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_ge_1
% 5.06/5.41 thf(fact_8115_fact__mono,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_mono
% 5.06/5.41 thf(fact_8116_fact__mono,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_mono
% 5.06/5.41 thf(fact_8117_fact__mono,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_mono
% 5.06/5.41 thf(fact_8118_fact__mono,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_mono
% 5.06/5.41 thf(fact_8119_fact__dvd,axiom,
% 5.06/5.41 ! [N2: nat,M: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.41 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_dvd
% 5.06/5.41 thf(fact_8120_fact__dvd,axiom,
% 5.06/5.41 ! [N2: nat,M: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.41 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_dvd
% 5.06/5.41 thf(fact_8121_fact__dvd,axiom,
% 5.06/5.41 ! [N2: nat,M: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.41 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_dvd
% 5.06/5.41 thf(fact_8122_fact__dvd,axiom,
% 5.06/5.41 ! [N2: nat,M: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.41 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_dvd
% 5.06/5.41 thf(fact_8123_fact__less__mono,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.41 => ( ( ord_less_nat @ M @ N2 )
% 5.06/5.41 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_less_mono
% 5.06/5.41 thf(fact_8124_fact__less__mono,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.41 => ( ( ord_less_nat @ M @ N2 )
% 5.06/5.41 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_less_mono
% 5.06/5.41 thf(fact_8125_fact__less__mono,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.41 => ( ( ord_less_nat @ M @ N2 )
% 5.06/5.41 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_less_mono
% 5.06/5.41 thf(fact_8126_fact__less__mono,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.41 => ( ( ord_less_nat @ M @ N2 )
% 5.06/5.41 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_less_mono
% 5.06/5.41 thf(fact_8127_fact__fact__dvd__fact,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N2 ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_fact_dvd_fact
% 5.06/5.41 thf(fact_8128_fact__fact__dvd__fact,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N2 ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_fact_dvd_fact
% 5.06/5.41 thf(fact_8129_fact__fact__dvd__fact,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_fact_dvd_fact
% 5.06/5.41 thf(fact_8130_fact__fact__dvd__fact,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_fact_dvd_fact
% 5.06/5.41 thf(fact_8131_fact__fact__dvd__fact,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_fact_dvd_fact
% 5.06/5.41 thf(fact_8132_fact__mod,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.06/5.41 = zero_zero_int ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_mod
% 5.06/5.41 thf(fact_8133_fact__mod,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.06/5.41 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_mod
% 5.06/5.41 thf(fact_8134_fact__mod,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.06/5.41 = zero_zero_nat ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_mod
% 5.06/5.41 thf(fact_8135_fact__le__power,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_le3102999989581377725nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri4939895301339042750nteger @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_le_power
% 5.06/5.41 thf(fact_8136_fact__le__power,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_le_power
% 5.06/5.41 thf(fact_8137_fact__le__power,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_le_power
% 5.06/5.41 thf(fact_8138_fact__le__power,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_le_power
% 5.06/5.41 thf(fact_8139_fact__le__power,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_le_power
% 5.06/5.41 thf(fact_8140_tan__def,axiom,
% 5.06/5.41 ( tan_complex
% 5.06/5.41 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X2 ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_def
% 5.06/5.41 thf(fact_8141_tan__def,axiom,
% 5.06/5.41 ( tan_real
% 5.06/5.41 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ X2 ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_def
% 5.06/5.41 thf(fact_8142_choose__dvd,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_dvd
% 5.06/5.41 thf(fact_8143_choose__dvd,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_dvd
% 5.06/5.41 thf(fact_8144_choose__dvd,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_dvd
% 5.06/5.41 thf(fact_8145_choose__dvd,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_dvd
% 5.06/5.41 thf(fact_8146_choose__dvd,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_dvd
% 5.06/5.41 thf(fact_8147_fact__numeral,axiom,
% 5.06/5.41 ! [K: num] :
% 5.06/5.41 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.06/5.41 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_numeral
% 5.06/5.41 thf(fact_8148_fact__numeral,axiom,
% 5.06/5.41 ! [K: num] :
% 5.06/5.41 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.06/5.41 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_numeral
% 5.06/5.41 thf(fact_8149_fact__numeral,axiom,
% 5.06/5.41 ! [K: num] :
% 5.06/5.41 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.06/5.41 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_numeral
% 5.06/5.41 thf(fact_8150_fact__numeral,axiom,
% 5.06/5.41 ! [K: num] :
% 5.06/5.41 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.06/5.41 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_numeral
% 5.06/5.41 thf(fact_8151_fact__numeral,axiom,
% 5.06/5.41 ! [K: num] :
% 5.06/5.41 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.06/5.41 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_numeral
% 5.06/5.41 thf(fact_8152_square__fact__le__2__fact,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % square_fact_le_2_fact
% 5.06/5.41 thf(fact_8153_tan__45,axiom,
% 5.06/5.41 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % tan_45
% 5.06/5.41 thf(fact_8154_fact__num__eq__if,axiom,
% 5.06/5.41 ( semiri5044797733671781792omplex
% 5.06/5.41 = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_num_eq_if
% 5.06/5.41 thf(fact_8155_fact__num__eq__if,axiom,
% 5.06/5.41 ( semiri773545260158071498ct_rat
% 5.06/5.41 = ( ^ [M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M6 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_num_eq_if
% 5.06/5.41 thf(fact_8156_fact__num__eq__if,axiom,
% 5.06/5.41 ( semiri1406184849735516958ct_int
% 5.06/5.41 = ( ^ [M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_num_eq_if
% 5.06/5.41 thf(fact_8157_fact__num__eq__if,axiom,
% 5.06/5.41 ( semiri3624122377584611663nteger
% 5.06/5.41 = ( ^ [M6: nat] : ( if_Code_integer @ ( M6 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M6 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_num_eq_if
% 5.06/5.41 thf(fact_8158_fact__num__eq__if,axiom,
% 5.06/5.41 ( semiri2265585572941072030t_real
% 5.06/5.41 = ( ^ [M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M6 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_num_eq_if
% 5.06/5.41 thf(fact_8159_fact__num__eq__if,axiom,
% 5.06/5.41 ( semiri1408675320244567234ct_nat
% 5.06/5.41 = ( ^ [M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M6 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_num_eq_if
% 5.06/5.41 thf(fact_8160_fact__code,axiom,
% 5.06/5.41 ( semiri1406184849735516958ct_int
% 5.06/5.41 = ( ^ [N: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_code
% 5.06/5.41 thf(fact_8161_fact__code,axiom,
% 5.06/5.41 ( semiri3624122377584611663nteger
% 5.06/5.41 = ( ^ [N: nat] : ( semiri4939895301339042750nteger @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_code
% 5.06/5.41 thf(fact_8162_fact__code,axiom,
% 5.06/5.41 ( semiri2265585572941072030t_real
% 5.06/5.41 = ( ^ [N: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_code
% 5.06/5.41 thf(fact_8163_fact__code,axiom,
% 5.06/5.41 ( semiri1408675320244567234ct_nat
% 5.06/5.41 = ( ^ [N: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_code
% 5.06/5.41 thf(fact_8164_fact__reduce,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( semiri773545260158071498ct_rat @ N2 )
% 5.06/5.41 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_reduce
% 5.06/5.41 thf(fact_8165_fact__reduce,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( semiri1406184849735516958ct_int @ N2 )
% 5.06/5.41 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_reduce
% 5.06/5.41 thf(fact_8166_fact__reduce,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( semiri3624122377584611663nteger @ N2 )
% 5.06/5.41 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_reduce
% 5.06/5.41 thf(fact_8167_fact__reduce,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( semiri2265585572941072030t_real @ N2 )
% 5.06/5.41 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_reduce
% 5.06/5.41 thf(fact_8168_fact__reduce,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 5.06/5.41 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_reduce
% 5.06/5.41 thf(fact_8169_tan__gt__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_gt_zero
% 5.06/5.41 thf(fact_8170_lemma__tan__total,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.41 => ? [X3: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X3 )
% 5.06/5.41 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 & ( ord_less_real @ Y @ ( tan_real @ X3 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % lemma_tan_total
% 5.06/5.41 thf(fact_8171_tan__total,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ? [X3: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.06/5.41 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 & ( ( tan_real @ X3 )
% 5.06/5.41 = Y )
% 5.06/5.41 & ! [Y3: real] :
% 5.06/5.41 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.06/5.41 & ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 & ( ( tan_real @ Y3 )
% 5.06/5.41 = Y ) )
% 5.06/5.41 => ( Y3 = X3 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_total
% 5.06/5.41 thf(fact_8172_tan__monotone,axiom,
% 5.06/5.41 ! [Y: real,X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_real @ Y @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_monotone
% 5.06/5.41 thf(fact_8173_tan__monotone_H,axiom,
% 5.06/5.41 ! [Y: real,X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_real @ Y @ X )
% 5.06/5.41 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_monotone'
% 5.06/5.41 thf(fact_8174_tan__mono__lt__eq,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.06/5.41 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_mono_lt_eq
% 5.06/5.41 thf(fact_8175_lemma__tan__total1,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ? [X3: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.06/5.41 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 & ( ( tan_real @ X3 )
% 5.06/5.41 = Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % lemma_tan_total1
% 5.06/5.41 thf(fact_8176_tan__minus__45,axiom,
% 5.06/5.41 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.41 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_minus_45
% 5.06/5.41 thf(fact_8177_tan__inverse,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 5.06/5.41 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_inverse
% 5.06/5.41 thf(fact_8178_add__tan__eq,axiom,
% 5.06/5.41 ! [X: complex,Y: complex] :
% 5.06/5.41 ( ( ( cos_complex @ X )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( ( cos_complex @ Y )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % add_tan_eq
% 5.06/5.41 thf(fact_8179_add__tan__eq,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( cos_real @ X )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( ( cos_real @ Y )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.06/5.41 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % add_tan_eq
% 5.06/5.41 thf(fact_8180_tan__pos__pi2__le,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_pos_pi2_le
% 5.06/5.41 thf(fact_8181_tan__total__pos,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ? [X3: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.06/5.41 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 & ( ( tan_real @ X3 )
% 5.06/5.41 = Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_total_pos
% 5.06/5.41 thf(fact_8182_tan__less__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.06/5.41 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_less_zero
% 5.06/5.41 thf(fact_8183_tan__mono__le__eq,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.06/5.41 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_mono_le_eq
% 5.06/5.41 thf(fact_8184_tan__mono__le,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.41 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_mono_le
% 5.06/5.41 thf(fact_8185_tan__bound__pi2,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_bound_pi2
% 5.06/5.41 thf(fact_8186_arctan,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.06/5.41 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 & ( ( tan_real @ ( arctan @ Y ) )
% 5.06/5.41 = Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % arctan
% 5.06/5.41 thf(fact_8187_arctan__tan,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( arctan @ ( tan_real @ X ) )
% 5.06/5.41 = X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arctan_tan
% 5.06/5.41 thf(fact_8188_arctan__unique,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ( tan_real @ X )
% 5.06/5.41 = Y )
% 5.06/5.41 => ( ( arctan @ Y )
% 5.06/5.41 = X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arctan_unique
% 5.06/5.41 thf(fact_8189_Maclaurin__zero,axiom,
% 5.06/5.41 ! [X: real,N2: nat,Diff: nat > complex > real] :
% 5.06/5.41 ( ( X = zero_zero_real )
% 5.06/5.41 => ( ( N2 != zero_zero_nat )
% 5.06/5.41 => ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_zero
% 5.06/5.41 thf(fact_8190_Maclaurin__zero,axiom,
% 5.06/5.41 ! [X: real,N2: nat,Diff: nat > real > real] :
% 5.06/5.41 ( ( X = zero_zero_real )
% 5.06/5.41 => ( ( N2 != zero_zero_nat )
% 5.06/5.41 => ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_zero
% 5.06/5.41 thf(fact_8191_Maclaurin__zero,axiom,
% 5.06/5.41 ! [X: real,N2: nat,Diff: nat > rat > real] :
% 5.06/5.41 ( ( X = zero_zero_real )
% 5.06/5.41 => ( ( N2 != zero_zero_nat )
% 5.06/5.41 => ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_zero
% 5.06/5.41 thf(fact_8192_Maclaurin__zero,axiom,
% 5.06/5.41 ! [X: real,N2: nat,Diff: nat > nat > real] :
% 5.06/5.41 ( ( X = zero_zero_real )
% 5.06/5.41 => ( ( N2 != zero_zero_nat )
% 5.06/5.41 => ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_zero
% 5.06/5.41 thf(fact_8193_Maclaurin__zero,axiom,
% 5.06/5.41 ! [X: real,N2: nat,Diff: nat > int > real] :
% 5.06/5.41 ( ( X = zero_zero_real )
% 5.06/5.41 => ( ( N2 != zero_zero_nat )
% 5.06/5.41 => ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_zero
% 5.06/5.41 thf(fact_8194_Maclaurin__lemma,axiom,
% 5.06/5.41 ! [H2: real,F: real > real,J: nat > real,N2: nat] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.06/5.41 => ? [B8: real] :
% 5.06/5.41 ( ( F @ H2 )
% 5.06/5.41 = ( plus_plus_real
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_lemma
% 5.06/5.41 thf(fact_8195_lemma__tan__add1,axiom,
% 5.06/5.41 ! [X: complex,Y: complex] :
% 5.06/5.41 ( ( ( cos_complex @ X )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( ( cos_complex @ Y )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % lemma_tan_add1
% 5.06/5.41 thf(fact_8196_lemma__tan__add1,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( cos_real @ X )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( ( cos_real @ Y )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) )
% 5.06/5.41 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % lemma_tan_add1
% 5.06/5.41 thf(fact_8197_tan__diff,axiom,
% 5.06/5.41 ! [X: complex,Y: complex] :
% 5.06/5.41 ( ( ( cos_complex @ X )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( ( cos_complex @ Y )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( ( cos_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( tan_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_diff
% 5.06/5.41 thf(fact_8198_tan__diff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( cos_real @ X )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( ( cos_real @ Y )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( tan_real @ ( minus_minus_real @ X @ Y ) )
% 5.06/5.41 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_diff
% 5.06/5.41 thf(fact_8199_tan__add,axiom,
% 5.06/5.41 ! [X: complex,Y: complex] :
% 5.06/5.41 ( ( ( cos_complex @ X )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( ( cos_complex @ Y )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( ( cos_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.06/5.41 != zero_zero_complex )
% 5.06/5.41 => ( ( tan_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_add
% 5.06/5.41 thf(fact_8200_tan__add,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( cos_real @ X )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( ( cos_real @ Y )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 5.06/5.41 != zero_zero_real )
% 5.06/5.41 => ( ( tan_real @ ( plus_plus_real @ X @ Y ) )
% 5.06/5.41 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_add
% 5.06/5.41 thf(fact_8201_tan__total__pi4,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.41 => ? [Z4: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z4 )
% 5.06/5.41 & ( ord_less_real @ Z4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 & ( ( tan_real @ Z4 )
% 5.06/5.41 = X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_total_pi4
% 5.06/5.41 thf(fact_8202_tan__half,axiom,
% 5.06/5.41 ( tan_complex
% 5.06/5.41 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_complex ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_half
% 5.06/5.41 thf(fact_8203_tan__half,axiom,
% 5.06/5.41 ( tan_real
% 5.06/5.41 = ( ^ [X2: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_half
% 5.06/5.41 thf(fact_8204_cos__coeff__def,axiom,
% 5.06/5.41 ( cos_coeff
% 5.06/5.41 = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ zero_zero_real ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_coeff_def
% 5.06/5.41 thf(fact_8205_Maclaurin__sin__expansion3,axiom,
% 5.06/5.41 ! [N2: nat,X: real] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ? [T5: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ T5 )
% 5.06/5.41 & ( ord_less_real @ T5 @ X )
% 5.06/5.41 & ( ( sin_real @ X )
% 5.06/5.41 = ( plus_plus_real
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_sin_expansion3
% 5.06/5.41 thf(fact_8206_Maclaurin__sin__expansion4,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ? [T5: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ T5 )
% 5.06/5.41 & ( ord_less_eq_real @ T5 @ X )
% 5.06/5.41 & ( ( sin_real @ X )
% 5.06/5.41 = ( plus_plus_real
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_sin_expansion4
% 5.06/5.41 thf(fact_8207_Maclaurin__sin__expansion2,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ? [T5: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X ) )
% 5.06/5.41 & ( ( sin_real @ X )
% 5.06/5.41 = ( plus_plus_real
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_sin_expansion2
% 5.06/5.41 thf(fact_8208_Maclaurin__sin__expansion,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ? [T5: real] :
% 5.06/5.41 ( ( sin_real @ X )
% 5.06/5.41 = ( plus_plus_real
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_sin_expansion
% 5.06/5.41 thf(fact_8209_sin__coeff__def,axiom,
% 5.06/5.41 ( sin_coeff
% 5.06/5.41 = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_coeff_def
% 5.06/5.41 thf(fact_8210_fact__ge__self,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_ge_self
% 5.06/5.41 thf(fact_8211_fact__mono__nat,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_mono_nat
% 5.06/5.41 thf(fact_8212_fact__less__mono__nat,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.41 => ( ( ord_less_nat @ M @ N2 )
% 5.06/5.41 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_less_mono_nat
% 5.06/5.41 thf(fact_8213_fact__ge__Suc__0__nat,axiom,
% 5.06/5.41 ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_ge_Suc_0_nat
% 5.06/5.41 thf(fact_8214_dvd__fact,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.06/5.41 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % dvd_fact
% 5.06/5.41 thf(fact_8215_fact__diff__Suc,axiom,
% 5.06/5.41 ! [N2: nat,M: nat] :
% 5.06/5.41 ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.06/5.41 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) )
% 5.06/5.41 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_diff_Suc
% 5.06/5.41 thf(fact_8216_fact__div__fact__le__pow,axiom,
% 5.06/5.41 ! [R2: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ R2 @ N2 )
% 5.06/5.41 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R2 ) ) ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_div_fact_le_pow
% 5.06/5.41 thf(fact_8217_sin__coeff__Suc,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( sin_coeff @ ( suc @ N2 ) )
% 5.06/5.41 = ( divide_divide_real @ ( cos_coeff @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_coeff_Suc
% 5.06/5.41 thf(fact_8218_cos__coeff__Suc,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( cos_coeff @ ( suc @ N2 ) )
% 5.06/5.41 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N2 ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_coeff_Suc
% 5.06/5.41 thf(fact_8219_sin__tan,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( sin_real @ X )
% 5.06/5.41 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_tan
% 5.06/5.41 thf(fact_8220_cos__tan,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( cos_real @ X )
% 5.06/5.41 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_tan
% 5.06/5.41 thf(fact_8221_complex__unimodular__polar,axiom,
% 5.06/5.41 ! [Z: complex] :
% 5.06/5.41 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.06/5.41 = one_one_real )
% 5.06/5.41 => ~ ! [T5: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.06/5.41 => ( ( ord_less_real @ T5 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.06/5.41 => ( Z
% 5.06/5.41 != ( complex2 @ ( cos_real @ T5 ) @ ( sin_real @ T5 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % complex_unimodular_polar
% 5.06/5.41 thf(fact_8222_Maclaurin__exp__lt,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ( ( X != zero_zero_real )
% 5.06/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ? [T5: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T5 ) )
% 5.06/5.41 & ( ord_less_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X ) )
% 5.06/5.41 & ( ( exp_real @ X )
% 5.06/5.41 = ( plus_plus_real
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_exp_lt
% 5.06/5.41 thf(fact_8223_sin__paired,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.06/5.41 @ ( sin_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_paired
% 5.06/5.41 thf(fact_8224_real__sqrt__eq__iff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( sqrt @ X )
% 5.06/5.41 = ( sqrt @ Y ) )
% 5.06/5.41 = ( X = Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_eq_iff
% 5.06/5.41 thf(fact_8225_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ( sqrt @ X )
% 5.06/5.41 = zero_zero_real )
% 5.06/5.41 = ( X = zero_zero_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_eq_zero_cancel_iff
% 5.06/5.41 thf(fact_8226_real__sqrt__zero,axiom,
% 5.06/5.41 ( ( sqrt @ zero_zero_real )
% 5.06/5.41 = zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_zero
% 5.06/5.41 thf(fact_8227_real__sqrt__less__iff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 5.06/5.41 = ( ord_less_real @ X @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_less_iff
% 5.06/5.41 thf(fact_8228_real__sqrt__le__iff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 5.06/5.41 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_le_iff
% 5.06/5.41 thf(fact_8229_real__sqrt__eq__1__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ( sqrt @ X )
% 5.06/5.41 = one_one_real )
% 5.06/5.41 = ( X = one_one_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_eq_1_iff
% 5.06/5.41 thf(fact_8230_real__sqrt__one,axiom,
% 5.06/5.41 ( ( sqrt @ one_one_real )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_one
% 5.06/5.41 thf(fact_8231_exp__le__cancel__iff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.06/5.41 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_le_cancel_iff
% 5.06/5.41 thf(fact_8232_sums__zero,axiom,
% 5.06/5.41 ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : zero_zero_complex
% 5.06/5.41 @ zero_zero_complex ) ).
% 5.06/5.41
% 5.06/5.41 % sums_zero
% 5.06/5.41 thf(fact_8233_sums__zero,axiom,
% 5.06/5.41 ( sums_real
% 5.06/5.41 @ ^ [N: nat] : zero_zero_real
% 5.06/5.41 @ zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % sums_zero
% 5.06/5.41 thf(fact_8234_sums__zero,axiom,
% 5.06/5.41 ( sums_nat
% 5.06/5.41 @ ^ [N: nat] : zero_zero_nat
% 5.06/5.41 @ zero_zero_nat ) ).
% 5.06/5.41
% 5.06/5.41 % sums_zero
% 5.06/5.41 thf(fact_8235_sums__zero,axiom,
% 5.06/5.41 ( sums_int
% 5.06/5.41 @ ^ [N: nat] : zero_zero_int
% 5.06/5.41 @ zero_zero_int ) ).
% 5.06/5.41
% 5.06/5.41 % sums_zero
% 5.06/5.41 thf(fact_8236_exp__zero,axiom,
% 5.06/5.41 ( ( exp_complex @ zero_zero_complex )
% 5.06/5.41 = one_one_complex ) ).
% 5.06/5.41
% 5.06/5.41 % exp_zero
% 5.06/5.41 thf(fact_8237_exp__zero,axiom,
% 5.06/5.41 ( ( exp_real @ zero_zero_real )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % exp_zero
% 5.06/5.41 thf(fact_8238_real__sqrt__gt__0__iff,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.06/5.41 = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_gt_0_iff
% 5.06/5.41 thf(fact_8239_real__sqrt__lt__0__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.06/5.41 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_lt_0_iff
% 5.06/5.41 thf(fact_8240_real__sqrt__le__0__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.06/5.41 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_le_0_iff
% 5.06/5.41 thf(fact_8241_real__sqrt__ge__0__iff,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.06/5.41 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_ge_0_iff
% 5.06/5.41 thf(fact_8242_real__sqrt__gt__1__iff,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 5.06/5.41 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_gt_1_iff
% 5.06/5.41 thf(fact_8243_real__sqrt__lt__1__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 5.06/5.41 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_lt_1_iff
% 5.06/5.41 thf(fact_8244_real__sqrt__ge__1__iff,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 5.06/5.41 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_ge_1_iff
% 5.06/5.41 thf(fact_8245_real__sqrt__le__1__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 5.06/5.41 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_le_1_iff
% 5.06/5.41 thf(fact_8246_real__sqrt__mult__self,axiom,
% 5.06/5.41 ! [A: real] :
% 5.06/5.41 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.06/5.41 = ( abs_abs_real @ A ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_mult_self
% 5.06/5.41 thf(fact_8247_real__sqrt__abs2,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 5.06/5.41 = ( abs_abs_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_abs2
% 5.06/5.41 thf(fact_8248_real__sqrt__four,axiom,
% 5.06/5.41 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_four
% 5.06/5.41 thf(fact_8249_one__le__exp__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 5.06/5.41 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % one_le_exp_iff
% 5.06/5.41 thf(fact_8250_exp__le__one__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 5.06/5.41 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_le_one_iff
% 5.06/5.41 thf(fact_8251_powser__sums__zero__iff,axiom,
% 5.06/5.41 ! [A: nat > complex,X: complex] :
% 5.06/5.41 ( ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 5.06/5.41 @ X )
% 5.06/5.41 = ( ( A @ zero_zero_nat )
% 5.06/5.41 = X ) ) ).
% 5.06/5.41
% 5.06/5.41 % powser_sums_zero_iff
% 5.06/5.41 thf(fact_8252_powser__sums__zero__iff,axiom,
% 5.06/5.41 ! [A: nat > real,X: real] :
% 5.06/5.41 ( ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 5.06/5.41 @ X )
% 5.06/5.41 = ( ( A @ zero_zero_nat )
% 5.06/5.41 = X ) ) ).
% 5.06/5.41
% 5.06/5.41 % powser_sums_zero_iff
% 5.06/5.41 thf(fact_8253_real__sqrt__abs,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 = ( abs_abs_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_abs
% 5.06/5.41 thf(fact_8254_real__sqrt__pow2__iff,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = X )
% 5.06/5.41 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_pow2_iff
% 5.06/5.41 thf(fact_8255_real__sqrt__pow2,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = X ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_pow2
% 5.06/5.41 thf(fact_8256_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.06/5.41 ! [X: real,Y: real,Xa2: real,Ya: real] :
% 5.06/5.41 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_sum_squares_mult_squared_eq
% 5.06/5.41 thf(fact_8257_real__sqrt__less__mono,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_real @ X @ Y )
% 5.06/5.41 => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_less_mono
% 5.06/5.41 thf(fact_8258_real__sqrt__le__mono,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.41 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_le_mono
% 5.06/5.41 thf(fact_8259_sums__le,axiom,
% 5.06/5.41 ! [F: nat > real,G: nat > real,S2: real,T: real] :
% 5.06/5.41 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.06/5.41 => ( ( sums_real @ F @ S2 )
% 5.06/5.41 => ( ( sums_real @ G @ T )
% 5.06/5.41 => ( ord_less_eq_real @ S2 @ T ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_le
% 5.06/5.41 thf(fact_8260_sums__le,axiom,
% 5.06/5.41 ! [F: nat > nat,G: nat > nat,S2: nat,T: nat] :
% 5.06/5.41 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.06/5.41 => ( ( sums_nat @ F @ S2 )
% 5.06/5.41 => ( ( sums_nat @ G @ T )
% 5.06/5.41 => ( ord_less_eq_nat @ S2 @ T ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_le
% 5.06/5.41 thf(fact_8261_sums__le,axiom,
% 5.06/5.41 ! [F: nat > int,G: nat > int,S2: int,T: int] :
% 5.06/5.41 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.06/5.41 => ( ( sums_int @ F @ S2 )
% 5.06/5.41 => ( ( sums_int @ G @ T )
% 5.06/5.41 => ( ord_less_eq_int @ S2 @ T ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_le
% 5.06/5.41 thf(fact_8262_norm__exp,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % norm_exp
% 5.06/5.41 thf(fact_8263_norm__exp,axiom,
% 5.06/5.41 ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % norm_exp
% 5.06/5.41 thf(fact_8264_real__sqrt__minus,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_minus
% 5.06/5.41 thf(fact_8265_real__sqrt__power,axiom,
% 5.06/5.41 ! [X: real,K: nat] :
% 5.06/5.41 ( ( sqrt @ ( power_power_real @ X @ K ) )
% 5.06/5.41 = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_power
% 5.06/5.41 thf(fact_8266_real__sqrt__mult,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( sqrt @ ( times_times_real @ X @ Y ) )
% 5.06/5.41 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_mult
% 5.06/5.41 thf(fact_8267_real__sqrt__divide,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( sqrt @ ( divide_divide_real @ X @ Y ) )
% 5.06/5.41 = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_divide
% 5.06/5.41 thf(fact_8268_exp__times__arg__commute,axiom,
% 5.06/5.41 ! [A2: complex] :
% 5.06/5.41 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.06/5.41 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_times_arg_commute
% 5.06/5.41 thf(fact_8269_exp__times__arg__commute,axiom,
% 5.06/5.41 ! [A2: real] :
% 5.06/5.41 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.06/5.41 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_times_arg_commute
% 5.06/5.41 thf(fact_8270_complex__diff,axiom,
% 5.06/5.41 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.41 ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.06/5.41 = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % complex_diff
% 5.06/5.41 thf(fact_8271_sums__single,axiom,
% 5.06/5.41 ! [I2: nat,F: nat > complex] :
% 5.06/5.41 ( sums_complex
% 5.06/5.41 @ ^ [R5: nat] : ( if_complex @ ( R5 = I2 ) @ ( F @ R5 ) @ zero_zero_complex )
% 5.06/5.41 @ ( F @ I2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_single
% 5.06/5.41 thf(fact_8272_sums__single,axiom,
% 5.06/5.41 ! [I2: nat,F: nat > real] :
% 5.06/5.41 ( sums_real
% 5.06/5.41 @ ^ [R5: nat] : ( if_real @ ( R5 = I2 ) @ ( F @ R5 ) @ zero_zero_real )
% 5.06/5.41 @ ( F @ I2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_single
% 5.06/5.41 thf(fact_8273_sums__single,axiom,
% 5.06/5.41 ! [I2: nat,F: nat > nat] :
% 5.06/5.41 ( sums_nat
% 5.06/5.41 @ ^ [R5: nat] : ( if_nat @ ( R5 = I2 ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.06/5.41 @ ( F @ I2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_single
% 5.06/5.41 thf(fact_8274_sums__single,axiom,
% 5.06/5.41 ! [I2: nat,F: nat > int] :
% 5.06/5.41 ( sums_int
% 5.06/5.41 @ ^ [R5: nat] : ( if_int @ ( R5 = I2 ) @ ( F @ R5 ) @ zero_zero_int )
% 5.06/5.41 @ ( F @ I2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_single
% 5.06/5.41 thf(fact_8275_sums__mult,axiom,
% 5.06/5.41 ! [F: nat > complex,A: complex,C: complex] :
% 5.06/5.41 ( ( sums_complex @ F @ A )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 5.06/5.41 @ ( times_times_complex @ C @ A ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_mult
% 5.06/5.41 thf(fact_8276_sums__mult,axiom,
% 5.06/5.41 ! [F: nat > real,A: real,C: real] :
% 5.06/5.41 ( ( sums_real @ F @ A )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 5.06/5.41 @ ( times_times_real @ C @ A ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_mult
% 5.06/5.41 thf(fact_8277_sums__mult2,axiom,
% 5.06/5.41 ! [F: nat > complex,A: complex,C: complex] :
% 5.06/5.41 ( ( sums_complex @ F @ A )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C )
% 5.06/5.41 @ ( times_times_complex @ A @ C ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_mult2
% 5.06/5.41 thf(fact_8278_sums__mult2,axiom,
% 5.06/5.41 ! [F: nat > real,A: real,C: real] :
% 5.06/5.41 ( ( sums_real @ F @ A )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C )
% 5.06/5.41 @ ( times_times_real @ A @ C ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_mult2
% 5.06/5.41 thf(fact_8279_sums__add,axiom,
% 5.06/5.41 ! [F: nat > complex,A: complex,G: nat > complex,B: complex] :
% 5.06/5.41 ( ( sums_complex @ F @ A )
% 5.06/5.41 => ( ( sums_complex @ G @ B )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( plus_plus_complex @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.41 @ ( plus_plus_complex @ A @ B ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_add
% 5.06/5.41 thf(fact_8280_sums__add,axiom,
% 5.06/5.41 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.06/5.41 ( ( sums_real @ F @ A )
% 5.06/5.41 => ( ( sums_real @ G @ B )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.41 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_add
% 5.06/5.41 thf(fact_8281_sums__add,axiom,
% 5.06/5.41 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.06/5.41 ( ( sums_nat @ F @ A )
% 5.06/5.41 => ( ( sums_nat @ G @ B )
% 5.06/5.41 => ( sums_nat
% 5.06/5.41 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.41 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_add
% 5.06/5.41 thf(fact_8282_sums__add,axiom,
% 5.06/5.41 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.06/5.41 ( ( sums_int @ F @ A )
% 5.06/5.41 => ( ( sums_int @ G @ B )
% 5.06/5.41 => ( sums_int
% 5.06/5.41 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.41 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_add
% 5.06/5.41 thf(fact_8283_sums__diff,axiom,
% 5.06/5.41 ! [F: nat > complex,A: complex,G: nat > complex,B: complex] :
% 5.06/5.41 ( ( sums_complex @ F @ A )
% 5.06/5.41 => ( ( sums_complex @ G @ B )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( minus_minus_complex @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.41 @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_diff
% 5.06/5.41 thf(fact_8284_sums__diff,axiom,
% 5.06/5.41 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.06/5.41 ( ( sums_real @ F @ A )
% 5.06/5.41 => ( ( sums_real @ G @ B )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.41 @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_diff
% 5.06/5.41 thf(fact_8285_sums__divide,axiom,
% 5.06/5.41 ! [F: nat > complex,A: complex,C: complex] :
% 5.06/5.41 ( ( sums_complex @ F @ A )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C )
% 5.06/5.41 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_divide
% 5.06/5.41 thf(fact_8286_sums__divide,axiom,
% 5.06/5.41 ! [F: nat > real,A: real,C: real] :
% 5.06/5.41 ( ( sums_real @ F @ A )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C )
% 5.06/5.41 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_divide
% 5.06/5.41 thf(fact_8287_sums__minus,axiom,
% 5.06/5.41 ! [F: nat > real,A: real] :
% 5.06/5.41 ( ( sums_real @ F @ A )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( uminus_uminus_real @ ( F @ N ) )
% 5.06/5.41 @ ( uminus_uminus_real @ A ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_minus
% 5.06/5.41 thf(fact_8288_sums__minus,axiom,
% 5.06/5.41 ! [F: nat > complex,A: complex] :
% 5.06/5.41 ( ( sums_complex @ F @ A )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( uminus1482373934393186551omplex @ ( F @ N ) )
% 5.06/5.41 @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_minus
% 5.06/5.41 thf(fact_8289_sums__sum,axiom,
% 5.06/5.41 ! [I6: set_complex,F: complex > nat > real,X: complex > real] :
% 5.06/5.41 ( ! [I3: complex] :
% 5.06/5.41 ( ( member_complex @ I3 @ I6 )
% 5.06/5.41 => ( sums_real @ ( F @ I3 ) @ ( X @ I3 ) ) )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] :
% 5.06/5.41 ( groups5808333547571424918x_real
% 5.06/5.41 @ ^ [I5: complex] : ( F @ I5 @ N )
% 5.06/5.41 @ I6 )
% 5.06/5.41 @ ( groups5808333547571424918x_real @ X @ I6 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_sum
% 5.06/5.41 thf(fact_8290_sums__sum,axiom,
% 5.06/5.41 ! [I6: set_real,F: real > nat > real,X: real > real] :
% 5.06/5.41 ( ! [I3: real] :
% 5.06/5.41 ( ( member_real @ I3 @ I6 )
% 5.06/5.41 => ( sums_real @ ( F @ I3 ) @ ( X @ I3 ) ) )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] :
% 5.06/5.41 ( groups8097168146408367636l_real
% 5.06/5.41 @ ^ [I5: real] : ( F @ I5 @ N )
% 5.06/5.41 @ I6 )
% 5.06/5.41 @ ( groups8097168146408367636l_real @ X @ I6 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_sum
% 5.06/5.41 thf(fact_8291_sums__sum,axiom,
% 5.06/5.41 ! [I6: set_int,F: int > nat > real,X: int > real] :
% 5.06/5.41 ( ! [I3: int] :
% 5.06/5.41 ( ( member_int @ I3 @ I6 )
% 5.06/5.41 => ( sums_real @ ( F @ I3 ) @ ( X @ I3 ) ) )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] :
% 5.06/5.41 ( groups8778361861064173332t_real
% 5.06/5.41 @ ^ [I5: int] : ( F @ I5 @ N )
% 5.06/5.41 @ I6 )
% 5.06/5.41 @ ( groups8778361861064173332t_real @ X @ I6 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_sum
% 5.06/5.41 thf(fact_8292_sums__sum,axiom,
% 5.06/5.41 ! [I6: set_real,F: real > nat > complex,X: real > complex] :
% 5.06/5.41 ( ! [I3: real] :
% 5.06/5.41 ( ( member_real @ I3 @ I6 )
% 5.06/5.41 => ( sums_complex @ ( F @ I3 ) @ ( X @ I3 ) ) )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] :
% 5.06/5.41 ( groups5754745047067104278omplex
% 5.06/5.41 @ ^ [I5: real] : ( F @ I5 @ N )
% 5.06/5.41 @ I6 )
% 5.06/5.41 @ ( groups5754745047067104278omplex @ X @ I6 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_sum
% 5.06/5.41 thf(fact_8293_sums__sum,axiom,
% 5.06/5.41 ! [I6: set_nat,F: nat > nat > complex,X: nat > complex] :
% 5.06/5.41 ( ! [I3: nat] :
% 5.06/5.41 ( ( member_nat @ I3 @ I6 )
% 5.06/5.41 => ( sums_complex @ ( F @ I3 ) @ ( X @ I3 ) ) )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] :
% 5.06/5.41 ( groups2073611262835488442omplex
% 5.06/5.41 @ ^ [I5: nat] : ( F @ I5 @ N )
% 5.06/5.41 @ I6 )
% 5.06/5.41 @ ( groups2073611262835488442omplex @ X @ I6 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_sum
% 5.06/5.41 thf(fact_8294_sums__sum,axiom,
% 5.06/5.41 ! [I6: set_int,F: int > nat > complex,X: int > complex] :
% 5.06/5.41 ( ! [I3: int] :
% 5.06/5.41 ( ( member_int @ I3 @ I6 )
% 5.06/5.41 => ( sums_complex @ ( F @ I3 ) @ ( X @ I3 ) ) )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] :
% 5.06/5.41 ( groups3049146728041665814omplex
% 5.06/5.41 @ ^ [I5: int] : ( F @ I5 @ N )
% 5.06/5.41 @ I6 )
% 5.06/5.41 @ ( groups3049146728041665814omplex @ X @ I6 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_sum
% 5.06/5.41 thf(fact_8295_sums__sum,axiom,
% 5.06/5.41 ! [I6: set_int,F: int > nat > int,X: int > int] :
% 5.06/5.41 ( ! [I3: int] :
% 5.06/5.41 ( ( member_int @ I3 @ I6 )
% 5.06/5.41 => ( sums_int @ ( F @ I3 ) @ ( X @ I3 ) ) )
% 5.06/5.41 => ( sums_int
% 5.06/5.41 @ ^ [N: nat] :
% 5.06/5.41 ( groups4538972089207619220nt_int
% 5.06/5.41 @ ^ [I5: int] : ( F @ I5 @ N )
% 5.06/5.41 @ I6 )
% 5.06/5.41 @ ( groups4538972089207619220nt_int @ X @ I6 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_sum
% 5.06/5.41 thf(fact_8296_sums__sum,axiom,
% 5.06/5.41 ! [I6: set_complex,F: complex > nat > complex,X: complex > complex] :
% 5.06/5.41 ( ! [I3: complex] :
% 5.06/5.41 ( ( member_complex @ I3 @ I6 )
% 5.06/5.41 => ( sums_complex @ ( F @ I3 ) @ ( X @ I3 ) ) )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] :
% 5.06/5.41 ( groups7754918857620584856omplex
% 5.06/5.41 @ ^ [I5: complex] : ( F @ I5 @ N )
% 5.06/5.41 @ I6 )
% 5.06/5.41 @ ( groups7754918857620584856omplex @ X @ I6 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_sum
% 5.06/5.41 thf(fact_8297_sums__sum,axiom,
% 5.06/5.41 ! [I6: set_nat,F: nat > nat > nat,X: nat > nat] :
% 5.06/5.41 ( ! [I3: nat] :
% 5.06/5.41 ( ( member_nat @ I3 @ I6 )
% 5.06/5.41 => ( sums_nat @ ( F @ I3 ) @ ( X @ I3 ) ) )
% 5.06/5.41 => ( sums_nat
% 5.06/5.41 @ ^ [N: nat] :
% 5.06/5.41 ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [I5: nat] : ( F @ I5 @ N )
% 5.06/5.41 @ I6 )
% 5.06/5.41 @ ( groups3542108847815614940at_nat @ X @ I6 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_sum
% 5.06/5.41 thf(fact_8298_sums__sum,axiom,
% 5.06/5.41 ! [I6: set_nat,F: nat > nat > real,X: nat > real] :
% 5.06/5.41 ( ! [I3: nat] :
% 5.06/5.41 ( ( member_nat @ I3 @ I6 )
% 5.06/5.41 => ( sums_real @ ( F @ I3 ) @ ( X @ I3 ) ) )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] :
% 5.06/5.41 ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( F @ I5 @ N )
% 5.06/5.41 @ I6 )
% 5.06/5.41 @ ( groups6591440286371151544t_real @ X @ I6 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_sum
% 5.06/5.41 thf(fact_8299_real__sqrt__gt__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_gt_zero
% 5.06/5.41 thf(fact_8300_real__sqrt__ge__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_ge_zero
% 5.06/5.41 thf(fact_8301_real__sqrt__eq__zero__cancel,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ( sqrt @ X )
% 5.06/5.41 = zero_zero_real )
% 5.06/5.41 => ( X = zero_zero_real ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_eq_zero_cancel
% 5.06/5.41 thf(fact_8302_exp__ge__zero,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_ge_zero
% 5.06/5.41 thf(fact_8303_not__exp__le__zero,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.06/5.41
% 5.06/5.41 % not_exp_le_zero
% 5.06/5.41 thf(fact_8304_real__sqrt__ge__one,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.06/5.41 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_ge_one
% 5.06/5.41 thf(fact_8305_exp__add__commuting,axiom,
% 5.06/5.41 ! [X: complex,Y: complex] :
% 5.06/5.41 ( ( ( times_times_complex @ X @ Y )
% 5.06/5.41 = ( times_times_complex @ Y @ X ) )
% 5.06/5.41 => ( ( exp_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.06/5.41 = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_add_commuting
% 5.06/5.41 thf(fact_8306_exp__add__commuting,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( times_times_real @ X @ Y )
% 5.06/5.41 = ( times_times_real @ Y @ X ) )
% 5.06/5.41 => ( ( exp_real @ ( plus_plus_real @ X @ Y ) )
% 5.06/5.41 = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_add_commuting
% 5.06/5.41 thf(fact_8307_mult__exp__exp,axiom,
% 5.06/5.41 ! [X: complex,Y: complex] :
% 5.06/5.41 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) )
% 5.06/5.41 = ( exp_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % mult_exp_exp
% 5.06/5.41 thf(fact_8308_mult__exp__exp,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.06/5.41 = ( exp_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % mult_exp_exp
% 5.06/5.41 thf(fact_8309_exp__diff,axiom,
% 5.06/5.41 ! [X: complex,Y: complex] :
% 5.06/5.41 ( ( exp_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_diff
% 5.06/5.41 thf(fact_8310_exp__diff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( exp_real @ ( minus_minus_real @ X @ Y ) )
% 5.06/5.41 = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_diff
% 5.06/5.41 thf(fact_8311_sums__mult__iff,axiom,
% 5.06/5.41 ! [C: complex,F: nat > complex,D: complex] :
% 5.06/5.41 ( ( C != zero_zero_complex )
% 5.06/5.41 => ( ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 5.06/5.41 @ ( times_times_complex @ C @ D ) )
% 5.06/5.41 = ( sums_complex @ F @ D ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_mult_iff
% 5.06/5.41 thf(fact_8312_sums__mult__iff,axiom,
% 5.06/5.41 ! [C: real,F: nat > real,D: real] :
% 5.06/5.41 ( ( C != zero_zero_real )
% 5.06/5.41 => ( ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 5.06/5.41 @ ( times_times_real @ C @ D ) )
% 5.06/5.41 = ( sums_real @ F @ D ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_mult_iff
% 5.06/5.41 thf(fact_8313_sums__mult2__iff,axiom,
% 5.06/5.41 ! [C: complex,F: nat > complex,D: complex] :
% 5.06/5.41 ( ( C != zero_zero_complex )
% 5.06/5.41 => ( ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ C )
% 5.06/5.41 @ ( times_times_complex @ D @ C ) )
% 5.06/5.41 = ( sums_complex @ F @ D ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_mult2_iff
% 5.06/5.41 thf(fact_8314_sums__mult2__iff,axiom,
% 5.06/5.41 ! [C: real,F: nat > real,D: real] :
% 5.06/5.41 ( ( C != zero_zero_real )
% 5.06/5.41 => ( ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ C )
% 5.06/5.41 @ ( times_times_real @ D @ C ) )
% 5.06/5.41 = ( sums_real @ F @ D ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_mult2_iff
% 5.06/5.41 thf(fact_8315_Complex__eq__numeral,axiom,
% 5.06/5.41 ! [A: real,B: real,W: num] :
% 5.06/5.41 ( ( ( complex2 @ A @ B )
% 5.06/5.41 = ( numera6690914467698888265omplex @ W ) )
% 5.06/5.41 = ( ( A
% 5.06/5.41 = ( numeral_numeral_real @ W ) )
% 5.06/5.41 & ( B = zero_zero_real ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Complex_eq_numeral
% 5.06/5.41 thf(fact_8316_complex__add,axiom,
% 5.06/5.41 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.41 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.06/5.41 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % complex_add
% 5.06/5.41 thf(fact_8317_complex__norm,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y ) )
% 5.06/5.41 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % complex_norm
% 5.06/5.41 thf(fact_8318_real__div__sqrt,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 5.06/5.41 = ( sqrt @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_div_sqrt
% 5.06/5.41 thf(fact_8319_sqrt__add__le__add__sqrt,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sqrt_add_le_add_sqrt
% 5.06/5.41 thf(fact_8320_sums__mult__D,axiom,
% 5.06/5.41 ! [C: complex,F: nat > complex,A: complex] :
% 5.06/5.41 ( ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 5.06/5.41 @ A )
% 5.06/5.41 => ( ( C != zero_zero_complex )
% 5.06/5.41 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_mult_D
% 5.06/5.41 thf(fact_8321_sums__mult__D,axiom,
% 5.06/5.41 ! [C: real,F: nat > real,A: real] :
% 5.06/5.41 ( ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 5.06/5.41 @ A )
% 5.06/5.41 => ( ( C != zero_zero_real )
% 5.06/5.41 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_mult_D
% 5.06/5.41 thf(fact_8322_sums__Suc__imp,axiom,
% 5.06/5.41 ! [F: nat > complex,S2: complex] :
% 5.06/5.41 ( ( ( F @ zero_zero_nat )
% 5.06/5.41 = zero_zero_complex )
% 5.06/5.41 => ( ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.06/5.41 @ S2 )
% 5.06/5.41 => ( sums_complex @ F @ S2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_Suc_imp
% 5.06/5.41 thf(fact_8323_sums__Suc__imp,axiom,
% 5.06/5.41 ! [F: nat > real,S2: real] :
% 5.06/5.41 ( ( ( F @ zero_zero_nat )
% 5.06/5.41 = zero_zero_real )
% 5.06/5.41 => ( ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.06/5.41 @ S2 )
% 5.06/5.41 => ( sums_real @ F @ S2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_Suc_imp
% 5.06/5.41 thf(fact_8324_exp__ge__add__one__self,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_ge_add_one_self
% 5.06/5.41 thf(fact_8325_le__real__sqrt__sumsq,axiom,
% 5.06/5.41 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % le_real_sqrt_sumsq
% 5.06/5.41 thf(fact_8326_sums__Suc__iff,axiom,
% 5.06/5.41 ! [F: nat > complex,S2: complex] :
% 5.06/5.41 ( ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.06/5.41 @ S2 )
% 5.06/5.41 = ( sums_complex @ F @ ( plus_plus_complex @ S2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_Suc_iff
% 5.06/5.41 thf(fact_8327_sums__Suc__iff,axiom,
% 5.06/5.41 ! [F: nat > real,S2: real] :
% 5.06/5.41 ( ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.06/5.41 @ S2 )
% 5.06/5.41 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_Suc_iff
% 5.06/5.41 thf(fact_8328_sums__Suc,axiom,
% 5.06/5.41 ! [F: nat > complex,L2: complex] :
% 5.06/5.41 ( ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.06/5.41 @ L2 )
% 5.06/5.41 => ( sums_complex @ F @ ( plus_plus_complex @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_Suc
% 5.06/5.41 thf(fact_8329_sums__Suc,axiom,
% 5.06/5.41 ! [F: nat > real,L2: real] :
% 5.06/5.41 ( ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.06/5.41 @ L2 )
% 5.06/5.41 => ( sums_real @ F @ ( plus_plus_real @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_Suc
% 5.06/5.41 thf(fact_8330_sums__Suc,axiom,
% 5.06/5.41 ! [F: nat > nat,L2: nat] :
% 5.06/5.41 ( ( sums_nat
% 5.06/5.41 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.06/5.41 @ L2 )
% 5.06/5.41 => ( sums_nat @ F @ ( plus_plus_nat @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_Suc
% 5.06/5.41 thf(fact_8331_sums__Suc,axiom,
% 5.06/5.41 ! [F: nat > int,L2: int] :
% 5.06/5.41 ( ( sums_int
% 5.06/5.41 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.06/5.41 @ L2 )
% 5.06/5.41 => ( sums_int @ F @ ( plus_plus_int @ L2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_Suc
% 5.06/5.41 thf(fact_8332_sums__zero__iff__shift,axiom,
% 5.06/5.41 ! [N2: nat,F: nat > complex,S2: complex] :
% 5.06/5.41 ( ! [I3: nat] :
% 5.06/5.41 ( ( ord_less_nat @ I3 @ N2 )
% 5.06/5.41 => ( ( F @ I3 )
% 5.06/5.41 = zero_zero_complex ) )
% 5.06/5.41 => ( ( sums_complex
% 5.06/5.41 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.06/5.41 @ S2 )
% 5.06/5.41 = ( sums_complex @ F @ S2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_zero_iff_shift
% 5.06/5.41 thf(fact_8333_sums__zero__iff__shift,axiom,
% 5.06/5.41 ! [N2: nat,F: nat > real,S2: real] :
% 5.06/5.41 ( ! [I3: nat] :
% 5.06/5.41 ( ( ord_less_nat @ I3 @ N2 )
% 5.06/5.41 => ( ( F @ I3 )
% 5.06/5.41 = zero_zero_real ) )
% 5.06/5.41 => ( ( sums_real
% 5.06/5.41 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.06/5.41 @ S2 )
% 5.06/5.41 = ( sums_real @ F @ S2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_zero_iff_shift
% 5.06/5.41 thf(fact_8334_exp__minus__inverse,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 5.06/5.41 = one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % exp_minus_inverse
% 5.06/5.41 thf(fact_8335_exp__minus__inverse,axiom,
% 5.06/5.41 ! [X: complex] :
% 5.06/5.41 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 5.06/5.41 = one_one_complex ) ).
% 5.06/5.41
% 5.06/5.41 % exp_minus_inverse
% 5.06/5.41 thf(fact_8336_exp__of__nat__mult,axiom,
% 5.06/5.41 ! [N2: nat,X: complex] :
% 5.06/5.41 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ X ) )
% 5.06/5.41 = ( power_power_complex @ ( exp_complex @ X ) @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_of_nat_mult
% 5.06/5.41 thf(fact_8337_exp__of__nat__mult,axiom,
% 5.06/5.41 ! [N2: nat,X: real] :
% 5.06/5.41 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) )
% 5.06/5.41 = ( power_power_real @ ( exp_real @ X ) @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_of_nat_mult
% 5.06/5.41 thf(fact_8338_exp__of__nat2__mult,axiom,
% 5.06/5.41 ! [X: complex,N2: nat] :
% 5.06/5.41 ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.06/5.41 = ( power_power_complex @ ( exp_complex @ X ) @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_of_nat2_mult
% 5.06/5.41 thf(fact_8339_exp__of__nat2__mult,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.06/5.41 = ( power_power_real @ ( exp_real @ X ) @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_of_nat2_mult
% 5.06/5.41 thf(fact_8340_Complex__eq__neg__numeral,axiom,
% 5.06/5.41 ! [A: real,B: real,W: num] :
% 5.06/5.41 ( ( ( complex2 @ A @ B )
% 5.06/5.41 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.41 = ( ( A
% 5.06/5.41 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.06/5.41 & ( B = zero_zero_real ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Complex_eq_neg_numeral
% 5.06/5.41 thf(fact_8341_sums__If__finite__set,axiom,
% 5.06/5.41 ! [A2: set_nat,F: nat > complex] :
% 5.06/5.41 ( ( finite_finite_nat @ A2 )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [R5: nat] : ( if_complex @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_complex )
% 5.06/5.41 @ ( groups2073611262835488442omplex @ F @ A2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_If_finite_set
% 5.06/5.41 thf(fact_8342_sums__If__finite__set,axiom,
% 5.06/5.41 ! [A2: set_nat,F: nat > int] :
% 5.06/5.41 ( ( finite_finite_nat @ A2 )
% 5.06/5.41 => ( sums_int
% 5.06/5.41 @ ^ [R5: nat] : ( if_int @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_int )
% 5.06/5.41 @ ( groups3539618377306564664at_int @ F @ A2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_If_finite_set
% 5.06/5.41 thf(fact_8343_sums__If__finite__set,axiom,
% 5.06/5.41 ! [A2: set_nat,F: nat > nat] :
% 5.06/5.41 ( ( finite_finite_nat @ A2 )
% 5.06/5.41 => ( sums_nat
% 5.06/5.41 @ ^ [R5: nat] : ( if_nat @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.06/5.41 @ ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_If_finite_set
% 5.06/5.41 thf(fact_8344_sums__If__finite__set,axiom,
% 5.06/5.41 ! [A2: set_nat,F: nat > real] :
% 5.06/5.41 ( ( finite_finite_nat @ A2 )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [R5: nat] : ( if_real @ ( member_nat @ R5 @ A2 ) @ ( F @ R5 ) @ zero_zero_real )
% 5.06/5.41 @ ( groups6591440286371151544t_real @ F @ A2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_If_finite_set
% 5.06/5.41 thf(fact_8345_sums__If__finite,axiom,
% 5.06/5.41 ! [P: nat > $o,F: nat > complex] :
% 5.06/5.41 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [R5: nat] : ( if_complex @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_complex )
% 5.06/5.41 @ ( groups2073611262835488442omplex @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_If_finite
% 5.06/5.41 thf(fact_8346_sums__If__finite,axiom,
% 5.06/5.41 ! [P: nat > $o,F: nat > int] :
% 5.06/5.41 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.41 => ( sums_int
% 5.06/5.41 @ ^ [R5: nat] : ( if_int @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_int )
% 5.06/5.41 @ ( groups3539618377306564664at_int @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_If_finite
% 5.06/5.41 thf(fact_8347_sums__If__finite,axiom,
% 5.06/5.41 ! [P: nat > $o,F: nat > nat] :
% 5.06/5.41 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.41 => ( sums_nat
% 5.06/5.41 @ ^ [R5: nat] : ( if_nat @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.06/5.41 @ ( groups3542108847815614940at_nat @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_If_finite
% 5.06/5.41 thf(fact_8348_sums__If__finite,axiom,
% 5.06/5.41 ! [P: nat > $o,F: nat > real] :
% 5.06/5.41 ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [R5: nat] : ( if_real @ ( P @ R5 ) @ ( F @ R5 ) @ zero_zero_real )
% 5.06/5.41 @ ( groups6591440286371151544t_real @ F @ ( collect_nat @ P ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_If_finite
% 5.06/5.41 thf(fact_8349_sums__finite,axiom,
% 5.06/5.41 ! [N4: set_nat,F: nat > complex] :
% 5.06/5.41 ( ( finite_finite_nat @ N4 )
% 5.06/5.41 => ( ! [N3: nat] :
% 5.06/5.41 ( ~ ( member_nat @ N3 @ N4 )
% 5.06/5.41 => ( ( F @ N3 )
% 5.06/5.41 = zero_zero_complex ) )
% 5.06/5.41 => ( sums_complex @ F @ ( groups2073611262835488442omplex @ F @ N4 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_finite
% 5.06/5.41 thf(fact_8350_sums__finite,axiom,
% 5.06/5.41 ! [N4: set_nat,F: nat > int] :
% 5.06/5.41 ( ( finite_finite_nat @ N4 )
% 5.06/5.41 => ( ! [N3: nat] :
% 5.06/5.41 ( ~ ( member_nat @ N3 @ N4 )
% 5.06/5.41 => ( ( F @ N3 )
% 5.06/5.41 = zero_zero_int ) )
% 5.06/5.41 => ( sums_int @ F @ ( groups3539618377306564664at_int @ F @ N4 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_finite
% 5.06/5.41 thf(fact_8351_sums__finite,axiom,
% 5.06/5.41 ! [N4: set_nat,F: nat > nat] :
% 5.06/5.41 ( ( finite_finite_nat @ N4 )
% 5.06/5.41 => ( ! [N3: nat] :
% 5.06/5.41 ( ~ ( member_nat @ N3 @ N4 )
% 5.06/5.41 => ( ( F @ N3 )
% 5.06/5.41 = zero_zero_nat ) )
% 5.06/5.41 => ( sums_nat @ F @ ( groups3542108847815614940at_nat @ F @ N4 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_finite
% 5.06/5.41 thf(fact_8352_sums__finite,axiom,
% 5.06/5.41 ! [N4: set_nat,F: nat > real] :
% 5.06/5.41 ( ( finite_finite_nat @ N4 )
% 5.06/5.41 => ( ! [N3: nat] :
% 5.06/5.41 ( ~ ( member_nat @ N3 @ N4 )
% 5.06/5.41 => ( ( F @ N3 )
% 5.06/5.41 = zero_zero_real ) )
% 5.06/5.41 => ( sums_real @ F @ ( groups6591440286371151544t_real @ F @ N4 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_finite
% 5.06/5.41 thf(fact_8353_complex__mult,axiom,
% 5.06/5.41 ! [A: real,B: real,C: real,D: real] :
% 5.06/5.41 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.06/5.41 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % complex_mult
% 5.06/5.41 thf(fact_8354_powser__sums__if,axiom,
% 5.06/5.41 ! [M: nat,Z: complex] :
% 5.06/5.41 ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( if_complex @ ( N = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N ) )
% 5.06/5.41 @ ( power_power_complex @ Z @ M ) ) ).
% 5.06/5.41
% 5.06/5.41 % powser_sums_if
% 5.06/5.41 thf(fact_8355_powser__sums__if,axiom,
% 5.06/5.41 ! [M: nat,Z: real] :
% 5.06/5.41 ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( if_real @ ( N = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N ) )
% 5.06/5.41 @ ( power_power_real @ Z @ M ) ) ).
% 5.06/5.41
% 5.06/5.41 % powser_sums_if
% 5.06/5.41 thf(fact_8356_powser__sums__if,axiom,
% 5.06/5.41 ! [M: nat,Z: int] :
% 5.06/5.41 ( sums_int
% 5.06/5.41 @ ^ [N: nat] : ( times_times_int @ ( if_int @ ( N = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N ) )
% 5.06/5.41 @ ( power_power_int @ Z @ M ) ) ).
% 5.06/5.41
% 5.06/5.41 % powser_sums_if
% 5.06/5.41 thf(fact_8357_sqrt2__less__2,axiom,
% 5.06/5.41 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.06/5.41
% 5.06/5.41 % sqrt2_less_2
% 5.06/5.41 thf(fact_8358_powser__sums__zero,axiom,
% 5.06/5.41 ! [A: nat > complex] :
% 5.06/5.41 ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 5.06/5.41 @ ( A @ zero_zero_nat ) ) ).
% 5.06/5.41
% 5.06/5.41 % powser_sums_zero
% 5.06/5.41 thf(fact_8359_powser__sums__zero,axiom,
% 5.06/5.41 ! [A: nat > real] :
% 5.06/5.41 ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 5.06/5.41 @ ( A @ zero_zero_nat ) ) ).
% 5.06/5.41
% 5.06/5.41 % powser_sums_zero
% 5.06/5.41 thf(fact_8360_exp__ge__add__one__self__aux,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_ge_add_one_self_aux
% 5.06/5.41 thf(fact_8361_lemma__exp__total,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ one_one_real @ Y )
% 5.06/5.41 => ? [X3: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.06/5.41 & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y @ one_one_real ) )
% 5.06/5.41 & ( ( exp_real @ X3 )
% 5.06/5.41 = Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % lemma_exp_total
% 5.06/5.41 thf(fact_8362_ln__ge__iff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 5.06/5.41 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % ln_ge_iff
% 5.06/5.41 thf(fact_8363_ln__x__over__x__mono,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.41 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % ln_x_over_x_mono
% 5.06/5.41 thf(fact_8364_sums__iff__shift,axiom,
% 5.06/5.41 ! [F: nat > complex,N2: nat,S2: complex] :
% 5.06/5.41 ( ( sums_complex
% 5.06/5.41 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.06/5.41 @ S2 )
% 5.06/5.41 = ( sums_complex @ F @ ( plus_plus_complex @ S2 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_iff_shift
% 5.06/5.41 thf(fact_8365_sums__iff__shift,axiom,
% 5.06/5.41 ! [F: nat > real,N2: nat,S2: real] :
% 5.06/5.41 ( ( sums_real
% 5.06/5.41 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.06/5.41 @ S2 )
% 5.06/5.41 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_iff_shift
% 5.06/5.41 thf(fact_8366_sums__split__initial__segment,axiom,
% 5.06/5.41 ! [F: nat > complex,S2: complex,N2: nat] :
% 5.06/5.41 ( ( sums_complex @ F @ S2 )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.06/5.41 @ ( minus_minus_complex @ S2 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_split_initial_segment
% 5.06/5.41 thf(fact_8367_sums__split__initial__segment,axiom,
% 5.06/5.41 ! [F: nat > real,S2: real,N2: nat] :
% 5.06/5.41 ( ( sums_real @ F @ S2 )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.06/5.41 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_split_initial_segment
% 5.06/5.41 thf(fact_8368_sums__iff__shift_H,axiom,
% 5.06/5.41 ! [F: nat > complex,N2: nat,S2: complex] :
% 5.06/5.41 ( ( sums_complex
% 5.06/5.41 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.06/5.41 @ ( minus_minus_complex @ S2 @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.06/5.41 = ( sums_complex @ F @ S2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_iff_shift'
% 5.06/5.41 thf(fact_8369_sums__iff__shift_H,axiom,
% 5.06/5.41 ! [F: nat > real,N2: nat,S2: real] :
% 5.06/5.41 ( ( sums_real
% 5.06/5.41 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.06/5.41 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.06/5.41 = ( sums_real @ F @ S2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_iff_shift'
% 5.06/5.41 thf(fact_8370_sums__If__finite__set_H,axiom,
% 5.06/5.41 ! [G: nat > complex,S3: complex,A2: set_nat,S4: complex,F: nat > complex] :
% 5.06/5.41 ( ( sums_complex @ G @ S3 )
% 5.06/5.41 => ( ( finite_finite_nat @ A2 )
% 5.06/5.41 => ( ( S4
% 5.06/5.41 = ( plus_plus_complex @ S3
% 5.06/5.41 @ ( groups2073611262835488442omplex
% 5.06/5.41 @ ^ [N: nat] : ( minus_minus_complex @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.41 @ A2 ) ) )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( if_complex @ ( member_nat @ N @ A2 ) @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.41 @ S4 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_If_finite_set'
% 5.06/5.41 thf(fact_8371_sums__If__finite__set_H,axiom,
% 5.06/5.41 ! [G: nat > real,S3: real,A2: set_nat,S4: real,F: nat > real] :
% 5.06/5.41 ( ( sums_real @ G @ S3 )
% 5.06/5.41 => ( ( finite_finite_nat @ A2 )
% 5.06/5.41 => ( ( S4
% 5.06/5.41 = ( plus_plus_real @ S3
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.41 @ A2 ) ) )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( if_real @ ( member_nat @ N @ A2 ) @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.41 @ S4 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_If_finite_set'
% 5.06/5.41 thf(fact_8372_Complex__sum_H,axiom,
% 5.06/5.41 ! [F: nat > real,S2: set_nat] :
% 5.06/5.41 ( ( groups2073611262835488442omplex
% 5.06/5.41 @ ^ [X2: nat] : ( complex2 @ ( F @ X2 ) @ zero_zero_real )
% 5.06/5.41 @ S2 )
% 5.06/5.41 = ( complex2 @ ( groups6591440286371151544t_real @ F @ S2 ) @ zero_zero_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % Complex_sum'
% 5.06/5.41 thf(fact_8373_Complex__sum_H,axiom,
% 5.06/5.41 ! [F: complex > real,S2: set_complex] :
% 5.06/5.41 ( ( groups7754918857620584856omplex
% 5.06/5.41 @ ^ [X2: complex] : ( complex2 @ ( F @ X2 ) @ zero_zero_real )
% 5.06/5.41 @ S2 )
% 5.06/5.41 = ( complex2 @ ( groups5808333547571424918x_real @ F @ S2 ) @ zero_zero_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % Complex_sum'
% 5.06/5.41 thf(fact_8374_real__less__rsqrt,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.06/5.41 => ( ord_less_real @ X @ ( sqrt @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_less_rsqrt
% 5.06/5.41 thf(fact_8375_real__le__rsqrt,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.06/5.41 => ( ord_less_eq_real @ X @ ( sqrt @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_le_rsqrt
% 5.06/5.41 thf(fact_8376_sqrt__le__D,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y )
% 5.06/5.41 => ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sqrt_le_D
% 5.06/5.41 thf(fact_8377_exp__le,axiom,
% 5.06/5.41 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_le
% 5.06/5.41 thf(fact_8378_exp__divide__power__eq,axiom,
% 5.06/5.41 ! [N2: nat,X: complex] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N2 ) ) ) @ N2 )
% 5.06/5.41 = ( exp_complex @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_divide_power_eq
% 5.06/5.41 thf(fact_8379_exp__divide__power__eq,axiom,
% 5.06/5.41 ! [N2: nat,X: real] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.06/5.41 = ( exp_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_divide_power_eq
% 5.06/5.41 thf(fact_8380_tanh__altdef,axiom,
% 5.06/5.41 ( tanh_real
% 5.06/5.41 = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tanh_altdef
% 5.06/5.41 thf(fact_8381_tanh__altdef,axiom,
% 5.06/5.41 ( tanh_complex
% 5.06/5.41 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tanh_altdef
% 5.06/5.41 thf(fact_8382_real__sqrt__unique,axiom,
% 5.06/5.41 ! [Y: real,X: real] :
% 5.06/5.41 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = X )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( sqrt @ X )
% 5.06/5.41 = Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_unique
% 5.06/5.41 thf(fact_8383_real__le__lsqrt,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_le_lsqrt
% 5.06/5.41 thf(fact_8384_lemma__real__divide__sqrt__less,axiom,
% 5.06/5.41 ! [U: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ U )
% 5.06/5.41 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.06/5.41
% 5.06/5.41 % lemma_real_divide_sqrt_less
% 5.06/5.41 thf(fact_8385_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 = Y )
% 5.06/5.41 => ( X = zero_zero_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_sum_squares_eq_cancel2
% 5.06/5.41 thf(fact_8386_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 = X )
% 5.06/5.41 => ( Y = zero_zero_real ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_sum_squares_eq_cancel
% 5.06/5.41 thf(fact_8387_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.06/5.41 ! [A: real,C: real,B: real,D: 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 @ D ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_sum_squares_triangle_ineq
% 5.06/5.41 thf(fact_8388_real__sqrt__sum__squares__ge2,axiom,
% 5.06/5.41 ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_sum_squares_ge2
% 5.06/5.41 thf(fact_8389_real__sqrt__sum__squares__ge1,axiom,
% 5.06/5.41 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_sum_squares_ge1
% 5.06/5.41 thf(fact_8390_exp__half__le2,axiom,
% 5.06/5.41 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_half_le2
% 5.06/5.41 thf(fact_8391_sqrt__ge__absD,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y ) )
% 5.06/5.41 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % sqrt_ge_absD
% 5.06/5.41 thf(fact_8392_cos__45,axiom,
% 5.06/5.41 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_45
% 5.06/5.41 thf(fact_8393_sin__45,axiom,
% 5.06/5.41 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_45
% 5.06/5.41 thf(fact_8394_tan__60,axiom,
% 5.06/5.41 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.06/5.41 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_60
% 5.06/5.41 thf(fact_8395_exp__double,axiom,
% 5.06/5.41 ! [Z: complex] :
% 5.06/5.41 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.06/5.41 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_double
% 5.06/5.41 thf(fact_8396_exp__double,axiom,
% 5.06/5.41 ! [Z: real] :
% 5.06/5.41 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.06/5.41 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_double
% 5.06/5.41 thf(fact_8397_geometric__sums,axiom,
% 5.06/5.41 ! [C: real] :
% 5.06/5.41 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.06/5.41 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % geometric_sums
% 5.06/5.41 thf(fact_8398_geometric__sums,axiom,
% 5.06/5.41 ! [C: complex] :
% 5.06/5.41 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.06/5.41 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % geometric_sums
% 5.06/5.41 thf(fact_8399_real__less__lsqrt,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( ord_less_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_less_lsqrt
% 5.06/5.41 thf(fact_8400_power__half__series,axiom,
% 5.06/5.41 ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N ) )
% 5.06/5.41 @ one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % power_half_series
% 5.06/5.41 thf(fact_8401_sqrt__sum__squares__le__sum,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sqrt_sum_squares_le_sum
% 5.06/5.41 thf(fact_8402_sqrt__even__pow2,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.41 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.41 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sqrt_even_pow2
% 5.06/5.41 thf(fact_8403_real__sqrt__ge__abs1,axiom,
% 5.06/5.41 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_ge_abs1
% 5.06/5.41 thf(fact_8404_real__sqrt__ge__abs2,axiom,
% 5.06/5.41 ! [Y: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_ge_abs2
% 5.06/5.41 thf(fact_8405_sqrt__sum__squares__le__sum__abs,axiom,
% 5.06/5.41 ! [X: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sqrt_sum_squares_le_sum_abs
% 5.06/5.41 thf(fact_8406_ln__sqrt,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 5.06/5.41 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % ln_sqrt
% 5.06/5.41 thf(fact_8407_cos__30,axiom,
% 5.06/5.41 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.06/5.41 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_30
% 5.06/5.41 thf(fact_8408_sin__60,axiom,
% 5.06/5.41 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.06/5.41 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_60
% 5.06/5.41 thf(fact_8409_exp__bound__half,axiom,
% 5.06/5.41 ! [Z: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_bound_half
% 5.06/5.41 thf(fact_8410_exp__bound__half,axiom,
% 5.06/5.41 ! [Z: complex] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_bound_half
% 5.06/5.41 thf(fact_8411_sums__if_H,axiom,
% 5.06/5.41 ! [G: nat > real,X: real] :
% 5.06/5.41 ( ( sums_real @ G @ X )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_if'
% 5.06/5.41 thf(fact_8412_sums__if,axiom,
% 5.06/5.41 ! [G: nat > real,X: real,F: nat > real,Y: real] :
% 5.06/5.41 ( ( sums_real @ G @ X )
% 5.06/5.41 => ( ( sums_real @ F @ Y )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( F @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sums_if
% 5.06/5.41 thf(fact_8413_arsinh__real__aux,axiom,
% 5.06/5.41 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arsinh_real_aux
% 5.06/5.41 thf(fact_8414_real__sqrt__power__even,axiom,
% 5.06/5.41 ! [N2: nat,X: real] :
% 5.06/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( power_power_real @ ( sqrt @ X ) @ N2 )
% 5.06/5.41 = ( power_power_real @ X @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_power_even
% 5.06/5.41 thf(fact_8415_exp__bound,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.41 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_bound
% 5.06/5.41 thf(fact_8416_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.06/5.41 ! [X: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_sum_squares_mult_ge_zero
% 5.06/5.41 thf(fact_8417_arith__geo__mean__sqrt,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arith_geo_mean_sqrt
% 5.06/5.41 thf(fact_8418_tan__30,axiom,
% 5.06/5.41 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.06/5.41 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tan_30
% 5.06/5.41 thf(fact_8419_real__exp__bound__lemma,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_exp_bound_lemma
% 5.06/5.41 thf(fact_8420_cos__x__y__le__one,axiom,
% 5.06/5.41 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.06/5.41
% 5.06/5.41 % cos_x_y_le_one
% 5.06/5.41 thf(fact_8421_real__sqrt__sum__squares__less,axiom,
% 5.06/5.41 ! [X: real,U: real,Y: real] :
% 5.06/5.41 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % real_sqrt_sum_squares_less
% 5.06/5.41 thf(fact_8422_arcosh__real__def,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.06/5.41 => ( ( arcosh_real @ X )
% 5.06/5.41 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcosh_real_def
% 5.06/5.41 thf(fact_8423_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.06/5.41 ! [N2: nat,X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X )
% 5.06/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_ge_one_plus_x_over_n_power_n
% 5.06/5.41 thf(fact_8424_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_ge_one_minus_x_over_n_power_n
% 5.06/5.41 thf(fact_8425_cos__arctan,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( cos_real @ ( arctan @ X ) )
% 5.06/5.41 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_arctan
% 5.06/5.41 thf(fact_8426_sin__arctan,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( sin_real @ ( arctan @ X ) )
% 5.06/5.41 = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_arctan
% 5.06/5.41 thf(fact_8427_exp__bound__lemma,axiom,
% 5.06/5.41 ! [Z: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( 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 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_bound_lemma
% 5.06/5.41 thf(fact_8428_exp__bound__lemma,axiom,
% 5.06/5.41 ! [Z: complex] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( 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 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_bound_lemma
% 5.06/5.41 thf(fact_8429_Maclaurin__exp__le,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ? [T5: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X ) )
% 5.06/5.41 & ( ( exp_real @ X )
% 5.06/5.41 = ( plus_plus_real
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.41 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Maclaurin_exp_le
% 5.06/5.41 thf(fact_8430_sqrt__sum__squares__half__less,axiom,
% 5.06/5.41 ! [X: real,U: real,Y: real] :
% 5.06/5.41 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sqrt_sum_squares_half_less
% 5.06/5.41 thf(fact_8431_exp__lower__Taylor__quadratic,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % exp_lower_Taylor_quadratic
% 5.06/5.41 thf(fact_8432_sin__cos__sqrt,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 5.06/5.41 => ( ( sin_real @ X )
% 5.06/5.41 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_cos_sqrt
% 5.06/5.41 thf(fact_8433_arctan__half,axiom,
% 5.06/5.41 ( arctan
% 5.06/5.41 = ( ^ [X2: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X2 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arctan_half
% 5.06/5.41 thf(fact_8434_tanh__real__altdef,axiom,
% 5.06/5.41 ( tanh_real
% 5.06/5.41 = ( ^ [X2: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % tanh_real_altdef
% 5.06/5.41 thf(fact_8435_cos__paired,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.06/5.41 @ ( cos_real @ X ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_paired
% 5.06/5.41 thf(fact_8436_geometric__deriv__sums,axiom,
% 5.06/5.41 ! [Z: real] :
% 5.06/5.41 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) )
% 5.06/5.41 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % geometric_deriv_sums
% 5.06/5.41 thf(fact_8437_geometric__deriv__sums,axiom,
% 5.06/5.41 ! [Z: complex] :
% 5.06/5.41 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) )
% 5.06/5.41 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % geometric_deriv_sums
% 5.06/5.41 thf(fact_8438_diffs__equiv,axiom,
% 5.06/5.41 ! [C: nat > complex,X: complex] :
% 5.06/5.41 ( ( summable_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X @ N ) ) )
% 5.06/5.41 => ( sums_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( C @ N ) ) @ ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.06/5.41 @ ( suminf_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_equiv
% 5.06/5.41 thf(fact_8439_diffs__equiv,axiom,
% 5.06/5.41 ! [C: nat > real,X: real] :
% 5.06/5.41 ( ( summable_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X @ N ) ) )
% 5.06/5.41 => ( sums_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( C @ N ) ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.06/5.41 @ ( suminf_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_equiv
% 5.06/5.41 thf(fact_8440_arsinh__real__def,axiom,
% 5.06/5.41 ( arsinh_real
% 5.06/5.41 = ( ^ [X2: real] : ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arsinh_real_def
% 5.06/5.41 thf(fact_8441_binomial__code,axiom,
% 5.06/5.41 ( binomial
% 5.06/5.41 = ( ^ [N: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N @ ( minus_minus_nat @ N @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N @ K3 ) @ one_one_nat ) @ N @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_code
% 5.06/5.41 thf(fact_8442_cos__arcsin,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.41 => ( ( cos_real @ ( arcsin @ X ) )
% 5.06/5.41 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_arcsin
% 5.06/5.41 thf(fact_8443_sin__arccos__abs,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.06/5.41 => ( ( sin_real @ ( arccos @ Y ) )
% 5.06/5.41 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_arccos_abs
% 5.06/5.41 thf(fact_8444_binomial__Suc__n,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( binomial @ ( suc @ N2 ) @ N2 )
% 5.06/5.41 = ( suc @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_Suc_n
% 5.06/5.41 thf(fact_8445_binomial__n__n,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( binomial @ N2 @ N2 )
% 5.06/5.41 = one_one_nat ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_n_n
% 5.06/5.41 thf(fact_8446_binomial__1,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( binomial @ N2 @ ( suc @ zero_zero_nat ) )
% 5.06/5.41 = N2 ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_1
% 5.06/5.41 thf(fact_8447_binomial__0__Suc,axiom,
% 5.06/5.41 ! [K: nat] :
% 5.06/5.41 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.06/5.41 = zero_zero_nat ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_0_Suc
% 5.06/5.41 thf(fact_8448_binomial__eq__0__iff,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] :
% 5.06/5.41 ( ( ( binomial @ N2 @ K )
% 5.06/5.41 = zero_zero_nat )
% 5.06/5.41 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_eq_0_iff
% 5.06/5.41 thf(fact_8449_binomial__Suc__Suc,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] :
% 5.06/5.41 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 5.06/5.41 = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_Suc_Suc
% 5.06/5.41 thf(fact_8450_binomial__n__0,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( binomial @ N2 @ zero_zero_nat )
% 5.06/5.41 = one_one_nat ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_n_0
% 5.06/5.41 thf(fact_8451_zero__less__binomial__iff,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 5.06/5.41 = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % zero_less_binomial_iff
% 5.06/5.41 thf(fact_8452_cos__arccos,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ( cos_real @ ( arccos @ Y ) )
% 5.06/5.41 = Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_arccos
% 5.06/5.41 thf(fact_8453_sin__arcsin,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ( sin_real @ ( arcsin @ Y ) )
% 5.06/5.41 = Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_arcsin
% 5.06/5.41 thf(fact_8454_arccos__0,axiom,
% 5.06/5.41 ( ( arccos @ zero_zero_real )
% 5.06/5.41 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_0
% 5.06/5.41 thf(fact_8455_arcsin__1,axiom,
% 5.06/5.41 ( ( arcsin @ one_one_real )
% 5.06/5.41 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_1
% 5.06/5.41 thf(fact_8456_arcsin__minus__1,axiom,
% 5.06/5.41 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_minus_1
% 5.06/5.41 thf(fact_8457_choose__one,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( binomial @ N2 @ one_one_nat )
% 5.06/5.41 = N2 ) ).
% 5.06/5.41
% 5.06/5.41 % choose_one
% 5.06/5.41 thf(fact_8458_binomial__eq__0,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] :
% 5.06/5.41 ( ( ord_less_nat @ N2 @ K )
% 5.06/5.41 => ( ( binomial @ N2 @ K )
% 5.06/5.41 = zero_zero_nat ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_eq_0
% 5.06/5.41 thf(fact_8459_Suc__times__binomial,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) )
% 5.06/5.41 = ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Suc_times_binomial
% 5.06/5.41 thf(fact_8460_Suc__times__binomial__eq,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] :
% 5.06/5.41 ( ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) )
% 5.06/5.41 = ( times_times_nat @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Suc_times_binomial_eq
% 5.06/5.41 thf(fact_8461_binomial__symmetric,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( binomial @ N2 @ K )
% 5.06/5.41 = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_symmetric
% 5.06/5.41 thf(fact_8462_choose__mult__lemma,axiom,
% 5.06/5.41 ! [M: nat,R2: nat,K: nat] :
% 5.06/5.41 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.06/5.41 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_mult_lemma
% 5.06/5.41 thf(fact_8463_binomial__le__pow,axiom,
% 5.06/5.41 ! [R2: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ R2 @ N2 )
% 5.06/5.41 => ( ord_less_eq_nat @ ( binomial @ N2 @ R2 ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_le_pow
% 5.06/5.41 thf(fact_8464_diffs__minus,axiom,
% 5.06/5.41 ! [C: nat > real] :
% 5.06/5.41 ( ( diffs_real
% 5.06/5.41 @ ^ [N: nat] : ( uminus_uminus_real @ ( C @ N ) ) )
% 5.06/5.41 = ( ^ [N: nat] : ( uminus_uminus_real @ ( diffs_real @ C @ N ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_minus
% 5.06/5.41 thf(fact_8465_diffs__minus,axiom,
% 5.06/5.41 ! [C: nat > int] :
% 5.06/5.41 ( ( diffs_int
% 5.06/5.41 @ ^ [N: nat] : ( uminus_uminus_int @ ( C @ N ) ) )
% 5.06/5.41 = ( ^ [N: nat] : ( uminus_uminus_int @ ( diffs_int @ C @ N ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_minus
% 5.06/5.41 thf(fact_8466_diffs__minus,axiom,
% 5.06/5.41 ! [C: nat > complex] :
% 5.06/5.41 ( ( diffs_complex
% 5.06/5.41 @ ^ [N: nat] : ( uminus1482373934393186551omplex @ ( C @ N ) ) )
% 5.06/5.41 = ( ^ [N: nat] : ( uminus1482373934393186551omplex @ ( diffs_complex @ C @ N ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_minus
% 5.06/5.41 thf(fact_8467_diffs__minus,axiom,
% 5.06/5.41 ! [C: nat > rat] :
% 5.06/5.41 ( ( diffs_rat
% 5.06/5.41 @ ^ [N: nat] : ( uminus_uminus_rat @ ( C @ N ) ) )
% 5.06/5.41 = ( ^ [N: nat] : ( uminus_uminus_rat @ ( diffs_rat @ C @ N ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_minus
% 5.06/5.41 thf(fact_8468_diffs__minus,axiom,
% 5.06/5.41 ! [C: nat > code_integer] :
% 5.06/5.41 ( ( diffs_Code_integer
% 5.06/5.41 @ ^ [N: nat] : ( uminus1351360451143612070nteger @ ( C @ N ) ) )
% 5.06/5.41 = ( ^ [N: nat] : ( uminus1351360451143612070nteger @ ( diffs_Code_integer @ C @ N ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_minus
% 5.06/5.41 thf(fact_8469_zero__less__binomial,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % zero_less_binomial
% 5.06/5.41 thf(fact_8470_Suc__times__binomial__add,axiom,
% 5.06/5.41 ! [A: nat,B: nat] :
% 5.06/5.41 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.06/5.41 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Suc_times_binomial_add
% 5.06/5.41 thf(fact_8471_binomial__Suc__Suc__eq__times,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] :
% 5.06/5.41 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 5.06/5.41 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) @ ( suc @ K ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_Suc_Suc_eq_times
% 5.06/5.41 thf(fact_8472_choose__mult,axiom,
% 5.06/5.41 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ M )
% 5.06/5.41 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K ) )
% 5.06/5.41 = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_mult
% 5.06/5.41 thf(fact_8473_binomial__absorb__comp,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] :
% 5.06/5.41 ( ( times_times_nat @ ( minus_minus_nat @ N2 @ K ) @ ( binomial @ N2 @ K ) )
% 5.06/5.41 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_absorb_comp
% 5.06/5.41 thf(fact_8474_arccos__le__arccos,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_le_arccos
% 5.06/5.41 thf(fact_8475_arccos__eq__iff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.41 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 5.06/5.41 => ( ( ( arccos @ X )
% 5.06/5.41 = ( arccos @ Y ) )
% 5.06/5.41 = ( X = Y ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_eq_iff
% 5.06/5.41 thf(fact_8476_arccos__le__mono,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 5.06/5.41 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_le_mono
% 5.06/5.41 thf(fact_8477_arcsin__le__arcsin,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_le_arcsin
% 5.06/5.41 thf(fact_8478_arcsin__minus,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.41 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 5.06/5.41 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_minus
% 5.06/5.41 thf(fact_8479_arcsin__eq__iff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.06/5.41 => ( ( ( arcsin @ X )
% 5.06/5.41 = ( arcsin @ Y ) )
% 5.06/5.41 = ( X = Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_eq_iff
% 5.06/5.41 thf(fact_8480_arcsin__le__mono,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 5.06/5.41 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_le_mono
% 5.06/5.41 thf(fact_8481_binomial__absorption,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) )
% 5.06/5.41 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_absorption
% 5.06/5.41 thf(fact_8482_binomial__fact__lemma,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 5.06/5.41 = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_fact_lemma
% 5.06/5.41 thf(fact_8483_diffs__def,axiom,
% 5.06/5.41 ( diffs_rat
% 5.06/5.41 = ( ^ [C4: nat > rat,N: nat] : ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( C4 @ ( suc @ N ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_def
% 5.06/5.41 thf(fact_8484_diffs__def,axiom,
% 5.06/5.41 ( diffs_int
% 5.06/5.41 = ( ^ [C4: nat > int,N: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( C4 @ ( suc @ N ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_def
% 5.06/5.41 thf(fact_8485_diffs__def,axiom,
% 5.06/5.41 ( diffs_real
% 5.06/5.41 = ( ^ [C4: nat > real,N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( C4 @ ( suc @ N ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_def
% 5.06/5.41 thf(fact_8486_diffs__def,axiom,
% 5.06/5.41 ( diffs_Code_integer
% 5.06/5.41 = ( ^ [C4: nat > code_integer,N: nat] : ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N ) ) @ ( C4 @ ( suc @ N ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % diffs_def
% 5.06/5.41 thf(fact_8487_binomial__ge__n__over__k__pow__k,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_ge_n_over_k_pow_k
% 5.06/5.41 thf(fact_8488_binomial__ge__n__over__k__pow__k,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_ge_n_over_k_pow_k
% 5.06/5.41 thf(fact_8489_binomial__mono,axiom,
% 5.06/5.41 ! [K: nat,K6: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ K6 )
% 5.06/5.41 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 5.06/5.41 => ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_mono
% 5.06/5.41 thf(fact_8490_binomial__maximum_H,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_maximum'
% 5.06/5.41 thf(fact_8491_binomial__maximum,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_maximum
% 5.06/5.41 thf(fact_8492_binomial__antimono,axiom,
% 5.06/5.41 ! [K: nat,K6: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ K6 )
% 5.06/5.41 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.06/5.41 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 5.06/5.41 => ( ord_less_eq_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_antimono
% 5.06/5.41 thf(fact_8493_binomial__le__pow2,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_le_pow2
% 5.06/5.41 thf(fact_8494_arccos__lbound,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_lbound
% 5.06/5.41 thf(fact_8495_arccos__less__arccos,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_less_arccos
% 5.06/5.41 thf(fact_8496_choose__reduce__nat,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.41 => ( ( binomial @ N2 @ K )
% 5.06/5.41 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_reduce_nat
% 5.06/5.41 thf(fact_8497_times__binomial__minus1__eq,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.41 => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 5.06/5.41 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % times_binomial_minus1_eq
% 5.06/5.41 thf(fact_8498_arccos__less__mono,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.06/5.41 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 5.06/5.41 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_less_mono
% 5.06/5.41 thf(fact_8499_arccos__ubound,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_ubound
% 5.06/5.41 thf(fact_8500_arccos__cos,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ pi )
% 5.06/5.41 => ( ( arccos @ ( cos_real @ X ) )
% 5.06/5.41 = X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_cos
% 5.06/5.41 thf(fact_8501_termdiff__converges__all,axiom,
% 5.06/5.41 ! [C: nat > complex,X: complex] :
% 5.06/5.41 ( ! [X3: complex] :
% 5.06/5.41 ( summable_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X3 @ N ) ) )
% 5.06/5.41 => ( summable_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % termdiff_converges_all
% 5.06/5.41 thf(fact_8502_termdiff__converges__all,axiom,
% 5.06/5.41 ! [C: nat > real,X: real] :
% 5.06/5.41 ( ! [X3: real] :
% 5.06/5.41 ( summable_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X3 @ N ) ) )
% 5.06/5.41 => ( summable_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % termdiff_converges_all
% 5.06/5.41 thf(fact_8503_arcsin__less__arcsin,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_real @ X @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_less_arcsin
% 5.06/5.41 thf(fact_8504_arcsin__less__mono,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.06/5.41 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 5.06/5.41 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_less_mono
% 5.06/5.41 thf(fact_8505_cos__arccos__abs,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.06/5.41 => ( ( cos_real @ ( arccos @ Y ) )
% 5.06/5.41 = Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % cos_arccos_abs
% 5.06/5.41 thf(fact_8506_arccos__cos__eq__abs,axiom,
% 5.06/5.41 ! [Theta: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.06/5.41 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.06/5.41 = ( abs_abs_real @ Theta ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_cos_eq_abs
% 5.06/5.41 thf(fact_8507_binomial__altdef__nat,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( binomial @ N2 @ K )
% 5.06/5.41 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_altdef_nat
% 5.06/5.41 thf(fact_8508_binomial__less__binomial__Suc,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_less_binomial_Suc
% 5.06/5.41 thf(fact_8509_binomial__strict__mono,axiom,
% 5.06/5.41 ! [K: nat,K6: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ K @ K6 )
% 5.06/5.41 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 5.06/5.41 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_strict_mono
% 5.06/5.41 thf(fact_8510_binomial__strict__antimono,axiom,
% 5.06/5.41 ! [K: nat,K6: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ K @ K6 )
% 5.06/5.41 => ( ( ord_less_eq_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.06/5.41 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 5.06/5.41 => ( ord_less_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_strict_antimono
% 5.06/5.41 thf(fact_8511_central__binomial__odd,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.41 => ( ( binomial @ N2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.41 = ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % central_binomial_odd
% 5.06/5.41 thf(fact_8512_binomial__addition__formula,axiom,
% 5.06/5.41 ! [N2: nat,K: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( binomial @ N2 @ ( suc @ K ) )
% 5.06/5.41 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_addition_formula
% 5.06/5.41 thf(fact_8513_fact__binomial,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_binomial
% 5.06/5.41 thf(fact_8514_fact__binomial,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) )
% 5.06/5.41 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_binomial
% 5.06/5.41 thf(fact_8515_fact__binomial,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) )
% 5.06/5.41 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % fact_binomial
% 5.06/5.41 thf(fact_8516_binomial__fact,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) )
% 5.06/5.41 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_fact
% 5.06/5.41 thf(fact_8517_binomial__fact,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) )
% 5.06/5.41 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_fact
% 5.06/5.41 thf(fact_8518_binomial__fact,axiom,
% 5.06/5.41 ! [K: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) )
% 5.06/5.41 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % binomial_fact
% 5.06/5.41 thf(fact_8519_arccos__bounded,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.06/5.41 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_bounded
% 5.06/5.41 thf(fact_8520_arccos__cos2,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.06/5.41 => ( ( arccos @ ( cos_real @ X ) )
% 5.06/5.41 = ( uminus_uminus_real @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_cos2
% 5.06/5.41 thf(fact_8521_arccos__minus,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.41 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.06/5.41 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_minus
% 5.06/5.41 thf(fact_8522_choose__two,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( binomial @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.41 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_two
% 5.06/5.41 thf(fact_8523_arccos,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.06/5.41 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 5.06/5.41 & ( ( cos_real @ ( arccos @ Y ) )
% 5.06/5.41 = Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos
% 5.06/5.41 thf(fact_8524_arccos__minus__abs,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.41 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.06/5.41 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_minus_abs
% 5.06/5.41 thf(fact_8525_termdiff__converges,axiom,
% 5.06/5.41 ! [X: real,K5: real,C: nat > real] :
% 5.06/5.41 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ K5 )
% 5.06/5.41 => ( ! [X3: real] :
% 5.06/5.41 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X3 ) @ K5 )
% 5.06/5.41 => ( summable_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X3 @ N ) ) ) )
% 5.06/5.41 => ( summable_real
% 5.06/5.41 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % termdiff_converges
% 5.06/5.41 thf(fact_8526_termdiff__converges,axiom,
% 5.06/5.41 ! [X: complex,K5: real,C: nat > complex] :
% 5.06/5.41 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ K5 )
% 5.06/5.41 => ( ! [X3: complex] :
% 5.06/5.41 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X3 ) @ K5 )
% 5.06/5.41 => ( summable_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X3 @ N ) ) ) )
% 5.06/5.41 => ( summable_complex
% 5.06/5.41 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % termdiff_converges
% 5.06/5.41 thf(fact_8527_arccos__le__pi2,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arccos_le_pi2
% 5.06/5.41 thf(fact_8528_arcsin__lt__bounded,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_real @ Y @ one_one_real )
% 5.06/5.41 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.06/5.41 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_lt_bounded
% 5.06/5.41 thf(fact_8529_arcsin__lbound,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_lbound
% 5.06/5.41 thf(fact_8530_arcsin__ubound,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_ubound
% 5.06/5.41 thf(fact_8531_arcsin__bounded,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.06/5.41 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_bounded
% 5.06/5.41 thf(fact_8532_arcsin__sin,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( arcsin @ ( sin_real @ X ) )
% 5.06/5.41 = X ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_sin
% 5.06/5.41 thf(fact_8533_le__arcsin__iff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 5.06/5.41 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % le_arcsin_iff
% 5.06/5.41 thf(fact_8534_arcsin__le__iff,axiom,
% 5.06/5.41 ! [X: real,Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 5.06/5.41 = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_le_iff
% 5.06/5.41 thf(fact_8535_arcsin__pi,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.06/5.41 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 5.06/5.41 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.06/5.41 = Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin_pi
% 5.06/5.41 thf(fact_8536_arcsin,axiom,
% 5.06/5.41 ! [Y: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.06/5.41 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.06/5.41 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.06/5.41 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.41 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.06/5.41 = Y ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % arcsin
% 5.06/5.41 thf(fact_8537_central__binomial__lower__bound,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % central_binomial_lower_bound
% 5.06/5.41 thf(fact_8538_sin__arccos,axiom,
% 5.06/5.41 ! [X: real] :
% 5.06/5.41 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.41 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.41 => ( ( sin_real @ ( arccos @ X ) )
% 5.06/5.41 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sin_arccos
% 5.06/5.41 thf(fact_8539_choose__odd__sum,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.06/5.41 @ ( groups2073611262835488442omplex
% 5.06/5.41 @ ^ [I5: nat] :
% 5.06/5.41 ( if_complex
% 5.06/5.41 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.06/5.41 @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) )
% 5.06/5.41 @ zero_zero_complex )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_odd_sum
% 5.06/5.41 thf(fact_8540_choose__odd__sum,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.06/5.41 @ ( groups2906978787729119204at_rat
% 5.06/5.41 @ ^ [I5: nat] :
% 5.06/5.41 ( if_rat
% 5.06/5.41 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.06/5.41 @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) )
% 5.06/5.41 @ zero_zero_rat )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_odd_sum
% 5.06/5.41 thf(fact_8541_choose__odd__sum,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.06/5.41 @ ( groups3539618377306564664at_int
% 5.06/5.41 @ ^ [I5: nat] :
% 5.06/5.41 ( if_int
% 5.06/5.41 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.06/5.41 @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) )
% 5.06/5.41 @ zero_zero_int )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_odd_sum
% 5.06/5.41 thf(fact_8542_choose__odd__sum,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.06/5.41 @ ( groups7501900531339628137nteger
% 5.06/5.41 @ ^ [I5: nat] :
% 5.06/5.41 ( if_Code_integer
% 5.06/5.41 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.06/5.41 @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) )
% 5.06/5.41 @ zero_z3403309356797280102nteger )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_odd_sum
% 5.06/5.41 thf(fact_8543_choose__odd__sum,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] :
% 5.06/5.41 ( if_real
% 5.06/5.41 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.06/5.41 @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) )
% 5.06/5.41 @ zero_zero_real )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_odd_sum
% 5.06/5.41 thf(fact_8544_choose__even__sum,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.06/5.41 @ ( groups2073611262835488442omplex
% 5.06/5.41 @ ^ [I5: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) @ zero_zero_complex )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_even_sum
% 5.06/5.41 thf(fact_8545_choose__even__sum,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.06/5.41 @ ( groups2906978787729119204at_rat
% 5.06/5.41 @ ^ [I5: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) ) @ zero_zero_rat )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_even_sum
% 5.06/5.41 thf(fact_8546_choose__even__sum,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.06/5.41 @ ( groups3539618377306564664at_int
% 5.06/5.41 @ ^ [I5: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) @ zero_zero_int )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_even_sum
% 5.06/5.41 thf(fact_8547_choose__even__sum,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.06/5.41 @ ( groups7501900531339628137nteger
% 5.06/5.41 @ ^ [I5: nat] : ( if_Code_integer @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) @ zero_z3403309356797280102nteger )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_even_sum
% 5.06/5.41 thf(fact_8548_choose__even__sum,axiom,
% 5.06/5.41 ! [N2: nat] :
% 5.06/5.41 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.41 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) @ zero_zero_real )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_even_sum
% 5.06/5.41 thf(fact_8549_monoseq__def,axiom,
% 5.06/5.41 ( topolo6980174941875973593q_real
% 5.06/5.41 = ( ^ [X4: nat > real] :
% 5.06/5.41 ( ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_real @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.06/5.41 | ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_real @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoseq_def
% 5.06/5.41 thf(fact_8550_monoseq__def,axiom,
% 5.06/5.41 ( topolo3100542954746470799et_int
% 5.06/5.41 = ( ^ [X4: nat > set_int] :
% 5.06/5.41 ( ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_set_int @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.06/5.41 | ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_set_int @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoseq_def
% 5.06/5.41 thf(fact_8551_monoseq__def,axiom,
% 5.06/5.41 ( topolo4267028734544971653eq_rat
% 5.06/5.41 = ( ^ [X4: nat > rat] :
% 5.06/5.41 ( ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_rat @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.06/5.41 | ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_rat @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoseq_def
% 5.06/5.41 thf(fact_8552_monoseq__def,axiom,
% 5.06/5.41 ( topolo1459490580787246023eq_num
% 5.06/5.41 = ( ^ [X4: nat > num] :
% 5.06/5.41 ( ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_num @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.06/5.41 | ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_num @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoseq_def
% 5.06/5.41 thf(fact_8553_monoseq__def,axiom,
% 5.06/5.41 ( topolo4902158794631467389eq_nat
% 5.06/5.41 = ( ^ [X4: nat > nat] :
% 5.06/5.41 ( ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_nat @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.06/5.41 | ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_nat @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoseq_def
% 5.06/5.41 thf(fact_8554_monoseq__def,axiom,
% 5.06/5.41 ( topolo4899668324122417113eq_int
% 5.06/5.41 = ( ^ [X4: nat > int] :
% 5.06/5.41 ( ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_int @ ( X4 @ M6 ) @ ( X4 @ N ) ) )
% 5.06/5.41 | ! [M6: nat,N: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M6 @ N )
% 5.06/5.41 => ( ord_less_eq_int @ ( X4 @ N ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoseq_def
% 5.06/5.41 thf(fact_8555_monoI2,axiom,
% 5.06/5.41 ! [X8: nat > real] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M2 ) ) )
% 5.06/5.41 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI2
% 5.06/5.41 thf(fact_8556_monoI2,axiom,
% 5.06/5.41 ! [X8: nat > set_int] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ M2 ) ) )
% 5.06/5.41 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI2
% 5.06/5.41 thf(fact_8557_monoI2,axiom,
% 5.06/5.41 ! [X8: nat > rat] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ M2 ) ) )
% 5.06/5.41 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI2
% 5.06/5.41 thf(fact_8558_monoI2,axiom,
% 5.06/5.41 ! [X8: nat > num] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M2 ) ) )
% 5.06/5.41 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI2
% 5.06/5.41 thf(fact_8559_monoI2,axiom,
% 5.06/5.41 ! [X8: nat > nat] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M2 ) ) )
% 5.06/5.41 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI2
% 5.06/5.41 thf(fact_8560_monoI2,axiom,
% 5.06/5.41 ! [X8: nat > int] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M2 ) ) )
% 5.06/5.41 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI2
% 5.06/5.41 thf(fact_8561_monoI1,axiom,
% 5.06/5.41 ! [X8: nat > real] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_real @ ( X8 @ M2 ) @ ( X8 @ N3 ) ) )
% 5.06/5.41 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI1
% 5.06/5.41 thf(fact_8562_monoI1,axiom,
% 5.06/5.41 ! [X8: nat > set_int] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_set_int @ ( X8 @ M2 ) @ ( X8 @ N3 ) ) )
% 5.06/5.41 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI1
% 5.06/5.41 thf(fact_8563_monoI1,axiom,
% 5.06/5.41 ! [X8: nat > rat] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_rat @ ( X8 @ M2 ) @ ( X8 @ N3 ) ) )
% 5.06/5.41 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI1
% 5.06/5.41 thf(fact_8564_monoI1,axiom,
% 5.06/5.41 ! [X8: nat > num] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_num @ ( X8 @ M2 ) @ ( X8 @ N3 ) ) )
% 5.06/5.41 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI1
% 5.06/5.41 thf(fact_8565_monoI1,axiom,
% 5.06/5.41 ! [X8: nat > nat] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_nat @ ( X8 @ M2 ) @ ( X8 @ N3 ) ) )
% 5.06/5.41 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI1
% 5.06/5.41 thf(fact_8566_monoI1,axiom,
% 5.06/5.41 ! [X8: nat > int] :
% 5.06/5.41 ( ! [M2: nat,N3: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M2 @ N3 )
% 5.06/5.41 => ( ord_less_eq_int @ ( X8 @ M2 ) @ ( X8 @ N3 ) ) )
% 5.06/5.41 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.06/5.41
% 5.06/5.41 % monoI1
% 5.06/5.41 thf(fact_8567_atMost__iff,axiom,
% 5.06/5.41 ! [I2: real,K: real] :
% 5.06/5.41 ( ( member_real @ I2 @ ( set_ord_atMost_real @ K ) )
% 5.06/5.41 = ( ord_less_eq_real @ I2 @ K ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_iff
% 5.06/5.41 thf(fact_8568_atMost__iff,axiom,
% 5.06/5.41 ! [I2: set_nat,K: set_nat] :
% 5.06/5.41 ( ( member_set_nat @ I2 @ ( set_or4236626031148496127et_nat @ K ) )
% 5.06/5.41 = ( ord_less_eq_set_nat @ I2 @ K ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_iff
% 5.06/5.41 thf(fact_8569_atMost__iff,axiom,
% 5.06/5.41 ! [I2: set_int,K: set_int] :
% 5.06/5.41 ( ( member_set_int @ I2 @ ( set_or58775011639299419et_int @ K ) )
% 5.06/5.41 = ( ord_less_eq_set_int @ I2 @ K ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_iff
% 5.06/5.41 thf(fact_8570_atMost__iff,axiom,
% 5.06/5.41 ! [I2: rat,K: rat] :
% 5.06/5.41 ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K ) )
% 5.06/5.41 = ( ord_less_eq_rat @ I2 @ K ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_iff
% 5.06/5.41 thf(fact_8571_atMost__iff,axiom,
% 5.06/5.41 ! [I2: num,K: num] :
% 5.06/5.41 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K ) )
% 5.06/5.41 = ( ord_less_eq_num @ I2 @ K ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_iff
% 5.06/5.41 thf(fact_8572_atMost__iff,axiom,
% 5.06/5.41 ! [I2: nat,K: nat] :
% 5.06/5.41 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K ) )
% 5.06/5.41 = ( ord_less_eq_nat @ I2 @ K ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_iff
% 5.06/5.41 thf(fact_8573_atMost__iff,axiom,
% 5.06/5.41 ! [I2: int,K: int] :
% 5.06/5.41 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K ) )
% 5.06/5.41 = ( ord_less_eq_int @ I2 @ K ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_iff
% 5.06/5.41 thf(fact_8574_atMost__subset__iff,axiom,
% 5.06/5.41 ! [X: set_int,Y: set_int] :
% 5.06/5.41 ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X ) @ ( set_or58775011639299419et_int @ Y ) )
% 5.06/5.41 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_subset_iff
% 5.06/5.41 thf(fact_8575_atMost__subset__iff,axiom,
% 5.06/5.41 ! [X: rat,Y: rat] :
% 5.06/5.41 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X ) @ ( set_ord_atMost_rat @ Y ) )
% 5.06/5.41 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_subset_iff
% 5.06/5.41 thf(fact_8576_atMost__subset__iff,axiom,
% 5.06/5.41 ! [X: num,Y: num] :
% 5.06/5.41 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y ) )
% 5.06/5.41 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_subset_iff
% 5.06/5.41 thf(fact_8577_atMost__subset__iff,axiom,
% 5.06/5.41 ! [X: nat,Y: nat] :
% 5.06/5.41 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
% 5.06/5.41 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_subset_iff
% 5.06/5.41 thf(fact_8578_atMost__subset__iff,axiom,
% 5.06/5.41 ! [X: int,Y: int] :
% 5.06/5.41 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y ) )
% 5.06/5.41 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_subset_iff
% 5.06/5.41 thf(fact_8579_Icc__subset__Iic__iff,axiom,
% 5.06/5.41 ! [L2: set_int,H2: set_int,H3: set_int] :
% 5.06/5.41 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L2 @ H2 ) @ ( set_or58775011639299419et_int @ H3 ) )
% 5.06/5.41 = ( ~ ( ord_less_eq_set_int @ L2 @ H2 )
% 5.06/5.41 | ( ord_less_eq_set_int @ H2 @ H3 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Icc_subset_Iic_iff
% 5.06/5.41 thf(fact_8580_Icc__subset__Iic__iff,axiom,
% 5.06/5.41 ! [L2: rat,H2: rat,H3: rat] :
% 5.06/5.41 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L2 @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.06/5.41 = ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.06/5.41 | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Icc_subset_Iic_iff
% 5.06/5.41 thf(fact_8581_Icc__subset__Iic__iff,axiom,
% 5.06/5.41 ! [L2: num,H2: num,H3: num] :
% 5.06/5.41 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L2 @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 5.06/5.41 = ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.06/5.41 | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Icc_subset_Iic_iff
% 5.06/5.41 thf(fact_8582_Icc__subset__Iic__iff,axiom,
% 5.06/5.41 ! [L2: nat,H2: nat,H3: nat] :
% 5.06/5.41 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L2 @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.06/5.41 = ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.06/5.41 | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Icc_subset_Iic_iff
% 5.06/5.41 thf(fact_8583_Icc__subset__Iic__iff,axiom,
% 5.06/5.41 ! [L2: int,H2: int,H3: int] :
% 5.06/5.41 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L2 @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 5.06/5.41 = ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.06/5.41 | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Icc_subset_Iic_iff
% 5.06/5.41 thf(fact_8584_Icc__subset__Iic__iff,axiom,
% 5.06/5.41 ! [L2: real,H2: real,H3: real] :
% 5.06/5.41 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L2 @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 5.06/5.41 = ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.06/5.41 | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % Icc_subset_Iic_iff
% 5.06/5.41 thf(fact_8585_sum_OatMost__Suc,axiom,
% 5.06/5.41 ! [G: nat > rat,N2: nat] :
% 5.06/5.41 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_Suc
% 5.06/5.41 thf(fact_8586_sum_OatMost__Suc,axiom,
% 5.06/5.41 ! [G: nat > int,N2: nat] :
% 5.06/5.41 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_Suc
% 5.06/5.41 thf(fact_8587_sum_OatMost__Suc,axiom,
% 5.06/5.41 ! [G: nat > nat,N2: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_Suc
% 5.06/5.41 thf(fact_8588_sum_OatMost__Suc,axiom,
% 5.06/5.41 ! [G: nat > real,N2: nat] :
% 5.06/5.41 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_Suc
% 5.06/5.41 thf(fact_8589_atMost__def,axiom,
% 5.06/5.41 ( set_or4236626031148496127et_nat
% 5.06/5.41 = ( ^ [U2: set_nat] :
% 5.06/5.41 ( collect_set_nat
% 5.06/5.41 @ ^ [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ U2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_def
% 5.06/5.41 thf(fact_8590_atMost__def,axiom,
% 5.06/5.41 ( set_or58775011639299419et_int
% 5.06/5.41 = ( ^ [U2: set_int] :
% 5.06/5.41 ( collect_set_int
% 5.06/5.41 @ ^ [X2: set_int] : ( ord_less_eq_set_int @ X2 @ U2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_def
% 5.06/5.41 thf(fact_8591_atMost__def,axiom,
% 5.06/5.41 ( set_ord_atMost_rat
% 5.06/5.41 = ( ^ [U2: rat] :
% 5.06/5.41 ( collect_rat
% 5.06/5.41 @ ^ [X2: rat] : ( ord_less_eq_rat @ X2 @ U2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_def
% 5.06/5.41 thf(fact_8592_atMost__def,axiom,
% 5.06/5.41 ( set_ord_atMost_num
% 5.06/5.41 = ( ^ [U2: num] :
% 5.06/5.41 ( collect_num
% 5.06/5.41 @ ^ [X2: num] : ( ord_less_eq_num @ X2 @ U2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_def
% 5.06/5.41 thf(fact_8593_atMost__def,axiom,
% 5.06/5.41 ( set_ord_atMost_nat
% 5.06/5.41 = ( ^ [U2: nat] :
% 5.06/5.41 ( collect_nat
% 5.06/5.41 @ ^ [X2: nat] : ( ord_less_eq_nat @ X2 @ U2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_def
% 5.06/5.41 thf(fact_8594_atMost__def,axiom,
% 5.06/5.41 ( set_ord_atMost_int
% 5.06/5.41 = ( ^ [U2: int] :
% 5.06/5.41 ( collect_int
% 5.06/5.41 @ ^ [X2: int] : ( ord_less_eq_int @ X2 @ U2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % atMost_def
% 5.06/5.41 thf(fact_8595_lessThan__Suc__atMost,axiom,
% 5.06/5.41 ! [K: nat] :
% 5.06/5.41 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.06/5.41 = ( set_ord_atMost_nat @ K ) ) ).
% 5.06/5.41
% 5.06/5.41 % lessThan_Suc_atMost
% 5.06/5.41 thf(fact_8596_not__Iic__le__Icc,axiom,
% 5.06/5.41 ! [H2: int,L3: int,H3: int] :
% 5.06/5.41 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H2 ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 5.06/5.41
% 5.06/5.41 % not_Iic_le_Icc
% 5.06/5.41 thf(fact_8597_not__Iic__le__Icc,axiom,
% 5.06/5.41 ! [H2: real,L3: real,H3: real] :
% 5.06/5.41 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H2 ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 5.06/5.41
% 5.06/5.41 % not_Iic_le_Icc
% 5.06/5.41 thf(fact_8598_finite__nat__iff__bounded__le,axiom,
% 5.06/5.41 ( finite_finite_nat
% 5.06/5.41 = ( ^ [S5: set_nat] :
% 5.06/5.41 ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % finite_nat_iff_bounded_le
% 5.06/5.41 thf(fact_8599_Iic__subset__Iio__iff,axiom,
% 5.06/5.41 ! [A: rat,B: rat] :
% 5.06/5.41 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 5.06/5.41 = ( ord_less_rat @ A @ B ) ) ).
% 5.06/5.41
% 5.06/5.41 % Iic_subset_Iio_iff
% 5.06/5.41 thf(fact_8600_Iic__subset__Iio__iff,axiom,
% 5.06/5.41 ! [A: num,B: num] :
% 5.06/5.41 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.06/5.41 = ( ord_less_num @ A @ B ) ) ).
% 5.06/5.41
% 5.06/5.41 % Iic_subset_Iio_iff
% 5.06/5.41 thf(fact_8601_Iic__subset__Iio__iff,axiom,
% 5.06/5.41 ! [A: nat,B: nat] :
% 5.06/5.41 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.06/5.41 = ( ord_less_nat @ A @ B ) ) ).
% 5.06/5.41
% 5.06/5.41 % Iic_subset_Iio_iff
% 5.06/5.41 thf(fact_8602_Iic__subset__Iio__iff,axiom,
% 5.06/5.41 ! [A: int,B: int] :
% 5.06/5.41 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.06/5.41 = ( ord_less_int @ A @ B ) ) ).
% 5.06/5.41
% 5.06/5.41 % Iic_subset_Iio_iff
% 5.06/5.41 thf(fact_8603_Iic__subset__Iio__iff,axiom,
% 5.06/5.41 ! [A: real,B: real] :
% 5.06/5.41 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 5.06/5.41 = ( ord_less_real @ A @ B ) ) ).
% 5.06/5.41
% 5.06/5.41 % Iic_subset_Iio_iff
% 5.06/5.41 thf(fact_8604_Iic__subset__Iio__iff,axiom,
% 5.06/5.41 ! [A: $o,B: $o] :
% 5.06/5.41 ( ( ord_less_eq_set_o @ ( set_ord_atMost_o @ A ) @ ( set_ord_lessThan_o @ B ) )
% 5.06/5.41 = ( ord_less_o @ A @ B ) ) ).
% 5.06/5.41
% 5.06/5.41 % Iic_subset_Iio_iff
% 5.06/5.41 thf(fact_8605_sum__choose__upper,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = ( binomial @ ( suc @ N2 ) @ ( suc @ M ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_choose_upper
% 5.06/5.41 thf(fact_8606_sum_OatMost__Suc__shift,axiom,
% 5.06/5.41 ! [G: nat > rat,N2: nat] :
% 5.06/5.41 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.06/5.41 @ ( groups2906978787729119204at_rat
% 5.06/5.41 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_Suc_shift
% 5.06/5.41 thf(fact_8607_sum_OatMost__Suc__shift,axiom,
% 5.06/5.41 ! [G: nat > int,N2: nat] :
% 5.06/5.41 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.06/5.41 @ ( groups3539618377306564664at_int
% 5.06/5.41 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_Suc_shift
% 5.06/5.41 thf(fact_8608_sum_OatMost__Suc__shift,axiom,
% 5.06/5.41 ! [G: nat > nat,N2: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.06/5.41 @ ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_Suc_shift
% 5.06/5.41 thf(fact_8609_sum_OatMost__Suc__shift,axiom,
% 5.06/5.41 ! [G: nat > real,N2: nat] :
% 5.06/5.41 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_Suc_shift
% 5.06/5.41 thf(fact_8610_sum__telescope,axiom,
% 5.06/5.41 ! [F: nat > rat,I2: nat] :
% 5.06/5.41 ( ( groups2906978787729119204at_rat
% 5.06/5.41 @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ I2 ) )
% 5.06/5.41 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_telescope
% 5.06/5.41 thf(fact_8611_sum__telescope,axiom,
% 5.06/5.41 ! [F: nat > int,I2: nat] :
% 5.06/5.41 ( ( groups3539618377306564664at_int
% 5.06/5.41 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ I2 ) )
% 5.06/5.41 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_telescope
% 5.06/5.41 thf(fact_8612_sum__telescope,axiom,
% 5.06/5.41 ! [F: nat > real,I2: nat] :
% 5.06/5.41 ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ I2 ) )
% 5.06/5.41 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_telescope
% 5.06/5.41 thf(fact_8613_polyfun__eq__coeffs,axiom,
% 5.06/5.41 ! [C: nat > complex,N2: nat,D: nat > complex] :
% 5.06/5.41 ( ( ! [X2: complex] :
% 5.06/5.41 ( ( groups2073611262835488442omplex
% 5.06/5.41 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = ( groups2073611262835488442omplex
% 5.06/5.41 @ ^ [I5: nat] : ( times_times_complex @ ( D @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 5.06/5.41 = ( ! [I5: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.06/5.41 => ( ( C @ I5 )
% 5.06/5.41 = ( D @ I5 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % polyfun_eq_coeffs
% 5.06/5.41 thf(fact_8614_polyfun__eq__coeffs,axiom,
% 5.06/5.41 ! [C: nat > real,N2: nat,D: nat > real] :
% 5.06/5.41 ( ( ! [X2: real] :
% 5.06/5.41 ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( times_times_real @ ( D @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 5.06/5.41 = ( ! [I5: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.06/5.41 => ( ( C @ I5 )
% 5.06/5.41 = ( D @ I5 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % polyfun_eq_coeffs
% 5.06/5.41 thf(fact_8615_bounded__imp__summable,axiom,
% 5.06/5.41 ! [A: nat > int,B3: int] :
% 5.06/5.41 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N3 ) )
% 5.06/5.41 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 5.06/5.41 => ( summable_int @ A ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % bounded_imp_summable
% 5.06/5.41 thf(fact_8616_bounded__imp__summable,axiom,
% 5.06/5.41 ! [A: nat > nat,B3: nat] :
% 5.06/5.41 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N3 ) )
% 5.06/5.41 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 5.06/5.41 => ( summable_nat @ A ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % bounded_imp_summable
% 5.06/5.41 thf(fact_8617_bounded__imp__summable,axiom,
% 5.06/5.41 ! [A: nat > real,B3: real] :
% 5.06/5.41 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.06/5.41 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 5.06/5.41 => ( summable_real @ A ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % bounded_imp_summable
% 5.06/5.41 thf(fact_8618_sum_Onested__swap_H,axiom,
% 5.06/5.41 ! [A: nat > nat > nat,N2: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [I5: nat] : ( groups3542108847815614940at_nat @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [J3: nat] :
% 5.06/5.41 ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 5.06/5.41 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.nested_swap'
% 5.06/5.41 thf(fact_8619_sum_Onested__swap_H,axiom,
% 5.06/5.41 ! [A: nat > nat > real,N2: nat] :
% 5.06/5.41 ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( groups6591440286371151544t_real @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [J3: nat] :
% 5.06/5.41 ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 5.06/5.41 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.nested_swap'
% 5.06/5.41 thf(fact_8620_sum__choose__lower,axiom,
% 5.06/5.41 ! [R2: nat,N2: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N2 ) ) @ N2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_choose_lower
% 5.06/5.41 thf(fact_8621_choose__rising__sum_I2_J,axiom,
% 5.06/5.41 ! [N2: nat,M: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.06/5.41 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.41 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_rising_sum(2)
% 5.06/5.41 thf(fact_8622_choose__rising__sum_I1_J,axiom,
% 5.06/5.41 ! [N2: nat,M: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.06/5.41 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.41 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % choose_rising_sum(1)
% 5.06/5.41 thf(fact_8623_polyfun__eq__0,axiom,
% 5.06/5.41 ! [C: nat > complex,N2: nat] :
% 5.06/5.41 ( ( ! [X2: complex] :
% 5.06/5.41 ( ( groups2073611262835488442omplex
% 5.06/5.41 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = zero_zero_complex ) )
% 5.06/5.41 = ( ! [I5: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.06/5.41 => ( ( C @ I5 )
% 5.06/5.41 = zero_zero_complex ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % polyfun_eq_0
% 5.06/5.41 thf(fact_8624_polyfun__eq__0,axiom,
% 5.06/5.41 ! [C: nat > real,N2: nat] :
% 5.06/5.41 ( ( ! [X2: real] :
% 5.06/5.41 ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = zero_zero_real ) )
% 5.06/5.41 = ( ! [I5: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.06/5.41 => ( ( C @ I5 )
% 5.06/5.41 = zero_zero_real ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % polyfun_eq_0
% 5.06/5.41 thf(fact_8625_zero__polynom__imp__zero__coeffs,axiom,
% 5.06/5.41 ! [C: nat > complex,N2: nat,K: nat] :
% 5.06/5.41 ( ! [W2: complex] :
% 5.06/5.41 ( ( groups2073611262835488442omplex
% 5.06/5.41 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ W2 @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = zero_zero_complex )
% 5.06/5.41 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( C @ K )
% 5.06/5.41 = zero_zero_complex ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % zero_polynom_imp_zero_coeffs
% 5.06/5.41 thf(fact_8626_zero__polynom__imp__zero__coeffs,axiom,
% 5.06/5.41 ! [C: nat > real,N2: nat,K: nat] :
% 5.06/5.41 ( ! [W2: real] :
% 5.06/5.41 ( ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ W2 @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = zero_zero_real )
% 5.06/5.41 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.41 => ( ( C @ K )
% 5.06/5.41 = zero_zero_real ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % zero_polynom_imp_zero_coeffs
% 5.06/5.41 thf(fact_8627_sum_OatMost__shift,axiom,
% 5.06/5.41 ! [G: nat > rat,N2: nat] :
% 5.06/5.41 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.06/5.41 @ ( groups2906978787729119204at_rat
% 5.06/5.41 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_shift
% 5.06/5.41 thf(fact_8628_sum_OatMost__shift,axiom,
% 5.06/5.41 ! [G: nat > int,N2: nat] :
% 5.06/5.41 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.06/5.41 @ ( groups3539618377306564664at_int
% 5.06/5.41 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_shift
% 5.06/5.41 thf(fact_8629_sum_OatMost__shift,axiom,
% 5.06/5.41 ! [G: nat > nat,N2: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.06/5.41 @ ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_shift
% 5.06/5.41 thf(fact_8630_sum_OatMost__shift,axiom,
% 5.06/5.41 ! [G: nat > real,N2: nat] :
% 5.06/5.41 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.41 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.06/5.41 @ ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.06/5.41 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.atMost_shift
% 5.06/5.41 thf(fact_8631_sum__up__index__split,axiom,
% 5.06/5.41 ! [F: nat > rat,M: nat,N2: nat] :
% 5.06/5.41 ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_up_index_split
% 5.06/5.41 thf(fact_8632_sum__up__index__split,axiom,
% 5.06/5.41 ! [F: nat > int,M: nat,N2: nat] :
% 5.06/5.41 ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_up_index_split
% 5.06/5.41 thf(fact_8633_sum__up__index__split,axiom,
% 5.06/5.41 ! [F: nat > nat,M: nat,N2: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_up_index_split
% 5.06/5.41 thf(fact_8634_sum__up__index__split,axiom,
% 5.06/5.41 ! [F: nat > real,M: nat,N2: nat] :
% 5.06/5.41 ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.06/5.41 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_up_index_split
% 5.06/5.41 thf(fact_8635_sum_Otriangle__reindex__eq,axiom,
% 5.06/5.41 ! [G: nat > nat > nat,N2: nat] :
% 5.06/5.41 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.06/5.41 @ ( collec3392354462482085612at_nat
% 5.06/5.41 @ ( produc6081775807080527818_nat_o
% 5.06/5.41 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.06/5.41 = ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [K3: nat] :
% 5.06/5.41 ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ K3 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.triangle_reindex_eq
% 5.06/5.41 thf(fact_8636_sum_Otriangle__reindex__eq,axiom,
% 5.06/5.41 ! [G: nat > nat > real,N2: nat] :
% 5.06/5.41 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.06/5.41 @ ( collec3392354462482085612at_nat
% 5.06/5.41 @ ( produc6081775807080527818_nat_o
% 5.06/5.41 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.06/5.41 = ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [K3: nat] :
% 5.06/5.41 ( groups6591440286371151544t_real
% 5.06/5.41 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ K3 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum.triangle_reindex_eq
% 5.06/5.41 thf(fact_8637_sum__choose__diagonal,axiom,
% 5.06/5.41 ! [M: nat,N2: nat] :
% 5.06/5.41 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.41 => ( ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.41 = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_choose_diagonal
% 5.06/5.41 thf(fact_8638_vandermonde,axiom,
% 5.06/5.41 ! [M: nat,N2: nat,R2: nat] :
% 5.06/5.41 ( ( groups3542108847815614940at_nat
% 5.06/5.41 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 5.06/5.41 @ ( set_ord_atMost_nat @ R2 ) )
% 5.06/5.41 = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R2 ) ) ).
% 5.06/5.41
% 5.06/5.41 % vandermonde
% 5.06/5.41 thf(fact_8639_sum__gp__basic,axiom,
% 5.06/5.41 ! [X: complex,N2: nat] :
% 5.06/5.41 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_gp_basic
% 5.06/5.41 thf(fact_8640_sum__gp__basic,axiom,
% 5.06/5.41 ! [X: rat,N2: nat] :
% 5.06/5.41 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_gp_basic
% 5.06/5.41 thf(fact_8641_sum__gp__basic,axiom,
% 5.06/5.41 ! [X: int,N2: nat] :
% 5.06/5.41 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_gp_basic
% 5.06/5.41 thf(fact_8642_sum__gp__basic,axiom,
% 5.06/5.41 ! [X: real,N2: nat] :
% 5.06/5.41 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.41 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N2 ) ) ) ) ).
% 5.06/5.41
% 5.06/5.41 % sum_gp_basic
% 5.06/5.41 thf(fact_8643_polyfun__finite__roots,axiom,
% 5.06/5.41 ! [C: nat > complex,N2: nat] :
% 5.06/5.42 ( ( finite3207457112153483333omplex
% 5.06/5.42 @ ( collect_complex
% 5.06/5.42 @ ^ [X2: complex] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_complex ) ) )
% 5.06/5.42 = ( ? [I5: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.06/5.42 & ( ( C @ I5 )
% 5.06/5.42 != zero_zero_complex ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_finite_roots
% 5.06/5.42 thf(fact_8644_polyfun__finite__roots,axiom,
% 5.06/5.42 ! [C: nat > real,N2: nat] :
% 5.06/5.42 ( ( finite_finite_real
% 5.06/5.42 @ ( collect_real
% 5.06/5.42 @ ^ [X2: real] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_real ) ) )
% 5.06/5.42 = ( ? [I5: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.06/5.42 & ( ( C @ I5 )
% 5.06/5.42 != zero_zero_real ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_finite_roots
% 5.06/5.42 thf(fact_8645_polyfun__roots__finite,axiom,
% 5.06/5.42 ! [C: nat > complex,K: nat,N2: nat] :
% 5.06/5.42 ( ( ( C @ K )
% 5.06/5.42 != zero_zero_complex )
% 5.06/5.42 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.42 => ( finite3207457112153483333omplex
% 5.06/5.42 @ ( collect_complex
% 5.06/5.42 @ ^ [Z2: complex] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z2 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_complex ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_roots_finite
% 5.06/5.42 thf(fact_8646_polyfun__roots__finite,axiom,
% 5.06/5.42 ! [C: nat > real,K: nat,N2: nat] :
% 5.06/5.42 ( ( ( C @ K )
% 5.06/5.42 != zero_zero_real )
% 5.06/5.42 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.42 => ( finite_finite_real
% 5.06/5.42 @ ( collect_real
% 5.06/5.42 @ ^ [Z2: real] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z2 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_real ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_roots_finite
% 5.06/5.42 thf(fact_8647_polyfun__linear__factor__root,axiom,
% 5.06/5.42 ! [C: nat > complex,A: complex,N2: nat] :
% 5.06/5.42 ( ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ A @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_complex )
% 5.06/5.42 => ~ ! [B2: nat > complex] :
% 5.06/5.42 ~ ! [Z5: complex] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( B2 @ I5 ) @ ( power_power_complex @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_linear_factor_root
% 5.06/5.42 thf(fact_8648_polyfun__linear__factor__root,axiom,
% 5.06/5.42 ! [C: nat > rat,A: rat,N2: nat] :
% 5.06/5.42 ( ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ A @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_rat )
% 5.06/5.42 => ~ ! [B2: nat > rat] :
% 5.06/5.42 ~ ! [Z5: rat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( B2 @ I5 ) @ ( power_power_rat @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_linear_factor_root
% 5.06/5.42 thf(fact_8649_polyfun__linear__factor__root,axiom,
% 5.06/5.42 ! [C: nat > int,A: int,N2: nat] :
% 5.06/5.42 ( ( ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ A @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_int )
% 5.06/5.42 => ~ ! [B2: nat > int] :
% 5.06/5.42 ~ ! [Z5: int] :
% 5.06/5.42 ( ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( B2 @ I5 ) @ ( power_power_int @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_linear_factor_root
% 5.06/5.42 thf(fact_8650_polyfun__linear__factor__root,axiom,
% 5.06/5.42 ! [C: nat > real,A: real,N2: nat] :
% 5.06/5.42 ( ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ A @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_real )
% 5.06/5.42 => ~ ! [B2: nat > real] :
% 5.06/5.42 ~ ! [Z5: real] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( B2 @ I5 ) @ ( power_power_real @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_linear_factor_root
% 5.06/5.42 thf(fact_8651_polyfun__linear__factor,axiom,
% 5.06/5.42 ! [C: nat > complex,N2: nat,A: complex] :
% 5.06/5.42 ? [B2: nat > complex] :
% 5.06/5.42 ! [Z5: complex] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( plus_plus_complex
% 5.06/5.42 @ ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( B2 @ I5 ) @ ( power_power_complex @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ A @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_linear_factor
% 5.06/5.42 thf(fact_8652_polyfun__linear__factor,axiom,
% 5.06/5.42 ! [C: nat > rat,N2: nat,A: rat] :
% 5.06/5.42 ? [B2: nat > rat] :
% 5.06/5.42 ! [Z5: rat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( plus_plus_rat
% 5.06/5.42 @ ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( B2 @ I5 ) @ ( power_power_rat @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ A @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_linear_factor
% 5.06/5.42 thf(fact_8653_polyfun__linear__factor,axiom,
% 5.06/5.42 ! [C: nat > int,N2: nat,A: int] :
% 5.06/5.42 ? [B2: nat > int] :
% 5.06/5.42 ! [Z5: int] :
% 5.06/5.42 ( ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( plus_plus_int
% 5.06/5.42 @ ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( B2 @ I5 ) @ ( power_power_int @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ A @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_linear_factor
% 5.06/5.42 thf(fact_8654_polyfun__linear__factor,axiom,
% 5.06/5.42 ! [C: nat > real,N2: nat,A: real] :
% 5.06/5.42 ? [B2: nat > real] :
% 5.06/5.42 ! [Z5: real] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( plus_plus_real
% 5.06/5.42 @ ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( B2 @ I5 ) @ ( power_power_real @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ A @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_linear_factor
% 5.06/5.42 thf(fact_8655_sum__power__shift,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,X: complex] :
% 5.06/5.42 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.42 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.42 = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum_power_shift
% 5.06/5.42 thf(fact_8656_sum__power__shift,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,X: rat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.42 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.42 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum_power_shift
% 5.06/5.42 thf(fact_8657_sum__power__shift,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,X: int] :
% 5.06/5.42 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.42 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.42 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum_power_shift
% 5.06/5.42 thf(fact_8658_sum__power__shift,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.42 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.06/5.42 = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum_power_shift
% 5.06/5.42 thf(fact_8659_sum_Otriangle__reindex,axiom,
% 5.06/5.42 ! [G: nat > nat > nat,N2: nat] :
% 5.06/5.42 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.06/5.42 @ ( collec3392354462482085612at_nat
% 5.06/5.42 @ ( produc6081775807080527818_nat_o
% 5.06/5.42 @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.06/5.42 = ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [K3: nat] :
% 5.06/5.42 ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ K3 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.triangle_reindex
% 5.06/5.42 thf(fact_8660_sum_Otriangle__reindex,axiom,
% 5.06/5.42 ! [G: nat > nat > real,N2: nat] :
% 5.06/5.42 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.06/5.42 @ ( collec3392354462482085612at_nat
% 5.06/5.42 @ ( produc6081775807080527818_nat_o
% 5.06/5.42 @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.06/5.42 = ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] :
% 5.06/5.42 ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ K3 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.triangle_reindex
% 5.06/5.42 thf(fact_8661_choose__row__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( groups3542108847815614940at_nat @ ( binomial @ N2 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_row_sum
% 5.06/5.42 thf(fact_8662_summable__Cauchy__product,axiom,
% 5.06/5.42 ! [A: nat > complex,B: nat > complex] :
% 5.06/5.42 ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.06/5.42 => ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.06/5.42 => ( summable_complex
% 5.06/5.42 @ ^ [K3: nat] :
% 5.06/5.42 ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % summable_Cauchy_product
% 5.06/5.42 thf(fact_8663_summable__Cauchy__product,axiom,
% 5.06/5.42 ! [A: nat > real,B: nat > real] :
% 5.06/5.42 ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.06/5.42 => ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.06/5.42 => ( summable_real
% 5.06/5.42 @ ^ [K3: nat] :
% 5.06/5.42 ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % summable_Cauchy_product
% 5.06/5.42 thf(fact_8664_Cauchy__product,axiom,
% 5.06/5.42 ! [A: nat > complex,B: nat > complex] :
% 5.06/5.42 ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.06/5.42 => ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.06/5.42 => ( ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) )
% 5.06/5.42 = ( suminf_complex
% 5.06/5.42 @ ^ [K3: nat] :
% 5.06/5.42 ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Cauchy_product
% 5.06/5.42 thf(fact_8665_Cauchy__product,axiom,
% 5.06/5.42 ! [A: nat > real,B: nat > real] :
% 5.06/5.42 ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.06/5.42 => ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.06/5.42 => ( ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) )
% 5.06/5.42 = ( suminf_real
% 5.06/5.42 @ ^ [K3: nat] :
% 5.06/5.42 ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Cauchy_product
% 5.06/5.42 thf(fact_8666_binomial,axiom,
% 5.06/5.42 ! [A: nat,B: nat,N2: nat] :
% 5.06/5.42 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % binomial
% 5.06/5.42 thf(fact_8667_sum_Oin__pairs__0,axiom,
% 5.06/5.42 ! [G: nat > rat,N2: nat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.42 = ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.in_pairs_0
% 5.06/5.42 thf(fact_8668_sum_Oin__pairs__0,axiom,
% 5.06/5.42 ! [G: nat > int,N2: nat] :
% 5.06/5.42 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.42 = ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.in_pairs_0
% 5.06/5.42 thf(fact_8669_sum_Oin__pairs__0,axiom,
% 5.06/5.42 ! [G: nat > nat,N2: nat] :
% 5.06/5.42 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.42 = ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.in_pairs_0
% 5.06/5.42 thf(fact_8670_sum_Oin__pairs__0,axiom,
% 5.06/5.42 ! [G: nat > real,N2: nat] :
% 5.06/5.42 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.06/5.42 = ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.in_pairs_0
% 5.06/5.42 thf(fact_8671_polynomial__product,axiom,
% 5.06/5.42 ! [M: nat,A: nat > complex,N2: nat,B: nat > complex,X: complex] :
% 5.06/5.42 ( ! [I3: nat] :
% 5.06/5.42 ( ( ord_less_nat @ M @ I3 )
% 5.06/5.42 => ( ( A @ I3 )
% 5.06/5.42 = zero_zero_complex ) )
% 5.06/5.42 => ( ! [J2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ N2 @ J2 )
% 5.06/5.42 => ( ( B @ J2 )
% 5.06/5.42 = zero_zero_complex ) )
% 5.06/5.42 => ( ( times_times_complex
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [R5: nat] :
% 5.06/5.42 ( times_times_complex
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ R5 ) )
% 5.06/5.42 @ ( power_power_complex @ X @ R5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polynomial_product
% 5.06/5.42 thf(fact_8672_polynomial__product,axiom,
% 5.06/5.42 ! [M: nat,A: nat > rat,N2: nat,B: nat > rat,X: rat] :
% 5.06/5.42 ( ! [I3: nat] :
% 5.06/5.42 ( ( ord_less_nat @ M @ I3 )
% 5.06/5.42 => ( ( A @ I3 )
% 5.06/5.42 = zero_zero_rat ) )
% 5.06/5.42 => ( ! [J2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ N2 @ J2 )
% 5.06/5.42 => ( ( B @ J2 )
% 5.06/5.42 = zero_zero_rat ) )
% 5.06/5.42 => ( ( times_times_rat
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [R5: nat] :
% 5.06/5.42 ( times_times_rat
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ R5 ) )
% 5.06/5.42 @ ( power_power_rat @ X @ R5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polynomial_product
% 5.06/5.42 thf(fact_8673_polynomial__product,axiom,
% 5.06/5.42 ! [M: nat,A: nat > int,N2: nat,B: nat > int,X: int] :
% 5.06/5.42 ( ! [I3: nat] :
% 5.06/5.42 ( ( ord_less_nat @ M @ I3 )
% 5.06/5.42 => ( ( A @ I3 )
% 5.06/5.42 = zero_zero_int ) )
% 5.06/5.42 => ( ! [J2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ N2 @ J2 )
% 5.06/5.42 => ( ( B @ J2 )
% 5.06/5.42 = zero_zero_int ) )
% 5.06/5.42 => ( ( times_times_int
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [R5: nat] :
% 5.06/5.42 ( times_times_int
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ R5 ) )
% 5.06/5.42 @ ( power_power_int @ X @ R5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polynomial_product
% 5.06/5.42 thf(fact_8674_polynomial__product,axiom,
% 5.06/5.42 ! [M: nat,A: nat > real,N2: nat,B: nat > real,X: real] :
% 5.06/5.42 ( ! [I3: nat] :
% 5.06/5.42 ( ( ord_less_nat @ M @ I3 )
% 5.06/5.42 => ( ( A @ I3 )
% 5.06/5.42 = zero_zero_real ) )
% 5.06/5.42 => ( ! [J2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ N2 @ J2 )
% 5.06/5.42 => ( ( B @ J2 )
% 5.06/5.42 = zero_zero_real ) )
% 5.06/5.42 => ( ( times_times_real
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [R5: nat] :
% 5.06/5.42 ( times_times_real
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ R5 ) )
% 5.06/5.42 @ ( power_power_real @ X @ R5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polynomial_product
% 5.06/5.42 thf(fact_8675_polyfun__eq__const,axiom,
% 5.06/5.42 ! [C: nat > complex,N2: nat,K: complex] :
% 5.06/5.42 ( ( ! [X2: complex] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = K ) )
% 5.06/5.42 = ( ( ( C @ zero_zero_nat )
% 5.06/5.42 = K )
% 5.06/5.42 & ! [X2: nat] :
% 5.06/5.42 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 5.06/5.42 => ( ( C @ X2 )
% 5.06/5.42 = zero_zero_complex ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_eq_const
% 5.06/5.42 thf(fact_8676_polyfun__eq__const,axiom,
% 5.06/5.42 ! [C: nat > real,N2: nat,K: real] :
% 5.06/5.42 ( ( ! [X2: real] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = K ) )
% 5.06/5.42 = ( ( ( C @ zero_zero_nat )
% 5.06/5.42 = K )
% 5.06/5.42 & ! [X2: nat] :
% 5.06/5.42 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 5.06/5.42 => ( ( C @ X2 )
% 5.06/5.42 = zero_zero_real ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_eq_const
% 5.06/5.42 thf(fact_8677_binomial__ring,axiom,
% 5.06/5.42 ! [A: complex,B: complex,N2: nat] :
% 5.06/5.42 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % binomial_ring
% 5.06/5.42 thf(fact_8678_binomial__ring,axiom,
% 5.06/5.42 ! [A: rat,B: rat,N2: nat] :
% 5.06/5.42 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % binomial_ring
% 5.06/5.42 thf(fact_8679_binomial__ring,axiom,
% 5.06/5.42 ! [A: int,B: int,N2: nat] :
% 5.06/5.42 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % binomial_ring
% 5.06/5.42 thf(fact_8680_binomial__ring,axiom,
% 5.06/5.42 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.06/5.42 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups7501900531339628137nteger
% 5.06/5.42 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K3 ) ) @ ( power_8256067586552552935nteger @ A @ K3 ) ) @ ( power_8256067586552552935nteger @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % binomial_ring
% 5.06/5.42 thf(fact_8681_binomial__ring,axiom,
% 5.06/5.42 ! [A: nat,B: nat,N2: nat] :
% 5.06/5.42 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % binomial_ring
% 5.06/5.42 thf(fact_8682_binomial__ring,axiom,
% 5.06/5.42 ! [A: real,B: real,N2: nat] :
% 5.06/5.42 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % binomial_ring
% 5.06/5.42 thf(fact_8683_polynomial__product__nat,axiom,
% 5.06/5.42 ! [M: nat,A: nat > nat,N2: nat,B: nat > nat,X: nat] :
% 5.06/5.42 ( ! [I3: nat] :
% 5.06/5.42 ( ( ord_less_nat @ M @ I3 )
% 5.06/5.42 => ( ( A @ I3 )
% 5.06/5.42 = zero_zero_nat ) )
% 5.06/5.42 => ( ! [J2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ N2 @ J2 )
% 5.06/5.42 => ( ( B @ J2 )
% 5.06/5.42 = zero_zero_nat ) )
% 5.06/5.42 => ( ( times_times_nat
% 5.06/5.42 @ ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( power_power_nat @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 @ ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [R5: nat] :
% 5.06/5.42 ( times_times_nat
% 5.06/5.42 @ ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ R5 ) )
% 5.06/5.42 @ ( power_power_nat @ X @ R5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polynomial_product_nat
% 5.06/5.42 thf(fact_8684_choose__square__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N2 @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_square_sum
% 5.06/5.42 thf(fact_8685_Cauchy__product__sums,axiom,
% 5.06/5.42 ! [A: nat > complex,B: nat > complex] :
% 5.06/5.42 ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.06/5.42 => ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.06/5.42 => ( sums_complex
% 5.06/5.42 @ ^ [K3: nat] :
% 5.06/5.42 ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ K3 ) )
% 5.06/5.42 @ ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Cauchy_product_sums
% 5.06/5.42 thf(fact_8686_Cauchy__product__sums,axiom,
% 5.06/5.42 ! [A: nat > real,B: nat > real] :
% 5.06/5.42 ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.06/5.42 => ( ( summable_real
% 5.06/5.42 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.06/5.42 => ( sums_real
% 5.06/5.42 @ ^ [K3: nat] :
% 5.06/5.42 ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ K3 ) )
% 5.06/5.42 @ ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Cauchy_product_sums
% 5.06/5.42 thf(fact_8687_sum_Ozero__middle,axiom,
% 5.06/5.42 ! [P4: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.06/5.42 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.06/5.42 => ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ zero_zero_complex @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ P4 ) )
% 5.06/5.42 = ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.zero_middle
% 5.06/5.42 thf(fact_8688_sum_Ozero__middle,axiom,
% 5.06/5.42 ! [P4: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.06/5.42 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.06/5.42 => ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ P4 ) )
% 5.06/5.42 = ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.zero_middle
% 5.06/5.42 thf(fact_8689_sum_Ozero__middle,axiom,
% 5.06/5.42 ! [P4: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.06/5.42 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.06/5.42 => ( ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ P4 ) )
% 5.06/5.42 = ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.zero_middle
% 5.06/5.42 thf(fact_8690_sum_Ozero__middle,axiom,
% 5.06/5.42 ! [P4: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.06/5.42 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.06/5.42 => ( ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ P4 ) )
% 5.06/5.42 = ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.zero_middle
% 5.06/5.42 thf(fact_8691_sum_Ozero__middle,axiom,
% 5.06/5.42 ! [P4: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 5.06/5.42 => ( ( ord_less_eq_nat @ K @ P4 )
% 5.06/5.42 => ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ zero_zero_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ P4 ) )
% 5.06/5.42 = ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum.zero_middle
% 5.06/5.42 thf(fact_8692_root__polyfun,axiom,
% 5.06/5.42 ! [N2: nat,Z: int,A: int] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( ( power_power_int @ Z @ N2 )
% 5.06/5.42 = A )
% 5.06/5.42 = ( ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( if_int @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I5 = N2 ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_int ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % root_polyfun
% 5.06/5.42 thf(fact_8693_root__polyfun,axiom,
% 5.06/5.42 ! [N2: nat,Z: complex,A: complex] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( ( power_power_complex @ Z @ N2 )
% 5.06/5.42 = A )
% 5.06/5.42 = ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( if_complex @ ( I5 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I5 = N2 ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_complex ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % root_polyfun
% 5.06/5.42 thf(fact_8694_root__polyfun,axiom,
% 5.06/5.42 ! [N2: nat,Z: rat,A: rat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( ( power_power_rat @ Z @ N2 )
% 5.06/5.42 = A )
% 5.06/5.42 = ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( if_rat @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I5 = N2 ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_rat ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % root_polyfun
% 5.06/5.42 thf(fact_8695_root__polyfun,axiom,
% 5.06/5.42 ! [N2: nat,Z: code_integer,A: code_integer] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( ( power_8256067586552552935nteger @ Z @ N2 )
% 5.06/5.42 = A )
% 5.06/5.42 = ( ( groups7501900531339628137nteger
% 5.06/5.42 @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I5 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I5 = N2 ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_z3403309356797280102nteger ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % root_polyfun
% 5.06/5.42 thf(fact_8696_root__polyfun,axiom,
% 5.06/5.42 ! [N2: nat,Z: real,A: real] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( ( power_power_real @ Z @ N2 )
% 5.06/5.42 = A )
% 5.06/5.42 = ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( if_real @ ( I5 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I5 = N2 ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % root_polyfun
% 5.06/5.42 thf(fact_8697_sum__gp0,axiom,
% 5.06/5.42 ! [X: complex,N2: nat] :
% 5.06/5.42 ( ( ( X = one_one_complex )
% 5.06/5.42 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 5.06/5.42 & ( ( X != one_one_complex )
% 5.06/5.42 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum_gp0
% 5.06/5.42 thf(fact_8698_sum__gp0,axiom,
% 5.06/5.42 ! [X: rat,N2: nat] :
% 5.06/5.42 ( ( ( X = one_one_rat )
% 5.06/5.42 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 5.06/5.42 & ( ( X != one_one_rat )
% 5.06/5.42 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum_gp0
% 5.06/5.42 thf(fact_8699_sum__gp0,axiom,
% 5.06/5.42 ! [X: real,N2: nat] :
% 5.06/5.42 ( ( ( X = one_one_real )
% 5.06/5.42 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 5.06/5.42 & ( ( X != one_one_real )
% 5.06/5.42 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sum_gp0
% 5.06/5.42 thf(fact_8700_choose__alternating__linear__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( N2 != one_one_nat )
% 5.06/5.42 => ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I5 ) @ ( semiri8010041392384452111omplex @ I5 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_complex ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_alternating_linear_sum
% 5.06/5.42 thf(fact_8701_choose__alternating__linear__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( N2 != one_one_nat )
% 5.06/5.42 => ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I5 ) @ ( semiri681578069525770553at_rat @ I5 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_rat ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_alternating_linear_sum
% 5.06/5.42 thf(fact_8702_choose__alternating__linear__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( N2 != one_one_nat )
% 5.06/5.42 => ( ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I5 ) @ ( semiri1314217659103216013at_int @ I5 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_int ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_alternating_linear_sum
% 5.06/5.42 thf(fact_8703_choose__alternating__linear__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( N2 != one_one_nat )
% 5.06/5.42 => ( ( groups7501900531339628137nteger
% 5.06/5.42 @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I5 ) @ ( semiri4939895301339042750nteger @ I5 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_alternating_linear_sum
% 5.06/5.42 thf(fact_8704_choose__alternating__linear__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( N2 != one_one_nat )
% 5.06/5.42 => ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( semiri5074537144036343181t_real @ I5 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_alternating_linear_sum
% 5.06/5.42 thf(fact_8705_polyfun__diff__alt,axiom,
% 5.06/5.42 ! [N2: nat,A: nat > complex,X: complex,Y: complex] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( minus_minus_complex
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [J3: nat] :
% 5.06/5.42 ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y @ K3 ) ) @ ( power_power_complex @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_diff_alt
% 5.06/5.42 thf(fact_8706_polyfun__diff__alt,axiom,
% 5.06/5.42 ! [N2: nat,A: nat > rat,X: rat,Y: rat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( minus_minus_rat
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ Y @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [J3: nat] :
% 5.06/5.42 ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y @ K3 ) ) @ ( power_power_rat @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_diff_alt
% 5.06/5.42 thf(fact_8707_polyfun__diff__alt,axiom,
% 5.06/5.42 ! [N2: nat,A: nat > int,X: int,Y: int] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( minus_minus_int
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [J3: nat] :
% 5.06/5.42 ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y @ K3 ) ) @ ( power_power_int @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_diff_alt
% 5.06/5.42 thf(fact_8708_polyfun__diff__alt,axiom,
% 5.06/5.42 ! [N2: nat,A: nat > real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( minus_minus_real
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [J3: nat] :
% 5.06/5.42 ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J3 @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y @ K3 ) ) @ ( power_power_real @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_diff_alt
% 5.06/5.42 thf(fact_8709_monoseq__minus,axiom,
% 5.06/5.42 ! [A: nat > int] :
% 5.06/5.42 ( ( topolo4899668324122417113eq_int @ A )
% 5.06/5.42 => ( topolo4899668324122417113eq_int
% 5.06/5.42 @ ^ [N: nat] : ( uminus_uminus_int @ ( A @ N ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % monoseq_minus
% 5.06/5.42 thf(fact_8710_monoseq__minus,axiom,
% 5.06/5.42 ! [A: nat > rat] :
% 5.06/5.42 ( ( topolo4267028734544971653eq_rat @ A )
% 5.06/5.42 => ( topolo4267028734544971653eq_rat
% 5.06/5.42 @ ^ [N: nat] : ( uminus_uminus_rat @ ( A @ N ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % monoseq_minus
% 5.06/5.42 thf(fact_8711_monoseq__minus,axiom,
% 5.06/5.42 ! [A: nat > code_integer] :
% 5.06/5.42 ( ( topolo2919662092509805066nteger @ A )
% 5.06/5.42 => ( topolo2919662092509805066nteger
% 5.06/5.42 @ ^ [N: nat] : ( uminus1351360451143612070nteger @ ( A @ N ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % monoseq_minus
% 5.06/5.42 thf(fact_8712_monoseq__minus,axiom,
% 5.06/5.42 ! [A: nat > real] :
% 5.06/5.42 ( ( topolo6980174941875973593q_real @ A )
% 5.06/5.42 => ( topolo6980174941875973593q_real
% 5.06/5.42 @ ^ [N: nat] : ( uminus_uminus_real @ ( A @ N ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % monoseq_minus
% 5.06/5.42 thf(fact_8713_binomial__r__part__sum,axiom,
% 5.06/5.42 ! [M: nat] :
% 5.06/5.42 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % binomial_r_part_sum
% 5.06/5.42 thf(fact_8714_choose__linear__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( groups3542108847815614940at_nat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_nat @ I5 @ ( binomial @ N2 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_linear_sum
% 5.06/5.42 thf(fact_8715_choose__alternating__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I5 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_complex ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_alternating_sum
% 5.06/5.42 thf(fact_8716_choose__alternating__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I5 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_rat ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_alternating_sum
% 5.06/5.42 thf(fact_8717_choose__alternating__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I5 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_int ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_alternating_sum
% 5.06/5.42 thf(fact_8718_choose__alternating__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( groups7501900531339628137nteger
% 5.06/5.42 @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I5 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_alternating_sum
% 5.06/5.42 thf(fact_8719_choose__alternating__sum,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = zero_zero_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % choose_alternating_sum
% 5.06/5.42 thf(fact_8720_polyfun__extremal__lemma,axiom,
% 5.06/5.42 ! [E: real,C: nat > complex,N2: nat] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ E )
% 5.06/5.42 => ? [M8: real] :
% 5.06/5.42 ! [Z5: complex] :
% 5.06/5.42 ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z5 ) )
% 5.06/5.42 => ( ord_less_eq_real
% 5.06/5.42 @ ( real_V1022390504157884413omplex
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 @ ( times_times_real @ E @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_extremal_lemma
% 5.06/5.42 thf(fact_8721_polyfun__extremal__lemma,axiom,
% 5.06/5.42 ! [E: real,C: nat > real,N2: nat] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ E )
% 5.06/5.42 => ? [M8: real] :
% 5.06/5.42 ! [Z5: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z5 ) )
% 5.06/5.42 => ( ord_less_eq_real
% 5.06/5.42 @ ( real_V7735802525324610683m_real
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z5 @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 @ ( times_times_real @ E @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z5 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_extremal_lemma
% 5.06/5.42 thf(fact_8722_polyfun__diff,axiom,
% 5.06/5.42 ! [N2: nat,A: nat > complex,X: complex,Y: complex] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( minus_minus_complex
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [J3: nat] :
% 5.06/5.42 ( times_times_complex
% 5.06/5.42 @ ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.06/5.42 @ ( power_power_complex @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_diff
% 5.06/5.42 thf(fact_8723_polyfun__diff,axiom,
% 5.06/5.42 ! [N2: nat,A: nat > rat,X: rat,Y: rat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( minus_minus_rat
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ Y @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [J3: nat] :
% 5.06/5.42 ( times_times_rat
% 5.06/5.42 @ ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.06/5.42 @ ( power_power_rat @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_diff
% 5.06/5.42 thf(fact_8724_polyfun__diff,axiom,
% 5.06/5.42 ! [N2: nat,A: nat > int,X: int,Y: int] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( minus_minus_int
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [J3: nat] :
% 5.06/5.42 ( times_times_int
% 5.06/5.42 @ ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.06/5.42 @ ( power_power_int @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_diff
% 5.06/5.42 thf(fact_8725_polyfun__diff,axiom,
% 5.06/5.42 ! [N2: nat,A: nat > real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.06/5.42 => ( ( minus_minus_real
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ I5 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.06/5.42 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [J3: nat] :
% 5.06/5.42 ( times_times_real
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I5 @ J3 ) @ one_one_nat ) ) )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.06/5.42 @ ( power_power_real @ X @ J3 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % polyfun_diff
% 5.06/5.42 thf(fact_8726_monoseq__Suc,axiom,
% 5.06/5.42 ( topolo6980174941875973593q_real
% 5.06/5.42 = ( ^ [X4: nat > real] :
% 5.06/5.42 ( ! [N: nat] : ( ord_less_eq_real @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.06/5.42 | ! [N: nat] : ( ord_less_eq_real @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % monoseq_Suc
% 5.06/5.42 thf(fact_8727_monoseq__Suc,axiom,
% 5.06/5.42 ( topolo3100542954746470799et_int
% 5.06/5.42 = ( ^ [X4: nat > set_int] :
% 5.06/5.42 ( ! [N: nat] : ( ord_less_eq_set_int @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.06/5.42 | ! [N: nat] : ( ord_less_eq_set_int @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % monoseq_Suc
% 5.06/5.42 thf(fact_8728_monoseq__Suc,axiom,
% 5.06/5.42 ( topolo4267028734544971653eq_rat
% 5.06/5.42 = ( ^ [X4: nat > rat] :
% 5.06/5.42 ( ! [N: nat] : ( ord_less_eq_rat @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.06/5.42 | ! [N: nat] : ( ord_less_eq_rat @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % monoseq_Suc
% 5.06/5.42 thf(fact_8729_monoseq__Suc,axiom,
% 5.06/5.42 ( topolo1459490580787246023eq_num
% 5.06/5.42 = ( ^ [X4: nat > num] :
% 5.06/5.42 ( ! [N: nat] : ( ord_less_eq_num @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.06/5.42 | ! [N: nat] : ( ord_less_eq_num @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % monoseq_Suc
% 5.06/5.42 thf(fact_8730_monoseq__Suc,axiom,
% 5.06/5.42 ( topolo4902158794631467389eq_nat
% 5.06/5.42 = ( ^ [X4: nat > nat] :
% 5.06/5.42 ( ! [N: nat] : ( ord_less_eq_nat @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.06/5.42 | ! [N: nat] : ( ord_less_eq_nat @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % monoseq_Suc
% 5.06/5.42 thf(fact_8731_monoseq__Suc,axiom,
% 5.06/5.42 ( topolo4899668324122417113eq_int
% 5.06/5.42 = ( ^ [X4: nat > int] :
% 5.06/5.42 ( ! [N: nat] : ( ord_less_eq_int @ ( X4 @ N ) @ ( X4 @ ( suc @ N ) ) )
% 5.06/5.42 | ! [N: nat] : ( ord_less_eq_int @ ( X4 @ ( suc @ N ) ) @ ( X4 @ N ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % monoseq_Suc
% 5.06/5.42 thf(fact_8732_mono__SucI2,axiom,
% 5.06/5.42 ! [X8: nat > real] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.06/5.42 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI2
% 5.06/5.42 thf(fact_8733_mono__SucI2,axiom,
% 5.06/5.42 ! [X8: nat > set_int] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.06/5.42 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI2
% 5.06/5.42 thf(fact_8734_mono__SucI2,axiom,
% 5.06/5.42 ! [X8: nat > rat] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.06/5.42 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI2
% 5.06/5.42 thf(fact_8735_mono__SucI2,axiom,
% 5.06/5.42 ! [X8: nat > num] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.06/5.42 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI2
% 5.06/5.42 thf(fact_8736_mono__SucI2,axiom,
% 5.06/5.42 ! [X8: nat > nat] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.06/5.42 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI2
% 5.06/5.42 thf(fact_8737_mono__SucI2,axiom,
% 5.06/5.42 ! [X8: nat > int] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.06/5.42 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI2
% 5.06/5.42 thf(fact_8738_mono__SucI1,axiom,
% 5.06/5.42 ! [X8: nat > real] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.06/5.42 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI1
% 5.06/5.42 thf(fact_8739_mono__SucI1,axiom,
% 5.06/5.42 ! [X8: nat > set_int] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.06/5.42 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI1
% 5.06/5.42 thf(fact_8740_mono__SucI1,axiom,
% 5.06/5.42 ! [X8: nat > rat] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.06/5.42 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI1
% 5.06/5.42 thf(fact_8741_mono__SucI1,axiom,
% 5.06/5.42 ! [X8: nat > num] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.06/5.42 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI1
% 5.06/5.42 thf(fact_8742_mono__SucI1,axiom,
% 5.06/5.42 ! [X8: nat > nat] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.06/5.42 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI1
% 5.06/5.42 thf(fact_8743_mono__SucI1,axiom,
% 5.06/5.42 ! [X8: nat > int] :
% 5.06/5.42 ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.06/5.42 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.06/5.42
% 5.06/5.42 % mono_SucI1
% 5.06/5.42 thf(fact_8744_gbinomial__partial__row__sum,axiom,
% 5.06/5.42 ! [A: complex,M: nat] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( 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 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_partial_row_sum
% 5.06/5.42 thf(fact_8745_gbinomial__partial__row__sum,axiom,
% 5.06/5.42 ! [A: rat,M: nat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( 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 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_partial_row_sum
% 5.06/5.42 thf(fact_8746_gbinomial__partial__row__sum,axiom,
% 5.06/5.42 ! [A: real,M: nat] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( 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 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_partial_row_sum
% 5.06/5.42 thf(fact_8747_gbinomial__r__part__sum,axiom,
% 5.06/5.42 ! [M: nat] :
% 5.06/5.42 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_r_part_sum
% 5.06/5.42 thf(fact_8748_gbinomial__r__part__sum,axiom,
% 5.06/5.42 ! [M: nat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_r_part_sum
% 5.06/5.42 thf(fact_8749_gbinomial__r__part__sum,axiom,
% 5.06/5.42 ! [M: nat] :
% 5.06/5.42 ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_r_part_sum
% 5.06/5.42 thf(fact_8750_pochhammer__double,axiom,
% 5.06/5.42 ! [Z: complex,N2: nat] :
% 5.06/5.42 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_double
% 5.06/5.42 thf(fact_8751_pochhammer__double,axiom,
% 5.06/5.42 ! [Z: rat,N2: nat] :
% 5.06/5.42 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_double
% 5.06/5.42 thf(fact_8752_pochhammer__double,axiom,
% 5.06/5.42 ! [Z: real,N2: nat] :
% 5.06/5.42 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_double
% 5.06/5.42 thf(fact_8753_of__nat__code,axiom,
% 5.06/5.42 ( semiri8010041392384452111omplex
% 5.06/5.42 = ( ^ [N: nat] :
% 5.06/5.42 ( semiri2816024913162550771omplex
% 5.06/5.42 @ ^ [I5: complex] : ( plus_plus_complex @ I5 @ one_one_complex )
% 5.06/5.42 @ N
% 5.06/5.42 @ zero_zero_complex ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % of_nat_code
% 5.06/5.42 thf(fact_8754_of__nat__code,axiom,
% 5.06/5.42 ( semiri681578069525770553at_rat
% 5.06/5.42 = ( ^ [N: nat] :
% 5.06/5.42 ( semiri7787848453975740701ux_rat
% 5.06/5.42 @ ^ [I5: rat] : ( plus_plus_rat @ I5 @ one_one_rat )
% 5.06/5.42 @ N
% 5.06/5.42 @ zero_zero_rat ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % of_nat_code
% 5.06/5.42 thf(fact_8755_of__nat__code,axiom,
% 5.06/5.42 ( semiri1314217659103216013at_int
% 5.06/5.42 = ( ^ [N: nat] :
% 5.06/5.42 ( semiri8420488043553186161ux_int
% 5.06/5.42 @ ^ [I5: int] : ( plus_plus_int @ I5 @ one_one_int )
% 5.06/5.42 @ N
% 5.06/5.42 @ zero_zero_int ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % of_nat_code
% 5.06/5.42 thf(fact_8756_of__nat__code,axiom,
% 5.06/5.42 ( semiri5074537144036343181t_real
% 5.06/5.42 = ( ^ [N: nat] :
% 5.06/5.42 ( semiri7260567687927622513x_real
% 5.06/5.42 @ ^ [I5: real] : ( plus_plus_real @ I5 @ one_one_real )
% 5.06/5.42 @ N
% 5.06/5.42 @ zero_zero_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % of_nat_code
% 5.06/5.42 thf(fact_8757_of__nat__code,axiom,
% 5.06/5.42 ( semiri1316708129612266289at_nat
% 5.06/5.42 = ( ^ [N: nat] :
% 5.06/5.42 ( semiri8422978514062236437ux_nat
% 5.06/5.42 @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ one_one_nat )
% 5.06/5.42 @ N
% 5.06/5.42 @ zero_zero_nat ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % of_nat_code
% 5.06/5.42 thf(fact_8758_of__nat__code,axiom,
% 5.06/5.42 ( semiri4939895301339042750nteger
% 5.06/5.42 = ( ^ [N: nat] :
% 5.06/5.42 ( semiri4055485073559036834nteger
% 5.06/5.42 @ ^ [I5: code_integer] : ( plus_p5714425477246183910nteger @ I5 @ one_one_Code_integer )
% 5.06/5.42 @ N
% 5.06/5.42 @ zero_z3403309356797280102nteger ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % of_nat_code
% 5.06/5.42 thf(fact_8759_gchoose__row__sum__weighted,axiom,
% 5.06/5.42 ! [R2: complex,M: nat] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R2 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.06/5.42 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R2 @ ( suc @ M ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gchoose_row_sum_weighted
% 5.06/5.42 thf(fact_8760_gchoose__row__sum__weighted,axiom,
% 5.06/5.42 ! [R2: rat,M: nat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R2 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.06/5.42 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R2 @ ( suc @ M ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gchoose_row_sum_weighted
% 5.06/5.42 thf(fact_8761_gchoose__row__sum__weighted,axiom,
% 5.06/5.42 ! [R2: real,M: nat] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R2 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.06/5.42 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R2 @ ( suc @ M ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gchoose_row_sum_weighted
% 5.06/5.42 thf(fact_8762_of__nat__id,axiom,
% 5.06/5.42 ( semiri1316708129612266289at_nat
% 5.06/5.42 = ( ^ [N: nat] : N ) ) ).
% 5.06/5.42
% 5.06/5.42 % of_nat_id
% 5.06/5.42 thf(fact_8763_gbinomial__0_I2_J,axiom,
% 5.06/5.42 ! [K: nat] :
% 5.06/5.42 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.06/5.42 = zero_zero_complex ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_0(2)
% 5.06/5.42 thf(fact_8764_gbinomial__0_I2_J,axiom,
% 5.06/5.42 ! [K: nat] :
% 5.06/5.42 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.06/5.42 = zero_zero_real ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_0(2)
% 5.06/5.42 thf(fact_8765_gbinomial__0_I2_J,axiom,
% 5.06/5.42 ! [K: nat] :
% 5.06/5.42 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.06/5.42 = zero_zero_rat ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_0(2)
% 5.06/5.42 thf(fact_8766_gbinomial__0_I2_J,axiom,
% 5.06/5.42 ! [K: nat] :
% 5.06/5.42 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.06/5.42 = zero_zero_nat ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_0(2)
% 5.06/5.42 thf(fact_8767_gbinomial__0_I2_J,axiom,
% 5.06/5.42 ! [K: nat] :
% 5.06/5.42 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.06/5.42 = zero_zero_int ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_0(2)
% 5.06/5.42 thf(fact_8768_gbinomial__0_I1_J,axiom,
% 5.06/5.42 ! [A: complex] :
% 5.06/5.42 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.06/5.42 = one_one_complex ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_0(1)
% 5.06/5.42 thf(fact_8769_gbinomial__0_I1_J,axiom,
% 5.06/5.42 ! [A: real] :
% 5.06/5.42 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.06/5.42 = one_one_real ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_0(1)
% 5.06/5.42 thf(fact_8770_gbinomial__0_I1_J,axiom,
% 5.06/5.42 ! [A: rat] :
% 5.06/5.42 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.06/5.42 = one_one_rat ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_0(1)
% 5.06/5.42 thf(fact_8771_gbinomial__0_I1_J,axiom,
% 5.06/5.42 ! [A: nat] :
% 5.06/5.42 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.06/5.42 = one_one_nat ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_0(1)
% 5.06/5.42 thf(fact_8772_gbinomial__0_I1_J,axiom,
% 5.06/5.42 ! [A: int] :
% 5.06/5.42 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.06/5.42 = one_one_int ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_0(1)
% 5.06/5.42 thf(fact_8773_pochhammer__0,axiom,
% 5.06/5.42 ! [A: complex] :
% 5.06/5.42 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.06/5.42 = one_one_complex ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_0
% 5.06/5.42 thf(fact_8774_pochhammer__0,axiom,
% 5.06/5.42 ! [A: real] :
% 5.06/5.42 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.06/5.42 = one_one_real ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_0
% 5.06/5.42 thf(fact_8775_pochhammer__0,axiom,
% 5.06/5.42 ! [A: rat] :
% 5.06/5.42 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.06/5.42 = one_one_rat ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_0
% 5.06/5.42 thf(fact_8776_pochhammer__0,axiom,
% 5.06/5.42 ! [A: nat] :
% 5.06/5.42 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.06/5.42 = one_one_nat ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_0
% 5.06/5.42 thf(fact_8777_pochhammer__0,axiom,
% 5.06/5.42 ! [A: int] :
% 5.06/5.42 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.06/5.42 = one_one_int ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_0
% 5.06/5.42 thf(fact_8778_pochhammer__pos,axiom,
% 5.06/5.42 ! [X: real,N2: nat] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_pos
% 5.06/5.42 thf(fact_8779_pochhammer__pos,axiom,
% 5.06/5.42 ! [X: rat,N2: nat] :
% 5.06/5.42 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.06/5.42 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_pos
% 5.06/5.42 thf(fact_8780_pochhammer__pos,axiom,
% 5.06/5.42 ! [X: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.06/5.42 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_pos
% 5.06/5.42 thf(fact_8781_pochhammer__pos,axiom,
% 5.06/5.42 ! [X: int,N2: nat] :
% 5.06/5.42 ( ( ord_less_int @ zero_zero_int @ X )
% 5.06/5.42 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_pos
% 5.06/5.42 thf(fact_8782_pochhammer__neq__0__mono,axiom,
% 5.06/5.42 ! [A: complex,M: nat,N2: nat] :
% 5.06/5.42 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.06/5.42 != zero_zero_complex )
% 5.06/5.42 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.42 => ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.06/5.42 != zero_zero_complex ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_neq_0_mono
% 5.06/5.42 thf(fact_8783_pochhammer__neq__0__mono,axiom,
% 5.06/5.42 ! [A: real,M: nat,N2: nat] :
% 5.06/5.42 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.06/5.42 != zero_zero_real )
% 5.06/5.42 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.42 => ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.06/5.42 != zero_zero_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_neq_0_mono
% 5.06/5.42 thf(fact_8784_pochhammer__neq__0__mono,axiom,
% 5.06/5.42 ! [A: rat,M: nat,N2: nat] :
% 5.06/5.42 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.06/5.42 != zero_zero_rat )
% 5.06/5.42 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.42 => ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.06/5.42 != zero_zero_rat ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_neq_0_mono
% 5.06/5.42 thf(fact_8785_pochhammer__eq__0__mono,axiom,
% 5.06/5.42 ! [A: complex,N2: nat,M: nat] :
% 5.06/5.42 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.06/5.42 = zero_zero_complex )
% 5.06/5.42 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.42 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.06/5.42 = zero_zero_complex ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_eq_0_mono
% 5.06/5.42 thf(fact_8786_pochhammer__eq__0__mono,axiom,
% 5.06/5.42 ! [A: real,N2: nat,M: nat] :
% 5.06/5.42 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.06/5.42 = zero_zero_real )
% 5.06/5.42 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.42 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.06/5.42 = zero_zero_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_eq_0_mono
% 5.06/5.42 thf(fact_8787_pochhammer__eq__0__mono,axiom,
% 5.06/5.42 ! [A: rat,N2: nat,M: nat] :
% 5.06/5.42 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.06/5.42 = zero_zero_rat )
% 5.06/5.42 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.42 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.06/5.42 = zero_zero_rat ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_eq_0_mono
% 5.06/5.42 thf(fact_8788_pochhammer__fact,axiom,
% 5.06/5.42 ( semiri5044797733671781792omplex
% 5.06/5.42 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_fact
% 5.06/5.42 thf(fact_8789_pochhammer__fact,axiom,
% 5.06/5.42 ( semiri773545260158071498ct_rat
% 5.06/5.42 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_fact
% 5.06/5.42 thf(fact_8790_pochhammer__fact,axiom,
% 5.06/5.42 ( semiri1406184849735516958ct_int
% 5.06/5.42 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_fact
% 5.06/5.42 thf(fact_8791_pochhammer__fact,axiom,
% 5.06/5.42 ( semiri2265585572941072030t_real
% 5.06/5.42 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_fact
% 5.06/5.42 thf(fact_8792_pochhammer__fact,axiom,
% 5.06/5.42 ( semiri1408675320244567234ct_nat
% 5.06/5.42 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_fact
% 5.06/5.42 thf(fact_8793_gbinomial__pochhammer,axiom,
% 5.06/5.42 ( gbinomial_complex
% 5.06/5.42 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A4 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_pochhammer
% 5.06/5.42 thf(fact_8794_gbinomial__pochhammer,axiom,
% 5.06/5.42 ( gbinomial_rat
% 5.06/5.42 = ( ^ [A4: rat,K3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A4 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_pochhammer
% 5.06/5.42 thf(fact_8795_gbinomial__pochhammer,axiom,
% 5.06/5.42 ( gbinomial_real
% 5.06/5.42 = ( ^ [A4: real,K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A4 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_pochhammer
% 5.06/5.42 thf(fact_8796_gbinomial__pochhammer_H,axiom,
% 5.06/5.42 ( gbinomial_complex
% 5.06/5.42 = ( ^ [A4: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_pochhammer'
% 5.06/5.42 thf(fact_8797_gbinomial__pochhammer_H,axiom,
% 5.06/5.42 ( gbinomial_rat
% 5.06/5.42 = ( ^ [A4: rat,K3: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_pochhammer'
% 5.06/5.42 thf(fact_8798_gbinomial__pochhammer_H,axiom,
% 5.06/5.42 ( gbinomial_real
% 5.06/5.42 = ( ^ [A4: real,K3: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ K3 ) ) @ one_one_real ) @ K3 ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_pochhammer'
% 5.06/5.42 thf(fact_8799_gbinomial__Suc__Suc,axiom,
% 5.06/5.42 ! [A: complex,K: nat] :
% 5.06/5.42 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.06/5.42 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_Suc_Suc
% 5.06/5.42 thf(fact_8800_gbinomial__Suc__Suc,axiom,
% 5.06/5.42 ! [A: real,K: nat] :
% 5.06/5.42 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.06/5.42 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_Suc_Suc
% 5.06/5.42 thf(fact_8801_gbinomial__Suc__Suc,axiom,
% 5.06/5.42 ! [A: rat,K: nat] :
% 5.06/5.42 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.06/5.42 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_Suc_Suc
% 5.06/5.42 thf(fact_8802_gbinomial__of__nat__symmetric,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.42 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ K )
% 5.06/5.42 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_of_nat_symmetric
% 5.06/5.42 thf(fact_8803_pochhammer__nonneg,axiom,
% 5.06/5.42 ! [X: real,N2: nat] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_nonneg
% 5.06/5.42 thf(fact_8804_pochhammer__nonneg,axiom,
% 5.06/5.42 ! [X: rat,N2: nat] :
% 5.06/5.42 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.06/5.42 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_nonneg
% 5.06/5.42 thf(fact_8805_pochhammer__nonneg,axiom,
% 5.06/5.42 ! [X: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.06/5.42 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_nonneg
% 5.06/5.42 thf(fact_8806_pochhammer__nonneg,axiom,
% 5.06/5.42 ! [X: int,N2: nat] :
% 5.06/5.42 ( ( ord_less_int @ zero_zero_int @ X )
% 5.06/5.42 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_nonneg
% 5.06/5.42 thf(fact_8807_pochhammer__0__left,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ( N2 = zero_zero_nat )
% 5.06/5.42 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 5.06/5.42 = one_one_complex ) )
% 5.06/5.42 & ( ( N2 != zero_zero_nat )
% 5.06/5.42 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 5.06/5.42 = zero_zero_complex ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_0_left
% 5.06/5.42 thf(fact_8808_pochhammer__0__left,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ( N2 = zero_zero_nat )
% 5.06/5.42 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 5.06/5.42 = one_one_real ) )
% 5.06/5.42 & ( ( N2 != zero_zero_nat )
% 5.06/5.42 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 5.06/5.42 = zero_zero_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_0_left
% 5.06/5.42 thf(fact_8809_pochhammer__0__left,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ( N2 = zero_zero_nat )
% 5.06/5.42 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 5.06/5.42 = one_one_rat ) )
% 5.06/5.42 & ( ( N2 != zero_zero_nat )
% 5.06/5.42 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 5.06/5.42 = zero_zero_rat ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_0_left
% 5.06/5.42 thf(fact_8810_pochhammer__0__left,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ( N2 = zero_zero_nat )
% 5.06/5.42 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 = one_one_nat ) )
% 5.06/5.42 & ( ( N2 != zero_zero_nat )
% 5.06/5.42 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 = zero_zero_nat ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_0_left
% 5.06/5.42 thf(fact_8811_pochhammer__0__left,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ( N2 = zero_zero_nat )
% 5.06/5.42 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 5.06/5.42 = one_one_int ) )
% 5.06/5.42 & ( ( N2 != zero_zero_nat )
% 5.06/5.42 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 5.06/5.42 = zero_zero_int ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_0_left
% 5.06/5.42 thf(fact_8812_gbinomial__addition__formula,axiom,
% 5.06/5.42 ! [A: complex,K: nat] :
% 5.06/5.42 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.06/5.42 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_addition_formula
% 5.06/5.42 thf(fact_8813_gbinomial__addition__formula,axiom,
% 5.06/5.42 ! [A: real,K: nat] :
% 5.06/5.42 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.06/5.42 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_addition_formula
% 5.06/5.42 thf(fact_8814_gbinomial__addition__formula,axiom,
% 5.06/5.42 ! [A: rat,K: nat] :
% 5.06/5.42 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.06/5.42 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_addition_formula
% 5.06/5.42 thf(fact_8815_gbinomial__absorb__comp,axiom,
% 5.06/5.42 ! [A: complex,K: nat] :
% 5.06/5.42 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.06/5.42 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_absorb_comp
% 5.06/5.42 thf(fact_8816_gbinomial__absorb__comp,axiom,
% 5.06/5.42 ! [A: rat,K: nat] :
% 5.06/5.42 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.06/5.42 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_absorb_comp
% 5.06/5.42 thf(fact_8817_gbinomial__absorb__comp,axiom,
% 5.06/5.42 ! [A: real,K: nat] :
% 5.06/5.42 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.06/5.42 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_absorb_comp
% 5.06/5.42 thf(fact_8818_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.06/5.42 ! [K: nat,A: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.06/5.42 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_ge_n_over_k_pow_k
% 5.06/5.42 thf(fact_8819_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.06/5.42 ! [K: nat,A: rat] :
% 5.06/5.42 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.06/5.42 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_ge_n_over_k_pow_k
% 5.06/5.42 thf(fact_8820_gbinomial__mult__1,axiom,
% 5.06/5.42 ! [A: rat,K: nat] :
% 5.06/5.42 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.06/5.42 = ( 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 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_mult_1
% 5.06/5.42 thf(fact_8821_gbinomial__mult__1,axiom,
% 5.06/5.42 ! [A: real,K: nat] :
% 5.06/5.42 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.06/5.42 = ( 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 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_mult_1
% 5.06/5.42 thf(fact_8822_gbinomial__mult__1_H,axiom,
% 5.06/5.42 ! [A: rat,K: nat] :
% 5.06/5.42 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.06/5.42 = ( 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 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_mult_1'
% 5.06/5.42 thf(fact_8823_gbinomial__mult__1_H,axiom,
% 5.06/5.42 ! [A: real,K: nat] :
% 5.06/5.42 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.06/5.42 = ( 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 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_mult_1'
% 5.06/5.42 thf(fact_8824_pochhammer__rec,axiom,
% 5.06/5.42 ! [A: complex,N2: nat] :
% 5.06/5.42 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_rec
% 5.06/5.42 thf(fact_8825_pochhammer__rec,axiom,
% 5.06/5.42 ! [A: real,N2: nat] :
% 5.06/5.42 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_rec
% 5.06/5.42 thf(fact_8826_pochhammer__rec,axiom,
% 5.06/5.42 ! [A: rat,N2: nat] :
% 5.06/5.42 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_rec
% 5.06/5.42 thf(fact_8827_pochhammer__rec,axiom,
% 5.06/5.42 ! [A: nat,N2: nat] :
% 5.06/5.42 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_rec
% 5.06/5.42 thf(fact_8828_pochhammer__rec,axiom,
% 5.06/5.42 ! [A: int,N2: nat] :
% 5.06/5.42 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_rec
% 5.06/5.42 thf(fact_8829_pochhammer__Suc,axiom,
% 5.06/5.42 ! [A: rat,N2: nat] :
% 5.06/5.42 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_Suc
% 5.06/5.42 thf(fact_8830_pochhammer__Suc,axiom,
% 5.06/5.42 ! [A: int,N2: nat] :
% 5.06/5.42 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_Suc
% 5.06/5.42 thf(fact_8831_pochhammer__Suc,axiom,
% 5.06/5.42 ! [A: real,N2: nat] :
% 5.06/5.42 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N2 ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_Suc
% 5.06/5.42 thf(fact_8832_pochhammer__Suc,axiom,
% 5.06/5.42 ! [A: nat,N2: nat] :
% 5.06/5.42 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_Suc
% 5.06/5.42 thf(fact_8833_pochhammer__Suc,axiom,
% 5.06/5.42 ! [A: code_integer,N2: nat] :
% 5.06/5.42 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N2 ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_Suc
% 5.06/5.42 thf(fact_8834_pochhammer__rec_H,axiom,
% 5.06/5.42 ! [Z: rat,N2: nat] :
% 5.06/5.42 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_rec'
% 5.06/5.42 thf(fact_8835_pochhammer__rec_H,axiom,
% 5.06/5.42 ! [Z: int,N2: nat] :
% 5.06/5.42 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_rec'
% 5.06/5.42 thf(fact_8836_pochhammer__rec_H,axiom,
% 5.06/5.42 ! [Z: real,N2: nat] :
% 5.06/5.42 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_rec'
% 5.06/5.42 thf(fact_8837_pochhammer__rec_H,axiom,
% 5.06/5.42 ! [Z: nat,N2: nat] :
% 5.06/5.42 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_rec'
% 5.06/5.42 thf(fact_8838_pochhammer__rec_H,axiom,
% 5.06/5.42 ! [Z: code_integer,N2: nat] :
% 5.06/5.42 ( ( comm_s8582702949713902594nteger @ Z @ ( suc @ N2 ) )
% 5.06/5.42 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N2 ) ) @ ( comm_s8582702949713902594nteger @ Z @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_rec'
% 5.06/5.42 thf(fact_8839_pochhammer__eq__0__iff,axiom,
% 5.06/5.42 ! [A: complex,N2: nat] :
% 5.06/5.42 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.06/5.42 = zero_zero_complex )
% 5.06/5.42 = ( ? [K3: nat] :
% 5.06/5.42 ( ( ord_less_nat @ K3 @ N2 )
% 5.06/5.42 & ( A
% 5.06/5.42 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_eq_0_iff
% 5.06/5.42 thf(fact_8840_pochhammer__eq__0__iff,axiom,
% 5.06/5.42 ! [A: rat,N2: nat] :
% 5.06/5.42 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.06/5.42 = zero_zero_rat )
% 5.06/5.42 = ( ? [K3: nat] :
% 5.06/5.42 ( ( ord_less_nat @ K3 @ N2 )
% 5.06/5.42 & ( A
% 5.06/5.42 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_eq_0_iff
% 5.06/5.42 thf(fact_8841_pochhammer__eq__0__iff,axiom,
% 5.06/5.42 ! [A: real,N2: nat] :
% 5.06/5.42 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.06/5.42 = zero_zero_real )
% 5.06/5.42 = ( ? [K3: nat] :
% 5.06/5.42 ( ( ord_less_nat @ K3 @ N2 )
% 5.06/5.42 & ( A
% 5.06/5.42 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_eq_0_iff
% 5.06/5.42 thf(fact_8842_pochhammer__of__nat__eq__0__iff,axiom,
% 5.06/5.42 ! [N2: nat,K: nat] :
% 5.06/5.42 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.06/5.42 = zero_zero_complex )
% 5.06/5.42 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_iff
% 5.06/5.42 thf(fact_8843_pochhammer__of__nat__eq__0__iff,axiom,
% 5.06/5.42 ! [N2: nat,K: nat] :
% 5.06/5.42 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.06/5.42 = zero_zero_rat )
% 5.06/5.42 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_iff
% 5.06/5.42 thf(fact_8844_pochhammer__of__nat__eq__0__iff,axiom,
% 5.06/5.42 ! [N2: nat,K: nat] :
% 5.06/5.42 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.06/5.42 = zero_zero_int )
% 5.06/5.42 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_iff
% 5.06/5.42 thf(fact_8845_pochhammer__of__nat__eq__0__iff,axiom,
% 5.06/5.42 ! [N2: nat,K: nat] :
% 5.06/5.42 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.06/5.42 = zero_zero_real )
% 5.06/5.42 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_iff
% 5.06/5.42 thf(fact_8846_pochhammer__of__nat__eq__0__iff,axiom,
% 5.06/5.42 ! [N2: nat,K: nat] :
% 5.06/5.42 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.06/5.42 = zero_z3403309356797280102nteger )
% 5.06/5.42 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_iff
% 5.06/5.42 thf(fact_8847_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.06/5.42 ! [N2: nat,K: nat] :
% 5.06/5.42 ( ( ord_less_nat @ N2 @ K )
% 5.06/5.42 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.06/5.42 = zero_zero_complex ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_lemma
% 5.06/5.42 thf(fact_8848_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.06/5.42 ! [N2: nat,K: nat] :
% 5.06/5.42 ( ( ord_less_nat @ N2 @ K )
% 5.06/5.42 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.06/5.42 = zero_zero_rat ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_lemma
% 5.06/5.42 thf(fact_8849_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.06/5.42 ! [N2: nat,K: nat] :
% 5.06/5.42 ( ( ord_less_nat @ N2 @ K )
% 5.06/5.42 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.06/5.42 = zero_zero_int ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_lemma
% 5.06/5.42 thf(fact_8850_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.06/5.42 ! [N2: nat,K: nat] :
% 5.06/5.42 ( ( ord_less_nat @ N2 @ K )
% 5.06/5.42 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.06/5.42 = zero_zero_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_lemma
% 5.06/5.42 thf(fact_8851_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.06/5.42 ! [N2: nat,K: nat] :
% 5.06/5.42 ( ( ord_less_nat @ N2 @ K )
% 5.06/5.42 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.06/5.42 = zero_z3403309356797280102nteger ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_lemma
% 5.06/5.42 thf(fact_8852_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.42 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.06/5.42 != zero_zero_complex ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_lemma'
% 5.06/5.42 thf(fact_8853_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.42 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.06/5.42 != zero_zero_rat ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_lemma'
% 5.06/5.42 thf(fact_8854_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.42 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.06/5.42 != zero_zero_int ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_lemma'
% 5.06/5.42 thf(fact_8855_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.42 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.06/5.42 != zero_zero_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_lemma'
% 5.06/5.42 thf(fact_8856_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ K @ N2 )
% 5.06/5.42 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.06/5.42 != zero_z3403309356797280102nteger ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_of_nat_eq_0_lemma'
% 5.06/5.42 thf(fact_8857_pochhammer__product_H,axiom,
% 5.06/5.42 ! [Z: rat,N2: nat,M: nat] :
% 5.06/5.42 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.06/5.42 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_product'
% 5.06/5.42 thf(fact_8858_pochhammer__product_H,axiom,
% 5.06/5.42 ! [Z: int,N2: nat,M: nat] :
% 5.06/5.42 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.06/5.42 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_product'
% 5.06/5.42 thf(fact_8859_pochhammer__product_H,axiom,
% 5.06/5.42 ! [Z: real,N2: nat,M: nat] :
% 5.06/5.42 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.06/5.42 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_product'
% 5.06/5.42 thf(fact_8860_pochhammer__product_H,axiom,
% 5.06/5.42 ! [Z: nat,N2: nat,M: nat] :
% 5.06/5.42 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.06/5.42 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_product'
% 5.06/5.42 thf(fact_8861_pochhammer__product_H,axiom,
% 5.06/5.42 ! [Z: code_integer,N2: nat,M: nat] :
% 5.06/5.42 ( ( comm_s8582702949713902594nteger @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.06/5.42 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ N2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N2 ) ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_product'
% 5.06/5.42 thf(fact_8862_Suc__times__gbinomial,axiom,
% 5.06/5.42 ! [K: nat,A: complex] :
% 5.06/5.42 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.06/5.42 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Suc_times_gbinomial
% 5.06/5.42 thf(fact_8863_Suc__times__gbinomial,axiom,
% 5.06/5.42 ! [K: nat,A: rat] :
% 5.06/5.42 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.06/5.42 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Suc_times_gbinomial
% 5.06/5.42 thf(fact_8864_Suc__times__gbinomial,axiom,
% 5.06/5.42 ! [K: nat,A: real] :
% 5.06/5.42 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.06/5.42 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Suc_times_gbinomial
% 5.06/5.42 thf(fact_8865_gbinomial__absorption,axiom,
% 5.06/5.42 ! [K: nat,A: complex] :
% 5.06/5.42 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.06/5.42 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_absorption
% 5.06/5.42 thf(fact_8866_gbinomial__absorption,axiom,
% 5.06/5.42 ! [K: nat,A: rat] :
% 5.06/5.42 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.06/5.42 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_absorption
% 5.06/5.42 thf(fact_8867_gbinomial__absorption,axiom,
% 5.06/5.42 ! [K: nat,A: real] :
% 5.06/5.42 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.06/5.42 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_absorption
% 5.06/5.42 thf(fact_8868_gbinomial__trinomial__revision,axiom,
% 5.06/5.42 ! [K: nat,M: nat,A: rat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ K @ M )
% 5.06/5.42 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.06/5.42 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_trinomial_revision
% 5.06/5.42 thf(fact_8869_gbinomial__trinomial__revision,axiom,
% 5.06/5.42 ! [K: nat,M: nat,A: real] :
% 5.06/5.42 ( ( ord_less_eq_nat @ K @ M )
% 5.06/5.42 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.06/5.42 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_trinomial_revision
% 5.06/5.42 thf(fact_8870_pochhammer__product,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,Z: rat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.42 => ( ( comm_s4028243227959126397er_rat @ Z @ N2 )
% 5.06/5.42 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_product
% 5.06/5.42 thf(fact_8871_pochhammer__product,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,Z: int] :
% 5.06/5.42 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.42 => ( ( comm_s4660882817536571857er_int @ Z @ N2 )
% 5.06/5.42 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_product
% 5.06/5.42 thf(fact_8872_pochhammer__product,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,Z: real] :
% 5.06/5.42 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.42 => ( ( comm_s7457072308508201937r_real @ Z @ N2 )
% 5.06/5.42 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_product
% 5.06/5.42 thf(fact_8873_pochhammer__product,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,Z: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.42 => ( ( comm_s4663373288045622133er_nat @ Z @ N2 )
% 5.06/5.42 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_product
% 5.06/5.42 thf(fact_8874_pochhammer__product,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,Z: code_integer] :
% 5.06/5.42 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.42 => ( ( comm_s8582702949713902594nteger @ Z @ N2 )
% 5.06/5.42 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ M ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_product
% 5.06/5.42 thf(fact_8875_gbinomial__parallel__sum,axiom,
% 5.06/5.42 ! [A: complex,N2: nat] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ N2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_parallel_sum
% 5.06/5.42 thf(fact_8876_gbinomial__parallel__sum,axiom,
% 5.06/5.42 ! [A: rat,N2: nat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_parallel_sum
% 5.06/5.42 thf(fact_8877_gbinomial__parallel__sum,axiom,
% 5.06/5.42 ! [A: real,N2: nat] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.42 = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ N2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_parallel_sum
% 5.06/5.42 thf(fact_8878_gbinomial__rec,axiom,
% 5.06/5.42 ! [A: complex,K: nat] :
% 5.06/5.42 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.06/5.42 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_rec
% 5.06/5.42 thf(fact_8879_gbinomial__rec,axiom,
% 5.06/5.42 ! [A: rat,K: nat] :
% 5.06/5.42 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.06/5.42 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_rec
% 5.06/5.42 thf(fact_8880_gbinomial__rec,axiom,
% 5.06/5.42 ! [A: real,K: nat] :
% 5.06/5.42 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.06/5.42 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_rec
% 5.06/5.42 thf(fact_8881_gbinomial__factors,axiom,
% 5.06/5.42 ! [A: complex,K: nat] :
% 5.06/5.42 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.06/5.42 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_factors
% 5.06/5.42 thf(fact_8882_gbinomial__factors,axiom,
% 5.06/5.42 ! [A: rat,K: nat] :
% 5.06/5.42 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.06/5.42 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_factors
% 5.06/5.42 thf(fact_8883_gbinomial__factors,axiom,
% 5.06/5.42 ! [A: real,K: nat] :
% 5.06/5.42 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.06/5.42 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_factors
% 5.06/5.42 thf(fact_8884_gbinomial__index__swap,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ K ) )
% 5.06/5.42 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_index_swap
% 5.06/5.42 thf(fact_8885_gbinomial__index__swap,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ K ) )
% 5.06/5.42 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_index_swap
% 5.06/5.42 thf(fact_8886_gbinomial__index__swap,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ K ) )
% 5.06/5.42 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_index_swap
% 5.06/5.42 thf(fact_8887_gbinomial__negated__upper,axiom,
% 5.06/5.42 ( gbinomial_complex
% 5.06/5.42 = ( ^ [A4: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A4 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_negated_upper
% 5.06/5.42 thf(fact_8888_gbinomial__negated__upper,axiom,
% 5.06/5.42 ( gbinomial_rat
% 5.06/5.42 = ( ^ [A4: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A4 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_negated_upper
% 5.06/5.42 thf(fact_8889_gbinomial__negated__upper,axiom,
% 5.06/5.42 ( gbinomial_real
% 5.06/5.42 = ( ^ [A4: real,K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A4 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_negated_upper
% 5.06/5.42 thf(fact_8890_pochhammer__absorb__comp,axiom,
% 5.06/5.42 ! [R2: complex,K: nat] :
% 5.06/5.42 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 5.06/5.42 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_absorb_comp
% 5.06/5.42 thf(fact_8891_pochhammer__absorb__comp,axiom,
% 5.06/5.42 ! [R2: rat,K: nat] :
% 5.06/5.42 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 5.06/5.42 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_absorb_comp
% 5.06/5.42 thf(fact_8892_pochhammer__absorb__comp,axiom,
% 5.06/5.42 ! [R2: int,K: nat] :
% 5.06/5.42 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 5.06/5.42 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_absorb_comp
% 5.06/5.42 thf(fact_8893_pochhammer__absorb__comp,axiom,
% 5.06/5.42 ! [R2: real,K: nat] :
% 5.06/5.42 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 5.06/5.42 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_absorb_comp
% 5.06/5.42 thf(fact_8894_pochhammer__absorb__comp,axiom,
% 5.06/5.42 ! [R2: code_integer,K: nat] :
% 5.06/5.42 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 5.06/5.42 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_absorb_comp
% 5.06/5.42 thf(fact_8895_pochhammer__same,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ N2 )
% 5.06/5.42 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_same
% 5.06/5.42 thf(fact_8896_pochhammer__same,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ N2 )
% 5.06/5.42 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_same
% 5.06/5.42 thf(fact_8897_pochhammer__same,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ N2 )
% 5.06/5.42 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_same
% 5.06/5.42 thf(fact_8898_pochhammer__same,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ N2 )
% 5.06/5.42 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_same
% 5.06/5.42 thf(fact_8899_pochhammer__same,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ N2 )
% 5.06/5.42 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_same
% 5.06/5.42 thf(fact_8900_gbinomial__minus,axiom,
% 5.06/5.42 ! [A: complex,K: nat] :
% 5.06/5.42 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.06/5.42 = ( 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 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_minus
% 5.06/5.42 thf(fact_8901_gbinomial__minus,axiom,
% 5.06/5.42 ! [A: rat,K: nat] :
% 5.06/5.42 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.06/5.42 = ( 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 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_minus
% 5.06/5.42 thf(fact_8902_gbinomial__minus,axiom,
% 5.06/5.42 ! [A: real,K: nat] :
% 5.06/5.42 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.06/5.42 = ( 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 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_minus
% 5.06/5.42 thf(fact_8903_gbinomial__reduce__nat,axiom,
% 5.06/5.42 ! [K: nat,A: complex] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.42 => ( ( gbinomial_complex @ A @ K )
% 5.06/5.42 = ( 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 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_reduce_nat
% 5.06/5.42 thf(fact_8904_gbinomial__reduce__nat,axiom,
% 5.06/5.42 ! [K: nat,A: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.42 => ( ( gbinomial_real @ A @ K )
% 5.06/5.42 = ( 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 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_reduce_nat
% 5.06/5.42 thf(fact_8905_gbinomial__reduce__nat,axiom,
% 5.06/5.42 ! [K: nat,A: rat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.42 => ( ( gbinomial_rat @ A @ K )
% 5.06/5.42 = ( 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 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_reduce_nat
% 5.06/5.42 thf(fact_8906_pochhammer__minus,axiom,
% 5.06/5.42 ! [B: complex,K: nat] :
% 5.06/5.42 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.06/5.42 = ( 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 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_minus
% 5.06/5.42 thf(fact_8907_pochhammer__minus,axiom,
% 5.06/5.42 ! [B: rat,K: nat] :
% 5.06/5.42 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.06/5.42 = ( 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 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_minus
% 5.06/5.42 thf(fact_8908_pochhammer__minus,axiom,
% 5.06/5.42 ! [B: int,K: nat] :
% 5.06/5.42 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.06/5.42 = ( 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 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_minus
% 5.06/5.42 thf(fact_8909_pochhammer__minus,axiom,
% 5.06/5.42 ! [B: real,K: nat] :
% 5.06/5.42 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.06/5.42 = ( 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 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_minus
% 5.06/5.42 thf(fact_8910_pochhammer__minus,axiom,
% 5.06/5.42 ! [B: code_integer,K: nat] :
% 5.06/5.42 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.06/5.42 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_minus
% 5.06/5.42 thf(fact_8911_pochhammer__minus_H,axiom,
% 5.06/5.42 ! [B: complex,K: nat] :
% 5.06/5.42 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.06/5.42 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_minus'
% 5.06/5.42 thf(fact_8912_pochhammer__minus_H,axiom,
% 5.06/5.42 ! [B: rat,K: nat] :
% 5.06/5.42 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.06/5.42 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_minus'
% 5.06/5.42 thf(fact_8913_pochhammer__minus_H,axiom,
% 5.06/5.42 ! [B: int,K: nat] :
% 5.06/5.42 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.06/5.42 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_minus'
% 5.06/5.42 thf(fact_8914_pochhammer__minus_H,axiom,
% 5.06/5.42 ! [B: real,K: nat] :
% 5.06/5.42 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.06/5.42 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_minus'
% 5.06/5.42 thf(fact_8915_pochhammer__minus_H,axiom,
% 5.06/5.42 ! [B: code_integer,K: nat] :
% 5.06/5.42 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.06/5.42 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_minus'
% 5.06/5.42 thf(fact_8916_gbinomial__sum__lower__neg,axiom,
% 5.06/5.42 ! [A: complex,M: nat] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_sum_lower_neg
% 5.06/5.42 thf(fact_8917_gbinomial__sum__lower__neg,axiom,
% 5.06/5.42 ! [A: rat,M: nat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_sum_lower_neg
% 5.06/5.42 thf(fact_8918_gbinomial__sum__lower__neg,axiom,
% 5.06/5.42 ! [A: real,M: nat] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_sum_lower_neg
% 5.06/5.42 thf(fact_8919_pochhammer__binomial__sum,axiom,
% 5.06/5.42 ! [A: rat,B: rat,N2: nat] :
% 5.06/5.42 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_binomial_sum
% 5.06/5.42 thf(fact_8920_pochhammer__binomial__sum,axiom,
% 5.06/5.42 ! [A: int,B: int,N2: nat] :
% 5.06/5.42 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups3539618377306564664at_int
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_binomial_sum
% 5.06/5.42 thf(fact_8921_pochhammer__binomial__sum,axiom,
% 5.06/5.42 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.06/5.42 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups7501900531339628137nteger
% 5.06/5.42 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K3 ) ) @ ( comm_s8582702949713902594nteger @ A @ K3 ) ) @ ( comm_s8582702949713902594nteger @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_binomial_sum
% 5.06/5.42 thf(fact_8922_pochhammer__binomial__sum,axiom,
% 5.06/5.42 ! [A: real,B: real,N2: nat] :
% 5.06/5.42 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 5.06/5.42 = ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_binomial_sum
% 5.06/5.42 thf(fact_8923_gbinomial__partial__sum__poly,axiom,
% 5.06/5.42 ! [M: nat,A: complex,X: complex,Y: complex] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_partial_sum_poly
% 5.06/5.42 thf(fact_8924_gbinomial__partial__sum__poly,axiom,
% 5.06/5.42 ! [M: nat,A: rat,X: rat,Y: rat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X ) @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_partial_sum_poly
% 5.06/5.42 thf(fact_8925_gbinomial__partial__sum__poly,axiom,
% 5.06/5.42 ! [M: nat,A: real,X: real,Y: real] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_partial_sum_poly
% 5.06/5.42 thf(fact_8926_gbinomial__sum__up__index,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.42 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_sum_up_index
% 5.06/5.42 thf(fact_8927_gbinomial__sum__up__index,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.42 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_sum_up_index
% 5.06/5.42 thf(fact_8928_gbinomial__sum__up__index,axiom,
% 5.06/5.42 ! [K: nat,N2: nat] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.42 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_sum_up_index
% 5.06/5.42 thf(fact_8929_gbinomial__absorption_H,axiom,
% 5.06/5.42 ! [K: nat,A: complex] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.42 => ( ( gbinomial_complex @ A @ K )
% 5.06/5.42 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_absorption'
% 5.06/5.42 thf(fact_8930_gbinomial__absorption_H,axiom,
% 5.06/5.42 ! [K: nat,A: rat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.42 => ( ( gbinomial_rat @ A @ K )
% 5.06/5.42 = ( 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 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_absorption'
% 5.06/5.42 thf(fact_8931_gbinomial__absorption_H,axiom,
% 5.06/5.42 ! [K: nat,A: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.42 => ( ( gbinomial_real @ A @ K )
% 5.06/5.42 = ( 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 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_absorption'
% 5.06/5.42 thf(fact_8932_pochhammer__code,axiom,
% 5.06/5.42 ( comm_s2602460028002588243omplex
% 5.06/5.42 = ( ^ [A4: complex,N: nat] :
% 5.06/5.42 ( if_complex @ ( N = zero_zero_nat ) @ one_one_complex
% 5.06/5.42 @ ( set_fo1517530859248394432omplex
% 5.06/5.42 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.06/5.42 @ zero_zero_nat
% 5.06/5.42 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.06/5.42 @ one_one_complex ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_code
% 5.06/5.42 thf(fact_8933_pochhammer__code,axiom,
% 5.06/5.42 ( comm_s4028243227959126397er_rat
% 5.06/5.42 = ( ^ [A4: rat,N: nat] :
% 5.06/5.42 ( if_rat @ ( N = zero_zero_nat ) @ one_one_rat
% 5.06/5.42 @ ( set_fo1949268297981939178at_rat
% 5.06/5.42 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.06/5.42 @ zero_zero_nat
% 5.06/5.42 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.06/5.42 @ one_one_rat ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_code
% 5.06/5.42 thf(fact_8934_pochhammer__code,axiom,
% 5.06/5.42 ( comm_s4660882817536571857er_int
% 5.06/5.42 = ( ^ [A4: int,N: nat] :
% 5.06/5.42 ( if_int @ ( N = zero_zero_nat ) @ one_one_int
% 5.06/5.42 @ ( set_fo2581907887559384638at_int
% 5.06/5.42 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.06/5.42 @ zero_zero_nat
% 5.06/5.42 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.06/5.42 @ one_one_int ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_code
% 5.06/5.42 thf(fact_8935_pochhammer__code,axiom,
% 5.06/5.42 ( comm_s7457072308508201937r_real
% 5.06/5.42 = ( ^ [A4: real,N: nat] :
% 5.06/5.42 ( if_real @ ( N = zero_zero_nat ) @ one_one_real
% 5.06/5.42 @ ( set_fo3111899725591712190t_real
% 5.06/5.42 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.06/5.42 @ zero_zero_nat
% 5.06/5.42 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.06/5.42 @ one_one_real ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_code
% 5.06/5.42 thf(fact_8936_pochhammer__code,axiom,
% 5.06/5.42 ( comm_s8582702949713902594nteger
% 5.06/5.42 = ( ^ [A4: code_integer,N: nat] :
% 5.06/5.42 ( if_Code_integer @ ( N = zero_zero_nat ) @ one_one_Code_integer
% 5.06/5.42 @ ( set_fo1084959871951514735nteger
% 5.06/5.42 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A4 @ ( semiri4939895301339042750nteger @ O ) ) )
% 5.06/5.42 @ zero_zero_nat
% 5.06/5.42 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.06/5.42 @ one_one_Code_integer ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_code
% 5.06/5.42 thf(fact_8937_pochhammer__code,axiom,
% 5.06/5.42 ( comm_s4663373288045622133er_nat
% 5.06/5.42 = ( ^ [A4: nat,N: nat] :
% 5.06/5.42 ( if_nat @ ( N = zero_zero_nat ) @ one_one_nat
% 5.06/5.42 @ ( set_fo2584398358068434914at_nat
% 5.06/5.42 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.06/5.42 @ zero_zero_nat
% 5.06/5.42 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.06/5.42 @ one_one_nat ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_code
% 5.06/5.42 thf(fact_8938_gbinomial__sum__nat__pow2,axiom,
% 5.06/5.42 ! [M: nat] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_sum_nat_pow2
% 5.06/5.42 thf(fact_8939_gbinomial__sum__nat__pow2,axiom,
% 5.06/5.42 ! [M: nat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( divide_divide_rat @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ K3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ M ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_sum_nat_pow2
% 5.06/5.42 thf(fact_8940_gbinomial__sum__nat__pow2,axiom,
% 5.06/5.42 ! [M: nat] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K3 ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_sum_nat_pow2
% 5.06/5.42 thf(fact_8941_gbinomial__partial__sum__poly__xpos,axiom,
% 5.06/5.42 ! [M: nat,A: complex,X: complex,Y: complex] :
% 5.06/5.42 ( ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A ) @ one_one_complex ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_partial_sum_poly_xpos
% 5.06/5.42 thf(fact_8942_gbinomial__partial__sum__poly__xpos,axiom,
% 5.06/5.42 ! [M: nat,A: rat,X: rat,Y: rat] :
% 5.06/5.42 ( ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( groups2906978787729119204at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A ) @ one_one_rat ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_partial_sum_poly_xpos
% 5.06/5.42 thf(fact_8943_gbinomial__partial__sum__poly__xpos,axiom,
% 5.06/5.42 ! [M: nat,A: real,X: real,Y: real] :
% 5.06/5.42 ( ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) )
% 5.06/5.42 = ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A ) @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.06/5.42 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_partial_sum_poly_xpos
% 5.06/5.42 thf(fact_8944_fact__double,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % fact_double
% 5.06/5.42 thf(fact_8945_fact__double,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % fact_double
% 5.06/5.42 thf(fact_8946_fact__double,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % fact_double
% 5.06/5.42 thf(fact_8947_gbinomial__code,axiom,
% 5.06/5.42 ( gbinomial_complex
% 5.06/5.42 = ( ^ [A4: complex,K3: nat] :
% 5.06/5.42 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 5.06/5.42 @ ( divide1717551699836669952omplex
% 5.06/5.42 @ ( set_fo1517530859248394432omplex
% 5.06/5.42 @ ^ [L: nat] : ( times_times_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ L ) ) )
% 5.06/5.42 @ zero_zero_nat
% 5.06/5.42 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.06/5.42 @ one_one_complex )
% 5.06/5.42 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_code
% 5.06/5.42 thf(fact_8948_gbinomial__code,axiom,
% 5.06/5.42 ( gbinomial_rat
% 5.06/5.42 = ( ^ [A4: rat,K3: nat] :
% 5.06/5.42 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 5.06/5.42 @ ( divide_divide_rat
% 5.06/5.42 @ ( set_fo1949268297981939178at_rat
% 5.06/5.42 @ ^ [L: nat] : ( times_times_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ L ) ) )
% 5.06/5.42 @ zero_zero_nat
% 5.06/5.42 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.06/5.42 @ one_one_rat )
% 5.06/5.42 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_code
% 5.06/5.42 thf(fact_8949_gbinomial__code,axiom,
% 5.06/5.42 ( gbinomial_real
% 5.06/5.42 = ( ^ [A4: real,K3: nat] :
% 5.06/5.42 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 5.06/5.42 @ ( divide_divide_real
% 5.06/5.42 @ ( set_fo3111899725591712190t_real
% 5.06/5.42 @ ^ [L: nat] : ( times_times_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ L ) ) )
% 5.06/5.42 @ zero_zero_nat
% 5.06/5.42 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.06/5.42 @ one_one_real )
% 5.06/5.42 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % gbinomial_code
% 5.06/5.42 thf(fact_8950_pochhammer__times__pochhammer__half,axiom,
% 5.06/5.42 ! [Z: complex,N2: nat] :
% 5.06/5.42 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.06/5.42 = ( groups6464643781859351333omplex
% 5.06/5.42 @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_times_pochhammer_half
% 5.06/5.42 thf(fact_8951_pochhammer__times__pochhammer__half,axiom,
% 5.06/5.42 ! [Z: rat,N2: nat] :
% 5.06/5.42 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.06/5.42 = ( groups73079841787564623at_rat
% 5.06/5.42 @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_times_pochhammer_half
% 5.06/5.42 thf(fact_8952_pochhammer__times__pochhammer__half,axiom,
% 5.06/5.42 ! [Z: real,N2: nat] :
% 5.06/5.42 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.06/5.42 = ( groups129246275422532515t_real
% 5.06/5.42 @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pochhammer_times_pochhammer_half
% 5.06/5.42 thf(fact_8953_sin__x__sin__y,axiom,
% 5.06/5.42 ! [X: real,Y: real] :
% 5.06/5.42 ( sums_real
% 5.06/5.42 @ ^ [P5: nat] :
% 5.06/5.42 ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [N: nat] :
% 5.06/5.42 ( if_real
% 5.06/5.42 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 5.06/5.42 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.06/5.42 @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) ) @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 5.06/5.42 @ zero_zero_real )
% 5.06/5.42 @ ( set_ord_atMost_nat @ P5 ) )
% 5.06/5.42 @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sin_x_sin_y
% 5.06/5.42 thf(fact_8954_sin__x__sin__y,axiom,
% 5.06/5.42 ! [X: complex,Y: complex] :
% 5.06/5.42 ( sums_complex
% 5.06/5.42 @ ^ [P5: nat] :
% 5.06/5.42 ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [N: nat] :
% 5.06/5.42 ( if_complex
% 5.06/5.42 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 5.06/5.42 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.06/5.42 @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) ) @ ( power_power_complex @ X @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 5.06/5.42 @ zero_zero_complex )
% 5.06/5.42 @ ( set_ord_atMost_nat @ P5 ) )
% 5.06/5.42 @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sin_x_sin_y
% 5.06/5.42 thf(fact_8955_Maclaurin__sin__bound,axiom,
% 5.06/5.42 ! [X: real,N2: nat] :
% 5.06/5.42 ( ord_less_eq_real
% 5.06/5.42 @ ( abs_abs_real
% 5.06/5.42 @ ( minus_minus_real @ ( sin_real @ X )
% 5.06/5.42 @ ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.06/5.42 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Maclaurin_sin_bound
% 5.06/5.42 thf(fact_8956_sums__cos__x__plus__y,axiom,
% 5.06/5.42 ! [X: real,Y: real] :
% 5.06/5.42 ( sums_real
% 5.06/5.42 @ ^ [P5: nat] :
% 5.06/5.42 ( groups6591440286371151544t_real
% 5.06/5.42 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 ) @ ( times_times_real @ ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) ) @ zero_zero_real )
% 5.06/5.42 @ ( set_ord_atMost_nat @ P5 ) )
% 5.06/5.42 @ ( cos_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sums_cos_x_plus_y
% 5.06/5.42 thf(fact_8957_sums__cos__x__plus__y,axiom,
% 5.06/5.42 ! [X: complex,Y: complex] :
% 5.06/5.42 ( sums_complex
% 5.06/5.42 @ ^ [P5: nat] :
% 5.06/5.42 ( groups2073611262835488442omplex
% 5.06/5.42 @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 ) @ ( times_times_complex @ ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( ring_1_of_int_real @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( divide_divide_nat @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_complex @ X @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) ) @ zero_zero_complex )
% 5.06/5.42 @ ( set_ord_atMost_nat @ P5 ) )
% 5.06/5.42 @ ( cos_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sums_cos_x_plus_y
% 5.06/5.42 thf(fact_8958_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.06/5.42 ! [X: vEBT_VEBT,Y: $o] :
% 5.06/5.42 ( ( ( vEBT_VEBT_minNull @ X )
% 5.06/5.42 = Y )
% 5.06/5.42 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.06/5.42 => ( ( ( X
% 5.06/5.42 = ( vEBT_Leaf @ $false @ $false ) )
% 5.06/5.42 => ( Y
% 5.06/5.42 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.06/5.42 => ( ! [Uv2: $o] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.06/5.42 => ( ~ Y
% 5.06/5.42 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.06/5.42 => ( ! [Uu2: $o] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.06/5.42 => ( ~ Y
% 5.06/5.42 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.06/5.42 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.06/5.42 => ( Y
% 5.06/5.42 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.06/5.42 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.06/5.42 => ( ~ Y
% 5.06/5.42 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % VEBT_internal.minNull.pelims(1)
% 5.06/5.42 thf(fact_8959_mult__scaleR__right,axiom,
% 5.06/5.42 ! [X: real,A: real,Y: real] :
% 5.06/5.42 ( ( times_times_real @ X @ ( real_V1485227260804924795R_real @ A @ Y ) )
% 5.06/5.42 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % mult_scaleR_right
% 5.06/5.42 thf(fact_8960_mult__scaleR__right,axiom,
% 5.06/5.42 ! [X: complex,A: real,Y: complex] :
% 5.06/5.42 ( ( times_times_complex @ X @ ( real_V2046097035970521341omplex @ A @ Y ) )
% 5.06/5.42 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % mult_scaleR_right
% 5.06/5.42 thf(fact_8961_mult__scaleR__left,axiom,
% 5.06/5.42 ! [A: real,X: real,Y: real] :
% 5.06/5.42 ( ( times_times_real @ ( real_V1485227260804924795R_real @ A @ X ) @ Y )
% 5.06/5.42 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % mult_scaleR_left
% 5.06/5.42 thf(fact_8962_mult__scaleR__left,axiom,
% 5.06/5.42 ! [A: real,X: complex,Y: complex] :
% 5.06/5.42 ( ( times_times_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ Y )
% 5.06/5.42 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % mult_scaleR_left
% 5.06/5.42 thf(fact_8963_inverse__mult__distrib,axiom,
% 5.06/5.42 ! [A: real,B: real] :
% 5.06/5.42 ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.06/5.42 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_mult_distrib
% 5.06/5.42 thf(fact_8964_inverse__mult__distrib,axiom,
% 5.06/5.42 ! [A: complex,B: complex] :
% 5.06/5.42 ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.06/5.42 = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_mult_distrib
% 5.06/5.42 thf(fact_8965_inverse__mult__distrib,axiom,
% 5.06/5.42 ! [A: rat,B: rat] :
% 5.06/5.42 ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.06/5.42 = ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_mult_distrib
% 5.06/5.42 thf(fact_8966_inverse__eq__1__iff,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ( inverse_inverse_real @ X )
% 5.06/5.42 = one_one_real )
% 5.06/5.42 = ( X = one_one_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_eq_1_iff
% 5.06/5.42 thf(fact_8967_inverse__eq__1__iff,axiom,
% 5.06/5.42 ! [X: complex] :
% 5.06/5.42 ( ( ( invers8013647133539491842omplex @ X )
% 5.06/5.42 = one_one_complex )
% 5.06/5.42 = ( X = one_one_complex ) ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_eq_1_iff
% 5.06/5.42 thf(fact_8968_inverse__eq__1__iff,axiom,
% 5.06/5.42 ! [X: rat] :
% 5.06/5.42 ( ( ( inverse_inverse_rat @ X )
% 5.06/5.42 = one_one_rat )
% 5.06/5.42 = ( X = one_one_rat ) ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_eq_1_iff
% 5.06/5.42 thf(fact_8969_inverse__1,axiom,
% 5.06/5.42 ( ( inverse_inverse_real @ one_one_real )
% 5.06/5.42 = one_one_real ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_1
% 5.06/5.42 thf(fact_8970_inverse__1,axiom,
% 5.06/5.42 ( ( invers8013647133539491842omplex @ one_one_complex )
% 5.06/5.42 = one_one_complex ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_1
% 5.06/5.42 thf(fact_8971_inverse__1,axiom,
% 5.06/5.42 ( ( inverse_inverse_rat @ one_one_rat )
% 5.06/5.42 = one_one_rat ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_1
% 5.06/5.42 thf(fact_8972_inverse__divide,axiom,
% 5.06/5.42 ! [A: real,B: real] :
% 5.06/5.42 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 5.06/5.42 = ( divide_divide_real @ B @ A ) ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_divide
% 5.06/5.42 thf(fact_8973_inverse__divide,axiom,
% 5.06/5.42 ! [A: complex,B: complex] :
% 5.06/5.42 ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.06/5.42 = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_divide
% 5.06/5.42 thf(fact_8974_inverse__divide,axiom,
% 5.06/5.42 ! [A: rat,B: rat] :
% 5.06/5.42 ( ( inverse_inverse_rat @ ( divide_divide_rat @ A @ B ) )
% 5.06/5.42 = ( divide_divide_rat @ B @ A ) ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_divide
% 5.06/5.42 thf(fact_8975_scaleR__scaleR,axiom,
% 5.06/5.42 ! [A: real,B: real,X: real] :
% 5.06/5.42 ( ( real_V1485227260804924795R_real @ A @ ( real_V1485227260804924795R_real @ B @ X ) )
% 5.06/5.42 = ( real_V1485227260804924795R_real @ ( times_times_real @ A @ B ) @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % scaleR_scaleR
% 5.06/5.42 thf(fact_8976_scaleR__scaleR,axiom,
% 5.06/5.42 ! [A: real,B: real,X: complex] :
% 5.06/5.42 ( ( real_V2046097035970521341omplex @ A @ ( real_V2046097035970521341omplex @ B @ X ) )
% 5.06/5.42 = ( real_V2046097035970521341omplex @ ( times_times_real @ A @ B ) @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % scaleR_scaleR
% 5.06/5.42 thf(fact_8977_prod_Oneutral__const,axiom,
% 5.06/5.42 ! [A2: set_nat] :
% 5.06/5.42 ( ( groups705719431365010083at_int
% 5.06/5.42 @ ^ [Uu3: nat] : one_one_int
% 5.06/5.42 @ A2 )
% 5.06/5.42 = one_one_int ) ).
% 5.06/5.42
% 5.06/5.42 % prod.neutral_const
% 5.06/5.42 thf(fact_8978_prod_Oneutral__const,axiom,
% 5.06/5.42 ! [A2: set_int] :
% 5.06/5.42 ( ( groups1705073143266064639nt_int
% 5.06/5.42 @ ^ [Uu3: int] : one_one_int
% 5.06/5.42 @ A2 )
% 5.06/5.42 = one_one_int ) ).
% 5.06/5.42
% 5.06/5.42 % prod.neutral_const
% 5.06/5.42 thf(fact_8979_sin__npi__int,axiom,
% 5.06/5.42 ! [N2: int] :
% 5.06/5.42 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.06/5.42 = zero_zero_real ) ).
% 5.06/5.42
% 5.06/5.42 % sin_npi_int
% 5.06/5.42 thf(fact_8980_tan__periodic__int,axiom,
% 5.06/5.42 ! [X: real,I2: int] :
% 5.06/5.42 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 5.06/5.42 = ( tan_real @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % tan_periodic_int
% 5.06/5.42 thf(fact_8981_sin__int__2pin,axiom,
% 5.06/5.42 ! [N2: int] :
% 5.06/5.42 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 5.06/5.42 = zero_zero_real ) ).
% 5.06/5.42
% 5.06/5.42 % sin_int_2pin
% 5.06/5.42 thf(fact_8982_cos__int__2pin,axiom,
% 5.06/5.42 ! [N2: int] :
% 5.06/5.42 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 5.06/5.42 = one_one_real ) ).
% 5.06/5.42
% 5.06/5.42 % cos_int_2pin
% 5.06/5.42 thf(fact_8983_cos__npi__int,axiom,
% 5.06/5.42 ! [N2: int] :
% 5.06/5.42 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.42 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.06/5.42 = one_one_real ) )
% 5.06/5.42 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.42 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.06/5.42 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cos_npi_int
% 5.06/5.42 thf(fact_8984_real__scaleR__def,axiom,
% 5.06/5.42 real_V1485227260804924795R_real = times_times_real ).
% 5.06/5.42
% 5.06/5.42 % real_scaleR_def
% 5.06/5.42 thf(fact_8985_real__sqrt__inverse,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 5.06/5.42 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_sqrt_inverse
% 5.06/5.42 thf(fact_8986_divide__real__def,axiom,
% 5.06/5.42 ( divide_divide_real
% 5.06/5.42 = ( ^ [X2: real,Y2: real] : ( times_times_real @ X2 @ ( inverse_inverse_real @ Y2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % divide_real_def
% 5.06/5.42 thf(fact_8987_complex__scaleR,axiom,
% 5.06/5.42 ! [R2: real,A: real,B: real] :
% 5.06/5.42 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B ) )
% 5.06/5.42 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % complex_scaleR
% 5.06/5.42 thf(fact_8988_real__of__int__div4,axiom,
% 5.06/5.42 ! [N2: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_of_int_div4
% 5.06/5.42 thf(fact_8989_real__of__int__div,axiom,
% 5.06/5.42 ! [D: int,N2: int] :
% 5.06/5.42 ( ( dvd_dvd_int @ D @ N2 )
% 5.06/5.42 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ D ) )
% 5.06/5.42 = ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_of_int_div
% 5.06/5.42 thf(fact_8990_forall__pos__mono__1,axiom,
% 5.06/5.42 ! [P: real > $o,E: real] :
% 5.06/5.42 ( ! [D4: real,E2: real] :
% 5.06/5.42 ( ( ord_less_real @ D4 @ E2 )
% 5.06/5.42 => ( ( P @ D4 )
% 5.06/5.42 => ( P @ E2 ) ) )
% 5.06/5.42 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.06/5.42 => ( P @ E ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % forall_pos_mono_1
% 5.06/5.42 thf(fact_8991_forall__pos__mono,axiom,
% 5.06/5.42 ! [P: real > $o,E: real] :
% 5.06/5.42 ( ! [D4: real,E2: real] :
% 5.06/5.42 ( ( ord_less_real @ D4 @ E2 )
% 5.06/5.42 => ( ( P @ D4 )
% 5.06/5.42 => ( P @ E2 ) ) )
% 5.06/5.42 => ( ! [N3: nat] :
% 5.06/5.42 ( ( N3 != zero_zero_nat )
% 5.06/5.42 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.06/5.42 => ( P @ E ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % forall_pos_mono
% 5.06/5.42 thf(fact_8992_real__arch__inverse,axiom,
% 5.06/5.42 ! [E: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ E )
% 5.06/5.42 = ( ? [N: nat] :
% 5.06/5.42 ( ( N != zero_zero_nat )
% 5.06/5.42 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.06/5.42 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) @ E ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_arch_inverse
% 5.06/5.42 thf(fact_8993_int__le__real__less,axiom,
% 5.06/5.42 ( ord_less_eq_int
% 5.06/5.42 = ( ^ [N: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % int_le_real_less
% 5.06/5.42 thf(fact_8994_sqrt__divide__self__eq,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 5.06/5.42 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sqrt_divide_self_eq
% 5.06/5.42 thf(fact_8995_int__less__real__le,axiom,
% 5.06/5.42 ( ord_less_int
% 5.06/5.42 = ( ^ [N: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % int_less_real_le
% 5.06/5.42 thf(fact_8996_sin__zero__iff__int2,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ( sin_real @ X )
% 5.06/5.42 = zero_zero_real )
% 5.06/5.42 = ( ? [I5: int] :
% 5.06/5.42 ( X
% 5.06/5.42 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ pi ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sin_zero_iff_int2
% 5.06/5.42 thf(fact_8997_real__of__int__div__aux,axiom,
% 5.06/5.42 ! [X: int,D: int] :
% 5.06/5.42 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 5.06/5.42 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_of_int_div_aux
% 5.06/5.42 thf(fact_8998_real__of__int__div2,axiom,
% 5.06/5.42 ! [N2: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_of_int_div2
% 5.06/5.42 thf(fact_8999_real__of__int__div3,axiom,
% 5.06/5.42 ! [N2: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X ) ) ) @ one_one_real ) ).
% 5.06/5.42
% 5.06/5.42 % real_of_int_div3
% 5.06/5.42 thf(fact_9000_fact__eq__fact__times,axiom,
% 5.06/5.42 ! [N2: nat,M: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.42 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.06/5.42 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 5.06/5.42 @ ( groups708209901874060359at_nat
% 5.06/5.42 @ ^ [X2: nat] : X2
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % fact_eq_fact_times
% 5.06/5.42 thf(fact_9001_exp__plus__inverse__exp,axiom,
% 5.06/5.42 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % exp_plus_inverse_exp
% 5.06/5.42 thf(fact_9002_fact__div__fact,axiom,
% 5.06/5.42 ! [N2: nat,M: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.42 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 5.06/5.42 = ( groups708209901874060359at_nat
% 5.06/5.42 @ ^ [X2: nat] : X2
% 5.06/5.42 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % fact_div_fact
% 5.06/5.42 thf(fact_9003_plus__inverse__ge__2,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % plus_inverse_ge_2
% 5.06/5.42 thf(fact_9004_real__inv__sqrt__pow2,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.42 = ( inverse_inverse_real @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_inv_sqrt_pow2
% 5.06/5.42 thf(fact_9005_cos__one__2pi__int,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ( cos_real @ X )
% 5.06/5.42 = one_one_real )
% 5.06/5.42 = ( ? [X2: int] :
% 5.06/5.42 ( X
% 5.06/5.42 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cos_one_2pi_int
% 5.06/5.42 thf(fact_9006_tan__cot,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.06/5.42 = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % tan_cot
% 5.06/5.42 thf(fact_9007_real__le__x__sinh,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_le_x_sinh
% 5.06/5.42 thf(fact_9008_real__le__abs__sinh,axiom,
% 5.06/5.42 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_le_abs_sinh
% 5.06/5.42 thf(fact_9009_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.06/5.42 ! [X: vEBT_VEBT] :
% 5.06/5.42 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.06/5.42 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.06/5.42 => ( ! [Uv2: $o] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.06/5.42 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.06/5.42 => ( ! [Uu2: $o] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.06/5.42 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 5.06/5.42 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.06/5.42 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % VEBT_internal.minNull.pelims(3)
% 5.06/5.42 thf(fact_9010_arccos__cos__eq__abs__2pi,axiom,
% 5.06/5.42 ! [Theta: real] :
% 5.06/5.42 ~ ! [K2: int] :
% 5.06/5.42 ( ( arccos @ ( cos_real @ Theta ) )
% 5.06/5.42 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % arccos_cos_eq_abs_2pi
% 5.06/5.42 thf(fact_9011_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.06/5.42 ! [X: vEBT_VEBT] :
% 5.06/5.42 ( ( vEBT_VEBT_minNull @ X )
% 5.06/5.42 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.06/5.42 => ( ( ( X
% 5.06/5.42 = ( vEBT_Leaf @ $false @ $false ) )
% 5.06/5.42 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.06/5.42 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.06/5.42 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % VEBT_internal.minNull.pelims(2)
% 5.06/5.42 thf(fact_9012_cos__zero__iff__int,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ( cos_real @ X )
% 5.06/5.42 = zero_zero_real )
% 5.06/5.42 = ( ? [I5: int] :
% 5.06/5.42 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 5.06/5.42 & ( X
% 5.06/5.42 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cos_zero_iff_int
% 5.06/5.42 thf(fact_9013_sin__zero__iff__int,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ( sin_real @ X )
% 5.06/5.42 = zero_zero_real )
% 5.06/5.42 = ( ? [I5: int] :
% 5.06/5.42 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 5.06/5.42 & ( X
% 5.06/5.42 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sin_zero_iff_int
% 5.06/5.42 thf(fact_9014_sinh__real__le__iff,axiom,
% 5.06/5.42 ! [X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 5.06/5.42 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.06/5.42
% 5.06/5.42 % sinh_real_le_iff
% 5.06/5.42 thf(fact_9015_sinh__real__nonneg__iff,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.06/5.42 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % sinh_real_nonneg_iff
% 5.06/5.42 thf(fact_9016_sinh__real__nonpos__iff,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.06/5.42 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % sinh_real_nonpos_iff
% 5.06/5.42 thf(fact_9017_divide__complex__def,axiom,
% 5.06/5.42 ( divide1717551699836669952omplex
% 5.06/5.42 = ( ^ [X2: complex,Y2: complex] : ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ Y2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % divide_complex_def
% 5.06/5.42 thf(fact_9018_prod__int__eq,axiom,
% 5.06/5.42 ! [I2: nat,J: nat] :
% 5.06/5.42 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 5.06/5.42 = ( groups1705073143266064639nt_int
% 5.06/5.42 @ ^ [X2: int] : X2
% 5.06/5.42 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % prod_int_eq
% 5.06/5.42 thf(fact_9019_prod__int__plus__eq,axiom,
% 5.06/5.42 ! [I2: nat,J: nat] :
% 5.06/5.42 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 5.06/5.42 = ( groups1705073143266064639nt_int
% 5.06/5.42 @ ^ [X2: int] : X2
% 5.06/5.42 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % prod_int_plus_eq
% 5.06/5.42 thf(fact_9020_complex__inverse,axiom,
% 5.06/5.42 ! [A: real,B: real] :
% 5.06/5.42 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.06/5.42 = ( 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 ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % complex_inverse
% 5.06/5.42 thf(fact_9021_sinh__ln__real,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 5.06/5.42 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sinh_ln_real
% 5.06/5.42 thf(fact_9022_or__int__unfold,axiom,
% 5.06/5.42 ( bit_se1409905431419307370or_int
% 5.06/5.42 = ( ^ [K3: int,L: int] :
% 5.06/5.42 ( if_int
% 5.06/5.42 @ ( ( K3
% 5.06/5.42 = ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.42 | ( L
% 5.06/5.42 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.06/5.42 @ ( uminus_uminus_int @ one_one_int )
% 5.06/5.42 @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( 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 @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_int_unfold
% 5.06/5.42 thf(fact_9023_divmod__BitM__2__eq,axiom,
% 5.06/5.42 ! [M: num] :
% 5.06/5.42 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.06/5.42 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.06/5.42
% 5.06/5.42 % divmod_BitM_2_eq
% 5.06/5.42 thf(fact_9024_cot__less__zero,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.06/5.42 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.06/5.42 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cot_less_zero
% 5.06/5.42 thf(fact_9025_or__nonnegative__int__iff,axiom,
% 5.06/5.42 ! [K: int,L2: int] :
% 5.06/5.42 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 5.06/5.42 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.42 & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_nonnegative_int_iff
% 5.06/5.42 thf(fact_9026_or__negative__int__iff,axiom,
% 5.06/5.42 ! [K: int,L2: int] :
% 5.06/5.42 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 5.06/5.42 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.06/5.42 | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_negative_int_iff
% 5.06/5.42 thf(fact_9027_pred__numeral__simps_I2_J,axiom,
% 5.06/5.42 ! [K: num] :
% 5.06/5.42 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.06/5.42 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pred_numeral_simps(2)
% 5.06/5.42 thf(fact_9028_or__minus__numerals_I6_J,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 5.06/5.42 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_minus_numerals(6)
% 5.06/5.42 thf(fact_9029_or__minus__numerals_I2_J,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.06/5.42 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_minus_numerals(2)
% 5.06/5.42 thf(fact_9030_cot__npi,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.06/5.42 = zero_zero_real ) ).
% 5.06/5.42
% 5.06/5.42 % cot_npi
% 5.06/5.42 thf(fact_9031_cot__periodic,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.06/5.42 = ( cot_real @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % cot_periodic
% 5.06/5.42 thf(fact_9032_sinh__le__cosh__real,axiom,
% 5.06/5.42 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % sinh_le_cosh_real
% 5.06/5.42 thf(fact_9033_semiring__norm_I26_J,axiom,
% 5.06/5.42 ( ( bitM @ one )
% 5.06/5.42 = one ) ).
% 5.06/5.42
% 5.06/5.42 % semiring_norm(26)
% 5.06/5.42 thf(fact_9034_OR__lower,axiom,
% 5.06/5.42 ! [X: int,Y: int] :
% 5.06/5.42 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.42 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.42 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % OR_lower
% 5.06/5.42 thf(fact_9035_or__greater__eq,axiom,
% 5.06/5.42 ! [L2: int,K: int] :
% 5.06/5.42 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.06/5.42 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_greater_eq
% 5.06/5.42 thf(fact_9036_cosh__real__nonneg,axiom,
% 5.06/5.42 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % cosh_real_nonneg
% 5.06/5.42 thf(fact_9037_cosh__real__nonneg__le__iff,axiom,
% 5.06/5.42 ! [X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.06/5.42 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cosh_real_nonneg_le_iff
% 5.06/5.42 thf(fact_9038_cosh__real__nonpos__le__iff,axiom,
% 5.06/5.42 ! [X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.42 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.06/5.42 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cosh_real_nonpos_le_iff
% 5.06/5.42 thf(fact_9039_cosh__real__ge__1,axiom,
% 5.06/5.42 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % cosh_real_ge_1
% 5.06/5.42 thf(fact_9040_semiring__norm_I27_J,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( bitM @ ( bit0 @ N2 ) )
% 5.06/5.42 = ( bit1 @ ( bitM @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % semiring_norm(27)
% 5.06/5.42 thf(fact_9041_semiring__norm_I28_J,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( bitM @ ( bit1 @ N2 ) )
% 5.06/5.42 = ( bit1 @ ( bit0 @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % semiring_norm(28)
% 5.06/5.42 thf(fact_9042_cosh__real__strict__mono,axiom,
% 5.06/5.42 ! [X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ X @ Y )
% 5.06/5.42 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cosh_real_strict_mono
% 5.06/5.42 thf(fact_9043_cosh__real__nonneg__less__iff,axiom,
% 5.06/5.42 ! [X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.42 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.06/5.42 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cosh_real_nonneg_less_iff
% 5.06/5.42 thf(fact_9044_cosh__real__nonpos__less__iff,axiom,
% 5.06/5.42 ! [X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.42 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.06/5.42 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.06/5.42 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cosh_real_nonpos_less_iff
% 5.06/5.42 thf(fact_9045_arcosh__cosh__real,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 5.06/5.42 = X ) ) ).
% 5.06/5.42
% 5.06/5.42 % arcosh_cosh_real
% 5.06/5.42 thf(fact_9046_eval__nat__numeral_I2_J,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.06/5.42 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % eval_nat_numeral(2)
% 5.06/5.42 thf(fact_9047_one__plus__BitM,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 5.06/5.42 = ( bit0 @ N2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % one_plus_BitM
% 5.06/5.42 thf(fact_9048_BitM__plus__one,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 5.06/5.42 = ( bit0 @ N2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % BitM_plus_one
% 5.06/5.42 thf(fact_9049_OR__upper,axiom,
% 5.06/5.42 ! [X: int,N2: nat,Y: int] :
% 5.06/5.42 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.42 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % OR_upper
% 5.06/5.42 thf(fact_9050_or__int__rec,axiom,
% 5.06/5.42 ( bit_se1409905431419307370or_int
% 5.06/5.42 = ( ^ [K3: int,L: int] :
% 5.06/5.42 ( plus_plus_int
% 5.06/5.42 @ ( zero_n2684676970156552555ol_int
% 5.06/5.42 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.06/5.42 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.06/5.42 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_int_rec
% 5.06/5.42 thf(fact_9051_cosh__ln__real,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 5.06/5.42 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cosh_ln_real
% 5.06/5.42 thf(fact_9052_cot__gt__zero,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.42 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cot_gt_zero
% 5.06/5.42 thf(fact_9053_tan__cot_H,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.06/5.42 = ( cot_real @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % tan_cot'
% 5.06/5.42 thf(fact_9054_or__minus__numerals_I5_J,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 5.06/5.42 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_minus_numerals(5)
% 5.06/5.42 thf(fact_9055_or__minus__numerals_I1_J,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.06/5.42 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_minus_numerals(1)
% 5.06/5.42 thf(fact_9056_i__even__power,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.42 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % i_even_power
% 5.06/5.42 thf(fact_9057_log__base__10__eq1,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.42 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_base_10_eq1
% 5.06/5.42 thf(fact_9058_complex__i__mult__minus,axiom,
% 5.06/5.42 ! [X: complex] :
% 5.06/5.42 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 5.06/5.42 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % complex_i_mult_minus
% 5.06/5.42 thf(fact_9059_divide__i,axiom,
% 5.06/5.42 ! [X: complex] :
% 5.06/5.42 ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 5.06/5.42 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % divide_i
% 5.06/5.42 thf(fact_9060_i__squared,axiom,
% 5.06/5.42 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.06/5.42 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.42
% 5.06/5.42 % i_squared
% 5.06/5.42 thf(fact_9061_log__le__cancel__iff,axiom,
% 5.06/5.42 ! [A: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 5.06/5.42 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_le_cancel_iff
% 5.06/5.42 thf(fact_9062_log__le__one__cancel__iff,axiom,
% 5.06/5.42 ! [A: real,X: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 5.06/5.42 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_le_one_cancel_iff
% 5.06/5.42 thf(fact_9063_one__le__log__cancel__iff,axiom,
% 5.06/5.42 ! [A: real,X: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 5.06/5.42 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % one_le_log_cancel_iff
% 5.06/5.42 thf(fact_9064_log__le__zero__cancel__iff,axiom,
% 5.06/5.42 ! [A: real,X: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.06/5.42 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_le_zero_cancel_iff
% 5.06/5.42 thf(fact_9065_zero__le__log__cancel__iff,axiom,
% 5.06/5.42 ! [A: real,X: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ A )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.06/5.42 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % zero_le_log_cancel_iff
% 5.06/5.42 thf(fact_9066_or__nat__numerals_I2_J,axiom,
% 5.06/5.42 ! [Y: num] :
% 5.06/5.42 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.06/5.42 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_nat_numerals(2)
% 5.06/5.42 thf(fact_9067_or__nat__numerals_I4_J,axiom,
% 5.06/5.42 ! [X: num] :
% 5.06/5.42 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.06/5.42 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_nat_numerals(4)
% 5.06/5.42 thf(fact_9068_divide__numeral__i,axiom,
% 5.06/5.42 ! [Z: complex,N2: num] :
% 5.06/5.42 ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N2 ) @ imaginary_unit ) )
% 5.06/5.42 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % divide_numeral_i
% 5.06/5.42 thf(fact_9069_or__nat__numerals_I3_J,axiom,
% 5.06/5.42 ! [X: num] :
% 5.06/5.42 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.06/5.42 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_nat_numerals(3)
% 5.06/5.42 thf(fact_9070_or__nat__numerals_I1_J,axiom,
% 5.06/5.42 ! [Y: num] :
% 5.06/5.42 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.06/5.42 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_nat_numerals(1)
% 5.06/5.42 thf(fact_9071_log__pow__cancel,axiom,
% 5.06/5.42 ! [A: real,B: nat] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ( A != one_one_real )
% 5.06/5.42 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.06/5.42 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_pow_cancel
% 5.06/5.42 thf(fact_9072_or__minus__numerals_I8_J,axiom,
% 5.06/5.42 ! [N2: num,M: num] :
% 5.06/5.42 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.06/5.42 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_minus_numerals(8)
% 5.06/5.42 thf(fact_9073_or__minus__numerals_I4_J,axiom,
% 5.06/5.42 ! [M: num,N2: num] :
% 5.06/5.42 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.06/5.42 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_minus_numerals(4)
% 5.06/5.42 thf(fact_9074_or__minus__numerals_I7_J,axiom,
% 5.06/5.42 ! [N2: num,M: num] :
% 5.06/5.42 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.06/5.42 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_minus_numerals(7)
% 5.06/5.42 thf(fact_9075_or__minus__numerals_I3_J,axiom,
% 5.06/5.42 ! [M: num,N2: num] :
% 5.06/5.42 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.06/5.42 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_minus_numerals(3)
% 5.06/5.42 thf(fact_9076_power2__i,axiom,
% 5.06/5.42 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.42 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.42
% 5.06/5.42 % power2_i
% 5.06/5.42 thf(fact_9077_or__not__num__neg_Osimps_I1_J,axiom,
% 5.06/5.42 ( ( bit_or_not_num_neg @ one @ one )
% 5.06/5.42 = one ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.simps(1)
% 5.06/5.42 thf(fact_9078_complex__i__not__numeral,axiom,
% 5.06/5.42 ! [W: num] :
% 5.06/5.42 ( imaginary_unit
% 5.06/5.42 != ( numera6690914467698888265omplex @ W ) ) ).
% 5.06/5.42
% 5.06/5.42 % complex_i_not_numeral
% 5.06/5.42 thf(fact_9079_or__not__num__neg_Osimps_I4_J,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ one )
% 5.06/5.42 = ( bit0 @ one ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.simps(4)
% 5.06/5.42 thf(fact_9080_or__not__num__neg_Osimps_I6_J,axiom,
% 5.06/5.42 ! [N2: num,M: num] :
% 5.06/5.42 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit1 @ M ) )
% 5.06/5.42 = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.simps(6)
% 5.06/5.42 thf(fact_9081_or__not__num__neg_Osimps_I7_J,axiom,
% 5.06/5.42 ! [N2: num] :
% 5.06/5.42 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ one )
% 5.06/5.42 = one ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.simps(7)
% 5.06/5.42 thf(fact_9082_or__not__num__neg_Osimps_I3_J,axiom,
% 5.06/5.42 ! [M: num] :
% 5.06/5.42 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.06/5.42 = ( bit1 @ M ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.simps(3)
% 5.06/5.42 thf(fact_9083_i__times__eq__iff,axiom,
% 5.06/5.42 ! [W: complex,Z: complex] :
% 5.06/5.42 ( ( ( times_times_complex @ imaginary_unit @ W )
% 5.06/5.42 = Z )
% 5.06/5.42 = ( W
% 5.06/5.42 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % i_times_eq_iff
% 5.06/5.42 thf(fact_9084_or__not__num__neg_Osimps_I5_J,axiom,
% 5.06/5.42 ! [N2: num,M: num] :
% 5.06/5.42 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit0 @ M ) )
% 5.06/5.42 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.simps(5)
% 5.06/5.42 thf(fact_9085_or__not__num__neg_Osimps_I9_J,axiom,
% 5.06/5.42 ! [N2: num,M: num] :
% 5.06/5.42 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit1 @ M ) )
% 5.06/5.42 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.simps(9)
% 5.06/5.42 thf(fact_9086_complex__i__not__neg__numeral,axiom,
% 5.06/5.42 ! [W: num] :
% 5.06/5.42 ( imaginary_unit
% 5.06/5.42 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % complex_i_not_neg_numeral
% 5.06/5.42 thf(fact_9087_or__not__num__neg_Osimps_I2_J,axiom,
% 5.06/5.42 ! [M: num] :
% 5.06/5.42 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.06/5.42 = ( bit1 @ M ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.simps(2)
% 5.06/5.42 thf(fact_9088_Complex__mult__i,axiom,
% 5.06/5.42 ! [A: real,B: real] :
% 5.06/5.42 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.06/5.42 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.06/5.42
% 5.06/5.42 % Complex_mult_i
% 5.06/5.42 thf(fact_9089_i__mult__Complex,axiom,
% 5.06/5.42 ! [A: real,B: real] :
% 5.06/5.42 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.06/5.42 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.06/5.42
% 5.06/5.42 % i_mult_Complex
% 5.06/5.42 thf(fact_9090_less__log__of__power,axiom,
% 5.06/5.42 ! [B: real,N2: nat,M: real] :
% 5.06/5.42 ( ( ord_less_real @ ( power_power_real @ B @ N2 ) @ M )
% 5.06/5.42 => ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % less_log_of_power
% 5.06/5.42 thf(fact_9091_log__of__power__eq,axiom,
% 5.06/5.42 ! [M: nat,B: real,N2: nat] :
% 5.06/5.42 ( ( ( semiri5074537144036343181t_real @ M )
% 5.06/5.42 = ( power_power_real @ B @ N2 ) )
% 5.06/5.42 => ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ( semiri5074537144036343181t_real @ N2 )
% 5.06/5.42 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_of_power_eq
% 5.06/5.42 thf(fact_9092_or__not__num__neg_Osimps_I8_J,axiom,
% 5.06/5.42 ! [N2: num,M: num] :
% 5.06/5.42 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit0 @ M ) )
% 5.06/5.42 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.simps(8)
% 5.06/5.42 thf(fact_9093_log__mult,axiom,
% 5.06/5.42 ! [A: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ( A != one_one_real )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.42 => ( ( log @ A @ ( times_times_real @ X @ Y ) )
% 5.06/5.42 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_mult
% 5.06/5.42 thf(fact_9094_log__divide,axiom,
% 5.06/5.42 ! [A: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ( A != one_one_real )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.06/5.42 => ( ( log @ A @ ( divide_divide_real @ X @ Y ) )
% 5.06/5.42 = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_divide
% 5.06/5.42 thf(fact_9095_le__log__of__power,axiom,
% 5.06/5.42 ! [B: real,N2: nat,M: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ ( power_power_real @ B @ N2 ) @ M )
% 5.06/5.42 => ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % le_log_of_power
% 5.06/5.42 thf(fact_9096_log__base__pow,axiom,
% 5.06/5.42 ! [A: real,N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ( log @ ( power_power_real @ A @ N2 ) @ X )
% 5.06/5.42 = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_base_pow
% 5.06/5.42 thf(fact_9097_log__nat__power,axiom,
% 5.06/5.42 ! [X: real,B: real,N2: nat] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( log @ B @ ( power_power_real @ X @ N2 ) )
% 5.06/5.42 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_nat_power
% 5.06/5.42 thf(fact_9098_or__not__num__neg_Oelims,axiom,
% 5.06/5.42 ! [X: num,Xa2: num,Y: num] :
% 5.06/5.42 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 5.06/5.42 = Y )
% 5.06/5.42 => ( ( ( X = one )
% 5.06/5.42 => ( ( Xa2 = one )
% 5.06/5.42 => ( Y != one ) ) )
% 5.06/5.42 => ( ( ( X = one )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit0 @ M2 ) )
% 5.06/5.42 => ( Y
% 5.06/5.42 != ( bit1 @ M2 ) ) ) )
% 5.06/5.42 => ( ( ( X = one )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit1 @ M2 ) )
% 5.06/5.42 => ( Y
% 5.06/5.42 != ( bit1 @ M2 ) ) ) )
% 5.06/5.42 => ( ( ? [N3: num] :
% 5.06/5.42 ( X
% 5.06/5.42 = ( bit0 @ N3 ) )
% 5.06/5.42 => ( ( Xa2 = one )
% 5.06/5.42 => ( Y
% 5.06/5.42 != ( bit0 @ one ) ) ) )
% 5.06/5.42 => ( ! [N3: num] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( bit0 @ N3 ) )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit0 @ M2 ) )
% 5.06/5.42 => ( Y
% 5.06/5.42 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M2 ) ) ) ) )
% 5.06/5.42 => ( ! [N3: num] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( bit0 @ N3 ) )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit1 @ M2 ) )
% 5.06/5.42 => ( Y
% 5.06/5.42 != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M2 ) ) ) ) )
% 5.06/5.42 => ( ( ? [N3: num] :
% 5.06/5.42 ( X
% 5.06/5.42 = ( bit1 @ N3 ) )
% 5.06/5.42 => ( ( Xa2 = one )
% 5.06/5.42 => ( Y != one ) ) )
% 5.06/5.42 => ( ! [N3: num] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( bit1 @ N3 ) )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit0 @ M2 ) )
% 5.06/5.42 => ( Y
% 5.06/5.42 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M2 ) ) ) ) )
% 5.06/5.42 => ~ ! [N3: num] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( bit1 @ N3 ) )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit1 @ M2 ) )
% 5.06/5.42 => ( Y
% 5.06/5.42 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.elims
% 5.06/5.42 thf(fact_9099_log2__of__power__eq,axiom,
% 5.06/5.42 ! [M: nat,N2: nat] :
% 5.06/5.42 ( ( M
% 5.06/5.42 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 => ( ( semiri5074537144036343181t_real @ N2 )
% 5.06/5.42 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log2_of_power_eq
% 5.06/5.42 thf(fact_9100_log__of__power__less,axiom,
% 5.06/5.42 ! [M: nat,B: real,N2: nat] :
% 5.06/5.42 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.06/5.42 => ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.42 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_of_power_less
% 5.06/5.42 thf(fact_9101_log__eq__div__ln__mult__log,axiom,
% 5.06/5.42 ! [A: real,B: real,X: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ( A != one_one_real )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.42 => ( ( B != one_one_real )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( log @ A @ X )
% 5.06/5.42 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_eq_div_ln_mult_log
% 5.06/5.42 thf(fact_9102_log__of__power__le,axiom,
% 5.06/5.42 ! [M: nat,B: real,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.06/5.42 => ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.42 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_of_power_le
% 5.06/5.42 thf(fact_9103_less__log2__of__power,axiom,
% 5.06/5.42 ! [N2: nat,M: nat] :
% 5.06/5.42 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 5.06/5.42 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % less_log2_of_power
% 5.06/5.42 thf(fact_9104_le__log2__of__power,axiom,
% 5.06/5.42 ! [N2: nat,M: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 5.06/5.42 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % le_log2_of_power
% 5.06/5.42 thf(fact_9105_Suc__0__or__eq,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.42 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Suc_0_or_eq
% 5.06/5.42 thf(fact_9106_or__Suc__0__eq,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.06/5.42 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_Suc_0_eq
% 5.06/5.42 thf(fact_9107_or__nat__rec,axiom,
% 5.06/5.42 ( bit_se1412395901928357646or_nat
% 5.06/5.42 = ( ^ [M6: nat,N: nat] :
% 5.06/5.42 ( plus_plus_nat
% 5.06/5.42 @ ( zero_n2687167440665602831ol_nat
% 5.06/5.42 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.06/5.42 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.06/5.42 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_nat_rec
% 5.06/5.42 thf(fact_9108_log2__of__power__less,axiom,
% 5.06/5.42 ! [M: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.42 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log2_of_power_less
% 5.06/5.42 thf(fact_9109_or__nat__unfold,axiom,
% 5.06/5.42 ( bit_se1412395901928357646or_nat
% 5.06/5.42 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_nat_unfold
% 5.06/5.42 thf(fact_9110_log2__of__power__le,axiom,
% 5.06/5.42 ! [M: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.42 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.42 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log2_of_power_le
% 5.06/5.42 thf(fact_9111_log__base__10__eq2,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.06/5.42 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_base_10_eq2
% 5.06/5.42 thf(fact_9112_Arg__minus__ii,axiom,
% 5.06/5.42 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.06/5.42 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Arg_minus_ii
% 5.06/5.42 thf(fact_9113_ceiling__log__nat__eq__powr__iff,axiom,
% 5.06/5.42 ! [B: nat,K: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.06/5.42 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.42 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.06/5.42 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) )
% 5.06/5.42 = ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.06/5.42 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ceiling_log_nat_eq_powr_iff
% 5.06/5.42 thf(fact_9114_Arg__ii,axiom,
% 5.06/5.42 ( ( arg @ imaginary_unit )
% 5.06/5.42 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Arg_ii
% 5.06/5.42 thf(fact_9115_ceiling__log2__div2,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.42 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.06/5.42 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ceiling_log2_div2
% 5.06/5.42 thf(fact_9116_ceiling__divide__eq__div__numeral,axiom,
% 5.06/5.42 ! [A: num,B: num] :
% 5.06/5.42 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.06/5.42 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ceiling_divide_eq_div_numeral
% 5.06/5.42 thf(fact_9117_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.06/5.42 ! [A: num,B: num] :
% 5.06/5.42 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.06/5.42 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ceiling_minus_divide_eq_div_numeral
% 5.06/5.42 thf(fact_9118_Arg__bounded,axiom,
% 5.06/5.42 ! [Z: complex] :
% 5.06/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.06/5.42 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.06/5.42
% 5.06/5.42 % Arg_bounded
% 5.06/5.42 thf(fact_9119_ceiling__log__nat__eq__if,axiom,
% 5.06/5.42 ! [B: nat,N2: nat,K: nat] :
% 5.06/5.42 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.06/5.42 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 5.06/5.42 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.06/5.42 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.06/5.42 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ceiling_log_nat_eq_if
% 5.06/5.42 thf(fact_9120_cis__minus__pi__half,axiom,
% 5.06/5.42 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.06/5.42 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.06/5.42
% 5.06/5.42 % cis_minus_pi_half
% 5.06/5.42 thf(fact_9121_ceiling__log__eq__powr__iff,axiom,
% 5.06/5.42 ! [X: real,B: real,K: nat] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 5.06/5.42 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.06/5.42 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 5.06/5.42 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ceiling_log_eq_powr_iff
% 5.06/5.42 thf(fact_9122_or__not__num__neg_Opelims,axiom,
% 5.06/5.42 ! [X: num,Xa2: num,Y: num] :
% 5.06/5.42 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 5.06/5.42 = Y )
% 5.06/5.42 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 5.06/5.42 => ( ( ( X = one )
% 5.06/5.42 => ( ( Xa2 = one )
% 5.06/5.42 => ( ( Y = one )
% 5.06/5.42 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.06/5.42 => ( ( ( X = one )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit0 @ M2 ) )
% 5.06/5.42 => ( ( Y
% 5.06/5.42 = ( bit1 @ M2 ) )
% 5.06/5.42 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M2 ) ) ) ) ) )
% 5.06/5.42 => ( ( ( X = one )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit1 @ M2 ) )
% 5.06/5.42 => ( ( Y
% 5.06/5.42 = ( bit1 @ M2 ) )
% 5.06/5.42 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M2 ) ) ) ) ) )
% 5.06/5.42 => ( ! [N3: num] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( bit0 @ N3 ) )
% 5.06/5.42 => ( ( Xa2 = one )
% 5.06/5.42 => ( ( Y
% 5.06/5.42 = ( bit0 @ one ) )
% 5.06/5.42 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 5.06/5.42 => ( ! [N3: num] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( bit0 @ N3 ) )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit0 @ M2 ) )
% 5.06/5.42 => ( ( Y
% 5.06/5.42 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M2 ) ) )
% 5.06/5.42 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M2 ) ) ) ) ) )
% 5.06/5.42 => ( ! [N3: num] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( bit0 @ N3 ) )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit1 @ M2 ) )
% 5.06/5.42 => ( ( Y
% 5.06/5.42 = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M2 ) ) )
% 5.06/5.42 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M2 ) ) ) ) ) )
% 5.06/5.42 => ( ! [N3: num] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( bit1 @ N3 ) )
% 5.06/5.42 => ( ( Xa2 = one )
% 5.06/5.42 => ( ( Y = one )
% 5.06/5.42 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 5.06/5.42 => ( ! [N3: num] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( bit1 @ N3 ) )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit0 @ M2 ) )
% 5.06/5.42 => ( ( Y
% 5.06/5.42 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M2 ) ) )
% 5.06/5.42 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M2 ) ) ) ) ) )
% 5.06/5.42 => ~ ! [N3: num] :
% 5.06/5.42 ( ( X
% 5.06/5.42 = ( bit1 @ N3 ) )
% 5.06/5.42 => ! [M2: num] :
% 5.06/5.42 ( ( Xa2
% 5.06/5.42 = ( bit1 @ M2 ) )
% 5.06/5.42 => ( ( Y
% 5.06/5.42 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M2 ) ) )
% 5.06/5.42 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % or_not_num_neg.pelims
% 5.06/5.42 thf(fact_9123_floor__log__nat__eq__powr__iff,axiom,
% 5.06/5.42 ! [B: nat,K: nat,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.06/5.42 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.06/5.42 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.06/5.42 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.06/5.42 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.06/5.42 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_log_nat_eq_powr_iff
% 5.06/5.42 thf(fact_9124_powr__nonneg__iff,axiom,
% 5.06/5.42 ! [A: real,X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 5.06/5.42 = ( A = zero_zero_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_nonneg_iff
% 5.06/5.42 thf(fact_9125_powr__one,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( powr_real @ X @ one_one_real )
% 5.06/5.42 = X ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_one
% 5.06/5.42 thf(fact_9126_powr__one__gt__zero__iff,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ( powr_real @ X @ one_one_real )
% 5.06/5.42 = X )
% 5.06/5.42 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_one_gt_zero_iff
% 5.06/5.42 thf(fact_9127_powr__le__cancel__iff,axiom,
% 5.06/5.42 ! [X: real,A: real,B: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.06/5.42 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_le_cancel_iff
% 5.06/5.42 thf(fact_9128_numeral__powr__numeral__real,axiom,
% 5.06/5.42 ! [M: num,N2: num] :
% 5.06/5.42 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.06/5.42 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % numeral_powr_numeral_real
% 5.06/5.42 thf(fact_9129_floor__divide__eq__div__numeral,axiom,
% 5.06/5.42 ! [A: num,B: num] :
% 5.06/5.42 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.06/5.42 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_divide_eq_div_numeral
% 5.06/5.42 thf(fact_9130_powr__numeral,axiom,
% 5.06/5.42 ! [X: real,N2: num] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( powr_real @ X @ ( numeral_numeral_real @ N2 ) )
% 5.06/5.42 = ( power_power_real @ X @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_numeral
% 5.06/5.42 thf(fact_9131_cis__pi__half,axiom,
% 5.06/5.42 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.42 = imaginary_unit ) ).
% 5.06/5.42
% 5.06/5.42 % cis_pi_half
% 5.06/5.42 thf(fact_9132_floor__one__divide__eq__div__numeral,axiom,
% 5.06/5.42 ! [B: num] :
% 5.06/5.42 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.06/5.42 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_one_divide_eq_div_numeral
% 5.06/5.42 thf(fact_9133_cis__2pi,axiom,
% 5.06/5.42 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.06/5.42 = one_one_complex ) ).
% 5.06/5.42
% 5.06/5.42 % cis_2pi
% 5.06/5.42 thf(fact_9134_floor__minus__divide__eq__div__numeral,axiom,
% 5.06/5.42 ! [A: num,B: num] :
% 5.06/5.42 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.06/5.42 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_minus_divide_eq_div_numeral
% 5.06/5.42 thf(fact_9135_square__powr__half,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.42 = ( abs_abs_real @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % square_powr_half
% 5.06/5.42 thf(fact_9136_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.06/5.42 ! [B: num] :
% 5.06/5.42 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.06/5.42 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_minus_one_divide_eq_div_numeral
% 5.06/5.42 thf(fact_9137_powr__powr,axiom,
% 5.06/5.42 ! [X: real,A: real,B: real] :
% 5.06/5.42 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 5.06/5.42 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_powr
% 5.06/5.42 thf(fact_9138_powr__ge__pzero,axiom,
% 5.06/5.42 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_ge_pzero
% 5.06/5.42 thf(fact_9139_powr__mono2,axiom,
% 5.06/5.42 ! [A: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.42 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_mono2
% 5.06/5.42 thf(fact_9140_powr__mono,axiom,
% 5.06/5.42 ! [A: real,B: real,X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.42 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.06/5.42 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_mono
% 5.06/5.42 thf(fact_9141_cis__mult,axiom,
% 5.06/5.42 ! [A: real,B: real] :
% 5.06/5.42 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.06/5.42 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cis_mult
% 5.06/5.42 thf(fact_9142_cis__divide,axiom,
% 5.06/5.42 ! [A: real,B: real] :
% 5.06/5.42 ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 5.06/5.42 = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cis_divide
% 5.06/5.42 thf(fact_9143_powr__less__mono2,axiom,
% 5.06/5.42 ! [A: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ X @ Y )
% 5.06/5.42 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_less_mono2
% 5.06/5.42 thf(fact_9144_powr__mono2_H,axiom,
% 5.06/5.42 ! [A: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.42 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_mono2'
% 5.06/5.42 thf(fact_9145_powr__le1,axiom,
% 5.06/5.42 ! [A: real,X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.42 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_le1
% 5.06/5.42 thf(fact_9146_powr__mono__both,axiom,
% 5.06/5.42 ! [A: real,B: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ( ord_less_eq_real @ A @ B )
% 5.06/5.42 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.42 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_mono_both
% 5.06/5.42 thf(fact_9147_ge__one__powr__ge__zero,axiom,
% 5.06/5.42 ! [X: real,A: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ge_one_powr_ge_zero
% 5.06/5.42 thf(fact_9148_powr__divide,axiom,
% 5.06/5.42 ! [X: real,Y: real,A: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.42 => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 5.06/5.42 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_divide
% 5.06/5.42 thf(fact_9149_powr__mult,axiom,
% 5.06/5.42 ! [X: real,Y: real,A: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.42 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 5.06/5.42 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_mult
% 5.06/5.42 thf(fact_9150_inverse__powr,axiom,
% 5.06/5.42 ! [Y: real,A: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.42 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 5.06/5.42 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % inverse_powr
% 5.06/5.42 thf(fact_9151_divide__powr__uminus,axiom,
% 5.06/5.42 ! [A: real,B: real,C: real] :
% 5.06/5.42 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.06/5.42 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % divide_powr_uminus
% 5.06/5.42 thf(fact_9152_ln__powr,axiom,
% 5.06/5.42 ! [X: real,Y: real] :
% 5.06/5.42 ( ( X != zero_zero_real )
% 5.06/5.42 => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 5.06/5.42 = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ln_powr
% 5.06/5.42 thf(fact_9153_log__powr,axiom,
% 5.06/5.42 ! [X: real,B: real,Y: real] :
% 5.06/5.42 ( ( X != zero_zero_real )
% 5.06/5.42 => ( ( log @ B @ ( powr_real @ X @ Y ) )
% 5.06/5.42 = ( times_times_real @ Y @ ( log @ B @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_powr
% 5.06/5.42 thf(fact_9154_floor__log__eq__powr__iff,axiom,
% 5.06/5.42 ! [X: real,B: real,K: int] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 5.06/5.42 = K )
% 5.06/5.42 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 5.06/5.42 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_log_eq_powr_iff
% 5.06/5.42 thf(fact_9155_powr__realpow,axiom,
% 5.06/5.42 ! [X: real,N2: nat] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.06/5.42 = ( power_power_real @ X @ N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_realpow
% 5.06/5.42 thf(fact_9156_floor__eq,axiom,
% 5.06/5.42 ! [N2: int,X: real] :
% 5.06/5.42 ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X )
% 5.06/5.42 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.06/5.42 => ( ( archim6058952711729229775r_real @ X )
% 5.06/5.42 = N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_eq
% 5.06/5.42 thf(fact_9157_real__of__int__floor__add__one__gt,axiom,
% 5.06/5.42 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_of_int_floor_add_one_gt
% 5.06/5.42 thf(fact_9158_real__of__int__floor__add__one__ge,axiom,
% 5.06/5.42 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_of_int_floor_add_one_ge
% 5.06/5.42 thf(fact_9159_real__of__int__floor__gt__diff__one,axiom,
% 5.06/5.42 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_of_int_floor_gt_diff_one
% 5.06/5.42 thf(fact_9160_real__of__int__floor__ge__diff__one,axiom,
% 5.06/5.42 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_of_int_floor_ge_diff_one
% 5.06/5.42 thf(fact_9161_DeMoivre,axiom,
% 5.06/5.42 ! [A: real,N2: nat] :
% 5.06/5.42 ( ( power_power_complex @ ( cis @ A ) @ N2 )
% 5.06/5.42 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % DeMoivre
% 5.06/5.42 thf(fact_9162_powr__mult__base,axiom,
% 5.06/5.42 ! [X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 5.06/5.42 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_mult_base
% 5.06/5.42 thf(fact_9163_le__log__iff,axiom,
% 5.06/5.42 ! [B: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X ) )
% 5.06/5.42 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % le_log_iff
% 5.06/5.42 thf(fact_9164_log__le__iff,axiom,
% 5.06/5.42 ! [B: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y )
% 5.06/5.42 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_le_iff
% 5.06/5.42 thf(fact_9165_le__powr__iff,axiom,
% 5.06/5.42 ! [B: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 5.06/5.42 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % le_powr_iff
% 5.06/5.42 thf(fact_9166_powr__le__iff,axiom,
% 5.06/5.42 ! [B: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ B )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 5.06/5.42 = ( ord_less_eq_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_le_iff
% 5.06/5.42 thf(fact_9167_floor__eq2,axiom,
% 5.06/5.42 ! [N2: int,X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N2 ) @ X )
% 5.06/5.42 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.06/5.42 => ( ( archim6058952711729229775r_real @ X )
% 5.06/5.42 = N2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_eq2
% 5.06/5.42 thf(fact_9168_floor__divide__real__eq__div,axiom,
% 5.06/5.42 ! [B: int,A: real] :
% 5.06/5.42 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.06/5.42 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.06/5.42 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_divide_real_eq_div
% 5.06/5.42 thf(fact_9169_ln__powr__bound,axiom,
% 5.06/5.42 ! [X: real,A: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ln_powr_bound
% 5.06/5.42 thf(fact_9170_ln__powr__bound2,axiom,
% 5.06/5.42 ! [X: real,A: real] :
% 5.06/5.42 ( ( ord_less_real @ one_one_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ln_powr_bound2
% 5.06/5.42 thf(fact_9171_log__add__eq__powr,axiom,
% 5.06/5.42 ! [B: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.42 => ( ( B != one_one_real )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y )
% 5.06/5.42 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_add_eq_powr
% 5.06/5.42 thf(fact_9172_add__log__eq__powr,axiom,
% 5.06/5.42 ! [B: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.42 => ( ( B != one_one_real )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( plus_plus_real @ Y @ ( log @ B @ X ) )
% 5.06/5.42 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % add_log_eq_powr
% 5.06/5.42 thf(fact_9173_minus__log__eq__powr,axiom,
% 5.06/5.42 ! [B: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.42 => ( ( B != one_one_real )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( minus_minus_real @ Y @ ( log @ B @ X ) )
% 5.06/5.42 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % minus_log_eq_powr
% 5.06/5.42 thf(fact_9174_log__minus__eq__powr,axiom,
% 5.06/5.42 ! [B: real,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.42 => ( ( B != one_one_real )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y )
% 5.06/5.42 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_minus_eq_powr
% 5.06/5.42 thf(fact_9175_powr__half__sqrt,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.42 = ( sqrt @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_half_sqrt
% 5.06/5.42 thf(fact_9176_powr__neg__numeral,axiom,
% 5.06/5.42 ! [X: real,N2: num] :
% 5.06/5.42 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.06/5.42 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % powr_neg_numeral
% 5.06/5.42 thf(fact_9177_floor__log2__div2,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.42 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.06/5.42 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_log2_div2
% 5.06/5.42 thf(fact_9178_floor__log__nat__eq__if,axiom,
% 5.06/5.42 ! [B: nat,N2: nat,K: nat] :
% 5.06/5.42 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.06/5.42 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 5.06/5.42 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.06/5.42 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.06/5.42 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_log_nat_eq_if
% 5.06/5.42 thf(fact_9179_bij__betw__roots__unity,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( bij_betw_nat_complex
% 5.06/5.42 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.06/5.42 @ ( set_ord_lessThan_nat @ N2 )
% 5.06/5.42 @ ( collect_complex
% 5.06/5.42 @ ^ [Z2: complex] :
% 5.06/5.42 ( ( power_power_complex @ Z2 @ N2 )
% 5.06/5.42 = one_one_complex ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % bij_betw_roots_unity
% 5.06/5.42 thf(fact_9180_summable__complex__of__real,axiom,
% 5.06/5.42 ! [F: nat > real] :
% 5.06/5.42 ( ( summable_complex
% 5.06/5.42 @ ^ [N: nat] : ( real_V4546457046886955230omplex @ ( F @ N ) ) )
% 5.06/5.42 = ( summable_real @ F ) ) ).
% 5.06/5.42
% 5.06/5.42 % summable_complex_of_real
% 5.06/5.42 thf(fact_9181_exp__pi__i_H,axiom,
% 5.06/5.42 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.06/5.42 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.42
% 5.06/5.42 % exp_pi_i'
% 5.06/5.42 thf(fact_9182_exp__pi__i,axiom,
% 5.06/5.42 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.06/5.42 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.06/5.42
% 5.06/5.42 % exp_pi_i
% 5.06/5.42 thf(fact_9183_exp__two__pi__i,axiom,
% 5.06/5.42 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.06/5.42 = one_one_complex ) ).
% 5.06/5.42
% 5.06/5.42 % exp_two_pi_i
% 5.06/5.42 thf(fact_9184_exp__two__pi__i_H,axiom,
% 5.06/5.42 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.06/5.42 = one_one_complex ) ).
% 5.06/5.42
% 5.06/5.42 % exp_two_pi_i'
% 5.06/5.42 thf(fact_9185_complex__exp__exists,axiom,
% 5.06/5.42 ! [Z: complex] :
% 5.06/5.42 ? [A3: complex,R3: real] :
% 5.06/5.42 ( Z
% 5.06/5.42 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( exp_complex @ A3 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % complex_exp_exists
% 5.06/5.42 thf(fact_9186_complex__of__real__mult__Complex,axiom,
% 5.06/5.42 ! [R2: real,X: real,Y: real] :
% 5.06/5.42 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y ) )
% 5.06/5.42 = ( complex2 @ ( times_times_real @ R2 @ X ) @ ( times_times_real @ R2 @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % complex_of_real_mult_Complex
% 5.06/5.42 thf(fact_9187_Complex__mult__complex__of__real,axiom,
% 5.06/5.42 ! [X: real,Y: real,R2: real] :
% 5.06/5.42 ( ( times_times_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.06/5.42 = ( complex2 @ ( times_times_real @ X @ R2 ) @ ( times_times_real @ Y @ R2 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Complex_mult_complex_of_real
% 5.06/5.42 thf(fact_9188_complex__of__real__add__Complex,axiom,
% 5.06/5.42 ! [R2: real,X: real,Y: real] :
% 5.06/5.42 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y ) )
% 5.06/5.42 = ( complex2 @ ( plus_plus_real @ R2 @ X ) @ Y ) ) ).
% 5.06/5.42
% 5.06/5.42 % complex_of_real_add_Complex
% 5.06/5.42 thf(fact_9189_Complex__add__complex__of__real,axiom,
% 5.06/5.42 ! [X: real,Y: real,R2: real] :
% 5.06/5.42 ( ( plus_plus_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.06/5.42 = ( complex2 @ ( plus_plus_real @ X @ R2 ) @ Y ) ) ).
% 5.06/5.42
% 5.06/5.42 % Complex_add_complex_of_real
% 5.06/5.42 thf(fact_9190_cis__conv__exp,axiom,
% 5.06/5.42 ( cis
% 5.06/5.42 = ( ^ [B4: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B4 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cis_conv_exp
% 5.06/5.42 thf(fact_9191_i__complex__of__real,axiom,
% 5.06/5.42 ! [R2: real] :
% 5.06/5.42 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.06/5.42 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % i_complex_of_real
% 5.06/5.42 thf(fact_9192_complex__of__real__i,axiom,
% 5.06/5.42 ! [R2: real] :
% 5.06/5.42 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 5.06/5.42 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % complex_of_real_i
% 5.06/5.42 thf(fact_9193_Complex__eq,axiom,
% 5.06/5.42 ( complex2
% 5.06/5.42 = ( ^ [A4: real,B4: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A4 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B4 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Complex_eq
% 5.06/5.42 thf(fact_9194_complex__split__polar,axiom,
% 5.06/5.42 ! [Z: complex] :
% 5.06/5.42 ? [R3: real,A3: real] :
% 5.06/5.42 ( Z
% 5.06/5.42 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A3 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A3 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % complex_split_polar
% 5.06/5.42 thf(fact_9195_cmod__unit__one,axiom,
% 5.06/5.42 ! [A: real] :
% 5.06/5.42 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.06/5.42 = one_one_real ) ).
% 5.06/5.42
% 5.06/5.42 % cmod_unit_one
% 5.06/5.42 thf(fact_9196_cmod__complex__polar,axiom,
% 5.06/5.42 ! [R2: real,A: real] :
% 5.06/5.42 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 5.06/5.42 = ( abs_abs_real @ R2 ) ) ).
% 5.06/5.42
% 5.06/5.42 % cmod_complex_polar
% 5.06/5.42 thf(fact_9197_csqrt__ii,axiom,
% 5.06/5.42 ( ( csqrt @ imaginary_unit )
% 5.06/5.42 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % csqrt_ii
% 5.06/5.42 thf(fact_9198_int__ge__less__than2__def,axiom,
% 5.06/5.42 ( int_ge_less_than2
% 5.06/5.42 = ( ^ [D2: int] :
% 5.06/5.42 ( collec213857154873943460nt_int
% 5.06/5.42 @ ( produc4947309494688390418_int_o
% 5.06/5.42 @ ^ [Z6: int,Z2: int] :
% 5.06/5.42 ( ( ord_less_eq_int @ D2 @ Z2 )
% 5.06/5.42 & ( ord_less_int @ Z6 @ Z2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % int_ge_less_than2_def
% 5.06/5.42 thf(fact_9199_int__ge__less__than__def,axiom,
% 5.06/5.42 ( int_ge_less_than
% 5.06/5.42 = ( ^ [D2: int] :
% 5.06/5.42 ( collec213857154873943460nt_int
% 5.06/5.42 @ ( produc4947309494688390418_int_o
% 5.06/5.42 @ ^ [Z6: int,Z2: int] :
% 5.06/5.42 ( ( ord_less_eq_int @ D2 @ Z6 )
% 5.06/5.42 & ( ord_less_int @ Z6 @ Z2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % int_ge_less_than_def
% 5.06/5.42 thf(fact_9200_upto_Opinduct,axiom,
% 5.06/5.42 ! [A0: int,A12: int,P: int > int > $o] :
% 5.06/5.42 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.06/5.42 => ( ! [I3: int,J2: int] :
% 5.06/5.42 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 5.06/5.42 => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 5.06/5.42 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 5.06/5.42 => ( P @ I3 @ J2 ) ) )
% 5.06/5.42 => ( P @ A0 @ A12 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % upto.pinduct
% 5.06/5.42 thf(fact_9201_power2__csqrt,axiom,
% 5.06/5.42 ! [Z: complex] :
% 5.06/5.42 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.42 = Z ) ).
% 5.06/5.42
% 5.06/5.42 % power2_csqrt
% 5.06/5.42 thf(fact_9202_of__real__sqrt,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 5.06/5.42 = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % of_real_sqrt
% 5.06/5.42 thf(fact_9203_bij__betw__nth__root__unity,axiom,
% 5.06/5.42 ! [C: complex,N2: nat] :
% 5.06/5.42 ( ( C != zero_zero_complex )
% 5.06/5.42 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N2 @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 5.06/5.42 @ ( collect_complex
% 5.06/5.42 @ ^ [Z2: complex] :
% 5.06/5.42 ( ( power_power_complex @ Z2 @ N2 )
% 5.06/5.42 = one_one_complex ) )
% 5.06/5.42 @ ( collect_complex
% 5.06/5.42 @ ^ [Z2: complex] :
% 5.06/5.42 ( ( power_power_complex @ Z2 @ N2 )
% 5.06/5.42 = C ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % bij_betw_nth_root_unity
% 5.06/5.42 thf(fact_9204_arctan__def,axiom,
% 5.06/5.42 ( arctan
% 5.06/5.42 = ( ^ [Y2: real] :
% 5.06/5.42 ( the_real
% 5.06/5.42 @ ^ [X2: real] :
% 5.06/5.42 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.06/5.42 & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.42 & ( ( tan_real @ X2 )
% 5.06/5.42 = Y2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % arctan_def
% 5.06/5.42 thf(fact_9205_arcsin__def,axiom,
% 5.06/5.42 ( arcsin
% 5.06/5.42 = ( ^ [Y2: real] :
% 5.06/5.42 ( the_real
% 5.06/5.42 @ ^ [X2: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.06/5.42 & ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.42 & ( ( sin_real @ X2 )
% 5.06/5.42 = Y2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % arcsin_def
% 5.06/5.42 thf(fact_9206_modulo__int__unfold,axiom,
% 5.06/5.42 ! [L2: int,K: int,N2: nat,M: nat] :
% 5.06/5.42 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.06/5.42 = zero_zero_int )
% 5.06/5.42 | ( ( sgn_sgn_int @ K )
% 5.06/5.42 = zero_zero_int )
% 5.06/5.42 | ( N2 = zero_zero_nat ) )
% 5.06/5.42 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.06/5.42 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.06/5.42 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.06/5.42 = zero_zero_int )
% 5.06/5.42 | ( ( sgn_sgn_int @ K )
% 5.06/5.42 = zero_zero_int )
% 5.06/5.42 | ( N2 = zero_zero_nat ) )
% 5.06/5.42 => ( ( ( ( sgn_sgn_int @ K )
% 5.06/5.42 = ( sgn_sgn_int @ L2 ) )
% 5.06/5.42 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.06/5.42 = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) )
% 5.06/5.42 & ( ( ( sgn_sgn_int @ K )
% 5.06/5.42 != ( sgn_sgn_int @ L2 ) )
% 5.06/5.42 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.06/5.42 = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.06/5.42 @ ( minus_minus_int
% 5.06/5.42 @ ( semiri1314217659103216013at_int
% 5.06/5.42 @ ( times_times_nat @ N2
% 5.06/5.42 @ ( zero_n2687167440665602831ol_nat
% 5.06/5.42 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) )
% 5.06/5.42 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % modulo_int_unfold
% 5.06/5.42 thf(fact_9207_real__root__zero,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( root @ N2 @ zero_zero_real )
% 5.06/5.42 = zero_zero_real ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_zero
% 5.06/5.42 thf(fact_9208_real__root__Suc__0,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 5.06/5.42 = X ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_Suc_0
% 5.06/5.42 thf(fact_9209_real__root__eq__iff,axiom,
% 5.06/5.42 ! [N2: nat,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ( root @ N2 @ X )
% 5.06/5.42 = ( root @ N2 @ Y ) )
% 5.06/5.42 = ( X = Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_eq_iff
% 5.06/5.42 thf(fact_9210_root__0,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( root @ zero_zero_nat @ X )
% 5.06/5.42 = zero_zero_real ) ).
% 5.06/5.42
% 5.06/5.42 % root_0
% 5.06/5.42 thf(fact_9211_real__root__eq__0__iff,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ( root @ N2 @ X )
% 5.06/5.42 = zero_zero_real )
% 5.06/5.42 = ( X = zero_zero_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_eq_0_iff
% 5.06/5.42 thf(fact_9212_real__root__less__iff,axiom,
% 5.06/5.42 ! [N2: nat,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) )
% 5.06/5.42 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_less_iff
% 5.06/5.42 thf(fact_9213_real__root__le__iff,axiom,
% 5.06/5.42 ! [N2: nat,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) )
% 5.06/5.42 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_le_iff
% 5.06/5.42 thf(fact_9214_real__root__eq__1__iff,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ( root @ N2 @ X )
% 5.06/5.42 = one_one_real )
% 5.06/5.42 = ( X = one_one_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_eq_1_iff
% 5.06/5.42 thf(fact_9215_real__root__one,axiom,
% 5.06/5.42 ! [N2: nat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( root @ N2 @ one_one_real )
% 5.06/5.42 = one_one_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_one
% 5.06/5.42 thf(fact_9216_sgn__mult__dvd__iff,axiom,
% 5.06/5.42 ! [R2: int,L2: int,K: int] :
% 5.06/5.42 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L2 ) @ K )
% 5.06/5.42 = ( ( dvd_dvd_int @ L2 @ K )
% 5.06/5.42 & ( ( R2 = zero_zero_int )
% 5.06/5.42 => ( K = zero_zero_int ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sgn_mult_dvd_iff
% 5.06/5.42 thf(fact_9217_mult__sgn__dvd__iff,axiom,
% 5.06/5.42 ! [L2: int,R2: int,K: int] :
% 5.06/5.42 ( ( dvd_dvd_int @ ( times_times_int @ L2 @ ( sgn_sgn_int @ R2 ) ) @ K )
% 5.06/5.42 = ( ( dvd_dvd_int @ L2 @ K )
% 5.06/5.42 & ( ( R2 = zero_zero_int )
% 5.06/5.42 => ( K = zero_zero_int ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % mult_sgn_dvd_iff
% 5.06/5.42 thf(fact_9218_dvd__sgn__mult__iff,axiom,
% 5.06/5.42 ! [L2: int,R2: int,K: int] :
% 5.06/5.42 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 5.06/5.42 = ( ( dvd_dvd_int @ L2 @ K )
% 5.06/5.42 | ( R2 = zero_zero_int ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % dvd_sgn_mult_iff
% 5.06/5.42 thf(fact_9219_dvd__mult__sgn__iff,axiom,
% 5.06/5.42 ! [L2: int,K: int,R2: int] :
% 5.06/5.42 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 5.06/5.42 = ( ( dvd_dvd_int @ L2 @ K )
% 5.06/5.42 | ( R2 = zero_zero_int ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % dvd_mult_sgn_iff
% 5.06/5.42 thf(fact_9220_real__root__lt__0__iff,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ ( root @ N2 @ X ) @ zero_zero_real )
% 5.06/5.42 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_lt_0_iff
% 5.06/5.42 thf(fact_9221_real__root__gt__0__iff,axiom,
% 5.06/5.42 ! [N2: nat,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 5.06/5.42 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_gt_0_iff
% 5.06/5.42 thf(fact_9222_real__root__le__0__iff,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ zero_zero_real )
% 5.06/5.42 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_le_0_iff
% 5.06/5.42 thf(fact_9223_real__root__ge__0__iff,axiom,
% 5.06/5.42 ! [N2: nat,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 5.06/5.42 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_ge_0_iff
% 5.06/5.42 thf(fact_9224_real__root__lt__1__iff,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ ( root @ N2 @ X ) @ one_one_real )
% 5.06/5.42 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_lt_1_iff
% 5.06/5.42 thf(fact_9225_real__root__gt__1__iff,axiom,
% 5.06/5.42 ! [N2: nat,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ one_one_real @ ( root @ N2 @ Y ) )
% 5.06/5.42 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_gt_1_iff
% 5.06/5.42 thf(fact_9226_real__root__le__1__iff,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_real @ ( root @ N2 @ X ) @ one_one_real )
% 5.06/5.42 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_le_1_iff
% 5.06/5.42 thf(fact_9227_real__root__ge__1__iff,axiom,
% 5.06/5.42 ! [N2: nat,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N2 @ Y ) )
% 5.06/5.42 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_ge_1_iff
% 5.06/5.42 thf(fact_9228_real__root__pow__pos2,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 5.06/5.42 = X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_pow_pos2
% 5.06/5.42 thf(fact_9229_real__root__mult__exp,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,X: real] :
% 5.06/5.42 ( ( root @ ( times_times_nat @ M @ N2 ) @ X )
% 5.06/5.42 = ( root @ M @ ( root @ N2 @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_mult_exp
% 5.06/5.42 thf(fact_9230_real__root__mult,axiom,
% 5.06/5.42 ! [N2: nat,X: real,Y: real] :
% 5.06/5.42 ( ( root @ N2 @ ( times_times_real @ X @ Y ) )
% 5.06/5.42 = ( times_times_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_mult
% 5.06/5.42 thf(fact_9231_real__root__minus,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( root @ N2 @ ( uminus_uminus_real @ X ) )
% 5.06/5.42 = ( uminus_uminus_real @ ( root @ N2 @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_minus
% 5.06/5.42 thf(fact_9232_real__root__commute,axiom,
% 5.06/5.42 ! [M: nat,N2: nat,X: real] :
% 5.06/5.42 ( ( root @ M @ ( root @ N2 @ X ) )
% 5.06/5.42 = ( root @ N2 @ ( root @ M @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_commute
% 5.06/5.42 thf(fact_9233_real__root__divide,axiom,
% 5.06/5.42 ! [N2: nat,X: real,Y: real] :
% 5.06/5.42 ( ( root @ N2 @ ( divide_divide_real @ X @ Y ) )
% 5.06/5.42 = ( divide_divide_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_divide
% 5.06/5.42 thf(fact_9234_real__root__inverse,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( root @ N2 @ ( inverse_inverse_real @ X ) )
% 5.06/5.42 = ( inverse_inverse_real @ ( root @ N2 @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_inverse
% 5.06/5.42 thf(fact_9235_real__root__pos__pos__le,axiom,
% 5.06/5.42 ! [X: real,N2: nat] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_pos_pos_le
% 5.06/5.42 thf(fact_9236_int__sgnE,axiom,
% 5.06/5.42 ! [K: int] :
% 5.06/5.42 ~ ! [N3: nat,L4: int] :
% 5.06/5.42 ( K
% 5.06/5.42 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % int_sgnE
% 5.06/5.42 thf(fact_9237_real__root__less__mono,axiom,
% 5.06/5.42 ! [N2: nat,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ X @ Y )
% 5.06/5.42 => ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_less_mono
% 5.06/5.42 thf(fact_9238_real__root__le__mono,axiom,
% 5.06/5.42 ! [N2: nat,X: real,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_real @ X @ Y )
% 5.06/5.42 => ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N2 @ Y ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_le_mono
% 5.06/5.42 thf(fact_9239_ln__real__def,axiom,
% 5.06/5.42 ( ln_ln_real
% 5.06/5.42 = ( ^ [X2: real] :
% 5.06/5.42 ( the_real
% 5.06/5.42 @ ^ [U2: real] :
% 5.06/5.42 ( ( exp_real @ U2 )
% 5.06/5.42 = X2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ln_real_def
% 5.06/5.42 thf(fact_9240_real__root__power,axiom,
% 5.06/5.42 ! [N2: nat,X: real,K: nat] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( root @ N2 @ ( power_power_real @ X @ K ) )
% 5.06/5.42 = ( power_power_real @ ( root @ N2 @ X ) @ K ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_power
% 5.06/5.42 thf(fact_9241_real__root__abs,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( root @ N2 @ ( abs_abs_real @ X ) )
% 5.06/5.42 = ( abs_abs_real @ ( root @ N2 @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_abs
% 5.06/5.42 thf(fact_9242_sgn__mod,axiom,
% 5.06/5.42 ! [L2: int,K: int] :
% 5.06/5.42 ( ( L2 != zero_zero_int )
% 5.06/5.42 => ( ~ ( dvd_dvd_int @ L2 @ K )
% 5.06/5.42 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.06/5.42 = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sgn_mod
% 5.06/5.42 thf(fact_9243_ln__neg__is__const,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.42 => ( ( ln_ln_real @ X )
% 5.06/5.42 = ( the_real
% 5.06/5.42 @ ^ [X2: real] : $false ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ln_neg_is_const
% 5.06/5.42 thf(fact_9244_real__root__gt__zero,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ord_less_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_gt_zero
% 5.06/5.42 thf(fact_9245_real__root__strict__decreasing,axiom,
% 5.06/5.42 ! [N2: nat,N4: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_nat @ N2 @ N4 )
% 5.06/5.42 => ( ( ord_less_real @ one_one_real @ X )
% 5.06/5.42 => ( ord_less_real @ ( root @ N4 @ X ) @ ( root @ N2 @ X ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_strict_decreasing
% 5.06/5.42 thf(fact_9246_sqrt__def,axiom,
% 5.06/5.42 ( sqrt
% 5.06/5.42 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sqrt_def
% 5.06/5.42 thf(fact_9247_root__abs__power,axiom,
% 5.06/5.42 ! [N2: nat,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( abs_abs_real @ ( root @ N2 @ ( power_power_real @ Y @ N2 ) ) )
% 5.06/5.42 = ( abs_abs_real @ Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % root_abs_power
% 5.06/5.42 thf(fact_9248_div__sgn__abs__cancel,axiom,
% 5.06/5.42 ! [V: int,K: int,L2: int] :
% 5.06/5.42 ( ( V != zero_zero_int )
% 5.06/5.42 => ( ( 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 ) ) )
% 5.06/5.42 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % div_sgn_abs_cancel
% 5.06/5.42 thf(fact_9249_div__dvd__sgn__abs,axiom,
% 5.06/5.42 ! [L2: int,K: int] :
% 5.06/5.42 ( ( dvd_dvd_int @ L2 @ K )
% 5.06/5.42 => ( ( divide_divide_int @ K @ L2 )
% 5.06/5.42 = ( 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 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % div_dvd_sgn_abs
% 5.06/5.42 thf(fact_9250_real__root__pos__pos,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_pos_pos
% 5.06/5.42 thf(fact_9251_real__root__strict__increasing,axiom,
% 5.06/5.42 ! [N2: nat,N4: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_nat @ N2 @ N4 )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_real @ X @ one_one_real )
% 5.06/5.42 => ( ord_less_real @ ( root @ N2 @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_strict_increasing
% 5.06/5.42 thf(fact_9252_real__root__decreasing,axiom,
% 5.06/5.42 ! [N2: nat,N4: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.06/5.42 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.06/5.42 => ( ord_less_eq_real @ ( root @ N4 @ X ) @ ( root @ N2 @ X ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_decreasing
% 5.06/5.42 thf(fact_9253_real__root__pow__pos,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 5.06/5.42 = X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_pow_pos
% 5.06/5.42 thf(fact_9254_odd__real__root__power__cancel,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.42 => ( ( root @ N2 @ ( power_power_real @ X @ N2 ) )
% 5.06/5.42 = X ) ) ).
% 5.06/5.42
% 5.06/5.42 % odd_real_root_power_cancel
% 5.06/5.42 thf(fact_9255_odd__real__root__unique,axiom,
% 5.06/5.42 ! [N2: nat,Y: real,X: real] :
% 5.06/5.42 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.42 => ( ( ( power_power_real @ Y @ N2 )
% 5.06/5.42 = X )
% 5.06/5.42 => ( ( root @ N2 @ X )
% 5.06/5.42 = Y ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % odd_real_root_unique
% 5.06/5.42 thf(fact_9256_odd__real__root__pow,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.42 => ( ( power_power_real @ ( root @ N2 @ X ) @ N2 )
% 5.06/5.42 = X ) ) ).
% 5.06/5.42
% 5.06/5.42 % odd_real_root_pow
% 5.06/5.42 thf(fact_9257_real__root__pos__unique,axiom,
% 5.06/5.42 ! [N2: nat,Y: real,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.06/5.42 => ( ( ( power_power_real @ Y @ N2 )
% 5.06/5.42 = X )
% 5.06/5.42 => ( ( root @ N2 @ X )
% 5.06/5.42 = Y ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_pos_unique
% 5.06/5.42 thf(fact_9258_real__root__power__cancel,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( root @ N2 @ ( power_power_real @ X @ N2 ) )
% 5.06/5.42 = X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_power_cancel
% 5.06/5.42 thf(fact_9259_real__root__increasing,axiom,
% 5.06/5.42 ! [N2: nat,N4: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.06/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.42 => ( ord_less_eq_real @ ( root @ N2 @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % real_root_increasing
% 5.06/5.42 thf(fact_9260_arccos__def,axiom,
% 5.06/5.42 ( arccos
% 5.06/5.42 = ( ^ [Y2: real] :
% 5.06/5.42 ( the_real
% 5.06/5.42 @ ^ [X2: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.06/5.42 & ( ord_less_eq_real @ X2 @ pi )
% 5.06/5.42 & ( ( cos_real @ X2 )
% 5.06/5.42 = Y2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % arccos_def
% 5.06/5.42 thf(fact_9261_eucl__rel__int__remainderI,axiom,
% 5.06/5.42 ! [R2: int,L2: int,K: int,Q2: int] :
% 5.06/5.42 ( ( ( sgn_sgn_int @ R2 )
% 5.06/5.42 = ( sgn_sgn_int @ L2 ) )
% 5.06/5.42 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L2 ) )
% 5.06/5.42 => ( ( K
% 5.06/5.42 = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R2 ) )
% 5.06/5.42 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % eucl_rel_int_remainderI
% 5.06/5.42 thf(fact_9262_ln__root,axiom,
% 5.06/5.42 ! [N2: nat,B: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.42 => ( ( ln_ln_real @ ( root @ N2 @ B ) )
% 5.06/5.42 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % ln_root
% 5.06/5.42 thf(fact_9263_log__root,axiom,
% 5.06/5.42 ! [N2: nat,A: real,B: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.06/5.42 => ( ( log @ B @ ( root @ N2 @ A ) )
% 5.06/5.42 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_root
% 5.06/5.42 thf(fact_9264_log__base__root,axiom,
% 5.06/5.42 ! [N2: nat,B: real,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.06/5.42 => ( ( log @ ( root @ N2 @ B ) @ X )
% 5.06/5.42 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % log_base_root
% 5.06/5.42 thf(fact_9265_eucl__rel__int_Ocases,axiom,
% 5.06/5.42 ! [A12: int,A23: int,A32: product_prod_int_int] :
% 5.06/5.42 ( ( eucl_rel_int @ A12 @ A23 @ A32 )
% 5.06/5.42 => ( ( ( A23 = zero_zero_int )
% 5.06/5.42 => ( A32
% 5.06/5.42 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.06/5.42 => ( ! [Q3: int] :
% 5.06/5.42 ( ( A32
% 5.06/5.42 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.06/5.42 => ( ( A23 != zero_zero_int )
% 5.06/5.42 => ( A12
% 5.06/5.42 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 5.06/5.42 => ~ ! [R3: int,Q3: int] :
% 5.06/5.42 ( ( A32
% 5.06/5.42 = ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.06/5.42 => ( ( ( sgn_sgn_int @ R3 )
% 5.06/5.42 = ( sgn_sgn_int @ A23 ) )
% 5.06/5.42 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A23 ) )
% 5.06/5.42 => ( A12
% 5.06/5.42 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % eucl_rel_int.cases
% 5.06/5.42 thf(fact_9266_eucl__rel__int_Osimps,axiom,
% 5.06/5.42 ( eucl_rel_int
% 5.06/5.42 = ( ^ [A1: int,A22: int,A33: product_prod_int_int] :
% 5.06/5.42 ( ? [K3: int] :
% 5.06/5.42 ( ( A1 = K3 )
% 5.06/5.42 & ( A22 = zero_zero_int )
% 5.06/5.42 & ( A33
% 5.06/5.42 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.06/5.42 | ? [L: int,K3: int,Q4: int] :
% 5.06/5.42 ( ( A1 = K3 )
% 5.06/5.42 & ( A22 = L )
% 5.06/5.42 & ( A33
% 5.06/5.42 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.06/5.42 & ( L != zero_zero_int )
% 5.06/5.42 & ( K3
% 5.06/5.42 = ( times_times_int @ Q4 @ L ) ) )
% 5.06/5.42 | ? [R5: int,L: int,K3: int,Q4: int] :
% 5.06/5.42 ( ( A1 = K3 )
% 5.06/5.42 & ( A22 = L )
% 5.06/5.42 & ( A33
% 5.06/5.42 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.06/5.42 & ( ( sgn_sgn_int @ R5 )
% 5.06/5.42 = ( sgn_sgn_int @ L ) )
% 5.06/5.42 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 5.06/5.42 & ( K3
% 5.06/5.42 = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R5 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % eucl_rel_int.simps
% 5.06/5.42 thf(fact_9267_div__noneq__sgn__abs,axiom,
% 5.06/5.42 ! [L2: int,K: int] :
% 5.06/5.42 ( ( L2 != zero_zero_int )
% 5.06/5.42 => ( ( ( sgn_sgn_int @ K )
% 5.06/5.42 != ( sgn_sgn_int @ L2 ) )
% 5.06/5.42 => ( ( divide_divide_int @ K @ L2 )
% 5.06/5.42 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) )
% 5.06/5.42 @ ( zero_n2684676970156552555ol_int
% 5.06/5.42 @ ~ ( dvd_dvd_int @ L2 @ K ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % div_noneq_sgn_abs
% 5.06/5.42 thf(fact_9268_root__powr__inverse,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.42 => ( ( root @ N2 @ X )
% 5.06/5.42 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % root_powr_inverse
% 5.06/5.42 thf(fact_9269_pi__half,axiom,
% 5.06/5.42 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.42 = ( the_real
% 5.06/5.42 @ ^ [X2: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.06/5.42 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.42 & ( ( cos_real @ X2 )
% 5.06/5.42 = zero_zero_real ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pi_half
% 5.06/5.42 thf(fact_9270_pi__def,axiom,
% 5.06/5.42 ( pi
% 5.06/5.42 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.06/5.42 @ ( the_real
% 5.06/5.42 @ ^ [X2: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.06/5.42 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.06/5.42 & ( ( cos_real @ X2 )
% 5.06/5.42 = zero_zero_real ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % pi_def
% 5.06/5.42 thf(fact_9271_divide__int__unfold,axiom,
% 5.06/5.42 ! [L2: int,K: int,N2: nat,M: nat] :
% 5.06/5.42 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.06/5.42 = zero_zero_int )
% 5.06/5.42 | ( ( sgn_sgn_int @ K )
% 5.06/5.42 = zero_zero_int )
% 5.06/5.42 | ( N2 = zero_zero_nat ) )
% 5.06/5.42 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.06/5.42 = zero_zero_int ) )
% 5.06/5.42 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.06/5.42 = zero_zero_int )
% 5.06/5.42 | ( ( sgn_sgn_int @ K )
% 5.06/5.42 = zero_zero_int )
% 5.06/5.42 | ( N2 = zero_zero_nat ) )
% 5.06/5.42 => ( ( ( ( sgn_sgn_int @ K )
% 5.06/5.42 = ( sgn_sgn_int @ L2 ) )
% 5.06/5.42 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.06/5.42 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) )
% 5.06/5.42 & ( ( ( sgn_sgn_int @ K )
% 5.06/5.42 != ( sgn_sgn_int @ L2 ) )
% 5.06/5.42 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.06/5.42 = ( uminus_uminus_int
% 5.06/5.42 @ ( semiri1314217659103216013at_int
% 5.06/5.42 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N2 )
% 5.06/5.42 @ ( zero_n2687167440665602831ol_nat
% 5.06/5.42 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % divide_int_unfold
% 5.06/5.42 thf(fact_9272_zero__le__sgn__iff,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 5.06/5.42 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.06/5.42
% 5.06/5.42 % zero_le_sgn_iff
% 5.06/5.42 thf(fact_9273_sgn__le__0__iff,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 5.06/5.42 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.06/5.42
% 5.06/5.42 % sgn_le_0_iff
% 5.06/5.42 thf(fact_9274_sgn__root,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( sgn_sgn_real @ ( root @ N2 @ X ) )
% 5.06/5.42 = ( sgn_sgn_real @ X ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sgn_root
% 5.06/5.42 thf(fact_9275_sgn__real__def,axiom,
% 5.06/5.42 ( sgn_sgn_real
% 5.06/5.42 = ( ^ [A4: real] : ( if_real @ ( A4 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A4 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sgn_real_def
% 5.06/5.42 thf(fact_9276_sgn__power__injE,axiom,
% 5.06/5.42 ! [A: real,N2: nat,X: real,B: real] :
% 5.06/5.42 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 5.06/5.42 = X )
% 5.06/5.42 => ( ( X
% 5.06/5.42 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N2 ) ) )
% 5.06/5.42 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( A = B ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % sgn_power_injE
% 5.06/5.42 thf(fact_9277_sgn__power__root,axiom,
% 5.06/5.42 ! [N2: nat,X: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N2 @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N2 @ X ) ) @ N2 ) )
% 5.06/5.42 = X ) ) ).
% 5.06/5.42
% 5.06/5.42 % sgn_power_root
% 5.06/5.42 thf(fact_9278_root__sgn__power,axiom,
% 5.06/5.42 ! [N2: nat,Y: real] :
% 5.06/5.42 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ( ( root @ N2 @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) ) )
% 5.06/5.42 = Y ) ) ).
% 5.06/5.42
% 5.06/5.42 % root_sgn_power
% 5.06/5.42 thf(fact_9279_cis__Arg__unique,axiom,
% 5.06/5.42 ! [Z: complex,X: real] :
% 5.06/5.42 ( ( ( sgn_sgn_complex @ Z )
% 5.06/5.42 = ( cis @ X ) )
% 5.06/5.42 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.06/5.42 => ( ( ord_less_eq_real @ X @ pi )
% 5.06/5.42 => ( ( arg @ Z )
% 5.06/5.42 = X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % cis_Arg_unique
% 5.06/5.42 thf(fact_9280_split__root,axiom,
% 5.06/5.42 ! [P: real > $o,N2: nat,X: real] :
% 5.06/5.42 ( ( P @ ( root @ N2 @ X ) )
% 5.06/5.42 = ( ( ( N2 = zero_zero_nat )
% 5.06/5.42 => ( P @ zero_zero_real ) )
% 5.06/5.42 & ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.42 => ! [Y2: real] :
% 5.06/5.42 ( ( ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N2 ) )
% 5.06/5.42 = X )
% 5.06/5.42 => ( P @ Y2 ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % split_root
% 5.06/5.42 thf(fact_9281_floor__real__def,axiom,
% 5.06/5.42 ( archim6058952711729229775r_real
% 5.06/5.42 = ( ^ [X2: real] :
% 5.06/5.42 ( the_int
% 5.06/5.42 @ ^ [Z2: int] :
% 5.06/5.42 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X2 )
% 5.06/5.42 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % floor_real_def
% 5.06/5.42 thf(fact_9282_Arg__correct,axiom,
% 5.06/5.42 ! [Z: complex] :
% 5.06/5.42 ( ( Z != zero_zero_complex )
% 5.06/5.42 => ( ( ( sgn_sgn_complex @ Z )
% 5.06/5.42 = ( cis @ ( arg @ Z ) ) )
% 5.06/5.42 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.06/5.42 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % Arg_correct
% 5.06/5.42 thf(fact_9283_arctan__inverse,axiom,
% 5.06/5.42 ! [X: real] :
% 5.06/5.42 ( ( X != zero_zero_real )
% 5.06/5.42 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 5.06/5.42 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 5.06/5.42
% 5.06/5.42 % arctan_inverse
% 5.06/5.42 thf(fact_9284_modulo__int__def,axiom,
% 5.06/5.42 ( modulo_modulo_int
% 5.06/5.42 = ( ^ [K3: int,L: int] :
% 5.06/5.42 ( if_int @ ( L = zero_zero_int ) @ K3
% 5.06/5.42 @ ( if_int
% 5.06/5.42 @ ( ( sgn_sgn_int @ K3 )
% 5.06/5.42 = ( sgn_sgn_int @ L ) )
% 5.06/5.42 @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 5.06/5.43 @ ( times_times_int @ ( sgn_sgn_int @ L )
% 5.06/5.43 @ ( minus_minus_int
% 5.06/5.43 @ ( times_times_int @ ( abs_abs_int @ L )
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ~ ( dvd_dvd_int @ L @ K3 ) ) )
% 5.06/5.43 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % modulo_int_def
% 5.06/5.43 thf(fact_9285_divide__int__def,axiom,
% 5.06/5.43 ( divide_divide_int
% 5.06/5.43 = ( ^ [K3: int,L: int] :
% 5.06/5.43 ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 5.06/5.43 @ ( if_int
% 5.06/5.43 @ ( ( sgn_sgn_int @ K3 )
% 5.06/5.43 = ( sgn_sgn_int @ L ) )
% 5.06/5.43 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 5.06/5.43 @ ( uminus_uminus_int
% 5.06/5.43 @ ( semiri1314217659103216013at_int
% 5.06/5.43 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 5.06/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.06/5.43 @ ~ ( dvd_dvd_int @ L @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % divide_int_def
% 5.06/5.43 thf(fact_9286_even__set__encode__iff,axiom,
% 5.06/5.43 ! [A2: set_nat] :
% 5.06/5.43 ( ( finite_finite_nat @ A2 )
% 5.06/5.43 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.06/5.43 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % even_set_encode_iff
% 5.06/5.43 thf(fact_9287_mask__nat__positive__iff,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.06/5.43 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % mask_nat_positive_iff
% 5.06/5.43 thf(fact_9288_nat__numeral,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.06/5.43 = ( numeral_numeral_nat @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_numeral
% 5.06/5.43 thf(fact_9289_nat__1,axiom,
% 5.06/5.43 ( ( nat2 @ one_one_int )
% 5.06/5.43 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_1
% 5.06/5.43 thf(fact_9290_nat__0__iff,axiom,
% 5.06/5.43 ! [I2: int] :
% 5.06/5.43 ( ( ( nat2 @ I2 )
% 5.06/5.43 = zero_zero_nat )
% 5.06/5.43 = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_0_iff
% 5.06/5.43 thf(fact_9291_nat__le__0,axiom,
% 5.06/5.43 ! [Z: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.06/5.43 => ( ( nat2 @ Z )
% 5.06/5.43 = zero_zero_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_le_0
% 5.06/5.43 thf(fact_9292_zless__nat__conj,axiom,
% 5.06/5.43 ! [W: int,Z: int] :
% 5.06/5.43 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.06/5.43 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.06/5.43 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % zless_nat_conj
% 5.06/5.43 thf(fact_9293_nat__neg__numeral,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.06/5.43 = zero_zero_nat ) ).
% 5.06/5.43
% 5.06/5.43 % nat_neg_numeral
% 5.06/5.43 thf(fact_9294_int__nat__eq,axiom,
% 5.06/5.43 ! [Z: int] :
% 5.06/5.43 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.06/5.43 = Z ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.06/5.43 = zero_zero_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % int_nat_eq
% 5.06/5.43 thf(fact_9295_zero__less__nat__eq,axiom,
% 5.06/5.43 ! [Z: int] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.06/5.43 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.06/5.43
% 5.06/5.43 % zero_less_nat_eq
% 5.06/5.43 thf(fact_9296_diff__nat__numeral,axiom,
% 5.06/5.43 ! [V: num,V3: num] :
% 5.06/5.43 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.06/5.43 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % diff_nat_numeral
% 5.06/5.43 thf(fact_9297_numeral__power__eq__nat__cancel__iff,axiom,
% 5.06/5.43 ! [X: num,N2: nat,Y: int] :
% 5.06/5.43 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
% 5.06/5.43 = ( nat2 @ Y ) )
% 5.06/5.43 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 )
% 5.06/5.43 = Y ) ) ).
% 5.06/5.43
% 5.06/5.43 % numeral_power_eq_nat_cancel_iff
% 5.06/5.43 thf(fact_9298_nat__eq__numeral__power__cancel__iff,axiom,
% 5.06/5.43 ! [Y: int,X: num,N2: nat] :
% 5.06/5.43 ( ( ( nat2 @ Y )
% 5.06/5.43 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.06/5.43 = ( Y
% 5.06/5.43 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_eq_numeral_power_cancel_iff
% 5.06/5.43 thf(fact_9299_nat__ceiling__le__eq,axiom,
% 5.06/5.43 ! [X: real,A: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 5.06/5.43 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_ceiling_le_eq
% 5.06/5.43 thf(fact_9300_one__less__nat__eq,axiom,
% 5.06/5.43 ! [Z: int] :
% 5.06/5.43 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.06/5.43 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.06/5.43
% 5.06/5.43 % one_less_nat_eq
% 5.06/5.43 thf(fact_9301_nat__numeral__diff__1,axiom,
% 5.06/5.43 ! [V: num] :
% 5.06/5.43 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.06/5.43 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_numeral_diff_1
% 5.06/5.43 thf(fact_9302_nat__less__numeral__power__cancel__iff,axiom,
% 5.06/5.43 ! [A: int,X: num,N2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.06/5.43 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_less_numeral_power_cancel_iff
% 5.06/5.43 thf(fact_9303_numeral__power__less__nat__cancel__iff,axiom,
% 5.06/5.43 ! [X: num,N2: nat,A: int] :
% 5.06/5.43 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 5.06/5.43 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.06/5.43
% 5.06/5.43 % numeral_power_less_nat_cancel_iff
% 5.06/5.43 thf(fact_9304_nat__le__numeral__power__cancel__iff,axiom,
% 5.06/5.43 ! [A: int,X: num,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.06/5.43 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_le_numeral_power_cancel_iff
% 5.06/5.43 thf(fact_9305_numeral__power__le__nat__cancel__iff,axiom,
% 5.06/5.43 ! [X: num,N2: nat,A: int] :
% 5.06/5.43 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 5.06/5.43 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.06/5.43
% 5.06/5.43 % numeral_power_le_nat_cancel_iff
% 5.06/5.43 thf(fact_9306_less__eq__mask,axiom,
% 5.06/5.43 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_eq_mask
% 5.06/5.43 thf(fact_9307_nat__mask__eq,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.06/5.43 = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_mask_eq
% 5.06/5.43 thf(fact_9308_nat__numeral__as__int,axiom,
% 5.06/5.43 ( numeral_numeral_nat
% 5.06/5.43 = ( ^ [I5: num] : ( nat2 @ ( numeral_numeral_int @ I5 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_numeral_as_int
% 5.06/5.43 thf(fact_9309_nat__mono,axiom,
% 5.06/5.43 ! [X: int,Y: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ X @ Y )
% 5.06/5.43 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_mono
% 5.06/5.43 thf(fact_9310_ex__nat,axiom,
% 5.06/5.43 ( ( ^ [P2: nat > $o] :
% 5.06/5.43 ? [X6: nat] : ( P2 @ X6 ) )
% 5.06/5.43 = ( ^ [P3: nat > $o] :
% 5.06/5.43 ? [X2: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.06/5.43 & ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % ex_nat
% 5.06/5.43 thf(fact_9311_all__nat,axiom,
% 5.06/5.43 ( ( ^ [P2: nat > $o] :
% 5.06/5.43 ! [X6: nat] : ( P2 @ X6 ) )
% 5.06/5.43 = ( ^ [P3: nat > $o] :
% 5.06/5.43 ! [X2: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.06/5.43 => ( P3 @ ( nat2 @ X2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % all_nat
% 5.06/5.43 thf(fact_9312_eq__nat__nat__iff,axiom,
% 5.06/5.43 ! [Z: int,Z7: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.06/5.43 => ( ( ( nat2 @ Z )
% 5.06/5.43 = ( nat2 @ Z7 ) )
% 5.06/5.43 = ( Z = Z7 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % eq_nat_nat_iff
% 5.06/5.43 thf(fact_9313_nat__one__as__int,axiom,
% 5.06/5.43 ( one_one_nat
% 5.06/5.43 = ( nat2 @ one_one_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_one_as_int
% 5.06/5.43 thf(fact_9314_unset__bit__nat__def,axiom,
% 5.06/5.43 ( bit_se4205575877204974255it_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % unset_bit_nat_def
% 5.06/5.43 thf(fact_9315_mask__nonnegative__int,axiom,
% 5.06/5.43 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % mask_nonnegative_int
% 5.06/5.43 thf(fact_9316_not__mask__negative__int,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 5.06/5.43
% 5.06/5.43 % not_mask_negative_int
% 5.06/5.43 thf(fact_9317_nat__mono__iff,axiom,
% 5.06/5.43 ! [Z: int,W: int] :
% 5.06/5.43 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.06/5.43 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_mono_iff
% 5.06/5.43 thf(fact_9318_zless__nat__eq__int__zless,axiom,
% 5.06/5.43 ! [M: nat,Z: int] :
% 5.06/5.43 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.06/5.43 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.06/5.43
% 5.06/5.43 % zless_nat_eq_int_zless
% 5.06/5.43 thf(fact_9319_nat__le__iff,axiom,
% 5.06/5.43 ! [X: int,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N2 )
% 5.06/5.43 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_le_iff
% 5.06/5.43 thf(fact_9320_nat__0__le,axiom,
% 5.06/5.43 ! [Z: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.06/5.43 = Z ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_0_le
% 5.06/5.43 thf(fact_9321_int__eq__iff,axiom,
% 5.06/5.43 ! [M: nat,Z: int] :
% 5.06/5.43 ( ( ( semiri1314217659103216013at_int @ M )
% 5.06/5.43 = Z )
% 5.06/5.43 = ( ( M
% 5.06/5.43 = ( nat2 @ Z ) )
% 5.06/5.43 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % int_eq_iff
% 5.06/5.43 thf(fact_9322_nat__int__add,axiom,
% 5.06/5.43 ! [A: nat,B: nat] :
% 5.06/5.43 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.06/5.43 = ( plus_plus_nat @ A @ B ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_int_add
% 5.06/5.43 thf(fact_9323_int__minus,axiom,
% 5.06/5.43 ! [N2: nat,M: nat] :
% 5.06/5.43 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ M ) )
% 5.06/5.43 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % int_minus
% 5.06/5.43 thf(fact_9324_nat__abs__mult__distrib,axiom,
% 5.06/5.43 ! [W: int,Z: int] :
% 5.06/5.43 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.06/5.43 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_abs_mult_distrib
% 5.06/5.43 thf(fact_9325_nat__plus__as__int,axiom,
% 5.06/5.43 ( plus_plus_nat
% 5.06/5.43 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_plus_as_int
% 5.06/5.43 thf(fact_9326_nat__times__as__int,axiom,
% 5.06/5.43 ( times_times_nat
% 5.06/5.43 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_times_as_int
% 5.06/5.43 thf(fact_9327_or__nat__def,axiom,
% 5.06/5.43 ( bit_se1412395901928357646or_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_nat_def
% 5.06/5.43 thf(fact_9328_real__nat__ceiling__ge,axiom,
% 5.06/5.43 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % real_nat_ceiling_ge
% 5.06/5.43 thf(fact_9329_less__mask,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.43 => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_mask
% 5.06/5.43 thf(fact_9330_nat__minus__as__int,axiom,
% 5.06/5.43 ( minus_minus_nat
% 5.06/5.43 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_minus_as_int
% 5.06/5.43 thf(fact_9331_nat__div__as__int,axiom,
% 5.06/5.43 ( divide_divide_nat
% 5.06/5.43 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_div_as_int
% 5.06/5.43 thf(fact_9332_nat__mod__as__int,axiom,
% 5.06/5.43 ( modulo_modulo_nat
% 5.06/5.43 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_mod_as_int
% 5.06/5.43 thf(fact_9333_nat__less__eq__zless,axiom,
% 5.06/5.43 ! [W: int,Z: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.06/5.43 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.06/5.43 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_less_eq_zless
% 5.06/5.43 thf(fact_9334_nat__le__eq__zle,axiom,
% 5.06/5.43 ! [W: int,Z: int] :
% 5.06/5.43 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.06/5.43 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.06/5.43 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.06/5.43 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_le_eq_zle
% 5.06/5.43 thf(fact_9335_nat__eq__iff,axiom,
% 5.06/5.43 ! [W: int,M: nat] :
% 5.06/5.43 ( ( ( nat2 @ W )
% 5.06/5.43 = M )
% 5.06/5.43 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.06/5.43 => ( W
% 5.06/5.43 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.06/5.43 => ( M = zero_zero_nat ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_eq_iff
% 5.06/5.43 thf(fact_9336_nat__eq__iff2,axiom,
% 5.06/5.43 ! [M: nat,W: int] :
% 5.06/5.43 ( ( M
% 5.06/5.43 = ( nat2 @ W ) )
% 5.06/5.43 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.06/5.43 => ( W
% 5.06/5.43 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.06/5.43 => ( M = zero_zero_nat ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_eq_iff2
% 5.06/5.43 thf(fact_9337_le__nat__iff,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.43 => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 5.06/5.43 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % le_nat_iff
% 5.06/5.43 thf(fact_9338_nat__add__distrib,axiom,
% 5.06/5.43 ! [Z: int,Z7: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.06/5.43 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 5.06/5.43 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_add_distrib
% 5.06/5.43 thf(fact_9339_nat__mult__distrib,axiom,
% 5.06/5.43 ! [Z: int,Z7: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.06/5.43 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_mult_distrib
% 5.06/5.43 thf(fact_9340_Suc__as__int,axiom,
% 5.06/5.43 ( suc
% 5.06/5.43 = ( ^ [A4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ one_one_int ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Suc_as_int
% 5.06/5.43 thf(fact_9341_nat__diff__distrib,axiom,
% 5.06/5.43 ! [Z7: int,Z: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.06/5.43 => ( ( ord_less_eq_int @ Z7 @ Z )
% 5.06/5.43 => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 5.06/5.43 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_diff_distrib
% 5.06/5.43 thf(fact_9342_nat__diff__distrib_H,axiom,
% 5.06/5.43 ! [X: int,Y: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 5.06/5.43 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_diff_distrib'
% 5.06/5.43 thf(fact_9343_nat__abs__triangle__ineq,axiom,
% 5.06/5.43 ! [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 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_abs_triangle_ineq
% 5.06/5.43 thf(fact_9344_nat__div__distrib_H,axiom,
% 5.06/5.43 ! [Y: int,X: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.06/5.43 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_div_distrib'
% 5.06/5.43 thf(fact_9345_nat__div__distrib,axiom,
% 5.06/5.43 ! [X: int,Y: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.43 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.06/5.43 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_div_distrib
% 5.06/5.43 thf(fact_9346_nat__power__eq,axiom,
% 5.06/5.43 ! [Z: int,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( ( nat2 @ ( power_power_int @ Z @ N2 ) )
% 5.06/5.43 = ( power_power_nat @ ( nat2 @ Z ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_power_eq
% 5.06/5.43 thf(fact_9347_nat__floor__neg,axiom,
% 5.06/5.43 ! [X: real] :
% 5.06/5.43 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.06/5.43 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.06/5.43 = zero_zero_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_floor_neg
% 5.06/5.43 thf(fact_9348_nat__mod__distrib,axiom,
% 5.06/5.43 ! [X: int,Y: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 5.06/5.43 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_mod_distrib
% 5.06/5.43 thf(fact_9349_div__abs__eq__div__nat,axiom,
% 5.06/5.43 ! [K: int,L2: int] :
% 5.06/5.43 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.06/5.43 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % div_abs_eq_div_nat
% 5.06/5.43 thf(fact_9350_floor__eq3,axiom,
% 5.06/5.43 ! [N2: nat,X: real] :
% 5.06/5.43 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ X )
% 5.06/5.43 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.06/5.43 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.06/5.43 = N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % floor_eq3
% 5.06/5.43 thf(fact_9351_le__nat__floor,axiom,
% 5.06/5.43 ! [X: nat,A: real] :
% 5.06/5.43 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 5.06/5.43 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % le_nat_floor
% 5.06/5.43 thf(fact_9352_nat__2,axiom,
% 5.06/5.43 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.43 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_2
% 5.06/5.43 thf(fact_9353_Suc__nat__eq__nat__zadd1,axiom,
% 5.06/5.43 ! [Z: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( ( suc @ ( nat2 @ Z ) )
% 5.06/5.43 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Suc_nat_eq_nat_zadd1
% 5.06/5.43 thf(fact_9354_nat__less__iff,axiom,
% 5.06/5.43 ! [W: int,M: nat] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.06/5.43 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.06/5.43 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_less_iff
% 5.06/5.43 thf(fact_9355_nat__mult__distrib__neg,axiom,
% 5.06/5.43 ! [Z: int,Z7: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.06/5.43 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.06/5.43 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_mult_distrib_neg
% 5.06/5.43 thf(fact_9356_nat__abs__int__diff,axiom,
% 5.06/5.43 ! [A: nat,B: nat] :
% 5.06/5.43 ( ( ( ord_less_eq_nat @ A @ B )
% 5.06/5.43 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.06/5.43 = ( minus_minus_nat @ B @ A ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.06/5.43 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.06/5.43 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_abs_int_diff
% 5.06/5.43 thf(fact_9357_floor__eq4,axiom,
% 5.06/5.43 ! [N2: nat,X: real] :
% 5.06/5.43 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ X )
% 5.06/5.43 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.06/5.43 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.06/5.43 = N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % floor_eq4
% 5.06/5.43 thf(fact_9358_diff__nat__eq__if,axiom,
% 5.06/5.43 ! [Z7: int,Z: int] :
% 5.06/5.43 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 5.06/5.43 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.06/5.43 = ( nat2 @ Z ) ) )
% 5.06/5.43 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 5.06/5.43 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.06/5.43 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % diff_nat_eq_if
% 5.06/5.43 thf(fact_9359_Suc__mask__eq__exp,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.06/5.43 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % Suc_mask_eq_exp
% 5.06/5.43 thf(fact_9360_mask__nat__less__exp,axiom,
% 5.06/5.43 ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % mask_nat_less_exp
% 5.06/5.43 thf(fact_9361_nat__dvd__iff,axiom,
% 5.06/5.43 ! [Z: int,M: nat] :
% 5.06/5.43 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.06/5.43 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.06/5.43 => ( M = zero_zero_nat ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_dvd_iff
% 5.06/5.43 thf(fact_9362_mask__nat__def,axiom,
% 5.06/5.43 ( bit_se2002935070580805687sk_nat
% 5.06/5.43 = ( ^ [N: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % mask_nat_def
% 5.06/5.43 thf(fact_9363_mask__half__int,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.43 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % mask_half_int
% 5.06/5.43 thf(fact_9364_mask__int__def,axiom,
% 5.06/5.43 ( bit_se2000444600071755411sk_int
% 5.06/5.43 = ( ^ [N: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % mask_int_def
% 5.06/5.43 thf(fact_9365_even__nat__iff,axiom,
% 5.06/5.43 ! [K: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.43 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.06/5.43 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % even_nat_iff
% 5.06/5.43 thf(fact_9366_set__encode__def,axiom,
% 5.06/5.43 ( nat_set_encode
% 5.06/5.43 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % set_encode_def
% 5.06/5.43 thf(fact_9367_powr__real__of__int,axiom,
% 5.06/5.43 ! [X: real,N2: int] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.43 => ( ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.06/5.43 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N2 ) )
% 5.06/5.43 = ( power_power_real @ X @ ( nat2 @ N2 ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.06/5.43 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N2 ) )
% 5.06/5.43 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N2 ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % powr_real_of_int
% 5.06/5.43 thf(fact_9368_powr__int,axiom,
% 5.06/5.43 ! [X: real,I2: int] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.43 => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.06/5.43 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 5.06/5.43 = ( power_power_real @ X @ ( nat2 @ I2 ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.06/5.43 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 5.06/5.43 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % powr_int
% 5.06/5.43 thf(fact_9369_floor__rat__def,axiom,
% 5.06/5.43 ( archim3151403230148437115or_rat
% 5.06/5.43 = ( ^ [X2: rat] :
% 5.06/5.43 ( the_int
% 5.06/5.43 @ ^ [Z2: int] :
% 5.06/5.43 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 )
% 5.06/5.43 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % floor_rat_def
% 5.06/5.43 thf(fact_9370_Arg__def,axiom,
% 5.06/5.43 ( arg
% 5.06/5.43 = ( ^ [Z2: complex] :
% 5.06/5.43 ( if_real @ ( Z2 = zero_zero_complex ) @ zero_zero_real
% 5.06/5.43 @ ( fChoice_real
% 5.06/5.43 @ ^ [A4: real] :
% 5.06/5.43 ( ( ( sgn_sgn_complex @ Z2 )
% 5.06/5.43 = ( cis @ A4 ) )
% 5.06/5.43 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 5.06/5.43 & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Arg_def
% 5.06/5.43 thf(fact_9371_num_Osize__gen_I3_J,axiom,
% 5.06/5.43 ! [X32: num] :
% 5.06/5.43 ( ( size_num @ ( bit1 @ X32 ) )
% 5.06/5.43 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % num.size_gen(3)
% 5.06/5.43 thf(fact_9372_concat__bit__of__zero__2,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( bit_concat_bit @ N2 @ K @ zero_zero_int )
% 5.06/5.43 = ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % concat_bit_of_zero_2
% 5.06/5.43 thf(fact_9373_take__bit__of__Suc__0,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.06/5.43 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_of_Suc_0
% 5.06/5.43 thf(fact_9374_take__bit__nat__eq,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.43 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) )
% 5.06/5.43 = ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_nat_eq
% 5.06/5.43 thf(fact_9375_nat__take__bit__eq,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.43 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.06/5.43 = ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_take_bit_eq
% 5.06/5.43 thf(fact_9376_obtain__pos__sum,axiom,
% 5.06/5.43 ! [R2: rat] :
% 5.06/5.43 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.06/5.43 => ~ ! [S: rat] :
% 5.06/5.43 ( ( ord_less_rat @ zero_zero_rat @ S )
% 5.06/5.43 => ! [T5: rat] :
% 5.06/5.43 ( ( ord_less_rat @ zero_zero_rat @ T5 )
% 5.06/5.43 => ( R2
% 5.06/5.43 != ( plus_plus_rat @ S @ T5 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % obtain_pos_sum
% 5.06/5.43 thf(fact_9377_less__eq__rat__def,axiom,
% 5.06/5.43 ( ord_less_eq_rat
% 5.06/5.43 = ( ^ [X2: rat,Y2: rat] :
% 5.06/5.43 ( ( ord_less_rat @ X2 @ Y2 )
% 5.06/5.43 | ( X2 = Y2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_eq_rat_def
% 5.06/5.43 thf(fact_9378_take__bit__nat__less__eq__self,axiom,
% 5.06/5.43 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_nat_less_eq_self
% 5.06/5.43 thf(fact_9379_take__bit__tightened__less__eq__nat,axiom,
% 5.06/5.43 ! [M: nat,N2: nat,Q2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.43 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_tightened_less_eq_nat
% 5.06/5.43 thf(fact_9380_take__bit__diff,axiom,
% 5.06/5.43 ! [N2: nat,K: int,L2: int] :
% 5.06/5.43 ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L2 ) ) )
% 5.06/5.43 = ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_diff
% 5.06/5.43 thf(fact_9381_take__bit__mult,axiom,
% 5.06/5.43 ! [N2: nat,K: int,L2: int] :
% 5.06/5.43 ( ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L2 ) ) )
% 5.06/5.43 = ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_mult
% 5.06/5.43 thf(fact_9382_take__bit__minus,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 5.06/5.43 = ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_minus
% 5.06/5.43 thf(fact_9383_concat__bit__take__bit__eq,axiom,
% 5.06/5.43 ! [N2: nat,B: int] :
% 5.06/5.43 ( ( bit_concat_bit @ N2 @ ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 5.06/5.43 = ( bit_concat_bit @ N2 @ B ) ) ).
% 5.06/5.43
% 5.06/5.43 % concat_bit_take_bit_eq
% 5.06/5.43 thf(fact_9384_concat__bit__eq__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int,L2: int,R2: int,S2: int] :
% 5.06/5.43 ( ( ( bit_concat_bit @ N2 @ K @ L2 )
% 5.06/5.43 = ( bit_concat_bit @ N2 @ R2 @ S2 ) )
% 5.06/5.43 = ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.06/5.43 = ( bit_se2923211474154528505it_int @ N2 @ R2 ) )
% 5.06/5.43 & ( L2 = S2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % concat_bit_eq_iff
% 5.06/5.43 thf(fact_9385_take__bit__tightened__less__eq__int,axiom,
% 5.06/5.43 ! [M: nat,N2: nat,K: int] :
% 5.06/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.43 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_tightened_less_eq_int
% 5.06/5.43 thf(fact_9386_take__bit__int__less__eq__self__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.06/5.43 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_int_less_eq_self_iff
% 5.06/5.43 thf(fact_9387_take__bit__nonnegative,axiom,
% 5.06/5.43 ! [N2: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_nonnegative
% 5.06/5.43 thf(fact_9388_take__bit__int__greater__self__iff,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.06/5.43 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_int_greater_self_iff
% 5.06/5.43 thf(fact_9389_not__take__bit__negative,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ zero_zero_int ) ).
% 5.06/5.43
% 5.06/5.43 % not_take_bit_negative
% 5.06/5.43 thf(fact_9390_take__bit__eq__mask__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.06/5.43 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.06/5.43 = ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 5.06/5.43 = zero_zero_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_eq_mask_iff
% 5.06/5.43 thf(fact_9391_take__bit__decr__eq,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.06/5.43 != zero_zero_int )
% 5.06/5.43 => ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ one_one_int ) )
% 5.06/5.43 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ one_one_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_decr_eq
% 5.06/5.43 thf(fact_9392_take__bit__nat__eq__self,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.43 => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.06/5.43 = M ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_nat_eq_self
% 5.06/5.43 thf(fact_9393_take__bit__nat__less__exp,axiom,
% 5.06/5.43 ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_nat_less_exp
% 5.06/5.43 thf(fact_9394_take__bit__nat__eq__self__iff,axiom,
% 5.06/5.43 ! [N2: nat,M: nat] :
% 5.06/5.43 ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.06/5.43 = M )
% 5.06/5.43 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_nat_eq_self_iff
% 5.06/5.43 thf(fact_9395_take__bit__nat__def,axiom,
% 5.06/5.43 ( bit_se2925701944663578781it_nat
% 5.06/5.43 = ( ^ [N: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_nat_def
% 5.06/5.43 thf(fact_9396_take__bit__int__less__exp,axiom,
% 5.06/5.43 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_int_less_exp
% 5.06/5.43 thf(fact_9397_take__bit__int__def,axiom,
% 5.06/5.43 ( bit_se2923211474154528505it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_int_def
% 5.06/5.43 thf(fact_9398_num_Osize__gen_I1_J,axiom,
% 5.06/5.43 ( ( size_num @ one )
% 5.06/5.43 = zero_zero_nat ) ).
% 5.06/5.43
% 5.06/5.43 % num.size_gen(1)
% 5.06/5.43 thf(fact_9399_take__bit__nat__less__self__iff,axiom,
% 5.06/5.43 ! [N2: nat,M: nat] :
% 5.06/5.43 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 5.06/5.43 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_nat_less_self_iff
% 5.06/5.43 thf(fact_9400_take__bit__Suc__minus__bit0,axiom,
% 5.06/5.43 ! [N2: nat,K: num] :
% 5.06/5.43 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.06/5.43 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_Suc_minus_bit0
% 5.06/5.43 thf(fact_9401_take__bit__int__less__self__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.06/5.43 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_int_less_self_iff
% 5.06/5.43 thf(fact_9402_take__bit__int__greater__eq__self__iff,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.06/5.43 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_int_greater_eq_self_iff
% 5.06/5.43 thf(fact_9403_take__bit__int__eq__self__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.06/5.43 = K )
% 5.06/5.43 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.43 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_int_eq_self_iff
% 5.06/5.43 thf(fact_9404_take__bit__int__eq__self,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.43 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.43 => ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.06/5.43 = K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_int_eq_self
% 5.06/5.43 thf(fact_9405_take__bit__numeral__minus__bit0,axiom,
% 5.06/5.43 ! [L2: num,K: num] :
% 5.06/5.43 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.06/5.43 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_numeral_minus_bit0
% 5.06/5.43 thf(fact_9406_take__bit__incr__eq,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.06/5.43 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 5.06/5.43 => ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 5.06/5.43 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_incr_eq
% 5.06/5.43 thf(fact_9407_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.06/5.43 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.06/5.43 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_eq_mask_iff_exp_dvd
% 5.06/5.43 thf(fact_9408_take__bit__int__less__eq,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.06/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_int_less_eq
% 5.06/5.43 thf(fact_9409_take__bit__int__greater__eq,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( ord_less_int @ K @ zero_zero_int )
% 5.06/5.43 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_int_greater_eq
% 5.06/5.43 thf(fact_9410_signed__take__bit__eq__take__bit__shift,axiom,
% 5.06/5.43 ( bit_ri631733984087533419it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % signed_take_bit_eq_take_bit_shift
% 5.06/5.43 thf(fact_9411_take__bit__minus__small__eq,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( ord_less_int @ zero_zero_int @ K )
% 5.06/5.43 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.43 => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) )
% 5.06/5.43 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_minus_small_eq
% 5.06/5.43 thf(fact_9412_num_Osize__gen_I2_J,axiom,
% 5.06/5.43 ! [X22: num] :
% 5.06/5.43 ( ( size_num @ ( bit0 @ X22 ) )
% 5.06/5.43 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % num.size_gen(2)
% 5.06/5.43 thf(fact_9413_take__bit__numeral__minus__bit1,axiom,
% 5.06/5.43 ! [L2: num,K: num] :
% 5.06/5.43 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.06/5.43 = ( 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 ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_numeral_minus_bit1
% 5.06/5.43 thf(fact_9414_pred__numeral__inc,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( pred_numeral @ ( inc @ K ) )
% 5.06/5.43 = ( numeral_numeral_nat @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % pred_numeral_inc
% 5.06/5.43 thf(fact_9415_diff__rat__def,axiom,
% 5.06/5.43 ( minus_minus_rat
% 5.06/5.43 = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % diff_rat_def
% 5.06/5.43 thf(fact_9416_num__induct,axiom,
% 5.06/5.43 ! [P: num > $o,X: num] :
% 5.06/5.43 ( ( P @ one )
% 5.06/5.43 => ( ! [X3: num] :
% 5.06/5.43 ( ( P @ X3 )
% 5.06/5.43 => ( P @ ( inc @ X3 ) ) )
% 5.06/5.43 => ( P @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % num_induct
% 5.06/5.43 thf(fact_9417_add__inc,axiom,
% 5.06/5.43 ! [X: num,Y: num] :
% 5.06/5.43 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 5.06/5.43 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % add_inc
% 5.06/5.43 thf(fact_9418_inc_Osimps_I1_J,axiom,
% 5.06/5.43 ( ( inc @ one )
% 5.06/5.43 = ( bit0 @ one ) ) ).
% 5.06/5.43
% 5.06/5.43 % inc.simps(1)
% 5.06/5.43 thf(fact_9419_inc_Osimps_I2_J,axiom,
% 5.06/5.43 ! [X: num] :
% 5.06/5.43 ( ( inc @ ( bit0 @ X ) )
% 5.06/5.43 = ( bit1 @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % inc.simps(2)
% 5.06/5.43 thf(fact_9420_inc_Osimps_I3_J,axiom,
% 5.06/5.43 ! [X: num] :
% 5.06/5.43 ( ( inc @ ( bit1 @ X ) )
% 5.06/5.43 = ( bit0 @ ( inc @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % inc.simps(3)
% 5.06/5.43 thf(fact_9421_add__One,axiom,
% 5.06/5.43 ! [X: num] :
% 5.06/5.43 ( ( plus_plus_num @ X @ one )
% 5.06/5.43 = ( inc @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % add_One
% 5.06/5.43 thf(fact_9422_inc__BitM__eq,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( inc @ ( bitM @ N2 ) )
% 5.06/5.43 = ( bit0 @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % inc_BitM_eq
% 5.06/5.43 thf(fact_9423_BitM__inc__eq,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( bitM @ ( inc @ N2 ) )
% 5.06/5.43 = ( bit1 @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % BitM_inc_eq
% 5.06/5.43 thf(fact_9424_mult__inc,axiom,
% 5.06/5.43 ! [X: num,Y: num] :
% 5.06/5.43 ( ( times_times_num @ X @ ( inc @ Y ) )
% 5.06/5.43 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % mult_inc
% 5.06/5.43 thf(fact_9425_take__bit__Suc__minus__bit1,axiom,
% 5.06/5.43 ! [N2: nat,K: num] :
% 5.06/5.43 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.06/5.43 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_Suc_minus_bit1
% 5.06/5.43 thf(fact_9426_signed__take__bit__eq__take__bit__minus,axiom,
% 5.06/5.43 ( bit_ri631733984087533419it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % signed_take_bit_eq_take_bit_minus
% 5.06/5.43 thf(fact_9427_and__int__unfold,axiom,
% 5.06/5.43 ( bit_se725231765392027082nd_int
% 5.06/5.43 = ( ^ [K3: int,L: int] :
% 5.06/5.43 ( if_int
% 5.06/5.43 @ ( ( K3 = zero_zero_int )
% 5.06/5.43 | ( L = zero_zero_int ) )
% 5.06/5.43 @ zero_zero_int
% 5.06/5.43 @ ( if_int
% 5.06/5.43 @ ( K3
% 5.06/5.43 = ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.43 @ L
% 5.06/5.43 @ ( if_int
% 5.06/5.43 @ ( L
% 5.06/5.43 = ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.43 @ K3
% 5.06/5.43 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( 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 @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_int_unfold
% 5.06/5.43 thf(fact_9428_and__nonnegative__int__iff,axiom,
% 5.06/5.43 ! [K: int,L2: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.06/5.43 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.43 | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_nonnegative_int_iff
% 5.06/5.43 thf(fact_9429_and__negative__int__iff,axiom,
% 5.06/5.43 ! [K: int,L2: int] :
% 5.06/5.43 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 5.06/5.43 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.06/5.43 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_negative_int_iff
% 5.06/5.43 thf(fact_9430_signed__take__bit__nonnegative__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.06/5.43 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % signed_take_bit_nonnegative_iff
% 5.06/5.43 thf(fact_9431_signed__take__bit__negative__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ zero_zero_int )
% 5.06/5.43 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % signed_take_bit_negative_iff
% 5.06/5.43 thf(fact_9432_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.06/5.43 ! [W: num,N2: nat] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N2 ) )
% 5.06/5.43 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_minus_numeral_Bit0_Suc_iff
% 5.06/5.43 thf(fact_9433_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.06/5.43 ! [W: num,N2: nat] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N2 ) )
% 5.06/5.43 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_minus_numeral_Bit1_Suc_iff
% 5.06/5.43 thf(fact_9434_and__minus__numerals_I2_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.06/5.43 = one_one_int ) ).
% 5.06/5.43
% 5.06/5.43 % and_minus_numerals(2)
% 5.06/5.43 thf(fact_9435_and__minus__numerals_I6_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 5.06/5.43 = one_one_int ) ).
% 5.06/5.43
% 5.06/5.43 % and_minus_numerals(6)
% 5.06/5.43 thf(fact_9436_and__minus__numerals_I5_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 5.06/5.43 = zero_zero_int ) ).
% 5.06/5.43
% 5.06/5.43 % and_minus_numerals(5)
% 5.06/5.43 thf(fact_9437_and__minus__numerals_I1_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.06/5.43 = zero_zero_int ) ).
% 5.06/5.43
% 5.06/5.43 % and_minus_numerals(1)
% 5.06/5.43 thf(fact_9438_bit__minus__numeral__int_I1_J,axiom,
% 5.06/5.43 ! [W: num,N2: num] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.06/5.43 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_minus_numeral_int(1)
% 5.06/5.43 thf(fact_9439_bit__minus__numeral__int_I2_J,axiom,
% 5.06/5.43 ! [W: num,N2: num] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.06/5.43 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_minus_numeral_int(2)
% 5.06/5.43 thf(fact_9440_bit__and__int__iff,axiom,
% 5.06/5.43 ! [K: int,L2: int,N2: nat] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N2 )
% 5.06/5.43 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.06/5.43 & ( bit_se1146084159140164899it_int @ L2 @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_and_int_iff
% 5.06/5.43 thf(fact_9441_bit__or__int__iff,axiom,
% 5.06/5.43 ! [K: int,L2: int,N2: nat] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N2 )
% 5.06/5.43 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.06/5.43 | ( bit_se1146084159140164899it_int @ L2 @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_or_int_iff
% 5.06/5.43 thf(fact_9442_AND__upper2_H,axiom,
% 5.06/5.43 ! [Y: int,Z: int,X: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( ( ord_less_eq_int @ Y @ Z )
% 5.06/5.43 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % AND_upper2'
% 5.06/5.43 thf(fact_9443_AND__upper1_H,axiom,
% 5.06/5.43 ! [Y: int,Z: int,Ya: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( ( ord_less_eq_int @ Y @ Z )
% 5.06/5.43 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % AND_upper1'
% 5.06/5.43 thf(fact_9444_AND__upper2,axiom,
% 5.06/5.43 ! [Y: int,X: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 5.06/5.43
% 5.06/5.43 % AND_upper2
% 5.06/5.43 thf(fact_9445_AND__upper1,axiom,
% 5.06/5.43 ! [X: int,Y: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.43 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % AND_upper1
% 5.06/5.43 thf(fact_9446_AND__lower,axiom,
% 5.06/5.43 ! [X: int,Y: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.43 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % AND_lower
% 5.06/5.43 thf(fact_9447_plus__and__or,axiom,
% 5.06/5.43 ! [X: int,Y: int] :
% 5.06/5.43 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Y ) )
% 5.06/5.43 = ( plus_plus_int @ X @ Y ) ) ).
% 5.06/5.43
% 5.06/5.43 % plus_and_or
% 5.06/5.43 thf(fact_9448_pow_Osimps_I1_J,axiom,
% 5.06/5.43 ! [X: num] :
% 5.06/5.43 ( ( pow @ X @ one )
% 5.06/5.43 = X ) ).
% 5.06/5.43
% 5.06/5.43 % pow.simps(1)
% 5.06/5.43 thf(fact_9449_and__less__eq,axiom,
% 5.06/5.43 ! [L2: int,K: int] :
% 5.06/5.43 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.06/5.43 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_less_eq
% 5.06/5.43 thf(fact_9450_AND__upper1_H_H,axiom,
% 5.06/5.43 ! [Y: int,Z: int,Ya: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( ( ord_less_int @ Y @ Z )
% 5.06/5.43 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % AND_upper1''
% 5.06/5.43 thf(fact_9451_AND__upper2_H_H,axiom,
% 5.06/5.43 ! [Y: int,Z: int,X: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( ( ord_less_int @ Y @ Z )
% 5.06/5.43 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % AND_upper2''
% 5.06/5.43 thf(fact_9452_bit__not__int__iff_H,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N2 )
% 5.06/5.43 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_not_int_iff'
% 5.06/5.43 thf(fact_9453_even__and__iff__int,axiom,
% 5.06/5.43 ! [K: int,L2: int] :
% 5.06/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.06/5.43 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.06/5.43 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % even_and_iff_int
% 5.06/5.43 thf(fact_9454_bit__imp__take__bit__positive,axiom,
% 5.06/5.43 ! [N2: nat,M: nat,K: int] :
% 5.06/5.43 ( ( ord_less_nat @ N2 @ M )
% 5.06/5.43 => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.06/5.43 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_imp_take_bit_positive
% 5.06/5.43 thf(fact_9455_bit__concat__bit__iff,axiom,
% 5.06/5.43 ! [M: nat,K: int,L2: int,N2: nat] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N2 )
% 5.06/5.43 = ( ( ( ord_less_nat @ N2 @ M )
% 5.06/5.43 & ( bit_se1146084159140164899it_int @ K @ N2 ) )
% 5.06/5.43 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.43 & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_concat_bit_iff
% 5.06/5.43 thf(fact_9456_signed__take__bit__eq__concat__bit,axiom,
% 5.06/5.43 ( bit_ri631733984087533419it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] : ( bit_concat_bit @ N @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % signed_take_bit_eq_concat_bit
% 5.06/5.43 thf(fact_9457_int__bit__bound,axiom,
% 5.06/5.43 ! [K: int] :
% 5.06/5.43 ~ ! [N3: nat] :
% 5.06/5.43 ( ! [M3: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ N3 @ M3 )
% 5.06/5.43 => ( ( bit_se1146084159140164899it_int @ K @ M3 )
% 5.06/5.43 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.06/5.43 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.06/5.43 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.06/5.43 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % int_bit_bound
% 5.06/5.43 thf(fact_9458_bit__int__def,axiom,
% 5.06/5.43 ( bit_se1146084159140164899it_int
% 5.06/5.43 = ( ^ [K3: int,N: nat] :
% 5.06/5.43 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_int_def
% 5.06/5.43 thf(fact_9459_and__int__rec,axiom,
% 5.06/5.43 ( bit_se725231765392027082nd_int
% 5.06/5.43 = ( ^ [K3: int,L: int] :
% 5.06/5.43 ( plus_plus_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.06/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.06/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_int_rec
% 5.06/5.43 thf(fact_9460_set__bit__eq,axiom,
% 5.06/5.43 ( bit_se7879613467334960850it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] :
% 5.06/5.43 ( plus_plus_int @ K3
% 5.06/5.43 @ ( times_times_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N ) )
% 5.06/5.43 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % set_bit_eq
% 5.06/5.43 thf(fact_9461_unset__bit__eq,axiom,
% 5.06/5.43 ( bit_se4203085406695923979it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % unset_bit_eq
% 5.06/5.43 thf(fact_9462_take__bit__Suc__from__most,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K )
% 5.06/5.43 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % take_bit_Suc_from_most
% 5.06/5.43 thf(fact_9463_and__int_Oelims,axiom,
% 5.06/5.43 ! [X: int,Xa2: int,Y: int] :
% 5.06/5.43 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.06/5.43 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( uminus_uminus_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.06/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.06/5.43 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.06/5.43 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( plus_plus_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.06/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.06/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_int.elims
% 5.06/5.43 thf(fact_9464_and__int_Osimps,axiom,
% 5.06/5.43 ( bit_se725231765392027082nd_int
% 5.06/5.43 = ( ^ [K3: int,L: int] :
% 5.06/5.43 ( if_int
% 5.06/5.43 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.06/5.43 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.06/5.43 @ ( uminus_uminus_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.06/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.06/5.43 @ ( plus_plus_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.06/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.06/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_int.simps
% 5.06/5.43 thf(fact_9465_and__int_Opelims,axiom,
% 5.06/5.43 ! [X: int,Xa2: int,Y: int] :
% 5.06/5.43 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.06/5.43 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.06/5.43 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( uminus_uminus_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.06/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.06/5.43 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.06/5.43 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( plus_plus_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.06/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.06/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.06/5.43 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_int.pelims
% 5.06/5.43 thf(fact_9466_and__int_Opsimps,axiom,
% 5.06/5.43 ! [K: int,L2: int] :
% 5.06/5.43 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 5.06/5.43 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.06/5.43 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.06/5.43 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.06/5.43 = ( uminus_uminus_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.06/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 5.06/5.43 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.06/5.43 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.06/5.43 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.06/5.43 = ( plus_plus_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.06/5.43 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.06/5.43 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_int.psimps
% 5.06/5.43 thf(fact_9467_and__nat__numerals_I1_J,axiom,
% 5.06/5.43 ! [Y: num] :
% 5.06/5.43 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.06/5.43 = zero_zero_nat ) ).
% 5.06/5.43
% 5.06/5.43 % and_nat_numerals(1)
% 5.06/5.43 thf(fact_9468_and__nat__numerals_I3_J,axiom,
% 5.06/5.43 ! [X: num] :
% 5.06/5.43 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.06/5.43 = zero_zero_nat ) ).
% 5.06/5.43
% 5.06/5.43 % and_nat_numerals(3)
% 5.06/5.43 thf(fact_9469_and__nat__numerals_I2_J,axiom,
% 5.06/5.43 ! [Y: num] :
% 5.06/5.43 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.06/5.43 = one_one_nat ) ).
% 5.06/5.43
% 5.06/5.43 % and_nat_numerals(2)
% 5.06/5.43 thf(fact_9470_and__nat__numerals_I4_J,axiom,
% 5.06/5.43 ! [X: num] :
% 5.06/5.43 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.06/5.43 = one_one_nat ) ).
% 5.06/5.43
% 5.06/5.43 % and_nat_numerals(4)
% 5.06/5.43 thf(fact_9471_and__Suc__0__eq,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( bit_se727722235901077358nd_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.06/5.43 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_Suc_0_eq
% 5.06/5.43 thf(fact_9472_Suc__0__and__eq,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.43 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Suc_0_and_eq
% 5.06/5.43 thf(fact_9473_bit__Suc__0__iff,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.43 = ( N2 = zero_zero_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_Suc_0_iff
% 5.06/5.43 thf(fact_9474_not__bit__Suc__0__Suc,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % not_bit_Suc_0_Suc
% 5.06/5.43 thf(fact_9475_not__bit__Suc__0__numeral,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % not_bit_Suc_0_numeral
% 5.06/5.43 thf(fact_9476_and__nat__def,axiom,
% 5.06/5.43 ( bit_se727722235901077358nd_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_nat_def
% 5.06/5.43 thf(fact_9477_bit__nat__iff,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N2 )
% 5.06/5.43 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.43 & ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_nat_iff
% 5.06/5.43 thf(fact_9478_atLeastAtMostPlus1__int__conv,axiom,
% 5.06/5.43 ! [M: int,N2: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 5.06/5.43 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 5.06/5.43 = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastAtMostPlus1_int_conv
% 5.06/5.43 thf(fact_9479_simp__from__to,axiom,
% 5.06/5.43 ( set_or1266510415728281911st_int
% 5.06/5.43 = ( ^ [I5: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I5 ) @ bot_bot_set_int @ ( insert_int @ I5 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % simp_from_to
% 5.06/5.43 thf(fact_9480_bit__nat__def,axiom,
% 5.06/5.43 ( bit_se1148574629649215175it_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] :
% 5.06/5.43 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_nat_def
% 5.06/5.43 thf(fact_9481_and__int_Opinduct,axiom,
% 5.06/5.43 ! [A0: int,A12: int,P: int > int > $o] :
% 5.06/5.43 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.06/5.43 => ( ! [K2: int,L4: int] :
% 5.06/5.43 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 5.06/5.43 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.06/5.43 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.06/5.43 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.06/5.43 => ( P @ K2 @ L4 ) ) )
% 5.06/5.43 => ( P @ A0 @ A12 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_int.pinduct
% 5.06/5.43 thf(fact_9482_and__nat__unfold,axiom,
% 5.06/5.43 ( bit_se727722235901077358nd_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] :
% 5.06/5.43 ( if_nat
% 5.06/5.43 @ ( ( M6 = zero_zero_nat )
% 5.06/5.43 | ( N = zero_zero_nat ) )
% 5.06/5.43 @ zero_zero_nat
% 5.06/5.43 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_nat_unfold
% 5.06/5.43 thf(fact_9483_and__nat__rec,axiom,
% 5.06/5.43 ( bit_se727722235901077358nd_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] :
% 5.06/5.43 ( plus_plus_nat
% 5.06/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.06/5.43 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.06/5.43 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.06/5.43 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_nat_rec
% 5.06/5.43 thf(fact_9484_cis__multiple__2pi,axiom,
% 5.06/5.43 ! [N2: real] :
% 5.06/5.43 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.06/5.43 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.06/5.43 = one_one_complex ) ) ).
% 5.06/5.43
% 5.06/5.43 % cis_multiple_2pi
% 5.06/5.43 thf(fact_9485_rat__inverse__code,axiom,
% 5.06/5.43 ! [P4: rat] :
% 5.06/5.43 ( ( quotient_of @ ( inverse_inverse_rat @ P4 ) )
% 5.06/5.43 = ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [A4: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( A4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A4 ) @ B4 ) @ ( abs_abs_int @ A4 ) ) )
% 5.06/5.43 @ ( quotient_of @ P4 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_inverse_code
% 5.06/5.43 thf(fact_9486_set__encode__insert,axiom,
% 5.06/5.43 ! [A2: set_nat,N2: nat] :
% 5.06/5.43 ( ( finite_finite_nat @ A2 )
% 5.06/5.43 => ( ~ ( member_nat @ N2 @ A2 )
% 5.06/5.43 => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 5.06/5.43 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % set_encode_insert
% 5.06/5.43 thf(fact_9487_quotient__of__number_I3_J,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.06/5.43 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % quotient_of_number(3)
% 5.06/5.43 thf(fact_9488_quotient__of__number_I5_J,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.06/5.43 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % quotient_of_number(5)
% 5.06/5.43 thf(fact_9489_divide__rat__def,axiom,
% 5.06/5.43 ( divide_divide_rat
% 5.06/5.43 = ( ^ [Q4: rat,R5: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % divide_rat_def
% 5.06/5.43 thf(fact_9490_lessThan__Suc,axiom,
% 5.06/5.43 ! [K: nat] :
% 5.06/5.43 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.06/5.43 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % lessThan_Suc
% 5.06/5.43 thf(fact_9491_atMost__Suc,axiom,
% 5.06/5.43 ! [K: nat] :
% 5.06/5.43 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.06/5.43 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atMost_Suc
% 5.06/5.43 thf(fact_9492_atLeast0__atMost__Suc,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.06/5.43 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeast0_atMost_Suc
% 5.06/5.43 thf(fact_9493_Icc__eq__insert__lb__nat,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.43 => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 5.06/5.43 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Icc_eq_insert_lb_nat
% 5.06/5.43 thf(fact_9494_atLeastAtMostSuc__conv,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.06/5.43 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 5.06/5.43 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastAtMostSuc_conv
% 5.06/5.43 thf(fact_9495_atLeastAtMost__insertL,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.43 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.06/5.43 = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastAtMost_insertL
% 5.06/5.43 thf(fact_9496_lessThan__nat__numeral,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.06/5.43 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % lessThan_nat_numeral
% 5.06/5.43 thf(fact_9497_atMost__nat__numeral,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.06/5.43 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atMost_nat_numeral
% 5.06/5.43 thf(fact_9498_sin__times__pi__eq__0,axiom,
% 5.06/5.43 ! [X: real] :
% 5.06/5.43 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % sin_times_pi_eq_0
% 5.06/5.43 thf(fact_9499_rat__abs__code,axiom,
% 5.06/5.43 ! [P4: rat] :
% 5.06/5.43 ( ( quotient_of @ ( abs_abs_rat @ P4 ) )
% 5.06/5.43 = ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [A4: int] : ( product_Pair_int_int @ ( abs_abs_int @ A4 ) )
% 5.06/5.43 @ ( quotient_of @ P4 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_abs_code
% 5.06/5.43 thf(fact_9500_atLeast1__atMost__eq__remove0,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.43 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeast1_atMost_eq_remove0
% 5.06/5.43 thf(fact_9501_rat__uminus__code,axiom,
% 5.06/5.43 ! [P4: rat] :
% 5.06/5.43 ( ( quotient_of @ ( uminus_uminus_rat @ P4 ) )
% 5.06/5.43 = ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [A4: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A4 ) )
% 5.06/5.43 @ ( quotient_of @ P4 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_uminus_code
% 5.06/5.43 thf(fact_9502_rat__less__code,axiom,
% 5.06/5.43 ( ord_less_rat
% 5.06/5.43 = ( ^ [P5: rat,Q4: rat] :
% 5.06/5.43 ( produc4947309494688390418_int_o
% 5.06/5.43 @ ^ [A4: int,C4: int] :
% 5.06/5.43 ( produc4947309494688390418_int_o
% 5.06/5.43 @ ^ [B4: int,D2: int] : ( ord_less_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C4 @ B4 ) )
% 5.06/5.43 @ ( quotient_of @ Q4 ) )
% 5.06/5.43 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_less_code
% 5.06/5.43 thf(fact_9503_rat__floor__code,axiom,
% 5.06/5.43 ( archim3151403230148437115or_rat
% 5.06/5.43 = ( ^ [P5: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P5 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_floor_code
% 5.06/5.43 thf(fact_9504_rat__less__eq__code,axiom,
% 5.06/5.43 ( ord_less_eq_rat
% 5.06/5.43 = ( ^ [P5: rat,Q4: rat] :
% 5.06/5.43 ( produc4947309494688390418_int_o
% 5.06/5.43 @ ^ [A4: int,C4: int] :
% 5.06/5.43 ( produc4947309494688390418_int_o
% 5.06/5.43 @ ^ [B4: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C4 @ B4 ) )
% 5.06/5.43 @ ( quotient_of @ Q4 ) )
% 5.06/5.43 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_less_eq_code
% 5.06/5.43 thf(fact_9505_set__decode__plus__power__2,axiom,
% 5.06/5.43 ! [N2: nat,Z: nat] :
% 5.06/5.43 ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z ) )
% 5.06/5.43 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z ) )
% 5.06/5.43 = ( insert_nat @ N2 @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % set_decode_plus_power_2
% 5.06/5.43 thf(fact_9506_sin__integer__2pi,axiom,
% 5.06/5.43 ! [N2: real] :
% 5.06/5.43 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.06/5.43 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.06/5.43 = zero_zero_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % sin_integer_2pi
% 5.06/5.43 thf(fact_9507_cos__integer__2pi,axiom,
% 5.06/5.43 ! [N2: real] :
% 5.06/5.43 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.06/5.43 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.06/5.43 = one_one_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % cos_integer_2pi
% 5.06/5.43 thf(fact_9508_rat__minus__code,axiom,
% 5.06/5.43 ! [P4: rat,Q2: rat] :
% 5.06/5.43 ( ( quotient_of @ ( minus_minus_rat @ P4 @ Q2 ) )
% 5.06/5.43 = ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [A4: int,C4: int] :
% 5.06/5.43 ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ B4 @ C4 ) ) @ ( times_times_int @ C4 @ D2 ) ) )
% 5.06/5.43 @ ( quotient_of @ Q2 ) )
% 5.06/5.43 @ ( quotient_of @ P4 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_minus_code
% 5.06/5.43 thf(fact_9509_rat__plus__code,axiom,
% 5.06/5.43 ! [P4: rat,Q2: rat] :
% 5.06/5.43 ( ( quotient_of @ ( plus_plus_rat @ P4 @ Q2 ) )
% 5.06/5.43 = ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [A4: int,C4: int] :
% 5.06/5.43 ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ B4 @ C4 ) ) @ ( times_times_int @ C4 @ D2 ) ) )
% 5.06/5.43 @ ( quotient_of @ Q2 ) )
% 5.06/5.43 @ ( quotient_of @ P4 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_plus_code
% 5.06/5.43 thf(fact_9510_normalize__crossproduct,axiom,
% 5.06/5.43 ! [Q2: int,S2: int,P4: int,R2: int] :
% 5.06/5.43 ( ( Q2 != zero_zero_int )
% 5.06/5.43 => ( ( S2 != zero_zero_int )
% 5.06/5.43 => ( ( ( normalize @ ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.06/5.43 = ( normalize @ ( product_Pair_int_int @ R2 @ S2 ) ) )
% 5.06/5.43 => ( ( times_times_int @ P4 @ S2 )
% 5.06/5.43 = ( times_times_int @ R2 @ Q2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % normalize_crossproduct
% 5.06/5.43 thf(fact_9511_rat__times__code,axiom,
% 5.06/5.43 ! [P4: rat,Q2: rat] :
% 5.06/5.43 ( ( quotient_of @ ( times_times_rat @ P4 @ Q2 ) )
% 5.06/5.43 = ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [A4: int,C4: int] :
% 5.06/5.43 ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ B4 ) @ ( times_times_int @ C4 @ D2 ) ) )
% 5.06/5.43 @ ( quotient_of @ Q2 ) )
% 5.06/5.43 @ ( quotient_of @ P4 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_times_code
% 5.06/5.43 thf(fact_9512_rat__divide__code,axiom,
% 5.06/5.43 ! [P4: rat,Q2: rat] :
% 5.06/5.43 ( ( quotient_of @ ( divide_divide_rat @ P4 @ Q2 ) )
% 5.06/5.43 = ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [A4: int,C4: int] :
% 5.06/5.43 ( produc4245557441103728435nt_int
% 5.06/5.43 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C4 @ B4 ) ) )
% 5.06/5.43 @ ( quotient_of @ Q2 ) )
% 5.06/5.43 @ ( quotient_of @ P4 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_divide_code
% 5.06/5.43 thf(fact_9513_Frct__code__post_I5_J,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.06/5.43 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Frct_code_post(5)
% 5.06/5.43 thf(fact_9514_xor__Suc__0__eq,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.06/5.43 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.06/5.43 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_Suc_0_eq
% 5.06/5.43 thf(fact_9515_xor__nat__numerals_I4_J,axiom,
% 5.06/5.43 ! [X: num] :
% 5.06/5.43 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.06/5.43 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_nat_numerals(4)
% 5.06/5.43 thf(fact_9516_xor__nat__numerals_I3_J,axiom,
% 5.06/5.43 ! [X: num] :
% 5.06/5.43 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.06/5.43 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_nat_numerals(3)
% 5.06/5.43 thf(fact_9517_xor__nat__numerals_I2_J,axiom,
% 5.06/5.43 ! [Y: num] :
% 5.06/5.43 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.06/5.43 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_nat_numerals(2)
% 5.06/5.43 thf(fact_9518_xor__nat__numerals_I1_J,axiom,
% 5.06/5.43 ! [Y: num] :
% 5.06/5.43 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.06/5.43 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_nat_numerals(1)
% 5.06/5.43 thf(fact_9519_Frct__code__post_I4_J,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.06/5.43 = ( numeral_numeral_rat @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % Frct_code_post(4)
% 5.06/5.43 thf(fact_9520_xor__nat__unfold,axiom,
% 5.06/5.43 ( bit_se6528837805403552850or_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_nat_unfold
% 5.06/5.43 thf(fact_9521_xor__nat__rec,axiom,
% 5.06/5.43 ( bit_se6528837805403552850or_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] :
% 5.06/5.43 ( plus_plus_nat
% 5.06/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.06/5.43 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 5.06/5.43 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.06/5.43 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_nat_rec
% 5.06/5.43 thf(fact_9522_Frct__code__post_I6_J,axiom,
% 5.06/5.43 ! [K: num,L2: num] :
% 5.06/5.43 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 5.06/5.43 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Frct_code_post(6)
% 5.06/5.43 thf(fact_9523_Suc__0__xor__eq,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.43 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.43 @ ( zero_n2687167440665602831ol_nat
% 5.06/5.43 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Suc_0_xor_eq
% 5.06/5.43 thf(fact_9524_horner__sum__of__bool__2__less,axiom,
% 5.06/5.43 ! [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 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % horner_sum_of_bool_2_less
% 5.06/5.43 thf(fact_9525_push__bit__nonnegative__int__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.06/5.43 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % push_bit_nonnegative_int_iff
% 5.06/5.43 thf(fact_9526_push__bit__negative__int__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K ) @ zero_zero_int )
% 5.06/5.43 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % push_bit_negative_int_iff
% 5.06/5.43 thf(fact_9527_concat__bit__of__zero__1,axiom,
% 5.06/5.43 ! [N2: nat,L2: int] :
% 5.06/5.43 ( ( bit_concat_bit @ N2 @ zero_zero_int @ L2 )
% 5.06/5.43 = ( bit_se545348938243370406it_int @ N2 @ L2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % concat_bit_of_zero_1
% 5.06/5.43 thf(fact_9528_xor__nonnegative__int__iff,axiom,
% 5.06/5.43 ! [K: int,L2: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 5.06/5.43 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.06/5.43 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_nonnegative_int_iff
% 5.06/5.43 thf(fact_9529_xor__negative__int__iff,axiom,
% 5.06/5.43 ! [K: int,L2: int] :
% 5.06/5.43 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 5.06/5.43 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.06/5.43 != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_negative_int_iff
% 5.06/5.43 thf(fact_9530_push__bit__of__Suc__0,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( bit_se547839408752420682it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.06/5.43 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % push_bit_of_Suc_0
% 5.06/5.43 thf(fact_9531_bit__xor__int__iff,axiom,
% 5.06/5.43 ! [K: int,L2: int,N2: nat] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N2 )
% 5.06/5.43 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.06/5.43 != ( bit_se1146084159140164899it_int @ L2 @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_xor_int_iff
% 5.06/5.43 thf(fact_9532_flip__bit__int__def,axiom,
% 5.06/5.43 ( bit_se2159334234014336723it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % flip_bit_int_def
% 5.06/5.43 thf(fact_9533_push__bit__nat__eq,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( bit_se547839408752420682it_nat @ N2 @ ( nat2 @ K ) )
% 5.06/5.43 = ( nat2 @ ( bit_se545348938243370406it_int @ N2 @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % push_bit_nat_eq
% 5.06/5.43 thf(fact_9534_XOR__lower,axiom,
% 5.06/5.43 ! [X: int,Y: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % XOR_lower
% 5.06/5.43 thf(fact_9535_set__bit__nat__def,axiom,
% 5.06/5.43 ( bit_se7882103937844011126it_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] : ( bit_se1412395901928357646or_nat @ N @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % set_bit_nat_def
% 5.06/5.43 thf(fact_9536_flip__bit__nat__def,axiom,
% 5.06/5.43 ( bit_se2161824704523386999it_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] : ( bit_se6528837805403552850or_nat @ N @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % flip_bit_nat_def
% 5.06/5.43 thf(fact_9537_bit__push__bit__iff__int,axiom,
% 5.06/5.43 ! [M: nat,K: int,N2: nat] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N2 )
% 5.06/5.43 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.43 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_push_bit_iff_int
% 5.06/5.43 thf(fact_9538_xor__nat__def,axiom,
% 5.06/5.43 ( bit_se6528837805403552850or_nat
% 5.06/5.43 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_nat_def
% 5.06/5.43 thf(fact_9539_bit__push__bit__iff__nat,axiom,
% 5.06/5.43 ! [M: nat,Q2: nat,N2: nat] :
% 5.06/5.43 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N2 )
% 5.06/5.43 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.43 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_push_bit_iff_nat
% 5.06/5.43 thf(fact_9540_concat__bit__eq,axiom,
% 5.06/5.43 ( bit_concat_bit
% 5.06/5.43 = ( ^ [N: nat,K3: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % concat_bit_eq
% 5.06/5.43 thf(fact_9541_concat__bit__def,axiom,
% 5.06/5.43 ( bit_concat_bit
% 5.06/5.43 = ( ^ [N: nat,K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % concat_bit_def
% 5.06/5.43 thf(fact_9542_set__bit__int__def,axiom,
% 5.06/5.43 ( bit_se7879613467334960850it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % set_bit_int_def
% 5.06/5.43 thf(fact_9543_push__bit__nat__def,axiom,
% 5.06/5.43 ( bit_se547839408752420682it_nat
% 5.06/5.43 = ( ^ [N: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % push_bit_nat_def
% 5.06/5.43 thf(fact_9544_push__bit__int__def,axiom,
% 5.06/5.43 ( bit_se545348938243370406it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % push_bit_int_def
% 5.06/5.43 thf(fact_9545_push__bit__minus__one,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.43 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % push_bit_minus_one
% 5.06/5.43 thf(fact_9546_XOR__upper,axiom,
% 5.06/5.43 ! [X: int,N2: nat,Y: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.43 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.43 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.06/5.43 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % XOR_upper
% 5.06/5.43 thf(fact_9547_xor__int__rec,axiom,
% 5.06/5.43 ( bit_se6526347334894502574or_int
% 5.06/5.43 = ( ^ [K3: int,L: int] :
% 5.06/5.43 ( plus_plus_int
% 5.06/5.43 @ ( zero_n2684676970156552555ol_int
% 5.06/5.43 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.06/5.43 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.06/5.43 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_int_rec
% 5.06/5.43 thf(fact_9548_xor__int__unfold,axiom,
% 5.06/5.43 ( bit_se6526347334894502574or_int
% 5.06/5.43 = ( ^ [K3: int,L: int] :
% 5.06/5.43 ( if_int
% 5.06/5.43 @ ( K3
% 5.06/5.43 = ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.43 @ ( bit_ri7919022796975470100ot_int @ L )
% 5.06/5.43 @ ( if_int
% 5.06/5.43 @ ( L
% 5.06/5.43 = ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.43 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.06/5.43 @ ( if_int @ ( K3 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_int_unfold
% 5.06/5.43 thf(fact_9549_Cauchy__iff2,axiom,
% 5.06/5.43 ( topolo4055970368930404560y_real
% 5.06/5.43 = ( ^ [X4: nat > real] :
% 5.06/5.43 ! [J3: nat] :
% 5.06/5.43 ? [M9: nat] :
% 5.06/5.43 ! [M6: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ M9 @ M6 )
% 5.06/5.43 => ! [N: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ M9 @ N )
% 5.06/5.43 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X4 @ M6 ) @ ( X4 @ N ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Cauchy_iff2
% 5.06/5.43 thf(fact_9550_not__negative__int__iff,axiom,
% 5.06/5.43 ! [K: int] :
% 5.06/5.43 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.06/5.43 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % not_negative_int_iff
% 5.06/5.43 thf(fact_9551_not__nonnegative__int__iff,axiom,
% 5.06/5.43 ! [K: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.06/5.43 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % not_nonnegative_int_iff
% 5.06/5.43 thf(fact_9552_or__minus__minus__numerals,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_minus_minus_numerals
% 5.06/5.43 thf(fact_9553_and__minus__minus__numerals,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_minus_minus_numerals
% 5.06/5.43 thf(fact_9554_bit__not__int__iff,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N2 )
% 5.06/5.43 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_not_int_iff
% 5.06/5.43 thf(fact_9555_or__int__def,axiom,
% 5.06/5.43 ( bit_se1409905431419307370or_int
% 5.06/5.43 = ( ^ [K3: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_int_def
% 5.06/5.43 thf(fact_9556_not__int__def,axiom,
% 5.06/5.43 ( bit_ri7919022796975470100ot_int
% 5.06/5.43 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % not_int_def
% 5.06/5.43 thf(fact_9557_and__not__numerals_I1_J,axiom,
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.06/5.43 = zero_zero_int ) ).
% 5.06/5.43
% 5.06/5.43 % and_not_numerals(1)
% 5.06/5.43 thf(fact_9558_or__not__numerals_I1_J,axiom,
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.06/5.43 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_not_numerals(1)
% 5.06/5.43 thf(fact_9559_unset__bit__int__def,axiom,
% 5.06/5.43 ( bit_se4203085406695923979it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % unset_bit_int_def
% 5.06/5.43 thf(fact_9560_xor__int__def,axiom,
% 5.06/5.43 ( bit_se6526347334894502574or_int
% 5.06/5.43 = ( ^ [K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_int_def
% 5.06/5.43 thf(fact_9561_not__int__div__2,axiom,
% 5.06/5.43 ! [K: int] :
% 5.06/5.43 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.43 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % not_int_div_2
% 5.06/5.43 thf(fact_9562_even__not__iff__int,axiom,
% 5.06/5.43 ! [K: int] :
% 5.06/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.06/5.43 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % even_not_iff_int
% 5.06/5.43 thf(fact_9563_and__not__numerals_I4_J,axiom,
% 5.06/5.43 ! [M: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.06/5.43 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_not_numerals(4)
% 5.06/5.43 thf(fact_9564_and__not__numerals_I2_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.06/5.43 = one_one_int ) ).
% 5.06/5.43
% 5.06/5.43 % and_not_numerals(2)
% 5.06/5.43 thf(fact_9565_or__not__numerals_I4_J,axiom,
% 5.06/5.43 ! [M: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.06/5.43 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_not_numerals(4)
% 5.06/5.43 thf(fact_9566_or__not__numerals_I2_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.06/5.43 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_not_numerals(2)
% 5.06/5.43 thf(fact_9567_bit__minus__int__iff,axiom,
% 5.06/5.43 ! [K: int,N2: nat] :
% 5.06/5.43 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N2 )
% 5.06/5.43 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_minus_int_iff
% 5.06/5.43 thf(fact_9568_numeral__or__not__num__eq,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) )
% 5.06/5.43 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % numeral_or_not_num_eq
% 5.06/5.43 thf(fact_9569_int__numeral__not__or__num__neg,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % int_numeral_not_or_num_neg
% 5.06/5.43 thf(fact_9570_int__numeral__or__not__num__neg,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % int_numeral_or_not_num_neg
% 5.06/5.43 thf(fact_9571_and__not__numerals_I5_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.06/5.43 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_not_numerals(5)
% 5.06/5.43 thf(fact_9572_and__not__numerals_I7_J,axiom,
% 5.06/5.43 ! [M: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.06/5.43 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_not_numerals(7)
% 5.06/5.43 thf(fact_9573_or__not__numerals_I3_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.06/5.43 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_not_numerals(3)
% 5.06/5.43 thf(fact_9574_and__not__numerals_I3_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.06/5.43 = zero_zero_int ) ).
% 5.06/5.43
% 5.06/5.43 % and_not_numerals(3)
% 5.06/5.43 thf(fact_9575_or__not__numerals_I7_J,axiom,
% 5.06/5.43 ! [M: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.06/5.43 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_not_numerals(7)
% 5.06/5.43 thf(fact_9576_and__not__numerals_I9_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.06/5.43 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_not_numerals(9)
% 5.06/5.43 thf(fact_9577_and__not__numerals_I6_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.06/5.43 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_not_numerals(6)
% 5.06/5.43 thf(fact_9578_or__not__numerals_I6_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.06/5.43 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_not_numerals(6)
% 5.06/5.43 thf(fact_9579_or__not__numerals_I5_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.06/5.43 = ( 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 @ N2 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_not_numerals(5)
% 5.06/5.43 thf(fact_9580_and__not__numerals_I8_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.06/5.43 = ( 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 @ N2 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % and_not_numerals(8)
% 5.06/5.43 thf(fact_9581_or__not__numerals_I8_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.06/5.43 = ( 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 @ N2 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_not_numerals(8)
% 5.06/5.43 thf(fact_9582_or__not__numerals_I9_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.06/5.43 = ( 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 @ N2 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % or_not_numerals(9)
% 5.06/5.43 thf(fact_9583_not__int__rec,axiom,
% 5.06/5.43 ( bit_ri7919022796975470100ot_int
% 5.06/5.43 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % not_int_rec
% 5.06/5.43 thf(fact_9584_Sum__Ico__nat,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( groups3542108847815614940at_nat
% 5.06/5.43 @ ^ [X2: nat] : X2
% 5.06/5.43 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.06/5.43 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Sum_Ico_nat
% 5.06/5.43 thf(fact_9585_VEBT_Osize_I3_J,axiom,
% 5.06/5.43 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.06/5.43 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.06/5.43 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % VEBT.size(3)
% 5.06/5.43 thf(fact_9586_atLeastLessThan__singleton,axiom,
% 5.06/5.43 ! [M: nat] :
% 5.06/5.43 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.06/5.43 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastLessThan_singleton
% 5.06/5.43 thf(fact_9587_all__nat__less__eq,axiom,
% 5.06/5.43 ! [N2: nat,P: nat > $o] :
% 5.06/5.43 ( ( ! [M6: nat] :
% 5.06/5.43 ( ( ord_less_nat @ M6 @ N2 )
% 5.06/5.43 => ( P @ M6 ) ) )
% 5.06/5.43 = ( ! [X2: nat] :
% 5.06/5.43 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.43 => ( P @ X2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % all_nat_less_eq
% 5.06/5.43 thf(fact_9588_ex__nat__less__eq,axiom,
% 5.06/5.43 ! [N2: nat,P: nat > $o] :
% 5.06/5.43 ( ( ? [M6: nat] :
% 5.06/5.43 ( ( ord_less_nat @ M6 @ N2 )
% 5.06/5.43 & ( P @ M6 ) ) )
% 5.06/5.43 = ( ? [X2: nat] :
% 5.06/5.43 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.43 & ( P @ X2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % ex_nat_less_eq
% 5.06/5.43 thf(fact_9589_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.06/5.43 ! [L2: nat,U: nat] :
% 5.06/5.43 ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 5.06/5.43 = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastLessThanSuc_atLeastAtMost
% 5.06/5.43 thf(fact_9590_atLeast0__lessThan__Suc,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.06/5.43 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeast0_lessThan_Suc
% 5.06/5.43 thf(fact_9591_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.06/5.43 ! [N4: set_nat,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.43 => ( finite_finite_nat @ N4 ) ) ).
% 5.06/5.43
% 5.06/5.43 % subset_eq_atLeast0_lessThan_finite
% 5.06/5.43 thf(fact_9592_atLeastLessThanSuc,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.43 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.06/5.43 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.43 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.06/5.43 = bot_bot_set_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastLessThanSuc
% 5.06/5.43 thf(fact_9593_prod__Suc__fact,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.43 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % prod_Suc_fact
% 5.06/5.43 thf(fact_9594_prod__Suc__Suc__fact,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.06/5.43 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % prod_Suc_Suc_fact
% 5.06/5.43 thf(fact_9595_atLeastLessThan__nat__numeral,axiom,
% 5.06/5.43 ! [M: nat,K: num] :
% 5.06/5.43 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.06/5.43 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.06/5.43 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.06/5.43 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.06/5.43 = bot_bot_set_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastLessThan_nat_numeral
% 5.06/5.43 thf(fact_9596_atLeast1__lessThan__eq__remove0,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.06/5.43 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeast1_lessThan_eq_remove0
% 5.06/5.43 thf(fact_9597_sum__power2,axiom,
% 5.06/5.43 ! [K: nat] :
% 5.06/5.43 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.06/5.43 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % sum_power2
% 5.06/5.43 thf(fact_9598_Chebyshev__sum__upper__nat,axiom,
% 5.06/5.43 ! [N2: nat,A: nat > nat,B: nat > nat] :
% 5.06/5.43 ( ! [I3: nat,J2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.06/5.43 => ( ( ord_less_nat @ J2 @ N2 )
% 5.06/5.43 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 5.06/5.43 => ( ! [I3: nat,J2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.06/5.43 => ( ( ord_less_nat @ J2 @ N2 )
% 5.06/5.43 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I3 ) ) ) )
% 5.06/5.43 => ( ord_less_eq_nat
% 5.06/5.43 @ ( times_times_nat @ N2
% 5.06/5.43 @ ( groups3542108847815614940at_nat
% 5.06/5.43 @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( B @ I5 ) )
% 5.06/5.43 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 5.06/5.43 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Chebyshev_sum_upper_nat
% 5.06/5.43 thf(fact_9599_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.06/5.43 ! [L2: int,U: int] :
% 5.06/5.43 ( ( set_or4662586982721622107an_int @ L2 @ ( plus_plus_int @ U @ one_one_int ) )
% 5.06/5.43 = ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.06/5.43 thf(fact_9600_VEBT_Osize__gen_I1_J,axiom,
% 5.06/5.43 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.06/5.43 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.06/5.43 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % VEBT.size_gen(1)
% 5.06/5.43 thf(fact_9601_valid__eq2,axiom,
% 5.06/5.43 ! [T: vEBT_VEBT,D: nat] :
% 5.06/5.43 ( ( vEBT_VEBT_valid @ T @ D )
% 5.06/5.43 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.06/5.43
% 5.06/5.43 % valid_eq2
% 5.06/5.43 thf(fact_9602_valid__eq1,axiom,
% 5.06/5.43 ! [T: vEBT_VEBT,D: nat] :
% 5.06/5.43 ( ( vEBT_invar_vebt @ T @ D )
% 5.06/5.43 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.06/5.43
% 5.06/5.43 % valid_eq1
% 5.06/5.43 thf(fact_9603_valid__eq,axiom,
% 5.06/5.43 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.06/5.43
% 5.06/5.43 % valid_eq
% 5.06/5.43 thf(fact_9604_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.06/5.43 ! [Uu: $o,Uv: $o,D: nat] :
% 5.06/5.43 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.06/5.43 = ( D = one_one_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % VEBT_internal.valid'.simps(1)
% 5.06/5.43 thf(fact_9605_VEBT_Osize__gen_I2_J,axiom,
% 5.06/5.43 ! [X21: $o,X222: $o] :
% 5.06/5.43 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.06/5.43 = zero_zero_nat ) ).
% 5.06/5.43
% 5.06/5.43 % VEBT.size_gen(2)
% 5.06/5.43 thf(fact_9606_Code__Target__Int_Opositive__def,axiom,
% 5.06/5.43 code_Target_positive = numeral_numeral_int ).
% 5.06/5.43
% 5.06/5.43 % Code_Target_Int.positive_def
% 5.06/5.43 thf(fact_9607_csqrt_Osimps_I1_J,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( re @ ( csqrt @ Z ) )
% 5.06/5.43 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % csqrt.simps(1)
% 5.06/5.43 thf(fact_9608_complex__Re__numeral,axiom,
% 5.06/5.43 ! [V: num] :
% 5.06/5.43 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.06/5.43 = ( numeral_numeral_real @ V ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_Re_numeral
% 5.06/5.43 thf(fact_9609_Re__divide__numeral,axiom,
% 5.06/5.43 ! [Z: complex,W: num] :
% 5.06/5.43 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.43 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_divide_numeral
% 5.06/5.43 thf(fact_9610_sums__Re,axiom,
% 5.06/5.43 ! [X8: nat > complex,A: complex] :
% 5.06/5.43 ( ( sums_complex @ X8 @ A )
% 5.06/5.43 => ( sums_real
% 5.06/5.43 @ ^ [N: nat] : ( re @ ( X8 @ N ) )
% 5.06/5.43 @ ( re @ A ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sums_Re
% 5.06/5.43 thf(fact_9611_Cauchy__Re,axiom,
% 5.06/5.43 ! [X8: nat > complex] :
% 5.06/5.43 ( ( topolo6517432010174082258omplex @ X8 )
% 5.06/5.43 => ( topolo4055970368930404560y_real
% 5.06/5.43 @ ^ [N: nat] : ( re @ ( X8 @ N ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Cauchy_Re
% 5.06/5.43 thf(fact_9612_complex__Re__le__cmod,axiom,
% 5.06/5.43 ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_Re_le_cmod
% 5.06/5.43 thf(fact_9613_plus__complex_Osimps_I1_J,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( re @ ( plus_plus_complex @ X @ Y ) )
% 5.06/5.43 = ( plus_plus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % plus_complex.simps(1)
% 5.06/5.43 thf(fact_9614_scaleR__complex_Osimps_I1_J,axiom,
% 5.06/5.43 ! [R2: real,X: complex] :
% 5.06/5.43 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 5.06/5.43 = ( times_times_real @ R2 @ ( re @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % scaleR_complex.simps(1)
% 5.06/5.43 thf(fact_9615_minus__complex_Osimps_I1_J,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( re @ ( minus_minus_complex @ X @ Y ) )
% 5.06/5.43 = ( minus_minus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % minus_complex.simps(1)
% 5.06/5.43 thf(fact_9616_summable__Re,axiom,
% 5.06/5.43 ! [F: nat > complex] :
% 5.06/5.43 ( ( summable_complex @ F )
% 5.06/5.43 => ( summable_real
% 5.06/5.43 @ ^ [X2: nat] : ( re @ ( F @ X2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % summable_Re
% 5.06/5.43 thf(fact_9617_abs__Re__le__cmod,axiom,
% 5.06/5.43 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % abs_Re_le_cmod
% 5.06/5.43 thf(fact_9618_Re__csqrt,axiom,
% 5.06/5.43 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_csqrt
% 5.06/5.43 thf(fact_9619_cmod__plus__Re__le__0__iff,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.06/5.43 = ( ( re @ Z )
% 5.06/5.43 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % cmod_plus_Re_le_0_iff
% 5.06/5.43 thf(fact_9620_cos__n__Re__cis__pow__n,axiom,
% 5.06/5.43 ! [N2: nat,A: real] :
% 5.06/5.43 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) )
% 5.06/5.43 = ( re @ ( power_power_complex @ ( cis @ A ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % cos_n_Re_cis_pow_n
% 5.06/5.43 thf(fact_9621_csqrt_Ocode,axiom,
% 5.06/5.43 ( csqrt
% 5.06/5.43 = ( ^ [Z2: complex] :
% 5.06/5.43 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.43 @ ( times_times_real
% 5.06/5.43 @ ( if_real
% 5.06/5.43 @ ( ( im @ Z2 )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 @ one_one_real
% 5.06/5.43 @ ( sgn_sgn_real @ ( im @ Z2 ) ) )
% 5.06/5.43 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z2 ) @ ( re @ Z2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % csqrt.code
% 5.06/5.43 thf(fact_9622_csqrt_Osimps_I2_J,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( im @ ( csqrt @ Z ) )
% 5.06/5.43 = ( times_times_real
% 5.06/5.43 @ ( if_real
% 5.06/5.43 @ ( ( im @ Z )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 @ one_one_real
% 5.06/5.43 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.06/5.43 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % csqrt.simps(2)
% 5.06/5.43 thf(fact_9623_csqrt__of__real__nonpos,axiom,
% 5.06/5.43 ! [X: complex] :
% 5.06/5.43 ( ( ( im @ X )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 5.06/5.43 => ( ( csqrt @ X )
% 5.06/5.43 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % csqrt_of_real_nonpos
% 5.06/5.43 thf(fact_9624_Im__power__real,axiom,
% 5.06/5.43 ! [X: complex,N2: nat] :
% 5.06/5.43 ( ( ( im @ X )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 => ( ( im @ ( power_power_complex @ X @ N2 ) )
% 5.06/5.43 = zero_zero_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_power_real
% 5.06/5.43 thf(fact_9625_complex__Im__numeral,axiom,
% 5.06/5.43 ! [V: num] :
% 5.06/5.43 ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 5.06/5.43 = zero_zero_real ) ).
% 5.06/5.43
% 5.06/5.43 % complex_Im_numeral
% 5.06/5.43 thf(fact_9626_Im__i__times,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.06/5.43 = ( re @ Z ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_i_times
% 5.06/5.43 thf(fact_9627_Re__power__real,axiom,
% 5.06/5.43 ! [X: complex,N2: nat] :
% 5.06/5.43 ( ( ( im @ X )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 => ( ( re @ ( power_power_complex @ X @ N2 ) )
% 5.06/5.43 = ( power_power_real @ ( re @ X ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_power_real
% 5.06/5.43 thf(fact_9628_Re__i__times,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.06/5.43 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_i_times
% 5.06/5.43 thf(fact_9629_Im__divide__numeral,axiom,
% 5.06/5.43 ! [Z: complex,W: num] :
% 5.06/5.43 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.43 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_divide_numeral
% 5.06/5.43 thf(fact_9630_csqrt__of__real__nonneg,axiom,
% 5.06/5.43 ! [X: complex] :
% 5.06/5.43 ( ( ( im @ X )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 5.06/5.43 => ( ( csqrt @ X )
% 5.06/5.43 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % csqrt_of_real_nonneg
% 5.06/5.43 thf(fact_9631_csqrt__minus,axiom,
% 5.06/5.43 ! [X: complex] :
% 5.06/5.43 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 5.06/5.43 | ( ( ( im @ X )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 5.06/5.43 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 5.06/5.43 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % csqrt_minus
% 5.06/5.43 thf(fact_9632_sums__Im,axiom,
% 5.06/5.43 ! [X8: nat > complex,A: complex] :
% 5.06/5.43 ( ( sums_complex @ X8 @ A )
% 5.06/5.43 => ( sums_real
% 5.06/5.43 @ ^ [N: nat] : ( im @ ( X8 @ N ) )
% 5.06/5.43 @ ( im @ A ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sums_Im
% 5.06/5.43 thf(fact_9633_Cauchy__Im,axiom,
% 5.06/5.43 ! [X8: nat > complex] :
% 5.06/5.43 ( ( topolo6517432010174082258omplex @ X8 )
% 5.06/5.43 => ( topolo4055970368930404560y_real
% 5.06/5.43 @ ^ [N: nat] : ( im @ ( X8 @ N ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Cauchy_Im
% 5.06/5.43 thf(fact_9634_plus__complex_Osimps_I2_J,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( im @ ( plus_plus_complex @ X @ Y ) )
% 5.06/5.43 = ( plus_plus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % plus_complex.simps(2)
% 5.06/5.43 thf(fact_9635_scaleR__complex_Osimps_I2_J,axiom,
% 5.06/5.43 ! [R2: real,X: complex] :
% 5.06/5.43 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 5.06/5.43 = ( times_times_real @ R2 @ ( im @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % scaleR_complex.simps(2)
% 5.06/5.43 thf(fact_9636_minus__complex_Osimps_I2_J,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( im @ ( minus_minus_complex @ X @ Y ) )
% 5.06/5.43 = ( minus_minus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % minus_complex.simps(2)
% 5.06/5.43 thf(fact_9637_sums__complex__iff,axiom,
% 5.06/5.43 ( sums_complex
% 5.06/5.43 = ( ^ [F3: nat > complex,X2: complex] :
% 5.06/5.43 ( ( sums_real
% 5.06/5.43 @ ^ [Y2: nat] : ( re @ ( F3 @ Y2 ) )
% 5.06/5.43 @ ( re @ X2 ) )
% 5.06/5.43 & ( sums_real
% 5.06/5.43 @ ^ [Y2: nat] : ( im @ ( F3 @ Y2 ) )
% 5.06/5.43 @ ( im @ X2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sums_complex_iff
% 5.06/5.43 thf(fact_9638_summable__Im,axiom,
% 5.06/5.43 ! [F: nat > complex] :
% 5.06/5.43 ( ( summable_complex @ F )
% 5.06/5.43 => ( summable_real
% 5.06/5.43 @ ^ [X2: nat] : ( im @ ( F @ X2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % summable_Im
% 5.06/5.43 thf(fact_9639_abs__Im__le__cmod,axiom,
% 5.06/5.43 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % abs_Im_le_cmod
% 5.06/5.43 thf(fact_9640_summable__complex__iff,axiom,
% 5.06/5.43 ( summable_complex
% 5.06/5.43 = ( ^ [F3: nat > complex] :
% 5.06/5.43 ( ( summable_real
% 5.06/5.43 @ ^ [X2: nat] : ( re @ ( F3 @ X2 ) ) )
% 5.06/5.43 & ( summable_real
% 5.06/5.43 @ ^ [X2: nat] : ( im @ ( F3 @ X2 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % summable_complex_iff
% 5.06/5.43 thf(fact_9641_times__complex_Osimps_I2_J,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( im @ ( times_times_complex @ X @ Y ) )
% 5.06/5.43 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % times_complex.simps(2)
% 5.06/5.43 thf(fact_9642_cmod__Re__le__iff,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( ( im @ X )
% 5.06/5.43 = ( im @ Y ) )
% 5.06/5.43 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.06/5.43 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % cmod_Re_le_iff
% 5.06/5.43 thf(fact_9643_cmod__Im__le__iff,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( ( re @ X )
% 5.06/5.43 = ( re @ Y ) )
% 5.06/5.43 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.06/5.43 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % cmod_Im_le_iff
% 5.06/5.43 thf(fact_9644_times__complex_Osimps_I1_J,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( re @ ( times_times_complex @ X @ Y ) )
% 5.06/5.43 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % times_complex.simps(1)
% 5.06/5.43 thf(fact_9645_plus__complex_Ocode,axiom,
% 5.06/5.43 ( plus_plus_complex
% 5.06/5.43 = ( ^ [X2: complex,Y2: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y2 ) ) @ ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % plus_complex.code
% 5.06/5.43 thf(fact_9646_scaleR__complex_Ocode,axiom,
% 5.06/5.43 ( real_V2046097035970521341omplex
% 5.06/5.43 = ( ^ [R5: real,X2: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X2 ) ) @ ( times_times_real @ R5 @ ( im @ X2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % scaleR_complex.code
% 5.06/5.43 thf(fact_9647_minus__complex_Ocode,axiom,
% 5.06/5.43 ( minus_minus_complex
% 5.06/5.43 = ( ^ [X2: complex,Y2: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X2 ) @ ( re @ Y2 ) ) @ ( minus_minus_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % minus_complex.code
% 5.06/5.43 thf(fact_9648_csqrt__principal,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.06/5.43 | ( ( ( re @ ( csqrt @ Z ) )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % csqrt_principal
% 5.06/5.43 thf(fact_9649_cmod__le,axiom,
% 5.06/5.43 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % cmod_le
% 5.06/5.43 thf(fact_9650_sin__n__Im__cis__pow__n,axiom,
% 5.06/5.43 ! [N2: nat,A: real] :
% 5.06/5.43 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) )
% 5.06/5.43 = ( im @ ( power_power_complex @ ( cis @ A ) @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sin_n_Im_cis_pow_n
% 5.06/5.43 thf(fact_9651_Re__exp,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( re @ ( exp_complex @ Z ) )
% 5.06/5.43 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_exp
% 5.06/5.43 thf(fact_9652_Im__exp,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( im @ ( exp_complex @ Z ) )
% 5.06/5.43 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_exp
% 5.06/5.43 thf(fact_9653_complex__eq,axiom,
% 5.06/5.43 ! [A: complex] :
% 5.06/5.43 ( A
% 5.06/5.43 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_eq
% 5.06/5.43 thf(fact_9654_times__complex_Ocode,axiom,
% 5.06/5.43 ( times_times_complex
% 5.06/5.43 = ( ^ [X2: complex,Y2: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y2 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y2 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % times_complex.code
% 5.06/5.43 thf(fact_9655_exp__eq__polar,axiom,
% 5.06/5.43 ( exp_complex
% 5.06/5.43 = ( ^ [Z2: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z2 ) ) ) @ ( cis @ ( im @ Z2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % exp_eq_polar
% 5.06/5.43 thf(fact_9656_cmod__power2,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.43 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % cmod_power2
% 5.06/5.43 thf(fact_9657_Im__power2,axiom,
% 5.06/5.43 ! [X: complex] :
% 5.06/5.43 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.43 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_power2
% 5.06/5.43 thf(fact_9658_Re__power2,axiom,
% 5.06/5.43 ! [X: complex] :
% 5.06/5.43 ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.43 = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_power2
% 5.06/5.43 thf(fact_9659_complex__eq__0,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( Z = zero_zero_complex )
% 5.06/5.43 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.43 = zero_zero_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_eq_0
% 5.06/5.43 thf(fact_9660_norm__complex__def,axiom,
% 5.06/5.43 ( real_V1022390504157884413omplex
% 5.06/5.43 = ( ^ [Z2: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % norm_complex_def
% 5.06/5.43 thf(fact_9661_inverse__complex_Osimps_I1_J,axiom,
% 5.06/5.43 ! [X: complex] :
% 5.06/5.43 ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 5.06/5.43 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % inverse_complex.simps(1)
% 5.06/5.43 thf(fact_9662_complex__neq__0,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( Z != zero_zero_complex )
% 5.06/5.43 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_neq_0
% 5.06/5.43 thf(fact_9663_Re__divide,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.06/5.43 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_divide
% 5.06/5.43 thf(fact_9664_csqrt__square,axiom,
% 5.06/5.43 ! [B: complex] :
% 5.06/5.43 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.06/5.43 | ( ( ( re @ B )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.06/5.43 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.43 = B ) ) ).
% 5.06/5.43
% 5.06/5.43 % csqrt_square
% 5.06/5.43 thf(fact_9665_csqrt__unique,axiom,
% 5.06/5.43 ! [W: complex,Z: complex] :
% 5.06/5.43 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.06/5.43 = Z )
% 5.06/5.43 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.06/5.43 | ( ( ( re @ W )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.06/5.43 => ( ( csqrt @ Z )
% 5.06/5.43 = W ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % csqrt_unique
% 5.06/5.43 thf(fact_9666_inverse__complex_Osimps_I2_J,axiom,
% 5.06/5.43 ! [X: complex] :
% 5.06/5.43 ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 5.06/5.43 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % inverse_complex.simps(2)
% 5.06/5.43 thf(fact_9667_Im__divide,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.06/5.43 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_divide
% 5.06/5.43 thf(fact_9668_complex__abs__le__norm,axiom,
% 5.06/5.43 ! [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 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_abs_le_norm
% 5.06/5.43 thf(fact_9669_complex__unit__circle,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( Z != zero_zero_complex )
% 5.06/5.43 => ( ( 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 ) ) ) )
% 5.06/5.43 = one_one_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_unit_circle
% 5.06/5.43 thf(fact_9670_inverse__complex_Ocode,axiom,
% 5.06/5.43 ( invers8013647133539491842omplex
% 5.06/5.43 = ( ^ [X2: complex] : ( complex2 @ ( 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 ) ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % inverse_complex.code
% 5.06/5.43 thf(fact_9671_Complex__divide,axiom,
% 5.06/5.43 ( divide1717551699836669952omplex
% 5.06/5.43 = ( ^ [X2: complex,Y2: complex] : ( complex2 @ ( 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 ) ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Complex_divide
% 5.06/5.43 thf(fact_9672_Im__Reals__divide,axiom,
% 5.06/5.43 ! [R2: complex,Z: complex] :
% 5.06/5.43 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.06/5.43 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.06/5.43 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_Reals_divide
% 5.06/5.43 thf(fact_9673_Re__Reals__divide,axiom,
% 5.06/5.43 ! [R2: complex,Z: complex] :
% 5.06/5.43 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.06/5.43 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.06/5.43 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_Reals_divide
% 5.06/5.43 thf(fact_9674_imaginary__eq__real__iff,axiom,
% 5.06/5.43 ! [Y: complex,X: complex] :
% 5.06/5.43 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.06/5.43 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.06/5.43 => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 5.06/5.43 = X )
% 5.06/5.43 = ( ( X = zero_zero_complex )
% 5.06/5.43 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % imaginary_eq_real_iff
% 5.06/5.43 thf(fact_9675_real__eq__imaginary__iff,axiom,
% 5.06/5.43 ! [Y: complex,X: complex] :
% 5.06/5.43 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.06/5.43 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.06/5.43 => ( ( X
% 5.06/5.43 = ( times_times_complex @ imaginary_unit @ Y ) )
% 5.06/5.43 = ( ( X = zero_zero_complex )
% 5.06/5.43 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % real_eq_imaginary_iff
% 5.06/5.43 thf(fact_9676_complex__diff__cnj,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.06/5.43 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_diff_cnj
% 5.06/5.43 thf(fact_9677_complex__mult__cnj,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.06/5.43 = ( 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 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_mult_cnj
% 5.06/5.43 thf(fact_9678_complex__cnj__mult,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( cnj @ ( times_times_complex @ X @ Y ) )
% 5.06/5.43 = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_cnj_mult
% 5.06/5.43 thf(fact_9679_complex__cnj__power,axiom,
% 5.06/5.43 ! [X: complex,N2: nat] :
% 5.06/5.43 ( ( cnj @ ( power_power_complex @ X @ N2 ) )
% 5.06/5.43 = ( power_power_complex @ ( cnj @ X ) @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_cnj_power
% 5.06/5.43 thf(fact_9680_complex__cnj__add,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( cnj @ ( plus_plus_complex @ X @ Y ) )
% 5.06/5.43 = ( plus_plus_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_cnj_add
% 5.06/5.43 thf(fact_9681_complex__cnj__numeral,axiom,
% 5.06/5.43 ! [W: num] :
% 5.06/5.43 ( ( cnj @ ( numera6690914467698888265omplex @ W ) )
% 5.06/5.43 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_cnj_numeral
% 5.06/5.43 thf(fact_9682_complex__cnj__diff,axiom,
% 5.06/5.43 ! [X: complex,Y: complex] :
% 5.06/5.43 ( ( cnj @ ( minus_minus_complex @ X @ Y ) )
% 5.06/5.43 = ( minus_minus_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_cnj_diff
% 5.06/5.43 thf(fact_9683_complex__cnj__neg__numeral,axiom,
% 5.06/5.43 ! [W: num] :
% 5.06/5.43 ( ( cnj @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.06/5.43 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_cnj_neg_numeral
% 5.06/5.43 thf(fact_9684_complex__In__mult__cnj__zero,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.06/5.43 = zero_zero_real ) ).
% 5.06/5.43
% 5.06/5.43 % complex_In_mult_cnj_zero
% 5.06/5.43 thf(fact_9685_sums__cnj,axiom,
% 5.06/5.43 ! [F: nat > complex,L2: complex] :
% 5.06/5.43 ( ( sums_complex
% 5.06/5.43 @ ^ [X2: nat] : ( cnj @ ( F @ X2 ) )
% 5.06/5.43 @ ( cnj @ L2 ) )
% 5.06/5.43 = ( sums_complex @ F @ L2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % sums_cnj
% 5.06/5.43 thf(fact_9686_Re__complex__div__eq__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.06/5.43 = zero_zero_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_complex_div_eq_0
% 5.06/5.43 thf(fact_9687_Im__complex__div__eq__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.06/5.43 = zero_zero_real )
% 5.06/5.43 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.06/5.43 = zero_zero_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_complex_div_eq_0
% 5.06/5.43 thf(fact_9688_complex__mod__sqrt__Re__mult__cnj,axiom,
% 5.06/5.43 ( real_V1022390504157884413omplex
% 5.06/5.43 = ( ^ [Z2: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z2 @ ( cnj @ Z2 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_mod_sqrt_Re_mult_cnj
% 5.06/5.43 thf(fact_9689_Re__complex__div__lt__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.06/5.43 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_complex_div_lt_0
% 5.06/5.43 thf(fact_9690_Re__complex__div__gt__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.06/5.43 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_complex_div_gt_0
% 5.06/5.43 thf(fact_9691_Re__complex__div__le__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.06/5.43 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_complex_div_le_0
% 5.06/5.43 thf(fact_9692_Re__complex__div__ge__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.06/5.43 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Re_complex_div_ge_0
% 5.06/5.43 thf(fact_9693_Im__complex__div__lt__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.06/5.43 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_complex_div_lt_0
% 5.06/5.43 thf(fact_9694_Im__complex__div__gt__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.06/5.43 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_complex_div_gt_0
% 5.06/5.43 thf(fact_9695_Im__complex__div__le__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.06/5.43 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_complex_div_le_0
% 5.06/5.43 thf(fact_9696_Im__complex__div__ge__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.06/5.43 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Im_complex_div_ge_0
% 5.06/5.43 thf(fact_9697_complex__mod__mult__cnj,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.06/5.43 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_mod_mult_cnj
% 5.06/5.43 thf(fact_9698_complex__div__gt__0,axiom,
% 5.06/5.43 ! [A: complex,B: complex] :
% 5.06/5.43 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.06/5.43 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.06/5.43 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.06/5.43 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_div_gt_0
% 5.06/5.43 thf(fact_9699_complex__norm__square,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.06/5.43 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_norm_square
% 5.06/5.43 thf(fact_9700_complex__add__cnj,axiom,
% 5.06/5.43 ! [Z: complex] :
% 5.06/5.43 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.06/5.43 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_add_cnj
% 5.06/5.43 thf(fact_9701_complex__div__cnj,axiom,
% 5.06/5.43 ( divide1717551699836669952omplex
% 5.06/5.43 = ( ^ [A4: complex,B4: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A4 @ ( cnj @ B4 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % complex_div_cnj
% 5.06/5.43 thf(fact_9702_cnj__add__mult__eq__Re,axiom,
% 5.06/5.43 ! [Z: complex,W: complex] :
% 5.06/5.43 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.06/5.43 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % cnj_add_mult_eq_Re
% 5.06/5.43 thf(fact_9703_divmod__step__integer__def,axiom,
% 5.06/5.43 ( unique4921790084139445826nteger
% 5.06/5.43 = ( ^ [L: num] :
% 5.06/5.43 ( produc6916734918728496179nteger
% 5.06/5.43 @ ^ [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 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % divmod_step_integer_def
% 5.06/5.43 thf(fact_9704_card__Collect__less__nat,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( finite_card_nat
% 5.06/5.43 @ ( collect_nat
% 5.06/5.43 @ ^ [I5: nat] : ( ord_less_nat @ I5 @ N2 ) ) )
% 5.06/5.43 = N2 ) ).
% 5.06/5.43
% 5.06/5.43 % card_Collect_less_nat
% 5.06/5.43 thf(fact_9705_card__atMost,axiom,
% 5.06/5.43 ! [U: nat] :
% 5.06/5.43 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.06/5.43 = ( suc @ U ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_atMost
% 5.06/5.43 thf(fact_9706_card__atLeastLessThan,axiom,
% 5.06/5.43 ! [L2: nat,U: nat] :
% 5.06/5.43 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) )
% 5.06/5.43 = ( minus_minus_nat @ U @ L2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_atLeastLessThan
% 5.06/5.43 thf(fact_9707_card__Collect__le__nat,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( finite_card_nat
% 5.06/5.43 @ ( collect_nat
% 5.06/5.43 @ ^ [I5: nat] : ( ord_less_eq_nat @ I5 @ N2 ) ) )
% 5.06/5.43 = ( suc @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_Collect_le_nat
% 5.06/5.43 thf(fact_9708_card__atLeastAtMost,axiom,
% 5.06/5.43 ! [L2: nat,U: nat] :
% 5.06/5.43 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.06/5.43 = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_atLeastAtMost
% 5.06/5.43 thf(fact_9709_card__atLeastLessThan__int,axiom,
% 5.06/5.43 ! [L2: int,U: int] :
% 5.06/5.43 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L2 @ U ) )
% 5.06/5.43 = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_atLeastLessThan_int
% 5.06/5.43 thf(fact_9710_card__atLeastAtMost__int,axiom,
% 5.06/5.43 ! [L2: int,U: int] :
% 5.06/5.43 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.06/5.43 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_atLeastAtMost_int
% 5.06/5.43 thf(fact_9711_minus__integer__code_I2_J,axiom,
% 5.06/5.43 ! [L2: code_integer] :
% 5.06/5.43 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.06/5.43 = ( uminus1351360451143612070nteger @ L2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % minus_integer_code(2)
% 5.06/5.43 thf(fact_9712_minus__integer__code_I1_J,axiom,
% 5.06/5.43 ! [K: code_integer] :
% 5.06/5.43 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 5.06/5.43 = K ) ).
% 5.06/5.43
% 5.06/5.43 % minus_integer_code(1)
% 5.06/5.43 thf(fact_9713_divmod__integer_H__def,axiom,
% 5.06/5.43 ( unique3479559517661332726nteger
% 5.06/5.43 = ( ^ [M6: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % divmod_integer'_def
% 5.06/5.43 thf(fact_9714_times__integer__code_I1_J,axiom,
% 5.06/5.43 ! [K: code_integer] :
% 5.06/5.43 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.06/5.43 = zero_z3403309356797280102nteger ) ).
% 5.06/5.43
% 5.06/5.43 % times_integer_code(1)
% 5.06/5.43 thf(fact_9715_times__integer__code_I2_J,axiom,
% 5.06/5.43 ! [L2: code_integer] :
% 5.06/5.43 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.06/5.43 = zero_z3403309356797280102nteger ) ).
% 5.06/5.43
% 5.06/5.43 % times_integer_code(2)
% 5.06/5.43 thf(fact_9716_less__eq__integer__code_I1_J,axiom,
% 5.06/5.43 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.06/5.43
% 5.06/5.43 % less_eq_integer_code(1)
% 5.06/5.43 thf(fact_9717_plus__integer__code_I1_J,axiom,
% 5.06/5.43 ! [K: code_integer] :
% 5.06/5.43 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 5.06/5.43 = K ) ).
% 5.06/5.43
% 5.06/5.43 % plus_integer_code(1)
% 5.06/5.43 thf(fact_9718_plus__integer__code_I2_J,axiom,
% 5.06/5.43 ! [L2: code_integer] :
% 5.06/5.43 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.06/5.43 = L2 ) ).
% 5.06/5.43
% 5.06/5.43 % plus_integer_code(2)
% 5.06/5.43 thf(fact_9719_nat_Odisc__eq__case_I2_J,axiom,
% 5.06/5.43 ! [Nat: nat] :
% 5.06/5.43 ( ( Nat != zero_zero_nat )
% 5.06/5.43 = ( case_nat_o @ $false
% 5.06/5.43 @ ^ [Uu3: nat] : $true
% 5.06/5.43 @ Nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat.disc_eq_case(2)
% 5.06/5.43 thf(fact_9720_nat_Odisc__eq__case_I1_J,axiom,
% 5.06/5.43 ! [Nat: nat] :
% 5.06/5.43 ( ( Nat = zero_zero_nat )
% 5.06/5.43 = ( case_nat_o @ $true
% 5.06/5.43 @ ^ [Uu3: nat] : $false
% 5.06/5.43 @ Nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat.disc_eq_case(1)
% 5.06/5.43 thf(fact_9721_card__less,axiom,
% 5.06/5.43 ! [M7: set_nat,I2: nat] :
% 5.06/5.43 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.06/5.43 => ( ( finite_card_nat
% 5.06/5.43 @ ( collect_nat
% 5.06/5.43 @ ^ [K3: nat] :
% 5.06/5.43 ( ( member_nat @ K3 @ M7 )
% 5.06/5.43 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 5.06/5.43 != zero_zero_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_less
% 5.06/5.43 thf(fact_9722_card__less__Suc,axiom,
% 5.06/5.43 ! [M7: set_nat,I2: nat] :
% 5.06/5.43 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.06/5.43 => ( ( suc
% 5.06/5.43 @ ( finite_card_nat
% 5.06/5.43 @ ( collect_nat
% 5.06/5.43 @ ^ [K3: nat] :
% 5.06/5.43 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.06/5.43 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 5.06/5.43 = ( finite_card_nat
% 5.06/5.43 @ ( collect_nat
% 5.06/5.43 @ ^ [K3: nat] :
% 5.06/5.43 ( ( member_nat @ K3 @ M7 )
% 5.06/5.43 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_less_Suc
% 5.06/5.43 thf(fact_9723_card__less__Suc2,axiom,
% 5.06/5.43 ! [M7: set_nat,I2: nat] :
% 5.06/5.43 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.06/5.43 => ( ( finite_card_nat
% 5.06/5.43 @ ( collect_nat
% 5.06/5.43 @ ^ [K3: nat] :
% 5.06/5.43 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.06/5.43 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 5.06/5.43 = ( finite_card_nat
% 5.06/5.43 @ ( collect_nat
% 5.06/5.43 @ ^ [K3: nat] :
% 5.06/5.43 ( ( member_nat @ K3 @ M7 )
% 5.06/5.43 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_less_Suc2
% 5.06/5.43 thf(fact_9724_subset__card__intvl__is__intvl,axiom,
% 5.06/5.43 ! [A2: set_nat,K: nat] :
% 5.06/5.43 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.06/5.43 => ( A2
% 5.06/5.43 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % subset_card_intvl_is_intvl
% 5.06/5.43 thf(fact_9725_one__natural_Orsp,axiom,
% 5.06/5.43 one_one_nat = one_one_nat ).
% 5.06/5.43
% 5.06/5.43 % one_natural.rsp
% 5.06/5.43 thf(fact_9726_less__eq__nat_Osimps_I2_J,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.06/5.43 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_eq_nat.simps(2)
% 5.06/5.43 thf(fact_9727_max__Suc2,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 5.06/5.43 = ( case_nat_nat @ ( suc @ N2 )
% 5.06/5.43 @ ^ [M4: nat] : ( suc @ ( ord_max_nat @ M4 @ N2 ) )
% 5.06/5.43 @ M ) ) ).
% 5.06/5.43
% 5.06/5.43 % max_Suc2
% 5.06/5.43 thf(fact_9728_max__Suc1,axiom,
% 5.06/5.43 ! [N2: nat,M: nat] :
% 5.06/5.43 ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 5.06/5.43 = ( case_nat_nat @ ( suc @ N2 )
% 5.06/5.43 @ ^ [M4: nat] : ( suc @ ( ord_max_nat @ N2 @ M4 ) )
% 5.06/5.43 @ M ) ) ).
% 5.06/5.43
% 5.06/5.43 % max_Suc1
% 5.06/5.43 thf(fact_9729_subset__eq__atLeast0__lessThan__card,axiom,
% 5.06/5.43 ! [N4: set_nat,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.06/5.43 => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % subset_eq_atLeast0_lessThan_card
% 5.06/5.43 thf(fact_9730_card__sum__le__nat__sum,axiom,
% 5.06/5.43 ! [S3: set_nat] :
% 5.06/5.43 ( ord_less_eq_nat
% 5.06/5.43 @ ( groups3542108847815614940at_nat
% 5.06/5.43 @ ^ [X2: nat] : X2
% 5.06/5.43 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 5.06/5.43 @ ( groups3542108847815614940at_nat
% 5.06/5.43 @ ^ [X2: nat] : X2
% 5.06/5.43 @ S3 ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_sum_le_nat_sum
% 5.06/5.43 thf(fact_9731_card__nth__roots,axiom,
% 5.06/5.43 ! [C: complex,N2: nat] :
% 5.06/5.43 ( ( C != zero_zero_complex )
% 5.06/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( finite_card_complex
% 5.06/5.43 @ ( collect_complex
% 5.06/5.43 @ ^ [Z2: complex] :
% 5.06/5.43 ( ( power_power_complex @ Z2 @ N2 )
% 5.06/5.43 = C ) ) )
% 5.06/5.43 = N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_nth_roots
% 5.06/5.43 thf(fact_9732_card__roots__unity__eq,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( finite_card_complex
% 5.06/5.43 @ ( collect_complex
% 5.06/5.43 @ ^ [Z2: complex] :
% 5.06/5.43 ( ( power_power_complex @ Z2 @ N2 )
% 5.06/5.43 = one_one_complex ) ) )
% 5.06/5.43 = N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_roots_unity_eq
% 5.06/5.43 thf(fact_9733_diff__Suc,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.06/5.43 = ( case_nat_nat @ zero_zero_nat
% 5.06/5.43 @ ^ [K3: nat] : K3
% 5.06/5.43 @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % diff_Suc
% 5.06/5.43 thf(fact_9734_integer__of__int__code,axiom,
% 5.06/5.43 ( code_integer_of_int
% 5.06/5.43 = ( ^ [K3: int] :
% 5.06/5.43 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.06/5.43 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.06/5.43 @ ( if_Code_integer
% 5.06/5.43 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.06/5.43 = zero_zero_int )
% 5.06/5.43 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.06/5.43 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % integer_of_int_code
% 5.06/5.43 thf(fact_9735_plus__integer_Oabs__eq,axiom,
% 5.06/5.43 ! [Xa2: int,X: int] :
% 5.06/5.43 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.06/5.43 = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % plus_integer.abs_eq
% 5.06/5.43 thf(fact_9736_times__integer_Oabs__eq,axiom,
% 5.06/5.43 ! [Xa2: int,X: int] :
% 5.06/5.43 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.06/5.43 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % times_integer.abs_eq
% 5.06/5.43 thf(fact_9737_less__eq__integer_Oabs__eq,axiom,
% 5.06/5.43 ! [Xa2: int,X: int] :
% 5.06/5.43 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.06/5.43 = ( ord_less_eq_int @ Xa2 @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_eq_integer.abs_eq
% 5.06/5.43 thf(fact_9738_minus__integer_Oabs__eq,axiom,
% 5.06/5.43 ! [Xa2: int,X: int] :
% 5.06/5.43 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.06/5.43 = ( code_integer_of_int @ ( minus_minus_int @ Xa2 @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % minus_integer.abs_eq
% 5.06/5.43 thf(fact_9739_Code__Numeral_Opositive__def,axiom,
% 5.06/5.43 code_positive = numera6620942414471956472nteger ).
% 5.06/5.43
% 5.06/5.43 % Code_Numeral.positive_def
% 5.06/5.43 thf(fact_9740_integer__of__num_I3_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( code_integer_of_num @ ( bit1 @ N2 ) )
% 5.06/5.43 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) @ one_one_Code_integer ) ) ).
% 5.06/5.43
% 5.06/5.43 % integer_of_num(3)
% 5.06/5.43 thf(fact_9741_integer__of__num__def,axiom,
% 5.06/5.43 code_integer_of_num = numera6620942414471956472nteger ).
% 5.06/5.43
% 5.06/5.43 % integer_of_num_def
% 5.06/5.43 thf(fact_9742_integer__of__num__triv_I1_J,axiom,
% 5.06/5.43 ( ( code_integer_of_num @ one )
% 5.06/5.43 = one_one_Code_integer ) ).
% 5.06/5.43
% 5.06/5.43 % integer_of_num_triv(1)
% 5.06/5.43 thf(fact_9743_integer__of__num_I2_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 5.06/5.43 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % integer_of_num(2)
% 5.06/5.43 thf(fact_9744_integer__of__num__triv_I2_J,axiom,
% 5.06/5.43 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.06/5.43 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % integer_of_num_triv(2)
% 5.06/5.43 thf(fact_9745_int__of__integer__code,axiom,
% 5.06/5.43 ( code_int_of_integer
% 5.06/5.43 = ( ^ [K3: code_integer] :
% 5.06/5.43 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.06/5.43 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.06/5.43 @ ( produc1553301316500091796er_int
% 5.06/5.43 @ ^ [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 ) )
% 5.06/5.43 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % int_of_integer_code
% 5.06/5.43 thf(fact_9746_bit__cut__integer__def,axiom,
% 5.06/5.43 ( code_bit_cut_integer
% 5.06/5.43 = ( ^ [K3: code_integer] :
% 5.06/5.43 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.06/5.43 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_cut_integer_def
% 5.06/5.43 thf(fact_9747_num__of__integer__code,axiom,
% 5.06/5.43 ( code_num_of_integer
% 5.06/5.43 = ( ^ [K3: code_integer] :
% 5.06/5.43 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.06/5.43 @ ( produc7336495610019696514er_num
% 5.06/5.43 @ ^ [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 ) )
% 5.06/5.43 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % num_of_integer_code
% 5.06/5.43 thf(fact_9748_int__of__integer__max,axiom,
% 5.06/5.43 ! [K: code_integer,L2: code_integer] :
% 5.06/5.43 ( ( code_int_of_integer @ ( ord_max_Code_integer @ K @ L2 ) )
% 5.06/5.43 = ( ord_max_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % int_of_integer_max
% 5.06/5.43 thf(fact_9749_int__of__integer__numeral,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.06/5.43 = ( numeral_numeral_int @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % int_of_integer_numeral
% 5.06/5.43 thf(fact_9750_plus__integer_Orep__eq,axiom,
% 5.06/5.43 ! [X: code_integer,Xa2: code_integer] :
% 5.06/5.43 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa2 ) )
% 5.06/5.43 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % plus_integer.rep_eq
% 5.06/5.43 thf(fact_9751_times__integer_Orep__eq,axiom,
% 5.06/5.43 ! [X: code_integer,Xa2: code_integer] :
% 5.06/5.43 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 5.06/5.43 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % times_integer.rep_eq
% 5.06/5.43 thf(fact_9752_minus__integer_Orep__eq,axiom,
% 5.06/5.43 ! [X: code_integer,Xa2: code_integer] :
% 5.06/5.43 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa2 ) )
% 5.06/5.43 = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % minus_integer.rep_eq
% 5.06/5.43 thf(fact_9753_less__eq__integer_Orep__eq,axiom,
% 5.06/5.43 ( ord_le3102999989581377725nteger
% 5.06/5.43 = ( ^ [X2: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_eq_integer.rep_eq
% 5.06/5.43 thf(fact_9754_integer__less__eq__iff,axiom,
% 5.06/5.43 ( ord_le3102999989581377725nteger
% 5.06/5.43 = ( ^ [K3: code_integer,L: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % integer_less_eq_iff
% 5.06/5.43 thf(fact_9755_bit__cut__integer__code,axiom,
% 5.06/5.43 ( code_bit_cut_integer
% 5.06/5.43 = ( ^ [K3: code_integer] :
% 5.06/5.43 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.06/5.43 @ ( produc9125791028180074456eger_o
% 5.06/5.43 @ ^ [R5: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 5.06/5.43 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bit_cut_integer_code
% 5.06/5.43 thf(fact_9756_nat__of__integer__code,axiom,
% 5.06/5.43 ( code_nat_of_integer
% 5.06/5.43 = ( ^ [K3: code_integer] :
% 5.06/5.43 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.06/5.43 @ ( produc1555791787009142072er_nat
% 5.06/5.43 @ ^ [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 ) )
% 5.06/5.43 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_of_integer_code
% 5.06/5.43 thf(fact_9757_of__nat__of__integer,axiom,
% 5.06/5.43 ! [K: code_integer] :
% 5.06/5.43 ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 5.06/5.43 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % of_nat_of_integer
% 5.06/5.43 thf(fact_9758_nat__of__integer__non__positive,axiom,
% 5.06/5.43 ! [K: code_integer] :
% 5.06/5.43 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.06/5.43 => ( ( code_nat_of_integer @ K )
% 5.06/5.43 = zero_zero_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_of_integer_non_positive
% 5.06/5.43 thf(fact_9759_nat__of__integer__code__post_I3_J,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.06/5.43 = ( numeral_numeral_nat @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_of_integer_code_post(3)
% 5.06/5.43 thf(fact_9760_nat__of__integer__code__post_I2_J,axiom,
% 5.06/5.43 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.06/5.43 = one_one_nat ) ).
% 5.06/5.43
% 5.06/5.43 % nat_of_integer_code_post(2)
% 5.06/5.43 thf(fact_9761_pred__def,axiom,
% 5.06/5.43 ( pred
% 5.06/5.43 = ( case_nat_nat @ zero_zero_nat
% 5.06/5.43 @ ^ [X24: nat] : X24 ) ) ).
% 5.06/5.43
% 5.06/5.43 % pred_def
% 5.06/5.43 thf(fact_9762_divmod__integer__code,axiom,
% 5.06/5.43 ( code_divmod_integer
% 5.06/5.43 = ( ^ [K3: code_integer,L: code_integer] :
% 5.06/5.43 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.06/5.43 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 5.06/5.43 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L )
% 5.06/5.43 @ ( produc6916734918728496179nteger
% 5.06/5.43 @ ^ [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 ) ) )
% 5.06/5.43 @ ( code_divmod_abs @ K3 @ L ) ) )
% 5.06/5.43 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.06/5.43 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.06/5.43 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L )
% 5.06/5.43 @ ( produc6916734918728496179nteger
% 5.06/5.43 @ ^ [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 ) ) )
% 5.06/5.43 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % divmod_integer_code
% 5.06/5.43 thf(fact_9763_binomial__def,axiom,
% 5.06/5.43 ( binomial
% 5.06/5.43 = ( ^ [N: nat,K3: nat] :
% 5.06/5.43 ( finite_card_set_nat
% 5.06/5.43 @ ( collect_set_nat
% 5.06/5.43 @ ^ [K7: set_nat] :
% 5.06/5.43 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.06/5.43 & ( ( finite_card_nat @ K7 )
% 5.06/5.43 = K3 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % binomial_def
% 5.06/5.43 thf(fact_9764_drop__bit__numeral__minus__bit1,axiom,
% 5.06/5.43 ! [L2: num,K: num] :
% 5.06/5.43 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.06/5.43 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_numeral_minus_bit1
% 5.06/5.43 thf(fact_9765_Suc__0__mod__numeral,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.06/5.43 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Suc_0_mod_numeral
% 5.06/5.43 thf(fact_9766_prod__decode__aux_Osimps,axiom,
% 5.06/5.43 ( nat_prod_decode_aux
% 5.06/5.43 = ( ^ [K3: nat,M6: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M6 @ K3 ) @ ( product_Pair_nat_nat @ M6 @ ( minus_minus_nat @ K3 @ M6 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M6 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % prod_decode_aux.simps
% 5.06/5.43 thf(fact_9767_drop__bit__nonnegative__int__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) )
% 5.06/5.43 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_nonnegative_int_iff
% 5.06/5.43 thf(fact_9768_drop__bit__negative__int__iff,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) @ zero_zero_int )
% 5.06/5.43 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_negative_int_iff
% 5.06/5.43 thf(fact_9769_drop__bit__minus__one,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.06/5.43 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_minus_one
% 5.06/5.43 thf(fact_9770_drop__bit__Suc__minus__bit0,axiom,
% 5.06/5.43 ! [N2: nat,K: num] :
% 5.06/5.43 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.06/5.43 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_Suc_minus_bit0
% 5.06/5.43 thf(fact_9771_drop__bit__numeral__minus__bit0,axiom,
% 5.06/5.43 ! [L2: num,K: num] :
% 5.06/5.43 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.06/5.43 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_numeral_minus_bit0
% 5.06/5.43 thf(fact_9772_drop__bit__Suc__minus__bit1,axiom,
% 5.06/5.43 ! [N2: nat,K: num] :
% 5.06/5.43 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.06/5.43 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_Suc_minus_bit1
% 5.06/5.43 thf(fact_9773_drop__bit__push__bit__int,axiom,
% 5.06/5.43 ! [M: nat,N2: nat,K: int] :
% 5.06/5.43 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.06/5.43 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N2 @ M ) @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_push_bit_int
% 5.06/5.43 thf(fact_9774_drop__bit__int__def,axiom,
% 5.06/5.43 ( bit_se8568078237143864401it_int
% 5.06/5.43 = ( ^ [N: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_int_def
% 5.06/5.43 thf(fact_9775_prod__decode__aux_Oelims,axiom,
% 5.06/5.43 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.06/5.43 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % prod_decode_aux.elims
% 5.06/5.43 thf(fact_9776_prod__decode__aux_Opelims,axiom,
% 5.06/5.43 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.06/5.43 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.06/5.43 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 5.06/5.43 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % prod_decode_aux.pelims
% 5.06/5.43 thf(fact_9777_Suc__0__div__numeral,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.06/5.43 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Suc_0_div_numeral
% 5.06/5.43 thf(fact_9778_finite__enumerate,axiom,
% 5.06/5.43 ! [S3: set_nat] :
% 5.06/5.43 ( ( finite_finite_nat @ S3 )
% 5.06/5.43 => ? [R3: nat > nat] :
% 5.06/5.43 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 5.06/5.43 & ! [N9: nat] :
% 5.06/5.43 ( ( ord_less_nat @ N9 @ ( finite_card_nat @ S3 ) )
% 5.06/5.43 => ( member_nat @ ( R3 @ N9 ) @ S3 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % finite_enumerate
% 5.06/5.43 thf(fact_9779_drop__bit__of__Suc__0,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( bit_se8570568707652914677it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.06/5.43 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_of_Suc_0
% 5.06/5.43 thf(fact_9780_fst__divmod__nat,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 5.06/5.43 = ( divide_divide_nat @ M @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % fst_divmod_nat
% 5.06/5.43 thf(fact_9781_drop__bit__nat__eq,axiom,
% 5.06/5.43 ! [N2: nat,K: int] :
% 5.06/5.43 ( ( bit_se8570568707652914677it_nat @ N2 @ ( nat2 @ K ) )
% 5.06/5.43 = ( nat2 @ ( bit_se8568078237143864401it_int @ N2 @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_nat_eq
% 5.06/5.43 thf(fact_9782_drop__bit__nat__def,axiom,
% 5.06/5.43 ( bit_se8570568707652914677it_nat
% 5.06/5.43 = ( ^ [N: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % drop_bit_nat_def
% 5.06/5.43 thf(fact_9783_one__mod__minus__numeral,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % one_mod_minus_numeral
% 5.06/5.43 thf(fact_9784_minus__one__mod__numeral,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % minus_one_mod_numeral
% 5.06/5.43 thf(fact_9785_numeral__mod__minus__numeral,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % numeral_mod_minus_numeral
% 5.06/5.43 thf(fact_9786_minus__numeral__mod__numeral,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % minus_numeral_mod_numeral
% 5.06/5.43 thf(fact_9787_Divides_Oadjust__mod__def,axiom,
% 5.06/5.43 ( adjust_mod
% 5.06/5.43 = ( ^ [L: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L @ R5 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Divides.adjust_mod_def
% 5.06/5.43 thf(fact_9788_bezw_Oelims,axiom,
% 5.06/5.43 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.06/5.43 ( ( ( bezw @ X @ Xa2 )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.06/5.43 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bezw.elims
% 5.06/5.43 thf(fact_9789_bezw_Osimps,axiom,
% 5.06/5.43 ( bezw
% 5.06/5.43 = ( ^ [X2: nat,Y2: nat] : ( if_Pro3027730157355071871nt_int @ ( Y2 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bezw.simps
% 5.06/5.43 thf(fact_9790_bezw_Opelims,axiom,
% 5.06/5.43 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.06/5.43 ( ( ( bezw @ X @ Xa2 )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.06/5.43 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.06/5.43 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 5.06/5.43 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bezw.pelims
% 5.06/5.43 thf(fact_9791_bezw__non__0,axiom,
% 5.06/5.43 ! [Y: nat,X: nat] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.06/5.43 => ( ( bezw @ X @ Y )
% 5.06/5.43 = ( 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 ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bezw_non_0
% 5.06/5.43 thf(fact_9792_normalize__def,axiom,
% 5.06/5.43 ( normalize
% 5.06/5.43 = ( ^ [P5: product_prod_int_int] :
% 5.06/5.43 ( 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 ) ) ) )
% 5.06/5.43 @ ( if_Pro3027730157355071871nt_int
% 5.06/5.43 @ ( ( product_snd_int_int @ P5 )
% 5.06/5.43 = zero_zero_int )
% 5.06/5.43 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.06/5.43 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % normalize_def
% 5.06/5.43 thf(fact_9793_gcd__neg__numeral__1__int,axiom,
% 5.06/5.43 ! [N2: num,X: int] :
% 5.06/5.43 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ X )
% 5.06/5.43 = ( gcd_gcd_int @ ( numeral_numeral_int @ N2 ) @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_neg_numeral_1_int
% 5.06/5.43 thf(fact_9794_gcd__neg__numeral__2__int,axiom,
% 5.06/5.43 ! [X: int,N2: num] :
% 5.06/5.43 ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_neg_numeral_2_int
% 5.06/5.43 thf(fact_9795_gcd__ge__0__int,axiom,
% 5.06/5.43 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_ge_0_int
% 5.06/5.43 thf(fact_9796_bezout__int,axiom,
% 5.06/5.43 ! [X: int,Y: int] :
% 5.06/5.43 ? [U3: int,V2: int] :
% 5.06/5.43 ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V2 @ Y ) )
% 5.06/5.43 = ( gcd_gcd_int @ X @ Y ) ) ).
% 5.06/5.43
% 5.06/5.43 % bezout_int
% 5.06/5.43 thf(fact_9797_gcd__mult__distrib__int,axiom,
% 5.06/5.43 ! [K: int,M: int,N2: int] :
% 5.06/5.43 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N2 ) )
% 5.06/5.43 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_mult_distrib_int
% 5.06/5.43 thf(fact_9798_gcd__le1__int,axiom,
% 5.06/5.43 ! [A: int,B: int] :
% 5.06/5.43 ( ( ord_less_int @ zero_zero_int @ A )
% 5.06/5.43 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_le1_int
% 5.06/5.43 thf(fact_9799_gcd__le2__int,axiom,
% 5.06/5.43 ! [B: int,A: int] :
% 5.06/5.43 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.43 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_le2_int
% 5.06/5.43 thf(fact_9800_gcd__cases__int,axiom,
% 5.06/5.43 ! [X: int,Y: int,P: int > $o] :
% 5.06/5.43 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 5.06/5.43 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.06/5.43 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.06/5.43 => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.06/5.43 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.06/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.06/5.43 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 5.06/5.43 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.06/5.43 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.06/5.43 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.06/5.43 => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_cases_int
% 5.06/5.43 thf(fact_9801_gcd__unique__int,axiom,
% 5.06/5.43 ! [D: int,A: int,B: int] :
% 5.06/5.43 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.06/5.43 & ( dvd_dvd_int @ D @ A )
% 5.06/5.43 & ( dvd_dvd_int @ D @ B )
% 5.06/5.43 & ! [E3: int] :
% 5.06/5.43 ( ( ( dvd_dvd_int @ E3 @ A )
% 5.06/5.43 & ( dvd_dvd_int @ E3 @ B ) )
% 5.06/5.43 => ( dvd_dvd_int @ E3 @ D ) ) )
% 5.06/5.43 = ( D
% 5.06/5.43 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_unique_int
% 5.06/5.43 thf(fact_9802_gcd__1__nat,axiom,
% 5.06/5.43 ! [M: nat] :
% 5.06/5.43 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.06/5.43 = one_one_nat ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_1_nat
% 5.06/5.43 thf(fact_9803_gcd__Suc__0,axiom,
% 5.06/5.43 ! [M: nat] :
% 5.06/5.43 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.06/5.43 = ( suc @ zero_zero_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_Suc_0
% 5.06/5.43 thf(fact_9804_gcd__pos__nat,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N2 ) )
% 5.06/5.43 = ( ( M != zero_zero_nat )
% 5.06/5.43 | ( N2 != zero_zero_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_pos_nat
% 5.06/5.43 thf(fact_9805_gcd__mult__distrib__nat,axiom,
% 5.06/5.43 ! [K: nat,M: nat,N2: nat] :
% 5.06/5.43 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N2 ) )
% 5.06/5.43 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_mult_distrib_nat
% 5.06/5.43 thf(fact_9806_gcd__le1__nat,axiom,
% 5.06/5.43 ! [A: nat,B: nat] :
% 5.06/5.43 ( ( A != zero_zero_nat )
% 5.06/5.43 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_le1_nat
% 5.06/5.43 thf(fact_9807_gcd__le2__nat,axiom,
% 5.06/5.43 ! [B: nat,A: nat] :
% 5.06/5.43 ( ( B != zero_zero_nat )
% 5.06/5.43 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_le2_nat
% 5.06/5.43 thf(fact_9808_gcd__diff1__nat,axiom,
% 5.06/5.43 ! [N2: nat,M: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ N2 @ M )
% 5.06/5.43 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 )
% 5.06/5.43 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_diff1_nat
% 5.06/5.43 thf(fact_9809_gcd__diff2__nat,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ M @ N2 )
% 5.06/5.43 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N2 @ M ) @ N2 )
% 5.06/5.43 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_diff2_nat
% 5.06/5.43 thf(fact_9810_bezout__nat,axiom,
% 5.06/5.43 ! [A: nat,B: nat] :
% 5.06/5.43 ( ( A != zero_zero_nat )
% 5.06/5.43 => ? [X3: nat,Y5: nat] :
% 5.06/5.43 ( ( times_times_nat @ A @ X3 )
% 5.06/5.43 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bezout_nat
% 5.06/5.43 thf(fact_9811_bezout__gcd__nat_H,axiom,
% 5.06/5.43 ! [B: nat,A: nat] :
% 5.06/5.43 ? [X3: nat,Y5: nat] :
% 5.06/5.43 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y5 ) @ ( times_times_nat @ A @ X3 ) )
% 5.06/5.43 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y5 ) )
% 5.06/5.43 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.06/5.43 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y5 ) @ ( times_times_nat @ B @ X3 ) )
% 5.06/5.43 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y5 ) )
% 5.06/5.43 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bezout_gcd_nat'
% 5.06/5.43 thf(fact_9812_bezw__aux,axiom,
% 5.06/5.43 ! [X: nat,Y: nat] :
% 5.06/5.43 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 5.06/5.43 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % bezw_aux
% 5.06/5.43 thf(fact_9813_nat__descend__induct,axiom,
% 5.06/5.43 ! [N2: nat,P: nat > $o,M: nat] :
% 5.06/5.43 ( ! [K2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ N2 @ K2 )
% 5.06/5.43 => ( P @ K2 ) )
% 5.06/5.43 => ( ! [K2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.06/5.43 => ( ! [I: nat] :
% 5.06/5.43 ( ( ord_less_nat @ K2 @ I )
% 5.06/5.43 => ( P @ I ) )
% 5.06/5.43 => ( P @ K2 ) ) )
% 5.06/5.43 => ( P @ M ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_descend_induct
% 5.06/5.43 thf(fact_9814_gcd__nat_Opelims,axiom,
% 5.06/5.43 ! [X: nat,Xa2: nat,Y: nat] :
% 5.06/5.43 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.06/5.43 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.06/5.43 => ( Y = X ) )
% 5.06/5.43 & ( ( Xa2 != zero_zero_nat )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 5.06/5.43 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_nat.pelims
% 5.06/5.43 thf(fact_9815_card__greaterThanLessThan__int,axiom,
% 5.06/5.43 ! [L2: int,U: int] :
% 5.06/5.43 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 5.06/5.43 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_greaterThanLessThan_int
% 5.06/5.43 thf(fact_9816_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.06/5.43 ! [L2: int,U: int] :
% 5.06/5.43 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 5.06/5.43 = ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.06/5.43 thf(fact_9817_xor__minus__numerals_I2_J,axiom,
% 5.06/5.43 ! [K: int,N2: num] :
% 5.06/5.43 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_minus_numerals(2)
% 5.06/5.43 thf(fact_9818_xor__minus__numerals_I1_J,axiom,
% 5.06/5.43 ! [N2: num,K: int] :
% 5.06/5.43 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ K )
% 5.06/5.43 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N2 @ one ) @ K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % xor_minus_numerals(1)
% 5.06/5.43 thf(fact_9819_card__greaterThanLessThan,axiom,
% 5.06/5.43 ! [L2: nat,U: nat] :
% 5.06/5.43 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 5.06/5.43 = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_greaterThanLessThan
% 5.06/5.43 thf(fact_9820_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.06/5.43 ! [L2: nat,U: nat] :
% 5.06/5.43 ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 5.06/5.43 = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastSucLessThan_greaterThanLessThan
% 5.06/5.43 thf(fact_9821_sub__BitM__One__eq,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( neg_numeral_sub_int @ ( bitM @ N2 ) @ one )
% 5.06/5.43 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sub_BitM_One_eq
% 5.06/5.43 thf(fact_9822_Suc__funpow,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( compow_nat_nat @ N2 @ suc )
% 5.06/5.43 = ( plus_plus_nat @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % Suc_funpow
% 5.06/5.43 thf(fact_9823_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.06/5.43 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] : ( ord_less_eq_nat @ Y2 @ X2 )
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] : ( ord_less_nat @ Y2 @ X2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % max_nat.semilattice_neutr_order_axioms
% 5.06/5.43 thf(fact_9824_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.06/5.43 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 5.06/5.43 @ ^ [M6: nat,N: nat] :
% 5.06/5.43 ( ( dvd_dvd_nat @ M6 @ N )
% 5.06/5.43 & ( M6 != N ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % gcd_nat.semilattice_neutr_order_axioms
% 5.06/5.43 thf(fact_9825_Gcd__remove0__nat,axiom,
% 5.06/5.43 ! [M7: set_nat] :
% 5.06/5.43 ( ( finite_finite_nat @ M7 )
% 5.06/5.43 => ( ( gcd_Gcd_nat @ M7 )
% 5.06/5.43 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Gcd_remove0_nat
% 5.06/5.43 thf(fact_9826_times__int_Oabs__eq,axiom,
% 5.06/5.43 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.06/5.43 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.06/5.43 = ( abs_Integ
% 5.06/5.43 @ ( produc27273713700761075at_nat
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] :
% 5.06/5.43 ( produc2626176000494625587at_nat
% 5.06/5.43 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y2 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y2 @ U2 ) ) ) )
% 5.06/5.43 @ Xa2
% 5.06/5.43 @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % times_int.abs_eq
% 5.06/5.43 thf(fact_9827_eq__Abs__Integ,axiom,
% 5.06/5.43 ! [Z: int] :
% 5.06/5.43 ~ ! [X3: nat,Y5: nat] :
% 5.06/5.43 ( Z
% 5.06/5.43 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y5 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % eq_Abs_Integ
% 5.06/5.43 thf(fact_9828_Gcd__nat__eq__one,axiom,
% 5.06/5.43 ! [N4: set_nat] :
% 5.06/5.43 ( ( member_nat @ one_one_nat @ N4 )
% 5.06/5.43 => ( ( gcd_Gcd_nat @ N4 )
% 5.06/5.43 = one_one_nat ) ) ).
% 5.06/5.43
% 5.06/5.43 % Gcd_nat_eq_one
% 5.06/5.43 thf(fact_9829_nat_Oabs__eq,axiom,
% 5.06/5.43 ! [X: product_prod_nat_nat] :
% 5.06/5.43 ( ( nat2 @ ( abs_Integ @ X ) )
% 5.06/5.43 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat.abs_eq
% 5.06/5.43 thf(fact_9830_zero__int__def,axiom,
% 5.06/5.43 ( zero_zero_int
% 5.06/5.43 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % zero_int_def
% 5.06/5.43 thf(fact_9831_int__def,axiom,
% 5.06/5.43 ( semiri1314217659103216013at_int
% 5.06/5.43 = ( ^ [N: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N @ zero_zero_nat ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % int_def
% 5.06/5.43 thf(fact_9832_uminus__int_Oabs__eq,axiom,
% 5.06/5.43 ! [X: product_prod_nat_nat] :
% 5.06/5.43 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 5.06/5.43 = ( abs_Integ
% 5.06/5.43 @ ( produc2626176000494625587at_nat
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] : ( product_Pair_nat_nat @ Y2 @ X2 )
% 5.06/5.43 @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % uminus_int.abs_eq
% 5.06/5.43 thf(fact_9833_one__int__def,axiom,
% 5.06/5.43 ( one_one_int
% 5.06/5.43 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % one_int_def
% 5.06/5.43 thf(fact_9834_less__int_Oabs__eq,axiom,
% 5.06/5.43 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.06/5.43 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.06/5.43 = ( produc8739625826339149834_nat_o
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] :
% 5.06/5.43 ( produc6081775807080527818_nat_o
% 5.06/5.43 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) )
% 5.06/5.43 @ Xa2
% 5.06/5.43 @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_int.abs_eq
% 5.06/5.43 thf(fact_9835_less__eq__int_Oabs__eq,axiom,
% 5.06/5.43 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.06/5.43 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.06/5.43 = ( produc8739625826339149834_nat_o
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] :
% 5.06/5.43 ( produc6081775807080527818_nat_o
% 5.06/5.43 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ U2 @ Y2 ) ) )
% 5.06/5.43 @ Xa2
% 5.06/5.43 @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_eq_int.abs_eq
% 5.06/5.43 thf(fact_9836_plus__int_Oabs__eq,axiom,
% 5.06/5.43 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.06/5.43 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.06/5.43 = ( abs_Integ
% 5.06/5.43 @ ( produc27273713700761075at_nat
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] :
% 5.06/5.43 ( produc2626176000494625587at_nat
% 5.06/5.43 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y2 @ V4 ) ) )
% 5.06/5.43 @ Xa2
% 5.06/5.43 @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % plus_int.abs_eq
% 5.06/5.43 thf(fact_9837_minus__int_Oabs__eq,axiom,
% 5.06/5.43 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.06/5.43 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.06/5.43 = ( abs_Integ
% 5.06/5.43 @ ( produc27273713700761075at_nat
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] :
% 5.06/5.43 ( produc2626176000494625587at_nat
% 5.06/5.43 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y2 @ U2 ) ) )
% 5.06/5.43 @ Xa2
% 5.06/5.43 @ X ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % minus_int.abs_eq
% 5.06/5.43 thf(fact_9838_Gcd__int__greater__eq__0,axiom,
% 5.06/5.43 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 5.06/5.43
% 5.06/5.43 % Gcd_int_greater_eq_0
% 5.06/5.43 thf(fact_9839_less__eq__int_Orep__eq,axiom,
% 5.06/5.43 ( ord_less_eq_int
% 5.06/5.43 = ( ^ [X2: int,Xa4: int] :
% 5.06/5.43 ( produc8739625826339149834_nat_o
% 5.06/5.43 @ ^ [Y2: nat,Z2: nat] :
% 5.06/5.43 ( produc6081775807080527818_nat_o
% 5.06/5.43 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y2 @ V4 ) @ ( plus_plus_nat @ U2 @ Z2 ) ) )
% 5.06/5.43 @ ( rep_Integ @ X2 )
% 5.06/5.43 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_eq_int.rep_eq
% 5.06/5.43 thf(fact_9840_less__int_Orep__eq,axiom,
% 5.06/5.43 ( ord_less_int
% 5.06/5.43 = ( ^ [X2: int,Xa4: int] :
% 5.06/5.43 ( produc8739625826339149834_nat_o
% 5.06/5.43 @ ^ [Y2: nat,Z2: nat] :
% 5.06/5.43 ( produc6081775807080527818_nat_o
% 5.06/5.43 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y2 @ V4 ) @ ( plus_plus_nat @ U2 @ Z2 ) ) )
% 5.06/5.43 @ ( rep_Integ @ X2 )
% 5.06/5.43 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_int.rep_eq
% 5.06/5.43 thf(fact_9841_nat_Orep__eq,axiom,
% 5.06/5.43 ( nat2
% 5.06/5.43 = ( ^ [X2: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat.rep_eq
% 5.06/5.43 thf(fact_9842_prod__encode__def,axiom,
% 5.06/5.43 ( nat_prod_encode
% 5.06/5.43 = ( produc6842872674320459806at_nat
% 5.06/5.43 @ ^ [M6: nat,N: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N ) ) @ M6 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % prod_encode_def
% 5.06/5.43 thf(fact_9843_uminus__int__def,axiom,
% 5.06/5.43 ( uminus_uminus_int
% 5.06/5.43 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.06/5.43 @ ( produc2626176000494625587at_nat
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] : ( product_Pair_nat_nat @ Y2 @ X2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % uminus_int_def
% 5.06/5.43 thf(fact_9844_le__prod__encode__2,axiom,
% 5.06/5.43 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % le_prod_encode_2
% 5.06/5.43 thf(fact_9845_le__prod__encode__1,axiom,
% 5.06/5.43 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % le_prod_encode_1
% 5.06/5.43 thf(fact_9846_prod__encode__prod__decode__aux,axiom,
% 5.06/5.43 ! [K: nat,M: nat] :
% 5.06/5.43 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.06/5.43 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.06/5.43
% 5.06/5.43 % prod_encode_prod_decode_aux
% 5.06/5.43 thf(fact_9847_times__int__def,axiom,
% 5.06/5.43 ( times_times_int
% 5.06/5.43 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.06/5.43 @ ( produc27273713700761075at_nat
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] :
% 5.06/5.43 ( produc2626176000494625587at_nat
% 5.06/5.43 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U2 ) @ ( times_times_nat @ Y2 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y2 @ U2 ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % times_int_def
% 5.06/5.43 thf(fact_9848_minus__int__def,axiom,
% 5.06/5.43 ( minus_minus_int
% 5.06/5.43 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.06/5.43 @ ( produc27273713700761075at_nat
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] :
% 5.06/5.43 ( produc2626176000494625587at_nat
% 5.06/5.43 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ V4 ) @ ( plus_plus_nat @ Y2 @ U2 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % minus_int_def
% 5.06/5.43 thf(fact_9849_plus__int__def,axiom,
% 5.06/5.43 ( plus_plus_int
% 5.06/5.43 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.06/5.43 @ ( produc27273713700761075at_nat
% 5.06/5.43 @ ^ [X2: nat,Y2: nat] :
% 5.06/5.43 ( produc2626176000494625587at_nat
% 5.06/5.43 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X2 @ U2 ) @ ( plus_plus_nat @ Y2 @ V4 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % plus_int_def
% 5.06/5.43 thf(fact_9850_pred__nat__def,axiom,
% 5.06/5.43 ( pred_nat
% 5.06/5.43 = ( collec3392354462482085612at_nat
% 5.06/5.43 @ ( produc6081775807080527818_nat_o
% 5.06/5.43 @ ^ [M6: nat,N: nat] :
% 5.06/5.43 ( N
% 5.06/5.43 = ( suc @ M6 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % pred_nat_def
% 5.06/5.43 thf(fact_9851_num__of__nat_Osimps_I2_J,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.06/5.43 = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.06/5.43 = one ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % num_of_nat.simps(2)
% 5.06/5.43 thf(fact_9852_num__of__nat__numeral__eq,axiom,
% 5.06/5.43 ! [Q2: num] :
% 5.06/5.43 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.06/5.43 = Q2 ) ).
% 5.06/5.43
% 5.06/5.43 % num_of_nat_numeral_eq
% 5.06/5.43 thf(fact_9853_num__of__nat_Osimps_I1_J,axiom,
% 5.06/5.43 ( ( num_of_nat @ zero_zero_nat )
% 5.06/5.43 = one ) ).
% 5.06/5.43
% 5.06/5.43 % num_of_nat.simps(1)
% 5.06/5.43 thf(fact_9854_numeral__num__of__nat,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 5.06/5.43 = N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % numeral_num_of_nat
% 5.06/5.43 thf(fact_9855_num__of__nat__One,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 5.06/5.43 => ( ( num_of_nat @ N2 )
% 5.06/5.43 = one ) ) ).
% 5.06/5.43
% 5.06/5.43 % num_of_nat_One
% 5.06/5.43 thf(fact_9856_num__of__nat__double,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 5.06/5.43 = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % num_of_nat_double
% 5.06/5.43 thf(fact_9857_num__of__nat__plus__distrib,axiom,
% 5.06/5.43 ! [M: nat,N2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.06/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.06/5.43 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % num_of_nat_plus_distrib
% 5.06/5.43 thf(fact_9858_pow_Osimps_I3_J,axiom,
% 5.06/5.43 ! [X: num,Y: num] :
% 5.06/5.43 ( ( pow @ X @ ( bit1 @ Y ) )
% 5.06/5.43 = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 5.06/5.43
% 5.06/5.43 % pow.simps(3)
% 5.06/5.43 thf(fact_9859_sqr_Osimps_I2_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( sqr @ ( bit0 @ N2 ) )
% 5.06/5.43 = ( bit0 @ ( bit0 @ ( sqr @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sqr.simps(2)
% 5.06/5.43 thf(fact_9860_sqr_Osimps_I1_J,axiom,
% 5.06/5.43 ( ( sqr @ one )
% 5.06/5.43 = one ) ).
% 5.06/5.43
% 5.06/5.43 % sqr.simps(1)
% 5.06/5.43 thf(fact_9861_sqr__conv__mult,axiom,
% 5.06/5.43 ( sqr
% 5.06/5.43 = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sqr_conv_mult
% 5.06/5.43 thf(fact_9862_pow_Osimps_I2_J,axiom,
% 5.06/5.43 ! [X: num,Y: num] :
% 5.06/5.43 ( ( pow @ X @ ( bit0 @ Y ) )
% 5.06/5.43 = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % pow.simps(2)
% 5.06/5.43 thf(fact_9863_sqr_Osimps_I3_J,axiom,
% 5.06/5.43 ! [N2: num] :
% 5.06/5.43 ( ( sqr @ ( bit1 @ N2 ) )
% 5.06/5.43 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sqr.simps(3)
% 5.06/5.43 thf(fact_9864_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.06/5.43 ! [N2: nat,J: nat,I2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 5.06/5.43 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N2 )
% 5.06/5.43 = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nth_sorted_list_of_set_greaterThanLessThan
% 5.06/5.43 thf(fact_9865_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.06/5.43 ! [N2: nat,J: nat,I2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I2 ) )
% 5.06/5.43 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N2 )
% 5.06/5.43 = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nth_sorted_list_of_set_greaterThanAtMost
% 5.06/5.43 thf(fact_9866_rat__floor__lemma,axiom,
% 5.06/5.43 ! [A: int,B: int] :
% 5.06/5.43 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.06/5.43 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_floor_lemma
% 5.06/5.43 thf(fact_9867_image__minus__const__atLeastLessThan__nat,axiom,
% 5.06/5.43 ! [C: nat,Y: nat,X: nat] :
% 5.06/5.43 ( ( ( ord_less_nat @ C @ Y )
% 5.06/5.43 => ( ( image_nat_nat
% 5.06/5.43 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.06/5.43 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.06/5.43 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_nat @ C @ Y )
% 5.06/5.43 => ( ( ( ord_less_nat @ X @ Y )
% 5.06/5.43 => ( ( image_nat_nat
% 5.06/5.43 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.06/5.43 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.06/5.43 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.06/5.43 & ( ~ ( ord_less_nat @ X @ Y )
% 5.06/5.43 => ( ( image_nat_nat
% 5.06/5.43 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.06/5.43 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.06/5.43 = bot_bot_set_nat ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % image_minus_const_atLeastLessThan_nat
% 5.06/5.43 thf(fact_9868_bij__betw__Suc,axiom,
% 5.06/5.43 ! [M7: set_nat,N4: set_nat] :
% 5.06/5.43 ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 5.06/5.43 = ( ( image_nat_nat @ suc @ M7 )
% 5.06/5.43 = N4 ) ) ).
% 5.06/5.43
% 5.06/5.43 % bij_betw_Suc
% 5.06/5.43 thf(fact_9869_image__Suc__atLeastAtMost,axiom,
% 5.06/5.43 ! [I2: nat,J: nat] :
% 5.06/5.43 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 5.06/5.43 = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % image_Suc_atLeastAtMost
% 5.06/5.43 thf(fact_9870_image__Suc__atLeastLessThan,axiom,
% 5.06/5.43 ! [I2: nat,J: nat] :
% 5.06/5.43 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 5.06/5.43 = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % image_Suc_atLeastLessThan
% 5.06/5.43 thf(fact_9871_mult__rat,axiom,
% 5.06/5.43 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.43 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.06/5.43 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % mult_rat
% 5.06/5.43 thf(fact_9872_divide__rat,axiom,
% 5.06/5.43 ! [A: int,B: int,C: int,D: int] :
% 5.06/5.43 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.06/5.43 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % divide_rat
% 5.06/5.43 thf(fact_9873_card__greaterThanAtMost,axiom,
% 5.06/5.43 ! [L2: nat,U: nat] :
% 5.06/5.43 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) )
% 5.06/5.43 = ( minus_minus_nat @ U @ L2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_greaterThanAtMost
% 5.06/5.43 thf(fact_9874_sgn__rat,axiom,
% 5.06/5.43 ! [A: int,B: int] :
% 5.06/5.43 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 5.06/5.43 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sgn_rat
% 5.06/5.43 thf(fact_9875_less__rat,axiom,
% 5.06/5.43 ! [B: int,D: int,A: int,C: int] :
% 5.06/5.43 ( ( B != zero_zero_int )
% 5.06/5.43 => ( ( D != zero_zero_int )
% 5.06/5.43 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.06/5.43 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % less_rat
% 5.06/5.43 thf(fact_9876_add__rat,axiom,
% 5.06/5.43 ! [B: int,D: int,A: int,C: int] :
% 5.06/5.43 ( ( B != zero_zero_int )
% 5.06/5.43 => ( ( D != zero_zero_int )
% 5.06/5.43 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.06/5.43 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % add_rat
% 5.06/5.43 thf(fact_9877_le__rat,axiom,
% 5.06/5.43 ! [B: int,D: int,A: int,C: int] :
% 5.06/5.43 ( ( B != zero_zero_int )
% 5.06/5.43 => ( ( D != zero_zero_int )
% 5.06/5.43 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.06/5.43 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % le_rat
% 5.06/5.43 thf(fact_9878_diff__rat,axiom,
% 5.06/5.43 ! [B: int,D: int,A: int,C: int] :
% 5.06/5.43 ( ( B != zero_zero_int )
% 5.06/5.43 => ( ( D != zero_zero_int )
% 5.06/5.43 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.06/5.43 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % diff_rat
% 5.06/5.43 thf(fact_9879_mult__rat__cancel,axiom,
% 5.06/5.43 ! [C: int,A: int,B: int] :
% 5.06/5.43 ( ( C != zero_zero_int )
% 5.06/5.43 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.06/5.43 = ( fract @ A @ B ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % mult_rat_cancel
% 5.06/5.43 thf(fact_9880_eq__rat_I1_J,axiom,
% 5.06/5.43 ! [B: int,D: int,A: int,C: int] :
% 5.06/5.43 ( ( B != zero_zero_int )
% 5.06/5.43 => ( ( D != zero_zero_int )
% 5.06/5.43 => ( ( ( fract @ A @ B )
% 5.06/5.43 = ( fract @ C @ D ) )
% 5.06/5.43 = ( ( times_times_int @ A @ D )
% 5.06/5.43 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % eq_rat(1)
% 5.06/5.43 thf(fact_9881_zero__notin__Suc__image,axiom,
% 5.06/5.43 ! [A2: set_nat] :
% 5.06/5.43 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % zero_notin_Suc_image
% 5.06/5.43 thf(fact_9882_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.06/5.43 ! [L2: nat,U: nat] :
% 5.06/5.43 ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 5.06/5.43 = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastSucAtMost_greaterThanAtMost
% 5.06/5.43 thf(fact_9883_rat__number__expand_I3_J,axiom,
% 5.06/5.43 ( numeral_numeral_rat
% 5.06/5.43 = ( ^ [K3: num] : ( fract @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_number_expand(3)
% 5.06/5.43 thf(fact_9884_rat__number__collapse_I3_J,axiom,
% 5.06/5.43 ! [W: num] :
% 5.06/5.43 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 5.06/5.43 = ( numeral_numeral_rat @ W ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_number_collapse(3)
% 5.06/5.43 thf(fact_9885_image__Suc__lessThan,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.43 = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % image_Suc_lessThan
% 5.06/5.43 thf(fact_9886_image__Suc__atMost,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 5.06/5.43 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % image_Suc_atMost
% 5.06/5.43 thf(fact_9887_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.06/5.43 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeast0_atMost_Suc_eq_insert_0
% 5.06/5.43 thf(fact_9888_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.06/5.43 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeast0_lessThan_Suc_eq_insert_0
% 5.06/5.43 thf(fact_9889_lessThan__Suc__eq__insert__0,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 5.06/5.43 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % lessThan_Suc_eq_insert_0
% 5.06/5.43 thf(fact_9890_atMost__Suc__eq__insert__0,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 5.06/5.43 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atMost_Suc_eq_insert_0
% 5.06/5.43 thf(fact_9891_Fract__add__one,axiom,
% 5.06/5.43 ! [N2: int,M: int] :
% 5.06/5.43 ( ( N2 != zero_zero_int )
% 5.06/5.43 => ( ( fract @ ( plus_plus_int @ M @ N2 ) @ N2 )
% 5.06/5.43 = ( plus_plus_rat @ ( fract @ M @ N2 ) @ one_one_rat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Fract_add_one
% 5.06/5.43 thf(fact_9892_zero__le__Fract__iff,axiom,
% 5.06/5.43 ! [B: int,A: int] :
% 5.06/5.43 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.06/5.43 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % zero_le_Fract_iff
% 5.06/5.43 thf(fact_9893_Fract__le__zero__iff,axiom,
% 5.06/5.43 ! [B: int,A: int] :
% 5.06/5.43 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.43 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.06/5.43 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Fract_le_zero_iff
% 5.06/5.43 thf(fact_9894_Fract__le__one__iff,axiom,
% 5.06/5.43 ! [B: int,A: int] :
% 5.06/5.43 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.43 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.06/5.43 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Fract_le_one_iff
% 5.06/5.43 thf(fact_9895_one__le__Fract__iff,axiom,
% 5.06/5.43 ! [B: int,A: int] :
% 5.06/5.43 ( ( ord_less_int @ zero_zero_int @ B )
% 5.06/5.43 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.06/5.43 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % one_le_Fract_iff
% 5.06/5.43 thf(fact_9896_rat__number__expand_I5_J,axiom,
% 5.06/5.43 ! [K: num] :
% 5.06/5.43 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.06/5.43 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_number_expand(5)
% 5.06/5.43 thf(fact_9897_rat__number__collapse_I4_J,axiom,
% 5.06/5.43 ! [W: num] :
% 5.06/5.43 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 5.06/5.43 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % rat_number_collapse(4)
% 5.06/5.43 thf(fact_9898_Gcd__abs__eq,axiom,
% 5.06/5.43 ! [K5: set_int] :
% 5.06/5.43 ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 5.06/5.43 = ( gcd_Gcd_int @ K5 ) ) ).
% 5.06/5.43
% 5.06/5.43 % Gcd_abs_eq
% 5.06/5.43 thf(fact_9899_card__greaterThanAtMost__int,axiom,
% 5.06/5.43 ! [L2: int,U: int] :
% 5.06/5.43 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L2 @ U ) )
% 5.06/5.43 = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_greaterThanAtMost_int
% 5.06/5.43 thf(fact_9900_Gcd__int__eq,axiom,
% 5.06/5.43 ! [N4: set_nat] :
% 5.06/5.43 ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N4 ) )
% 5.06/5.43 = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N4 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Gcd_int_eq
% 5.06/5.43 thf(fact_9901_Gcd__nat__abs__eq,axiom,
% 5.06/5.43 ! [K5: set_int] :
% 5.06/5.43 ( ( gcd_Gcd_nat
% 5.06/5.43 @ ( image_int_nat
% 5.06/5.43 @ ^ [K3: int] : ( nat2 @ ( abs_abs_int @ K3 ) )
% 5.06/5.43 @ K5 ) )
% 5.06/5.43 = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Gcd_nat_abs_eq
% 5.06/5.43 thf(fact_9902_Inf__real__def,axiom,
% 5.06/5.43 ( comple4887499456419720421f_real
% 5.06/5.43 = ( ^ [X4: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X4 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Inf_real_def
% 5.06/5.43 thf(fact_9903_finite__int__iff__bounded__le,axiom,
% 5.06/5.43 ( finite_finite_int
% 5.06/5.43 = ( ^ [S5: set_int] :
% 5.06/5.43 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % finite_int_iff_bounded_le
% 5.06/5.43 thf(fact_9904_finite__int__iff__bounded,axiom,
% 5.06/5.43 ( finite_finite_int
% 5.06/5.43 = ( ^ [S5: set_int] :
% 5.06/5.43 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % finite_int_iff_bounded
% 5.06/5.43 thf(fact_9905_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.06/5.43 ! [L2: int,U: int] :
% 5.06/5.43 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 5.06/5.43 = ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.06/5.43 thf(fact_9906_image__add__int__atLeastLessThan,axiom,
% 5.06/5.43 ! [L2: int,U: int] :
% 5.06/5.43 ( ( image_int_int
% 5.06/5.43 @ ^ [X2: int] : ( plus_plus_int @ X2 @ L2 )
% 5.06/5.43 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 5.06/5.43 = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 5.06/5.43
% 5.06/5.43 % image_add_int_atLeastLessThan
% 5.06/5.43 thf(fact_9907_image__atLeastZeroLessThan__int,axiom,
% 5.06/5.43 ! [U: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.06/5.43 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.06/5.43 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % image_atLeastZeroLessThan_int
% 5.06/5.43 thf(fact_9908_suminf__eq__SUP__real,axiom,
% 5.06/5.43 ! [X8: nat > real] :
% 5.06/5.43 ( ( summable_real @ X8 )
% 5.06/5.43 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I3 ) )
% 5.06/5.43 => ( ( suminf_real @ X8 )
% 5.06/5.43 = ( comple1385675409528146559p_real
% 5.06/5.43 @ ( image_nat_real
% 5.06/5.43 @ ^ [I5: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I5 ) )
% 5.06/5.43 @ top_top_set_nat ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % suminf_eq_SUP_real
% 5.06/5.43 thf(fact_9909_UN__lessThan__UNIV,axiom,
% 5.06/5.43 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.06/5.43 = top_top_set_nat ) ).
% 5.06/5.43
% 5.06/5.43 % UN_lessThan_UNIV
% 5.06/5.43 thf(fact_9910_UN__atMost__UNIV,axiom,
% 5.06/5.43 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.06/5.43 = top_top_set_nat ) ).
% 5.06/5.43
% 5.06/5.43 % UN_atMost_UNIV
% 5.06/5.43 thf(fact_9911_UNIV__nat__eq,axiom,
% 5.06/5.43 ( top_top_set_nat
% 5.06/5.43 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % UNIV_nat_eq
% 5.06/5.43 thf(fact_9912_range__mod,axiom,
% 5.06/5.43 ! [N2: nat] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( image_nat_nat
% 5.06/5.43 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N2 )
% 5.06/5.43 @ top_top_set_nat )
% 5.06/5.43 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % range_mod
% 5.06/5.43 thf(fact_9913_card__UNIV__unit,axiom,
% 5.06/5.43 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.06/5.43 = one_one_nat ) ).
% 5.06/5.43
% 5.06/5.43 % card_UNIV_unit
% 5.06/5.43 thf(fact_9914_card__UNIV__bool,axiom,
% 5.06/5.43 ( ( finite_card_o @ top_top_set_o )
% 5.06/5.43 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_UNIV_bool
% 5.06/5.43 thf(fact_9915_range__mult,axiom,
% 5.06/5.43 ! [A: real] :
% 5.06/5.43 ( ( ( A = zero_zero_real )
% 5.06/5.43 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.06/5.43 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.06/5.43 & ( ( A != zero_zero_real )
% 5.06/5.43 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.06/5.43 = top_top_set_real ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % range_mult
% 5.06/5.43 thf(fact_9916_root__def,axiom,
% 5.06/5.43 ( root
% 5.06/5.43 = ( ^ [N: nat,X2: real] :
% 5.06/5.43 ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 5.06/5.43 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.06/5.43 @ ^ [Y2: real] : ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N ) )
% 5.06/5.43 @ X2 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % root_def
% 5.06/5.43 thf(fact_9917_card__UNIV__char,axiom,
% 5.06/5.43 ( ( finite_card_char @ top_top_set_char )
% 5.06/5.43 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % card_UNIV_char
% 5.06/5.43 thf(fact_9918_UNIV__char__of__nat,axiom,
% 5.06/5.43 ( top_top_set_char
% 5.06/5.43 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % UNIV_char_of_nat
% 5.06/5.43 thf(fact_9919_char_Osize_I2_J,axiom,
% 5.06/5.43 ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.06/5.43 ( ( size_size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.06/5.43 = zero_zero_nat ) ).
% 5.06/5.43
% 5.06/5.43 % char.size(2)
% 5.06/5.43 thf(fact_9920_nat__of__char__less__256,axiom,
% 5.06/5.43 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nat_of_char_less_256
% 5.06/5.43 thf(fact_9921_range__nat__of__char,axiom,
% 5.06/5.43 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.06/5.43 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % range_nat_of_char
% 5.06/5.43 thf(fact_9922_integer__of__char__code,axiom,
% 5.06/5.43 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.06/5.43 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.06/5.43 = ( 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 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % integer_of_char_code
% 5.06/5.43 thf(fact_9923_char__of__integer__code,axiom,
% 5.06/5.43 ( char_of_integer
% 5.06/5.43 = ( ^ [K3: code_integer] :
% 5.06/5.43 ( produc4188289175737317920o_char
% 5.06/5.43 @ ^ [Q0: code_integer,B02: $o] :
% 5.06/5.43 ( produc4188289175737317920o_char
% 5.06/5.43 @ ^ [Q1: code_integer,B12: $o] :
% 5.06/5.43 ( produc4188289175737317920o_char
% 5.06/5.43 @ ^ [Q22: code_integer,B23: $o] :
% 5.06/5.43 ( produc4188289175737317920o_char
% 5.06/5.43 @ ^ [Q32: code_integer,B33: $o] :
% 5.06/5.43 ( produc4188289175737317920o_char
% 5.06/5.43 @ ^ [Q42: code_integer,B43: $o] :
% 5.06/5.43 ( produc4188289175737317920o_char
% 5.06/5.43 @ ^ [Q52: code_integer,B53: $o] :
% 5.06/5.43 ( produc4188289175737317920o_char
% 5.06/5.43 @ ^ [Q62: code_integer,B63: $o] :
% 5.06/5.43 ( produc4188289175737317920o_char
% 5.06/5.43 @ ^ [Uu3: code_integer] : ( char2 @ B02 @ B12 @ B23 @ B33 @ B43 @ B53 @ B63 )
% 5.06/5.43 @ ( code_bit_cut_integer @ Q62 ) )
% 5.06/5.43 @ ( code_bit_cut_integer @ Q52 ) )
% 5.06/5.43 @ ( code_bit_cut_integer @ Q42 ) )
% 5.06/5.43 @ ( code_bit_cut_integer @ Q32 ) )
% 5.06/5.43 @ ( code_bit_cut_integer @ Q22 ) )
% 5.06/5.43 @ ( code_bit_cut_integer @ Q1 ) )
% 5.06/5.43 @ ( code_bit_cut_integer @ Q0 ) )
% 5.06/5.43 @ ( code_bit_cut_integer @ K3 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % char_of_integer_code
% 5.06/5.43 thf(fact_9924_String_Ochar__of__ascii__of,axiom,
% 5.06/5.43 ! [C: char] :
% 5.06/5.43 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.06/5.43 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % String.char_of_ascii_of
% 5.06/5.43 thf(fact_9925_sorted__list__of__set__lessThan__Suc,axiom,
% 5.06/5.43 ! [K: nat] :
% 5.06/5.43 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.06/5.43 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sorted_list_of_set_lessThan_Suc
% 5.06/5.43 thf(fact_9926_sorted__list__of__set__atMost__Suc,axiom,
% 5.06/5.43 ! [K: nat] :
% 5.06/5.43 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.06/5.43 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sorted_list_of_set_atMost_Suc
% 5.06/5.43 thf(fact_9927_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.06/5.43 ! [I2: nat,J: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 5.06/5.43 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 5.06/5.43 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sorted_list_of_set_greaterThanAtMost
% 5.06/5.43 thf(fact_9928_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.06/5.43 ! [I2: nat,J: nat] :
% 5.06/5.43 ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 5.06/5.43 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 5.06/5.43 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % sorted_list_of_set_greaterThanLessThan
% 5.06/5.43 thf(fact_9929_list__encode_Oelims,axiom,
% 5.06/5.43 ! [X: list_nat,Y: nat] :
% 5.06/5.43 ( ( ( nat_list_encode @ X )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( ( X = nil_nat )
% 5.06/5.43 => ( Y != zero_zero_nat ) )
% 5.06/5.43 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.06/5.43 ( ( X
% 5.06/5.43 = ( cons_nat @ X3 @ Xs3 ) )
% 5.06/5.43 => ( Y
% 5.06/5.43 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % list_encode.elims
% 5.06/5.43 thf(fact_9930_upto__aux__rec,axiom,
% 5.06/5.43 ( upto_aux
% 5.06/5.43 = ( ^ [I5: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I5 ) @ Js @ ( upto_aux @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_aux_rec
% 5.06/5.43 thf(fact_9931_sup__nat__def,axiom,
% 5.06/5.43 sup_sup_nat = ord_max_nat ).
% 5.06/5.43
% 5.06/5.43 % sup_nat_def
% 5.06/5.43 thf(fact_9932_sup__enat__def,axiom,
% 5.06/5.43 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.06/5.43
% 5.06/5.43 % sup_enat_def
% 5.06/5.43 thf(fact_9933_sup__int__def,axiom,
% 5.06/5.43 sup_sup_int = ord_max_int ).
% 5.06/5.43
% 5.06/5.43 % sup_int_def
% 5.06/5.43 thf(fact_9934_atLeastLessThan__add__Un,axiom,
% 5.06/5.43 ! [I2: nat,J: nat,K: nat] :
% 5.06/5.43 ( ( ord_less_eq_nat @ I2 @ J )
% 5.06/5.43 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.06/5.43 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastLessThan_add_Un
% 5.06/5.43 thf(fact_9935_list__encode_Osimps_I2_J,axiom,
% 5.06/5.43 ! [X: nat,Xs2: list_nat] :
% 5.06/5.43 ( ( nat_list_encode @ ( cons_nat @ X @ Xs2 ) )
% 5.06/5.43 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % list_encode.simps(2)
% 5.06/5.43 thf(fact_9936_list__encode_Opelims,axiom,
% 5.06/5.43 ! [X: list_nat,Y: nat] :
% 5.06/5.43 ( ( ( nat_list_encode @ X )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 5.06/5.43 => ( ( ( X = nil_nat )
% 5.06/5.43 => ( ( Y = zero_zero_nat )
% 5.06/5.43 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.06/5.43 => ~ ! [X3: nat,Xs3: list_nat] :
% 5.06/5.43 ( ( X
% 5.06/5.43 = ( cons_nat @ X3 @ Xs3 ) )
% 5.06/5.43 => ( ( Y
% 5.06/5.43 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.06/5.43 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs3 ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % list_encode.pelims
% 5.06/5.43 thf(fact_9937_upto_Opelims,axiom,
% 5.06/5.43 ! [X: int,Xa2: int,Y: list_int] :
% 5.06/5.43 ( ( ( upto @ X @ Xa2 )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.06/5.43 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.06/5.43 => ( Y = nil_int ) ) )
% 5.06/5.43 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto.pelims
% 5.06/5.43 thf(fact_9938_upto_Opsimps,axiom,
% 5.06/5.43 ! [I2: int,J: int] :
% 5.06/5.43 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J ) )
% 5.06/5.43 => ( ( ( ord_less_eq_int @ I2 @ J )
% 5.06/5.43 => ( ( upto @ I2 @ J )
% 5.06/5.43 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ I2 @ J )
% 5.06/5.43 => ( ( upto @ I2 @ J )
% 5.06/5.43 = nil_int ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto.psimps
% 5.06/5.43 thf(fact_9939_upto__empty,axiom,
% 5.06/5.43 ! [J: int,I2: int] :
% 5.06/5.43 ( ( ord_less_int @ J @ I2 )
% 5.06/5.43 => ( ( upto @ I2 @ J )
% 5.06/5.43 = nil_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_empty
% 5.06/5.43 thf(fact_9940_upto__Nil2,axiom,
% 5.06/5.43 ! [I2: int,J: int] :
% 5.06/5.43 ( ( nil_int
% 5.06/5.43 = ( upto @ I2 @ J ) )
% 5.06/5.43 = ( ord_less_int @ J @ I2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_Nil2
% 5.06/5.43 thf(fact_9941_upto__Nil,axiom,
% 5.06/5.43 ! [I2: int,J: int] :
% 5.06/5.43 ( ( ( upto @ I2 @ J )
% 5.06/5.43 = nil_int )
% 5.06/5.43 = ( ord_less_int @ J @ I2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_Nil
% 5.06/5.43 thf(fact_9942_upto__single,axiom,
% 5.06/5.43 ! [I2: int] :
% 5.06/5.43 ( ( upto @ I2 @ I2 )
% 5.06/5.43 = ( cons_int @ I2 @ nil_int ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_single
% 5.06/5.43 thf(fact_9943_nth__upto,axiom,
% 5.06/5.43 ! [I2: int,K: nat,J: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.06/5.43 => ( ( nth_int @ ( upto @ I2 @ J ) @ K )
% 5.06/5.43 = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % nth_upto
% 5.06/5.43 thf(fact_9944_length__upto,axiom,
% 5.06/5.43 ! [I2: int,J: int] :
% 5.06/5.43 ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 5.06/5.43 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % length_upto
% 5.06/5.43 thf(fact_9945_upto__rec__numeral_I1_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 = nil_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_rec_numeral(1)
% 5.06/5.43 thf(fact_9946_upto__rec__numeral_I4_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = ( 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 @ N2 ) ) ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = nil_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_rec_numeral(4)
% 5.06/5.43 thf(fact_9947_upto__rec__numeral_I3_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 = ( 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 @ N2 ) ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.43 = nil_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_rec_numeral(3)
% 5.06/5.43 thf(fact_9948_upto__rec__numeral_I2_J,axiom,
% 5.06/5.43 ! [M: num,N2: num] :
% 5.06/5.43 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.43 = nil_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_rec_numeral(2)
% 5.06/5.43 thf(fact_9949_distinct__upto,axiom,
% 5.06/5.43 ! [I2: int,J: int] : ( distinct_int @ ( upto @ I2 @ J ) ) ).
% 5.06/5.43
% 5.06/5.43 % distinct_upto
% 5.06/5.43 thf(fact_9950_atLeastAtMost__upto,axiom,
% 5.06/5.43 ( set_or1266510415728281911st_int
% 5.06/5.43 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ J3 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastAtMost_upto
% 5.06/5.43 thf(fact_9951_upto__code,axiom,
% 5.06/5.43 ( upto
% 5.06/5.43 = ( ^ [I5: int,J3: int] : ( upto_aux @ I5 @ J3 @ nil_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_code
% 5.06/5.43 thf(fact_9952_upto__aux__def,axiom,
% 5.06/5.43 ( upto_aux
% 5.06/5.43 = ( ^ [I5: int,J3: int] : ( append_int @ ( upto @ I5 @ J3 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_aux_def
% 5.06/5.43 thf(fact_9953_upto__split2,axiom,
% 5.06/5.43 ! [I2: int,J: int,K: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ I2 @ J )
% 5.06/5.43 => ( ( ord_less_eq_int @ J @ K )
% 5.06/5.43 => ( ( upto @ I2 @ K )
% 5.06/5.43 = ( append_int @ ( upto @ I2 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_split2
% 5.06/5.43 thf(fact_9954_upto__split1,axiom,
% 5.06/5.43 ! [I2: int,J: int,K: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ I2 @ J )
% 5.06/5.43 => ( ( ord_less_eq_int @ J @ K )
% 5.06/5.43 => ( ( upto @ I2 @ K )
% 5.06/5.43 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_split1
% 5.06/5.43 thf(fact_9955_atLeastLessThan__upto,axiom,
% 5.06/5.43 ( set_or4662586982721622107an_int
% 5.06/5.43 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % atLeastLessThan_upto
% 5.06/5.43 thf(fact_9956_greaterThanAtMost__upto,axiom,
% 5.06/5.43 ( set_or6656581121297822940st_int
% 5.06/5.43 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % greaterThanAtMost_upto
% 5.06/5.43 thf(fact_9957_upto__rec1,axiom,
% 5.06/5.43 ! [I2: int,J: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ I2 @ J )
% 5.06/5.43 => ( ( upto @ I2 @ J )
% 5.06/5.43 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_rec1
% 5.06/5.43 thf(fact_9958_upto_Osimps,axiom,
% 5.06/5.43 ( upto
% 5.06/5.43 = ( ^ [I5: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I5 @ J3 ) @ ( cons_int @ I5 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto.simps
% 5.06/5.43 thf(fact_9959_upto_Oelims,axiom,
% 5.06/5.43 ! [X: int,Xa2: int,Y: list_int] :
% 5.06/5.43 ( ( ( upto @ X @ Xa2 )
% 5.06/5.43 = Y )
% 5.06/5.43 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.06/5.43 => ( Y
% 5.06/5.43 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.06/5.43 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.06/5.43 => ( Y = nil_int ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto.elims
% 5.06/5.43 thf(fact_9960_upto__rec2,axiom,
% 5.06/5.43 ! [I2: int,J: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ I2 @ J )
% 5.06/5.43 => ( ( upto @ I2 @ J )
% 5.06/5.43 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_rec2
% 5.06/5.43 thf(fact_9961_greaterThanLessThan__upto,axiom,
% 5.06/5.43 ( set_or5832277885323065728an_int
% 5.06/5.43 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % greaterThanLessThan_upto
% 5.06/5.43 thf(fact_9962_upto__split3,axiom,
% 5.06/5.43 ! [I2: int,J: int,K: int] :
% 5.06/5.43 ( ( ord_less_eq_int @ I2 @ J )
% 5.06/5.43 => ( ( ord_less_eq_int @ J @ K )
% 5.06/5.43 => ( ( upto @ I2 @ K )
% 5.06/5.43 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % upto_split3
% 5.06/5.43 thf(fact_9963_DERIV__real__root__generic,axiom,
% 5.06/5.43 ! [N2: nat,X: real,D3: real] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( X != zero_zero_real )
% 5.06/5.43 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.43 => ( D3
% 5.06/5.43 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.06/5.43 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.43 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.06/5.43 => ( D3
% 5.06/5.43 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.06/5.43 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.43 => ( D3
% 5.06/5.43 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ D3 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_real_root_generic
% 5.06/5.43 thf(fact_9964_DERIV__mirror,axiom,
% 5.06/5.43 ! [F: real > real,Y: real,X: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ Y @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ X ) @ top_top_set_real ) )
% 5.06/5.43 = ( has_fi5821293074295781190e_real
% 5.06/5.43 @ ^ [X2: real] : ( F @ ( uminus_uminus_real @ X2 ) )
% 5.06/5.43 @ ( uminus_uminus_real @ Y )
% 5.06/5.43 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_mirror
% 5.06/5.43 thf(fact_9965_DERIV__const__ratio__const,axiom,
% 5.06/5.43 ! [A: real,B: real,F: real > real,K: real] :
% 5.06/5.43 ( ( A != B )
% 5.06/5.43 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.43 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.06/5.43 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_const_ratio_const
% 5.06/5.43 thf(fact_9966_DERIV__const__ratio__const2,axiom,
% 5.06/5.43 ! [A: real,B: real,F: real > real,K: real] :
% 5.06/5.43 ( ( A != B )
% 5.06/5.43 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.43 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 5.06/5.43 = K ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_const_ratio_const2
% 5.06/5.43 thf(fact_9967_has__real__derivative__neg__dec__right,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real,S3: set_real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.06/5.43 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.06/5.43 => ? [D4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.06/5.43 & ! [H4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.06/5.43 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S3 )
% 5.06/5.43 => ( ( ord_less_real @ H4 @ D4 )
% 5.06/5.43 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % has_real_derivative_neg_dec_right
% 5.06/5.43 thf(fact_9968_has__real__derivative__pos__inc__right,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real,S3: set_real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.06/5.43 => ? [D4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.06/5.43 & ! [H4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.06/5.43 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S3 )
% 5.06/5.43 => ( ( ord_less_real @ H4 @ D4 )
% 5.06/5.43 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % has_real_derivative_pos_inc_right
% 5.06/5.43 thf(fact_9969_has__real__derivative__pos__inc__left,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real,S3: set_real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.06/5.43 => ? [D4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.06/5.43 & ! [H4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.06/5.43 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S3 )
% 5.06/5.43 => ( ( ord_less_real @ H4 @ D4 )
% 5.06/5.43 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % has_real_derivative_pos_inc_left
% 5.06/5.43 thf(fact_9970_has__real__derivative__neg__dec__left,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real,S3: set_real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 5.06/5.43 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.06/5.43 => ? [D4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.06/5.43 & ! [H4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.06/5.43 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S3 )
% 5.06/5.43 => ( ( ord_less_real @ H4 @ D4 )
% 5.06/5.43 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % has_real_derivative_neg_dec_left
% 5.06/5.43 thf(fact_9971_DERIV__local__const,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real,D: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.06/5.43 => ( ! [Y5: real] :
% 5.06/5.43 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 5.06/5.43 => ( ( F @ X )
% 5.06/5.43 = ( F @ Y5 ) ) )
% 5.06/5.43 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_local_const
% 5.06/5.43 thf(fact_9972_DERIV__pos__inc__left,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.06/5.43 => ? [D4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.06/5.43 & ! [H4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.06/5.43 => ( ( ord_less_real @ H4 @ D4 )
% 5.06/5.43 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_pos_inc_left
% 5.06/5.43 thf(fact_9973_DERIV__neg__dec__left,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.06/5.43 => ? [D4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.06/5.43 & ! [H4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.06/5.43 => ( ( ord_less_real @ H4 @ D4 )
% 5.06/5.43 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_neg_dec_left
% 5.06/5.43 thf(fact_9974_DERIV__neg__dec__right,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.06/5.43 => ? [D4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.06/5.43 & ! [H4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.06/5.43 => ( ( ord_less_real @ H4 @ D4 )
% 5.06/5.43 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_neg_dec_right
% 5.06/5.43 thf(fact_9975_DERIV__pos__inc__right,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.06/5.43 => ? [D4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ D4 )
% 5.06/5.43 & ! [H4: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.06/5.43 => ( ( ord_less_real @ H4 @ D4 )
% 5.06/5.43 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_pos_inc_right
% 5.06/5.43 thf(fact_9976_MVT2,axiom,
% 5.06/5.43 ! [A: real,B: real,F: real > real,F4: real > real] :
% 5.06/5.43 ( ( ord_less_real @ A @ B )
% 5.06/5.43 => ( ! [X3: real] :
% 5.06/5.43 ( ( ord_less_eq_real @ A @ X3 )
% 5.06/5.43 => ( ( ord_less_eq_real @ X3 @ B )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.06/5.43 => ? [Z4: real] :
% 5.06/5.43 ( ( ord_less_real @ A @ Z4 )
% 5.06/5.43 & ( ord_less_real @ Z4 @ B )
% 5.06/5.43 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.06/5.43 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z4 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % MVT2
% 5.06/5.43 thf(fact_9977_DERIV__pos__imp__increasing,axiom,
% 5.06/5.43 ! [A: real,B: real,F: real > real] :
% 5.06/5.43 ( ( ord_less_real @ A @ B )
% 5.06/5.43 => ( ! [X3: real] :
% 5.06/5.43 ( ( ord_less_eq_real @ A @ X3 )
% 5.06/5.43 => ( ( ord_less_eq_real @ X3 @ B )
% 5.06/5.43 => ? [Y3: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.43 & ( ord_less_real @ zero_zero_real @ Y3 ) ) ) )
% 5.06/5.43 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_pos_imp_increasing
% 5.06/5.43 thf(fact_9978_DERIV__neg__imp__decreasing,axiom,
% 5.06/5.43 ! [A: real,B: real,F: real > real] :
% 5.06/5.43 ( ( ord_less_real @ A @ B )
% 5.06/5.43 => ( ! [X3: real] :
% 5.06/5.43 ( ( ord_less_eq_real @ A @ X3 )
% 5.06/5.43 => ( ( ord_less_eq_real @ X3 @ B )
% 5.06/5.43 => ? [Y3: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.43 & ( ord_less_real @ Y3 @ zero_zero_real ) ) ) )
% 5.06/5.43 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_neg_imp_decreasing
% 5.06/5.43 thf(fact_9979_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.06/5.43 ! [A: real,B: real,F: real > real] :
% 5.06/5.43 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.43 => ( ! [X3: real] :
% 5.06/5.43 ( ( ord_less_eq_real @ A @ X3 )
% 5.06/5.43 => ( ( ord_less_eq_real @ X3 @ B )
% 5.06/5.43 => ? [Y3: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.43 & ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ) )
% 5.06/5.43 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_nonneg_imp_nondecreasing
% 5.06/5.43 thf(fact_9980_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.06/5.43 ! [A: real,B: real,F: real > real] :
% 5.06/5.43 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.43 => ( ! [X3: real] :
% 5.06/5.43 ( ( ord_less_eq_real @ A @ X3 )
% 5.06/5.43 => ( ( ord_less_eq_real @ X3 @ B )
% 5.06/5.43 => ? [Y3: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.43 & ( ord_less_eq_real @ Y3 @ zero_zero_real ) ) ) )
% 5.06/5.43 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_nonpos_imp_nonincreasing
% 5.06/5.43 thf(fact_9981_deriv__nonneg__imp__mono,axiom,
% 5.06/5.43 ! [A: real,B: real,G: real > real,G2: real > real] :
% 5.06/5.43 ( ! [X3: real] :
% 5.06/5.43 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.06/5.43 => ( ! [X3: real] :
% 5.06/5.43 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.06/5.43 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 5.06/5.43 => ( ( ord_less_eq_real @ A @ B )
% 5.06/5.43 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % deriv_nonneg_imp_mono
% 5.06/5.43 thf(fact_9982_DERIV__const__average,axiom,
% 5.06/5.43 ! [A: real,B: real,V: real > real,K: real] :
% 5.06/5.43 ( ( A != B )
% 5.06/5.43 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.43 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.06/5.43 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_const_average
% 5.06/5.43 thf(fact_9983_DERIV__local__max,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real,D: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.06/5.43 => ( ! [Y5: real] :
% 5.06/5.43 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 5.06/5.43 => ( ord_less_eq_real @ ( F @ Y5 ) @ ( F @ X ) ) )
% 5.06/5.43 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_local_max
% 5.06/5.43 thf(fact_9984_DERIV__local__min,axiom,
% 5.06/5.43 ! [F: real > real,L2: real,X: real,D: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.06/5.43 => ( ! [Y5: real] :
% 5.06/5.43 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 5.06/5.43 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y5 ) ) )
% 5.06/5.43 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_local_min
% 5.06/5.43 thf(fact_9985_DERIV__pow,axiom,
% 5.06/5.43 ! [N2: nat,X: real,S2: set_real] :
% 5.06/5.43 ( has_fi5821293074295781190e_real
% 5.06/5.43 @ ^ [X2: real] : ( power_power_real @ X2 @ N2 )
% 5.06/5.43 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ X @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.06/5.43 @ ( topolo2177554685111907308n_real @ X @ S2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_pow
% 5.06/5.43 thf(fact_9986_DERIV__fun__pow,axiom,
% 5.06/5.43 ! [G: real > real,M: real,X: real,N2: nat] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( has_fi5821293074295781190e_real
% 5.06/5.43 @ ^ [X2: real] : ( power_power_real @ ( G @ X2 ) @ N2 )
% 5.06/5.43 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) @ M )
% 5.06/5.43 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_fun_pow
% 5.06/5.43 thf(fact_9987_has__real__derivative__powr,axiom,
% 5.06/5.43 ! [Z: real,R2: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.06/5.43 => ( has_fi5821293074295781190e_real
% 5.06/5.43 @ ^ [Z2: real] : ( powr_real @ Z2 @ R2 )
% 5.06/5.43 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.06/5.43 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % has_real_derivative_powr
% 5.06/5.43 thf(fact_9988_DERIV__series_H,axiom,
% 5.06/5.43 ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.06/5.43 ( ! [N3: nat] :
% 5.06/5.43 ( has_fi5821293074295781190e_real
% 5.06/5.43 @ ^ [X2: real] : ( F @ X2 @ N3 )
% 5.06/5.43 @ ( F4 @ X0 @ N3 )
% 5.06/5.43 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.06/5.43 => ( ! [X3: real] :
% 5.06/5.43 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.06/5.43 => ( summable_real @ ( F @ X3 ) ) )
% 5.06/5.43 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.06/5.43 => ( ( summable_real @ ( F4 @ X0 ) )
% 5.06/5.43 => ( ( summable_real @ L5 )
% 5.06/5.43 => ( ! [N3: nat,X3: real,Y5: real] :
% 5.06/5.43 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.06/5.43 => ( ( member_real @ Y5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.06/5.43 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N3 ) @ ( F @ Y5 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y5 ) ) ) ) ) )
% 5.06/5.43 => ( has_fi5821293074295781190e_real
% 5.06/5.43 @ ^ [X2: real] : ( suminf_real @ ( F @ X2 ) )
% 5.06/5.43 @ ( suminf_real @ ( F4 @ X0 ) )
% 5.06/5.43 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_series'
% 5.06/5.43 thf(fact_9989_DERIV__log,axiom,
% 5.06/5.43 ! [X: real,B: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_log
% 5.06/5.43 thf(fact_9990_DERIV__fun__powr,axiom,
% 5.06/5.43 ! [G: real > real,M: real,X: real,R2: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.06/5.43 => ( has_fi5821293074295781190e_real
% 5.06/5.43 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R2 )
% 5.06/5.43 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.06/5.43 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_fun_powr
% 5.06/5.43 thf(fact_9991_DERIV__powr,axiom,
% 5.06/5.43 ! [G: real > real,M: real,X: real,F: real > real,R2: real] :
% 5.06/5.43 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.06/5.43 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.43 => ( has_fi5821293074295781190e_real
% 5.06/5.43 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 5.06/5.43 @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 5.06/5.43 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_powr
% 5.06/5.43 thf(fact_9992_artanh__real__has__field__derivative,axiom,
% 5.06/5.43 ! [X: real,A2: set_real] :
% 5.06/5.43 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % artanh_real_has_field_derivative
% 5.06/5.43 thf(fact_9993_DERIV__real__sqrt,axiom,
% 5.06/5.43 ! [X: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_real_sqrt
% 5.06/5.43 thf(fact_9994_DERIV__arctan,axiom,
% 5.06/5.43 ! [X: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_arctan
% 5.06/5.43 thf(fact_9995_arsinh__real__has__field__derivative,axiom,
% 5.06/5.43 ! [X: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ).
% 5.06/5.43
% 5.06/5.43 % arsinh_real_has_field_derivative
% 5.06/5.43 thf(fact_9996_DERIV__real__sqrt__generic,axiom,
% 5.06/5.43 ! [X: real,D3: real] :
% 5.06/5.43 ( ( X != zero_zero_real )
% 5.06/5.43 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.43 => ( D3
% 5.06/5.43 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.06/5.43 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 5.06/5.43 => ( D3
% 5.06/5.43 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ sqrt @ D3 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_real_sqrt_generic
% 5.06/5.43 thf(fact_9997_arcosh__real__has__field__derivative,axiom,
% 5.06/5.43 ! [X: real,A2: set_real] :
% 5.06/5.43 ( ( ord_less_real @ one_one_real @ X )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % arcosh_real_has_field_derivative
% 5.06/5.43 thf(fact_9998_DERIV__power__series_H,axiom,
% 5.06/5.43 ! [R: real,F: nat > real,X0: real] :
% 5.06/5.43 ( ! [X3: real] :
% 5.06/5.43 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.06/5.43 => ( summable_real
% 5.06/5.43 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X3 @ N ) ) ) )
% 5.06/5.43 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.06/5.43 => ( has_fi5821293074295781190e_real
% 5.06/5.43 @ ^ [X2: real] :
% 5.06/5.43 ( suminf_real
% 5.06/5.43 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) )
% 5.06/5.43 @ ( suminf_real
% 5.06/5.43 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X0 @ N ) ) )
% 5.06/5.43 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_power_series'
% 5.06/5.43 thf(fact_9999_DERIV__real__root,axiom,
% 5.06/5.43 ! [N2: nat,X: real] :
% 5.06/5.43 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_real_root
% 5.06/5.43 thf(fact_10000_DERIV__arccos,axiom,
% 5.06/5.43 ! [X: real] :
% 5.06/5.43 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.43 => ( ( ord_less_real @ X @ one_one_real )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_arccos
% 5.06/5.43 thf(fact_10001_DERIV__arcsin,axiom,
% 5.06/5.43 ! [X: real] :
% 5.06/5.43 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.06/5.43 => ( ( ord_less_real @ X @ one_one_real )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_arcsin
% 5.06/5.43 thf(fact_10002_Maclaurin__all__le,axiom,
% 5.06/5.43 ! [Diff: nat > real > real,F: real > real,X: real,N2: nat] :
% 5.06/5.43 ( ( ( Diff @ zero_zero_nat )
% 5.06/5.43 = F )
% 5.06/5.43 => ( ! [M2: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.43 => ? [T5: real] :
% 5.06/5.43 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X ) )
% 5.06/5.43 & ( ( F @ X )
% 5.06/5.43 = ( plus_plus_real
% 5.06/5.43 @ ( groups6591440286371151544t_real
% 5.06/5.43 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.43 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.43 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Maclaurin_all_le
% 5.06/5.43 thf(fact_10003_Maclaurin__all__le__objl,axiom,
% 5.06/5.43 ! [Diff: nat > real > real,F: real > real,X: real,N2: nat] :
% 5.06/5.43 ( ( ( ( Diff @ zero_zero_nat )
% 5.06/5.43 = F )
% 5.06/5.43 & ! [M2: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.06/5.43 => ? [T5: real] :
% 5.06/5.43 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X ) )
% 5.06/5.43 & ( ( F @ X )
% 5.06/5.43 = ( plus_plus_real
% 5.06/5.43 @ ( groups6591440286371151544t_real
% 5.06/5.43 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.43 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.43 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Maclaurin_all_le_objl
% 5.06/5.43 thf(fact_10004_DERIV__odd__real__root,axiom,
% 5.06/5.43 ! [N2: nat,X: real] :
% 5.06/5.43 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.43 => ( ( X != zero_zero_real )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % DERIV_odd_real_root
% 5.06/5.43 thf(fact_10005_Maclaurin__minus,axiom,
% 5.06/5.43 ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 5.06/5.43 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.06/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( ( Diff @ zero_zero_nat )
% 5.06/5.43 = F )
% 5.06/5.43 => ( ! [M2: nat,T5: real] :
% 5.06/5.43 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.06/5.43 & ( ord_less_eq_real @ H2 @ T5 )
% 5.06/5.43 & ( ord_less_eq_real @ T5 @ zero_zero_real ) )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.06/5.43 => ? [T5: real] :
% 5.06/5.43 ( ( ord_less_real @ H2 @ T5 )
% 5.06/5.43 & ( ord_less_real @ T5 @ zero_zero_real )
% 5.06/5.43 & ( ( F @ H2 )
% 5.06/5.43 = ( plus_plus_real
% 5.06/5.43 @ ( groups6591440286371151544t_real
% 5.06/5.43 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.06/5.43 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.43 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Maclaurin_minus
% 5.06/5.43 thf(fact_10006_Maclaurin2,axiom,
% 5.06/5.43 ! [H2: real,Diff: nat > real > real,F: real > real,N2: nat] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.06/5.43 => ( ( ( Diff @ zero_zero_nat )
% 5.06/5.43 = F )
% 5.06/5.43 => ( ! [M2: nat,T5: real] :
% 5.06/5.43 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.06/5.43 & ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.06/5.43 & ( ord_less_eq_real @ T5 @ H2 ) )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.06/5.43 => ? [T5: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ T5 )
% 5.06/5.43 & ( ord_less_eq_real @ T5 @ H2 )
% 5.06/5.43 & ( ( F @ H2 )
% 5.06/5.43 = ( plus_plus_real
% 5.06/5.43 @ ( groups6591440286371151544t_real
% 5.06/5.43 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.06/5.43 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.43 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Maclaurin2
% 5.06/5.43 thf(fact_10007_Maclaurin,axiom,
% 5.06/5.43 ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.06/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( ( Diff @ zero_zero_nat )
% 5.06/5.43 = F )
% 5.06/5.43 => ( ! [M2: nat,T5: real] :
% 5.06/5.43 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.06/5.43 & ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.06/5.43 & ( ord_less_eq_real @ T5 @ H2 ) )
% 5.06/5.43 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.06/5.43 => ? [T5: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ T5 )
% 5.06/5.43 & ( ord_less_real @ T5 @ H2 )
% 5.06/5.43 & ( ( F @ H2 )
% 5.06/5.43 = ( plus_plus_real
% 5.06/5.43 @ ( groups6591440286371151544t_real
% 5.06/5.43 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.06/5.43 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.43 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.43
% 5.06/5.43 % Maclaurin
% 5.06/5.43 thf(fact_10008_Maclaurin__all__lt,axiom,
% 5.06/5.43 ! [Diff: nat > real > real,F: real > real,N2: nat,X: real] :
% 5.06/5.43 ( ( ( Diff @ zero_zero_nat )
% 5.06/5.43 = F )
% 5.06/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.43 => ( ( X != zero_zero_real )
% 5.06/5.43 => ( ! [M2: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.43 => ? [T5: real] :
% 5.06/5.43 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T5 ) )
% 5.06/5.43 & ( ord_less_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X ) )
% 5.06/5.43 & ( ( F @ X )
% 5.06/5.43 = ( plus_plus_real
% 5.06/5.43 @ ( groups6591440286371151544t_real
% 5.06/5.43 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.43 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.43 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Maclaurin_all_lt
% 5.06/5.44 thf(fact_10009_Maclaurin__bi__le,axiom,
% 5.06/5.44 ! [Diff: nat > real > real,F: real > real,N2: nat,X: real] :
% 5.06/5.44 ( ( ( Diff @ zero_zero_nat )
% 5.06/5.44 = F )
% 5.06/5.44 => ( ! [M2: nat,T5: real] :
% 5.06/5.44 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.06/5.44 & ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X ) ) )
% 5.06/5.44 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.06/5.44 => ? [T5: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ ( abs_abs_real @ T5 ) @ ( abs_abs_real @ X ) )
% 5.06/5.44 & ( ( F @ X )
% 5.06/5.44 = ( plus_plus_real
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.44 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X @ N2 ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Maclaurin_bi_le
% 5.06/5.44 thf(fact_10010_Taylor__down,axiom,
% 5.06/5.44 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.06/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.44 => ( ( ( Diff @ zero_zero_nat )
% 5.06/5.44 = F )
% 5.06/5.44 => ( ! [M2: nat,T5: real] :
% 5.06/5.44 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.06/5.44 & ( ord_less_eq_real @ A @ T5 )
% 5.06/5.44 & ( ord_less_eq_real @ T5 @ B ) )
% 5.06/5.44 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.06/5.44 => ( ( ord_less_real @ A @ C )
% 5.06/5.44 => ( ( ord_less_eq_real @ C @ B )
% 5.06/5.44 => ? [T5: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ T5 )
% 5.06/5.44 & ( ord_less_real @ T5 @ C )
% 5.06/5.44 & ( ( F @ A )
% 5.06/5.44 = ( plus_plus_real
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.44 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Taylor_down
% 5.06/5.44 thf(fact_10011_Taylor__up,axiom,
% 5.06/5.44 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.06/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.44 => ( ( ( Diff @ zero_zero_nat )
% 5.06/5.44 = F )
% 5.06/5.44 => ( ! [M2: nat,T5: real] :
% 5.06/5.44 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.06/5.44 & ( ord_less_eq_real @ A @ T5 )
% 5.06/5.44 & ( ord_less_eq_real @ T5 @ B ) )
% 5.06/5.44 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.06/5.44 => ( ( ord_less_eq_real @ A @ C )
% 5.06/5.44 => ( ( ord_less_real @ C @ B )
% 5.06/5.44 => ? [T5: real] :
% 5.06/5.44 ( ( ord_less_real @ C @ T5 )
% 5.06/5.44 & ( ord_less_real @ T5 @ B )
% 5.06/5.44 & ( ( F @ B )
% 5.06/5.44 = ( plus_plus_real
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.44 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Taylor_up
% 5.06/5.44 thf(fact_10012_Taylor,axiom,
% 5.06/5.44 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 5.06/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.44 => ( ( ( Diff @ zero_zero_nat )
% 5.06/5.44 = F )
% 5.06/5.44 => ( ! [M2: nat,T5: real] :
% 5.06/5.44 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.06/5.44 & ( ord_less_eq_real @ A @ T5 )
% 5.06/5.44 & ( ord_less_eq_real @ T5 @ B ) )
% 5.06/5.44 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.06/5.44 => ( ( ord_less_eq_real @ A @ C )
% 5.06/5.44 => ( ( ord_less_eq_real @ C @ B )
% 5.06/5.44 => ( ( ord_less_eq_real @ A @ X )
% 5.06/5.44 => ( ( ord_less_eq_real @ X @ B )
% 5.06/5.44 => ( ( X != C )
% 5.06/5.44 => ? [T5: real] :
% 5.06/5.44 ( ( ( ord_less_real @ X @ C )
% 5.06/5.44 => ( ( ord_less_real @ X @ T5 )
% 5.06/5.44 & ( ord_less_real @ T5 @ C ) ) )
% 5.06/5.44 & ( ~ ( ord_less_real @ X @ C )
% 5.06/5.44 => ( ( ord_less_real @ C @ T5 )
% 5.06/5.44 & ( ord_less_real @ T5 @ X ) ) )
% 5.06/5.44 & ( ( F @ X )
% 5.06/5.44 = ( plus_plus_real
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M6 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.06/5.44 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T5 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Taylor
% 5.06/5.44 thf(fact_10013_Maclaurin__lemma2,axiom,
% 5.06/5.44 ! [N2: nat,H2: real,Diff: nat > real > real,K: nat,B3: real] :
% 5.06/5.44 ( ! [M2: nat,T5: real] :
% 5.06/5.44 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.06/5.44 & ( ord_less_eq_real @ zero_zero_real @ T5 )
% 5.06/5.44 & ( ord_less_eq_real @ T5 @ H2 ) )
% 5.06/5.44 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T5 ) @ ( topolo2177554685111907308n_real @ T5 @ top_top_set_real ) ) )
% 5.06/5.44 => ( ( N2
% 5.06/5.44 = ( suc @ K ) )
% 5.06/5.44 => ! [M3: nat,T6: real] :
% 5.06/5.44 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.06/5.44 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.06/5.44 & ( ord_less_eq_real @ T6 @ H2 ) )
% 5.06/5.44 => ( has_fi5821293074295781190e_real
% 5.06/5.44 @ ^ [U2: real] :
% 5.06/5.44 ( minus_minus_real @ ( Diff @ M3 @ U2 )
% 5.06/5.44 @ ( plus_plus_real
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M3 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ M3 ) ) )
% 5.06/5.44 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N2 @ M3 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ M3 ) ) ) ) ) )
% 5.06/5.44 @ ( minus_minus_real @ ( Diff @ ( suc @ M3 ) @ T6 )
% 5.06/5.44 @ ( plus_plus_real
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M3 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T6 @ P5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ M3 ) ) ) )
% 5.06/5.44 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T6 @ ( minus_minus_nat @ N2 @ ( suc @ M3 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ ( suc @ M3 ) ) ) ) ) ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Maclaurin_lemma2
% 5.06/5.44 thf(fact_10014_DERIV__arctan__series,axiom,
% 5.06/5.44 ! [X: real] :
% 5.06/5.44 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.44 => ( has_fi5821293074295781190e_real
% 5.06/5.44 @ ^ [X9: real] :
% 5.06/5.44 ( suminf_real
% 5.06/5.44 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.06/5.44 @ ( suminf_real
% 5.06/5.44 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % DERIV_arctan_series
% 5.06/5.44 thf(fact_10015_DERIV__even__real__root,axiom,
% 5.06/5.44 ! [N2: nat,X: real] :
% 5.06/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.44 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.44 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.06/5.44 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( power_power_real @ ( root @ N2 @ X ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % DERIV_even_real_root
% 5.06/5.44 thf(fact_10016_take__bit__numeral__minus__numeral__int,axiom,
% 5.06/5.44 ! [M: num,N2: num] :
% 5.06/5.44 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.44 = ( case_option_int_num @ zero_zero_int
% 5.06/5.44 @ ^ [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 ) ) )
% 5.06/5.44 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % take_bit_numeral_minus_numeral_int
% 5.06/5.44 thf(fact_10017_and__minus__numerals_I3_J,axiom,
% 5.06/5.44 ! [M: num,N2: num] :
% 5.06/5.44 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.06/5.44 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % and_minus_numerals(3)
% 5.06/5.44 thf(fact_10018_take__bit__num__simps_I1_J,axiom,
% 5.06/5.44 ! [M: num] :
% 5.06/5.44 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.06/5.44 = none_num ) ).
% 5.06/5.44
% 5.06/5.44 % take_bit_num_simps(1)
% 5.06/5.44 thf(fact_10019_take__bit__num__simps_I2_J,axiom,
% 5.06/5.44 ! [N2: nat] :
% 5.06/5.44 ( ( bit_take_bit_num @ ( suc @ N2 ) @ one )
% 5.06/5.44 = ( some_num @ one ) ) ).
% 5.06/5.44
% 5.06/5.44 % take_bit_num_simps(2)
% 5.06/5.44 thf(fact_10020_take__bit__num__simps_I5_J,axiom,
% 5.06/5.44 ! [R2: num] :
% 5.06/5.44 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 5.06/5.44 = ( some_num @ one ) ) ).
% 5.06/5.44
% 5.06/5.44 % take_bit_num_simps(5)
% 5.06/5.44 thf(fact_10021_take__bit__num__simps_I3_J,axiom,
% 5.06/5.44 ! [N2: nat,M: num] :
% 5.06/5.44 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M ) )
% 5.06/5.44 = ( case_o6005452278849405969um_num @ none_num
% 5.06/5.44 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.06/5.44 @ ( bit_take_bit_num @ N2 @ M ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % take_bit_num_simps(3)
% 5.06/5.44 thf(fact_10022_take__bit__num__simps_I4_J,axiom,
% 5.06/5.44 ! [N2: nat,M: num] :
% 5.06/5.44 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M ) )
% 5.06/5.44 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % take_bit_num_simps(4)
% 5.06/5.44 thf(fact_10023_take__bit__num__simps_I6_J,axiom,
% 5.06/5.44 ! [R2: num,M: num] :
% 5.06/5.44 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 5.06/5.44 = ( case_o6005452278849405969um_num @ none_num
% 5.06/5.44 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.06/5.44 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % take_bit_num_simps(6)
% 5.06/5.44 thf(fact_10024_take__bit__num__simps_I7_J,axiom,
% 5.06/5.44 ! [R2: num,M: num] :
% 5.06/5.44 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 5.06/5.44 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % take_bit_num_simps(7)
% 5.06/5.44 thf(fact_10025_and__minus__numerals_I8_J,axiom,
% 5.06/5.44 ! [N2: num,M: num] :
% 5.06/5.44 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.06/5.44 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % and_minus_numerals(8)
% 5.06/5.44 thf(fact_10026_and__minus__numerals_I4_J,axiom,
% 5.06/5.44 ! [M: num,N2: num] :
% 5.06/5.44 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.06/5.44 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % and_minus_numerals(4)
% 5.06/5.44 thf(fact_10027_and__minus__numerals_I7_J,axiom,
% 5.06/5.44 ! [N2: num,M: num] :
% 5.06/5.44 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.06/5.44 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % and_minus_numerals(7)
% 5.06/5.44 thf(fact_10028_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.06/5.44 ! [N2: nat,M: num] :
% 5.06/5.44 ( ( bit_take_bit_num @ N2 @ ( bit0 @ M ) )
% 5.06/5.44 = ( case_nat_option_num @ none_num
% 5.06/5.44 @ ^ [N: nat] :
% 5.06/5.44 ( case_o6005452278849405969um_num @ none_num
% 5.06/5.44 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.06/5.44 @ ( bit_take_bit_num @ N @ M ) )
% 5.06/5.44 @ N2 ) ) ).
% 5.06/5.44
% 5.06/5.44 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.06/5.44 thf(fact_10029_and__not__num_Osimps_I4_J,axiom,
% 5.06/5.44 ! [M: num] :
% 5.06/5.44 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.06/5.44 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % and_not_num.simps(4)
% 5.06/5.44 thf(fact_10030_and__not__num_Osimps_I2_J,axiom,
% 5.06/5.44 ! [N2: num] :
% 5.06/5.44 ( ( bit_and_not_num @ one @ ( bit0 @ N2 ) )
% 5.06/5.44 = ( some_num @ one ) ) ).
% 5.06/5.44
% 5.06/5.44 % and_not_num.simps(2)
% 5.06/5.44 thf(fact_10031_and__not__num_Osimps_I3_J,axiom,
% 5.06/5.44 ! [N2: num] :
% 5.06/5.44 ( ( bit_and_not_num @ one @ ( bit1 @ N2 ) )
% 5.06/5.44 = none_num ) ).
% 5.06/5.44
% 5.06/5.44 % and_not_num.simps(3)
% 5.06/5.44 thf(fact_10032_and__not__num_Osimps_I1_J,axiom,
% 5.06/5.44 ( ( bit_and_not_num @ one @ one )
% 5.06/5.44 = none_num ) ).
% 5.06/5.44
% 5.06/5.44 % and_not_num.simps(1)
% 5.06/5.44 thf(fact_10033_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.06/5.44 ! [N2: nat] :
% 5.06/5.44 ( ( bit_take_bit_num @ N2 @ one )
% 5.06/5.44 = ( case_nat_option_num @ none_num
% 5.06/5.44 @ ^ [N: nat] : ( some_num @ one )
% 5.06/5.44 @ N2 ) ) ).
% 5.06/5.44
% 5.06/5.44 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.06/5.44 thf(fact_10034_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.06/5.44 ! [N2: nat,M: num] :
% 5.06/5.44 ( ( bit_take_bit_num @ N2 @ ( bit1 @ M ) )
% 5.06/5.44 = ( case_nat_option_num @ none_num
% 5.06/5.44 @ ^ [N: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) )
% 5.06/5.44 @ N2 ) ) ).
% 5.06/5.44
% 5.06/5.44 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.06/5.44 thf(fact_10035_and__not__num_Osimps_I7_J,axiom,
% 5.06/5.44 ! [M: num] :
% 5.06/5.44 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.06/5.44 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % and_not_num.simps(7)
% 5.06/5.44 thf(fact_10036_and__not__num__eq__Some__iff,axiom,
% 5.06/5.44 ! [M: num,N2: num,Q2: num] :
% 5.06/5.44 ( ( ( bit_and_not_num @ M @ N2 )
% 5.06/5.44 = ( some_num @ Q2 ) )
% 5.06/5.44 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.44 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % and_not_num_eq_Some_iff
% 5.06/5.44 thf(fact_10037_and__not__num_Osimps_I8_J,axiom,
% 5.06/5.44 ! [M: num,N2: num] :
% 5.06/5.44 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.06/5.44 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.06/5.44 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.06/5.44 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % and_not_num.simps(8)
% 5.06/5.44 thf(fact_10038_and__not__num__eq__None__iff,axiom,
% 5.06/5.44 ! [M: num,N2: num] :
% 5.06/5.44 ( ( ( bit_and_not_num @ M @ N2 )
% 5.06/5.44 = none_num )
% 5.06/5.44 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.44 = zero_zero_int ) ) ).
% 5.06/5.44
% 5.06/5.44 % and_not_num_eq_None_iff
% 5.06/5.44 thf(fact_10039_int__numeral__not__and__num,axiom,
% 5.06/5.44 ! [M: num,N2: num] :
% 5.06/5.44 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.06/5.44 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % int_numeral_not_and_num
% 5.06/5.44 thf(fact_10040_int__numeral__and__not__num,axiom,
% 5.06/5.44 ! [M: num,N2: num] :
% 5.06/5.44 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.06/5.44 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % int_numeral_and_not_num
% 5.06/5.44 thf(fact_10041_take__bit__num__def,axiom,
% 5.06/5.44 ( bit_take_bit_num
% 5.06/5.44 = ( ^ [N: nat,M6: num] :
% 5.06/5.44 ( if_option_num
% 5.06/5.44 @ ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M6 ) )
% 5.06/5.44 = zero_zero_nat )
% 5.06/5.44 @ none_num
% 5.06/5.44 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % take_bit_num_def
% 5.06/5.44 thf(fact_10042_Bit__Operations_Otake__bit__num__code,axiom,
% 5.06/5.44 ( bit_take_bit_num
% 5.06/5.44 = ( ^ [N: nat,M6: num] :
% 5.06/5.44 ( produc478579273971653890on_num
% 5.06/5.44 @ ^ [A4: nat,X2: num] :
% 5.06/5.44 ( case_nat_option_num @ none_num
% 5.06/5.44 @ ^ [O: nat] :
% 5.06/5.44 ( case_num_option_num @ ( some_num @ one )
% 5.06/5.44 @ ^ [P5: num] :
% 5.06/5.44 ( case_o6005452278849405969um_num @ none_num
% 5.06/5.44 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.06/5.44 @ ( bit_take_bit_num @ O @ P5 ) )
% 5.06/5.44 @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 5.06/5.44 @ X2 )
% 5.06/5.44 @ A4 )
% 5.06/5.44 @ ( product_Pair_nat_num @ N @ M6 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Bit_Operations.take_bit_num_code
% 5.06/5.44 thf(fact_10043_isCont__Lb__Ub,axiom,
% 5.06/5.44 ! [A: real,B: real,F: real > real] :
% 5.06/5.44 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.06/5.44 & ( ord_less_eq_real @ X3 @ B ) )
% 5.06/5.44 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.06/5.44 => ? [L6: real,M8: real] :
% 5.06/5.44 ( ! [X5: real] :
% 5.06/5.44 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.06/5.44 & ( ord_less_eq_real @ X5 @ B ) )
% 5.06/5.44 => ( ( ord_less_eq_real @ L6 @ ( F @ X5 ) )
% 5.06/5.44 & ( ord_less_eq_real @ ( F @ X5 ) @ M8 ) ) )
% 5.06/5.44 & ! [Y3: real] :
% 5.06/5.44 ( ( ( ord_less_eq_real @ L6 @ Y3 )
% 5.06/5.44 & ( ord_less_eq_real @ Y3 @ M8 ) )
% 5.06/5.44 => ? [X3: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ A @ X3 )
% 5.06/5.44 & ( ord_less_eq_real @ X3 @ B )
% 5.06/5.44 & ( ( F @ X3 )
% 5.06/5.44 = Y3 ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % isCont_Lb_Ub
% 5.06/5.44 thf(fact_10044_isCont__real__sqrt,axiom,
% 5.06/5.44 ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 5.06/5.44
% 5.06/5.44 % isCont_real_sqrt
% 5.06/5.44 thf(fact_10045_isCont__real__root,axiom,
% 5.06/5.44 ! [X: real,N2: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N2 ) ) ).
% 5.06/5.44
% 5.06/5.44 % isCont_real_root
% 5.06/5.44 thf(fact_10046_isCont__inverse__function2,axiom,
% 5.06/5.44 ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 5.06/5.44 ( ( ord_less_real @ A @ X )
% 5.06/5.44 => ( ( ord_less_real @ X @ B )
% 5.06/5.44 => ( ! [Z4: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ A @ Z4 )
% 5.06/5.44 => ( ( ord_less_eq_real @ Z4 @ B )
% 5.06/5.44 => ( ( G @ ( F @ Z4 ) )
% 5.06/5.44 = Z4 ) ) )
% 5.06/5.44 => ( ! [Z4: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ A @ Z4 )
% 5.06/5.44 => ( ( ord_less_eq_real @ Z4 @ B )
% 5.06/5.44 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) ) )
% 5.06/5.44 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % isCont_inverse_function2
% 5.06/5.44 thf(fact_10047_LIM__less__bound,axiom,
% 5.06/5.44 ! [B: real,X: real,F: real > real] :
% 5.06/5.44 ( ( ord_less_real @ B @ X )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 5.06/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 5.06/5.44 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 5.06/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIM_less_bound
% 5.06/5.44 thf(fact_10048_isCont__inverse__function,axiom,
% 5.06/5.44 ! [D: real,X: real,G: real > real,F: real > real] :
% 5.06/5.44 ( ( ord_less_real @ zero_zero_real @ D )
% 5.06/5.44 => ( ! [Z4: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z4 @ X ) ) @ D )
% 5.06/5.44 => ( ( G @ ( F @ Z4 ) )
% 5.06/5.44 = Z4 ) )
% 5.06/5.44 => ( ! [Z4: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z4 @ X ) ) @ D )
% 5.06/5.44 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) )
% 5.06/5.44 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % isCont_inverse_function
% 5.06/5.44 thf(fact_10049_GMVT_H,axiom,
% 5.06/5.44 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 5.06/5.44 ( ( ord_less_real @ A @ B )
% 5.06/5.44 => ( ! [Z4: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ A @ Z4 )
% 5.06/5.44 => ( ( ord_less_eq_real @ Z4 @ B )
% 5.06/5.44 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ F ) ) )
% 5.06/5.44 => ( ! [Z4: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ A @ Z4 )
% 5.06/5.44 => ( ( ord_less_eq_real @ Z4 @ B )
% 5.06/5.44 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) @ G ) ) )
% 5.06/5.44 => ( ! [Z4: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ Z4 )
% 5.06/5.44 => ( ( ord_less_real @ Z4 @ B )
% 5.06/5.44 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z4 ) @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) ) ) )
% 5.06/5.44 => ( ! [Z4: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ Z4 )
% 5.06/5.44 => ( ( ord_less_real @ Z4 @ B )
% 5.06/5.44 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z4 ) @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) ) ) )
% 5.06/5.44 => ? [C3: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ C3 )
% 5.06/5.44 & ( ord_less_real @ C3 @ B )
% 5.06/5.44 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 5.06/5.44 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % GMVT'
% 5.06/5.44 thf(fact_10050_LIM__fun__gt__zero,axiom,
% 5.06/5.44 ! [F: real > real,L2: real,C: real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.06/5.44 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.06/5.44 => ? [R3: real] :
% 5.06/5.44 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.06/5.44 & ! [X5: real] :
% 5.06/5.44 ( ( ( X5 != C )
% 5.06/5.44 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.06/5.44 => ( ord_less_real @ zero_zero_real @ ( F @ X5 ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIM_fun_gt_zero
% 5.06/5.44 thf(fact_10051_LIM__fun__not__zero,axiom,
% 5.06/5.44 ! [F: real > real,L2: real,C: real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.06/5.44 => ( ( L2 != zero_zero_real )
% 5.06/5.44 => ? [R3: real] :
% 5.06/5.44 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.06/5.44 & ! [X5: real] :
% 5.06/5.44 ( ( ( X5 != C )
% 5.06/5.44 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.06/5.44 => ( ( F @ X5 )
% 5.06/5.44 != zero_zero_real ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIM_fun_not_zero
% 5.06/5.44 thf(fact_10052_LIM__fun__less__zero,axiom,
% 5.06/5.44 ! [F: real > real,L2: real,C: real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.06/5.44 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.06/5.44 => ? [R3: real] :
% 5.06/5.44 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.06/5.44 & ! [X5: real] :
% 5.06/5.44 ( ( ( X5 != C )
% 5.06/5.44 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.06/5.44 => ( ord_less_real @ ( F @ X5 ) @ zero_zero_real ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIM_fun_less_zero
% 5.06/5.44 thf(fact_10053_LIM__cos__div__sin,axiom,
% 5.06/5.44 ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIM_cos_div_sin
% 5.06/5.44 thf(fact_10054_summable__Leibniz_I3_J,axiom,
% 5.06/5.44 ! [A: nat > real] :
% 5.06/5.44 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ( ( topolo6980174941875973593q_real @ A )
% 5.06/5.44 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.06/5.44 => ! [N9: nat] :
% 5.06/5.44 ( member_real
% 5.06/5.44 @ ( suminf_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.06/5.44 @ ( set_or1222579329274155063t_real
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) )
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % summable_Leibniz(3)
% 5.06/5.44 thf(fact_10055_summable__Leibniz_I2_J,axiom,
% 5.06/5.44 ! [A: nat > real] :
% 5.06/5.44 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ( ( topolo6980174941875973593q_real @ A )
% 5.06/5.44 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.06/5.44 => ! [N9: nat] :
% 5.06/5.44 ( member_real
% 5.06/5.44 @ ( suminf_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.06/5.44 @ ( set_or1222579329274155063t_real
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % summable_Leibniz(2)
% 5.06/5.44 thf(fact_10056_filterlim__Suc,axiom,
% 5.06/5.44 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.06/5.44
% 5.06/5.44 % filterlim_Suc
% 5.06/5.44 thf(fact_10057_mult__nat__right__at__top,axiom,
% 5.06/5.44 ! [C: nat] :
% 5.06/5.44 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.06/5.44 => ( filterlim_nat_nat
% 5.06/5.44 @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 5.06/5.44 @ at_top_nat
% 5.06/5.44 @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % mult_nat_right_at_top
% 5.06/5.44 thf(fact_10058_mult__nat__left__at__top,axiom,
% 5.06/5.44 ! [C: nat] :
% 5.06/5.44 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.06/5.44 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % mult_nat_left_at_top
% 5.06/5.44 thf(fact_10059_monoseq__convergent,axiom,
% 5.06/5.44 ! [X8: nat > real,B3: real] :
% 5.06/5.44 ( ( topolo6980174941875973593q_real @ X8 )
% 5.06/5.44 => ( ! [I3: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I3 ) ) @ B3 )
% 5.06/5.44 => ~ ! [L6: real] :
% 5.06/5.44 ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % monoseq_convergent
% 5.06/5.44 thf(fact_10060_LIMSEQ__root,axiom,
% 5.06/5.44 ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( root @ N @ ( semiri5074537144036343181t_real @ N ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.06/5.44 @ at_top_nat ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_root
% 5.06/5.44 thf(fact_10061_nested__sequence__unique,axiom,
% 5.06/5.44 ! [F: nat > real,G: nat > real] :
% 5.06/5.44 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.06/5.44 => ( ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ at_top_nat )
% 5.06/5.44 => ? [L4: real] :
% 5.06/5.44 ( ! [N9: nat] : ( ord_less_eq_real @ ( F @ N9 ) @ L4 )
% 5.06/5.44 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.06/5.44 & ! [N9: nat] : ( ord_less_eq_real @ L4 @ ( G @ N9 ) )
% 5.06/5.44 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % nested_sequence_unique
% 5.06/5.44 thf(fact_10062_LIMSEQ__inverse__zero,axiom,
% 5.06/5.44 ! [X8: nat > real] :
% 5.06/5.44 ( ! [R3: real] :
% 5.06/5.44 ? [N7: nat] :
% 5.06/5.44 ! [N3: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.06/5.44 => ( ord_less_real @ R3 @ ( X8 @ N3 ) ) )
% 5.06/5.44 => ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( inverse_inverse_real @ ( X8 @ N ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_inverse_zero
% 5.06/5.44 thf(fact_10063_lim__inverse__n_H,axiom,
% 5.06/5.44 ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ at_top_nat ) ).
% 5.06/5.44
% 5.06/5.44 % lim_inverse_n'
% 5.06/5.44 thf(fact_10064_LIMSEQ__root__const,axiom,
% 5.06/5.44 ! [C: real] :
% 5.06/5.44 ( ( ord_less_real @ zero_zero_real @ C )
% 5.06/5.44 => ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( root @ N @ C )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.06/5.44 @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_root_const
% 5.06/5.44 thf(fact_10065_LIMSEQ__inverse__real__of__nat,axiom,
% 5.06/5.44 ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ at_top_nat ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_inverse_real_of_nat
% 5.06/5.44 thf(fact_10066_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.06/5.44 ! [R2: real] :
% 5.06/5.44 ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ R2 )
% 5.06/5.44 @ at_top_nat ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_inverse_real_of_nat_add
% 5.06/5.44 thf(fact_10067_increasing__LIMSEQ,axiom,
% 5.06/5.44 ! [F: nat > real,L2: real] :
% 5.06/5.44 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L2 )
% 5.06/5.44 => ( ! [E2: real] :
% 5.06/5.44 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.06/5.44 => ? [N9: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N9 ) @ E2 ) ) )
% 5.06/5.44 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % increasing_LIMSEQ
% 5.06/5.44 thf(fact_10068_LIMSEQ__realpow__zero,axiom,
% 5.06/5.44 ! [X: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.44 => ( ( ord_less_real @ X @ one_one_real )
% 5.06/5.44 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_realpow_zero
% 5.06/5.44 thf(fact_10069_LIMSEQ__divide__realpow__zero,axiom,
% 5.06/5.44 ! [X: real,A: real] :
% 5.06/5.44 ( ( ord_less_real @ one_one_real @ X )
% 5.06/5.44 => ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_divide_realpow_zero
% 5.06/5.44 thf(fact_10070_LIMSEQ__abs__realpow__zero,axiom,
% 5.06/5.44 ! [C: real] :
% 5.06/5.44 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.06/5.44 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_abs_realpow_zero
% 5.06/5.44 thf(fact_10071_LIMSEQ__abs__realpow__zero2,axiom,
% 5.06/5.44 ! [C: real] :
% 5.06/5.44 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.06/5.44 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_abs_realpow_zero2
% 5.06/5.44 thf(fact_10072_LIMSEQ__inverse__realpow__zero,axiom,
% 5.06/5.44 ! [X: real] :
% 5.06/5.44 ( ( ord_less_real @ one_one_real @ X )
% 5.06/5.44 => ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_inverse_realpow_zero
% 5.06/5.44 thf(fact_10073_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.06/5.44 ! [R2: real] :
% 5.06/5.44 ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ R2 )
% 5.06/5.44 @ at_top_nat ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.06/5.44 thf(fact_10074_tendsto__exp__limit__sequentially,axiom,
% 5.06/5.44 ! [X: real] :
% 5.06/5.44 ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.06/5.44 @ at_top_nat ) ).
% 5.06/5.44
% 5.06/5.44 % tendsto_exp_limit_sequentially
% 5.06/5.44 thf(fact_10075_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.06/5.44 ! [R2: real] :
% 5.06/5.44 ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ R2 )
% 5.06/5.44 @ at_top_nat ) ).
% 5.06/5.44
% 5.06/5.44 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.06/5.44 thf(fact_10076_summable__Leibniz_I1_J,axiom,
% 5.06/5.44 ! [A: nat > real] :
% 5.06/5.44 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ( ( topolo6980174941875973593q_real @ A )
% 5.06/5.44 => ( summable_real
% 5.06/5.44 @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % summable_Leibniz(1)
% 5.06/5.44 thf(fact_10077_summable,axiom,
% 5.06/5.44 ! [A: nat > real] :
% 5.06/5.44 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.06/5.44 => ( summable_real
% 5.06/5.44 @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % summable
% 5.06/5.44 thf(fact_10078_cos__diff__limit__1,axiom,
% 5.06/5.44 ! [Theta: nat > real,Theta2: real] :
% 5.06/5.44 ( ( filterlim_nat_real
% 5.06/5.44 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.06/5.44 @ at_top_nat )
% 5.06/5.44 => ~ ! [K2: nat > int] :
% 5.06/5.44 ~ ( filterlim_nat_real
% 5.06/5.44 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.06/5.44 @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % cos_diff_limit_1
% 5.06/5.44 thf(fact_10079_cos__limit__1,axiom,
% 5.06/5.44 ! [Theta: nat > real] :
% 5.06/5.44 ( ( filterlim_nat_real
% 5.06/5.44 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.06/5.44 @ at_top_nat )
% 5.06/5.44 => ? [K2: nat > int] :
% 5.06/5.44 ( filterlim_nat_real
% 5.06/5.44 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % cos_limit_1
% 5.06/5.44 thf(fact_10080_summable__Leibniz_I4_J,axiom,
% 5.06/5.44 ! [A: nat > real] :
% 5.06/5.44 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ( ( topolo6980174941875973593q_real @ A )
% 5.06/5.44 => ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] :
% 5.06/5.44 ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real
% 5.06/5.44 @ ( suminf_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.06/5.44 @ at_top_nat ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % summable_Leibniz(4)
% 5.06/5.44 thf(fact_10081_zeroseq__arctan__series,axiom,
% 5.06/5.44 ! [X: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.06/5.44 => ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % zeroseq_arctan_series
% 5.06/5.44 thf(fact_10082_summable__Leibniz_H_I2_J,axiom,
% 5.06/5.44 ! [A: nat > real,N2: nat] :
% 5.06/5.44 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.06/5.44 => ( ord_less_eq_real
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.06/5.44 @ ( suminf_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % summable_Leibniz'(2)
% 5.06/5.44 thf(fact_10083_summable__Leibniz_H_I3_J,axiom,
% 5.06/5.44 ! [A: nat > real] :
% 5.06/5.44 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.06/5.44 => ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] :
% 5.06/5.44 ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real
% 5.06/5.44 @ ( suminf_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.06/5.44 @ at_top_nat ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % summable_Leibniz'(3)
% 5.06/5.44 thf(fact_10084_sums__alternating__upper__lower,axiom,
% 5.06/5.44 ! [A: nat > real] :
% 5.06/5.44 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.06/5.44 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ? [L4: real] :
% 5.06/5.44 ( ! [N9: nat] :
% 5.06/5.44 ( ord_less_eq_real
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 5.06/5.44 @ L4 )
% 5.06/5.44 & ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] :
% 5.06/5.44 ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ L4 )
% 5.06/5.44 @ at_top_nat )
% 5.06/5.44 & ! [N9: nat] :
% 5.06/5.44 ( ord_less_eq_real @ L4
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) )
% 5.06/5.44 & ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] :
% 5.06/5.44 ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ L4 )
% 5.06/5.44 @ at_top_nat ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % sums_alternating_upper_lower
% 5.06/5.44 thf(fact_10085_summable__Leibniz_I5_J,axiom,
% 5.06/5.44 ! [A: nat > real] :
% 5.06/5.44 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ( ( topolo6980174941875973593q_real @ A )
% 5.06/5.44 => ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] :
% 5.06/5.44 ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real
% 5.06/5.44 @ ( suminf_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.06/5.44 @ at_top_nat ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % summable_Leibniz(5)
% 5.06/5.44 thf(fact_10086_summable__Leibniz_H_I4_J,axiom,
% 5.06/5.44 ! [A: nat > real,N2: nat] :
% 5.06/5.44 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.06/5.44 => ( ord_less_eq_real
% 5.06/5.44 @ ( suminf_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.06/5.44 @ ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % summable_Leibniz'(4)
% 5.06/5.44 thf(fact_10087_summable__Leibniz_H_I5_J,axiom,
% 5.06/5.44 ! [A: nat > real] :
% 5.06/5.44 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.06/5.44 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.06/5.44 => ( filterlim_nat_real
% 5.06/5.44 @ ^ [N: nat] :
% 5.06/5.44 ( groups6591440286371151544t_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.06/5.44 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real
% 5.06/5.44 @ ( suminf_real
% 5.06/5.44 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.06/5.44 @ at_top_nat ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % summable_Leibniz'(5)
% 5.06/5.44 thf(fact_10088_real__bounded__linear,axiom,
% 5.06/5.44 ( real_V5970128139526366754l_real
% 5.06/5.44 = ( ^ [F3: real > real] :
% 5.06/5.44 ? [C4: real] :
% 5.06/5.44 ( F3
% 5.06/5.44 = ( ^ [X2: real] : ( times_times_real @ X2 @ C4 ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % real_bounded_linear
% 5.06/5.44 thf(fact_10089_tendsto__exp__limit__at__right,axiom,
% 5.06/5.44 ! [X: real] :
% 5.06/5.44 ( filterlim_real_real
% 5.06/5.44 @ ^ [Y2: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y2 ) ) @ ( divide_divide_real @ one_one_real @ Y2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % tendsto_exp_limit_at_right
% 5.06/5.44 thf(fact_10090_dist__real__def,axiom,
% 5.06/5.44 ( real_V975177566351809787t_real
% 5.06/5.44 = ( ^ [X2: real,Y2: real] : ( abs_abs_real @ ( minus_minus_real @ X2 @ Y2 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % dist_real_def
% 5.06/5.44 thf(fact_10091_dist__complex__def,axiom,
% 5.06/5.44 ( real_V3694042436643373181omplex
% 5.06/5.44 = ( ^ [X2: complex,Y2: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y2 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % dist_complex_def
% 5.06/5.44 thf(fact_10092_INT__greaterThan__UNIV,axiom,
% 5.06/5.44 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.06/5.44 = bot_bot_set_nat ) ).
% 5.06/5.44
% 5.06/5.44 % INT_greaterThan_UNIV
% 5.06/5.44 thf(fact_10093_greaterThan__0,axiom,
% 5.06/5.44 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.06/5.44 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % greaterThan_0
% 5.06/5.44 thf(fact_10094_greaterThan__Suc,axiom,
% 5.06/5.44 ! [K: nat] :
% 5.06/5.44 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.06/5.44 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % greaterThan_Suc
% 5.06/5.44 thf(fact_10095_filterlim__tan__at__right,axiom,
% 5.06/5.44 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 ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % filterlim_tan_at_right
% 5.06/5.44 thf(fact_10096_atLeast__Suc__greaterThan,axiom,
% 5.06/5.44 ! [K: nat] :
% 5.06/5.44 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.06/5.44 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.06/5.44
% 5.06/5.44 % atLeast_Suc_greaterThan
% 5.06/5.44 thf(fact_10097_UN__atLeast__UNIV,axiom,
% 5.06/5.44 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.06/5.44 = top_top_set_nat ) ).
% 5.06/5.44
% 5.06/5.44 % UN_atLeast_UNIV
% 5.06/5.44 thf(fact_10098_atLeast__Suc,axiom,
% 5.06/5.44 ! [K: nat] :
% 5.06/5.44 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.06/5.44 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % atLeast_Suc
% 5.06/5.44 thf(fact_10099_ln__at__0,axiom,
% 5.06/5.44 filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.06/5.44
% 5.06/5.44 % ln_at_0
% 5.06/5.44 thf(fact_10100_filterlim__inverse__at__bot__neg,axiom,
% 5.06/5.44 filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 5.06/5.44
% 5.06/5.44 % filterlim_inverse_at_bot_neg
% 5.06/5.44 thf(fact_10101_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.06/5.44 ! [B: real,F: real > real,Flim: real] :
% 5.06/5.44 ( ! [X3: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ X3 @ B )
% 5.06/5.44 => ? [Y3: real] :
% 5.06/5.44 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.44 & ( ord_less_real @ zero_zero_real @ Y3 ) ) )
% 5.06/5.44 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.06/5.44 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % DERIV_pos_imp_increasing_at_bot
% 5.06/5.44 thf(fact_10102_filterlim__pow__at__bot__odd,axiom,
% 5.06/5.44 ! [N2: nat,F: real > real,F5: filter_real] :
% 5.06/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.44 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.06/5.44 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N2 )
% 5.06/5.44 @ at_bot_real
% 5.06/5.44 @ F5 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % filterlim_pow_at_bot_odd
% 5.06/5.44 thf(fact_10103_tendsto__arctan__at__bot,axiom,
% 5.06/5.44 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.06/5.44
% 5.06/5.44 % tendsto_arctan_at_bot
% 5.06/5.44 thf(fact_10104_Gcd__eq__Max,axiom,
% 5.06/5.44 ! [M7: set_nat] :
% 5.06/5.44 ( ( finite_finite_nat @ M7 )
% 5.06/5.44 => ( ( M7 != bot_bot_set_nat )
% 5.06/5.44 => ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.06/5.44 => ( ( gcd_Gcd_nat @ M7 )
% 5.06/5.44 = ( lattic8265883725875713057ax_nat
% 5.06/5.44 @ ( comple7806235888213564991et_nat
% 5.06/5.44 @ ( image_nat_set_nat
% 5.06/5.44 @ ^ [M6: nat] :
% 5.06/5.44 ( collect_nat
% 5.06/5.44 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M6 ) )
% 5.06/5.44 @ M7 ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Gcd_eq_Max
% 5.06/5.44 thf(fact_10105_Max__divisors__self__nat,axiom,
% 5.06/5.44 ! [N2: nat] :
% 5.06/5.44 ( ( N2 != zero_zero_nat )
% 5.06/5.44 => ( ( lattic8265883725875713057ax_nat
% 5.06/5.44 @ ( collect_nat
% 5.06/5.44 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ N2 ) ) )
% 5.06/5.44 = N2 ) ) ).
% 5.06/5.44
% 5.06/5.44 % Max_divisors_self_nat
% 5.06/5.44 thf(fact_10106_at__bot__le__at__infinity,axiom,
% 5.06/5.44 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 5.06/5.44
% 5.06/5.44 % at_bot_le_at_infinity
% 5.06/5.44 thf(fact_10107_sqrt__at__top,axiom,
% 5.06/5.44 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.06/5.44
% 5.06/5.44 % sqrt_at_top
% 5.06/5.44 thf(fact_10108_ln__at__top,axiom,
% 5.06/5.44 filterlim_real_real @ ln_ln_real @ at_top_real @ at_top_real ).
% 5.06/5.44
% 5.06/5.44 % ln_at_top
% 5.06/5.44 thf(fact_10109_exp__at__top,axiom,
% 5.06/5.44 filterlim_real_real @ exp_real @ at_top_real @ at_top_real ).
% 5.06/5.44
% 5.06/5.44 % exp_at_top
% 5.06/5.44 thf(fact_10110_filterlim__real__sequentially,axiom,
% 5.06/5.44 filterlim_nat_real @ semiri5074537144036343181t_real @ at_top_real @ at_top_nat ).
% 5.06/5.44
% 5.06/5.44 % filterlim_real_sequentially
% 5.06/5.44 thf(fact_10111_filterlim__uminus__at__top__at__bot,axiom,
% 5.06/5.44 filterlim_real_real @ uminus_uminus_real @ at_top_real @ at_bot_real ).
% 5.06/5.44
% 5.06/5.44 % filterlim_uminus_at_top_at_bot
% 5.06/5.44 thf(fact_10112_filterlim__uminus__at__bot__at__top,axiom,
% 5.06/5.44 filterlim_real_real @ uminus_uminus_real @ at_bot_real @ at_top_real ).
% 5.06/5.44
% 5.06/5.44 % filterlim_uminus_at_bot_at_top
% 5.06/5.44 thf(fact_10113_card__le__Suc__Max,axiom,
% 5.06/5.44 ! [S3: set_nat] :
% 5.06/5.44 ( ( finite_finite_nat @ S3 )
% 5.06/5.44 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % card_le_Suc_Max
% 5.06/5.44 thf(fact_10114_divide__nat__def,axiom,
% 5.06/5.44 ( divide_divide_nat
% 5.06/5.44 = ( ^ [M6: nat,N: nat] :
% 5.06/5.44 ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 5.06/5.44 @ ( lattic8265883725875713057ax_nat
% 5.06/5.44 @ ( collect_nat
% 5.06/5.44 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N ) @ M6 ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % divide_nat_def
% 5.06/5.44 thf(fact_10115_gcd__is__Max__divisors__nat,axiom,
% 5.06/5.44 ! [N2: nat,M: nat] :
% 5.06/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.44 => ( ( gcd_gcd_nat @ M @ N2 )
% 5.06/5.44 = ( lattic8265883725875713057ax_nat
% 5.06/5.44 @ ( collect_nat
% 5.06/5.44 @ ^ [D2: nat] :
% 5.06/5.44 ( ( dvd_dvd_nat @ D2 @ M )
% 5.06/5.44 & ( dvd_dvd_nat @ D2 @ N2 ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % gcd_is_Max_divisors_nat
% 5.06/5.44 thf(fact_10116_ln__x__over__x__tendsto__0,axiom,
% 5.06/5.44 ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ at_top_real ) ).
% 5.06/5.44
% 5.06/5.44 % ln_x_over_x_tendsto_0
% 5.06/5.44 thf(fact_10117_filterlim__inverse__at__top__right,axiom,
% 5.06/5.44 filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.06/5.44
% 5.06/5.44 % filterlim_inverse_at_top_right
% 5.06/5.44 thf(fact_10118_filterlim__inverse__at__right__top,axiom,
% 5.06/5.44 filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 5.06/5.44
% 5.06/5.44 % filterlim_inverse_at_right_top
% 5.06/5.44 thf(fact_10119_tendsto__power__div__exp__0,axiom,
% 5.06/5.44 ! [K: nat] :
% 5.06/5.44 ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( power_power_real @ X2 @ K ) @ ( exp_real @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.06/5.44 @ at_top_real ) ).
% 5.06/5.44
% 5.06/5.44 % tendsto_power_div_exp_0
% 5.06/5.44 thf(fact_10120_tendsto__exp__limit__at__top,axiom,
% 5.06/5.44 ! [X: real] :
% 5.06/5.44 ( filterlim_real_real
% 5.06/5.44 @ ^ [Y2: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y2 ) ) @ Y2 )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.06/5.44 @ at_top_real ) ).
% 5.06/5.44
% 5.06/5.44 % tendsto_exp_limit_at_top
% 5.06/5.44 thf(fact_10121_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.06/5.44 ! [B: real,F: real > real,Flim: real] :
% 5.06/5.44 ( ! [X3: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ B @ X3 )
% 5.06/5.44 => ? [Y3: real] :
% 5.06/5.44 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.06/5.44 & ( ord_less_real @ Y3 @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.06/5.44 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % DERIV_neg_imp_decreasing_at_top
% 5.06/5.44 thf(fact_10122_tendsto__arctan__at__top,axiom,
% 5.06/5.44 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.06/5.44
% 5.06/5.44 % tendsto_arctan_at_top
% 5.06/5.44 thf(fact_10123_filterlim__tan__at__left,axiom,
% 5.06/5.44 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 ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % filterlim_tan_at_left
% 5.06/5.44 thf(fact_10124_filterlim__pow__at__bot__even,axiom,
% 5.06/5.44 ! [N2: nat,F: real > real,F5: filter_real] :
% 5.06/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.44 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.06/5.44 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N2 )
% 5.06/5.44 @ at_top_real
% 5.06/5.44 @ F5 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % filterlim_pow_at_bot_even
% 5.06/5.44 thf(fact_10125_eventually__sequentially__Suc,axiom,
% 5.06/5.44 ! [P: nat > $o] :
% 5.06/5.44 ( ( eventually_nat
% 5.06/5.44 @ ^ [I5: nat] : ( P @ ( suc @ I5 ) )
% 5.06/5.44 @ at_top_nat )
% 5.06/5.44 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_sequentially_Suc
% 5.06/5.44 thf(fact_10126_eventually__sequentially__seg,axiom,
% 5.06/5.44 ! [P: nat > $o,K: nat] :
% 5.06/5.44 ( ( eventually_nat
% 5.06/5.44 @ ^ [N: nat] : ( P @ ( plus_plus_nat @ N @ K ) )
% 5.06/5.44 @ at_top_nat )
% 5.06/5.44 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_sequentially_seg
% 5.06/5.44 thf(fact_10127_Max__divisors__self__int,axiom,
% 5.06/5.44 ! [N2: int] :
% 5.06/5.44 ( ( N2 != zero_zero_int )
% 5.06/5.44 => ( ( lattic8263393255366662781ax_int
% 5.06/5.44 @ ( collect_int
% 5.06/5.44 @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ N2 ) ) )
% 5.06/5.44 = ( abs_abs_int @ N2 ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Max_divisors_self_int
% 5.06/5.44 thf(fact_10128_sequentially__offset,axiom,
% 5.06/5.44 ! [P: nat > $o,K: nat] :
% 5.06/5.44 ( ( eventually_nat @ P @ at_top_nat )
% 5.06/5.44 => ( eventually_nat
% 5.06/5.44 @ ^ [I5: nat] : ( P @ ( plus_plus_nat @ I5 @ K ) )
% 5.06/5.44 @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % sequentially_offset
% 5.06/5.44 thf(fact_10129_eventually__False__sequentially,axiom,
% 5.06/5.44 ~ ( eventually_nat
% 5.06/5.44 @ ^ [N: nat] : $false
% 5.06/5.44 @ at_top_nat ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_False_sequentially
% 5.06/5.44 thf(fact_10130_at__top__le__at__infinity,axiom,
% 5.06/5.44 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 5.06/5.44
% 5.06/5.44 % at_top_le_at_infinity
% 5.06/5.44 thf(fact_10131_le__sequentially,axiom,
% 5.06/5.44 ! [F5: filter_nat] :
% 5.06/5.44 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.06/5.44 = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F5 ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % le_sequentially
% 5.06/5.44 thf(fact_10132_eventually__sequentially,axiom,
% 5.06/5.44 ! [P: nat > $o] :
% 5.06/5.44 ( ( eventually_nat @ P @ at_top_nat )
% 5.06/5.44 = ( ? [N6: nat] :
% 5.06/5.44 ! [N: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ N6 @ N )
% 5.06/5.44 => ( P @ N ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_sequentially
% 5.06/5.44 thf(fact_10133_eventually__sequentiallyI,axiom,
% 5.06/5.44 ! [C: nat,P: nat > $o] :
% 5.06/5.44 ( ! [X3: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ C @ X3 )
% 5.06/5.44 => ( P @ X3 ) )
% 5.06/5.44 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_sequentiallyI
% 5.06/5.44 thf(fact_10134_open__bool__def,axiom,
% 5.06/5.44 ( topolo9180104560040979295open_o
% 5.06/5.44 = ( topolo4667128019001906403logy_o @ ( sup_sup_set_set_o @ ( image_o_set_o @ set_ord_lessThan_o @ top_top_set_o ) @ ( image_o_set_o @ set_or6416164934427428222Than_o @ top_top_set_o ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % open_bool_def
% 5.06/5.44 thf(fact_10135_open__int__def,axiom,
% 5.06/5.44 ( topolo4325760605701065253en_int
% 5.06/5.44 = ( topolo1611008123915946401gy_int @ ( sup_sup_set_set_int @ ( image_int_set_int @ set_ord_lessThan_int @ top_top_set_int ) @ ( image_int_set_int @ set_or1207661135979820486an_int @ top_top_set_int ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % open_int_def
% 5.06/5.44 thf(fact_10136_gcd__is__Max__divisors__int,axiom,
% 5.06/5.44 ! [N2: int,M: int] :
% 5.06/5.44 ( ( N2 != zero_zero_int )
% 5.06/5.44 => ( ( gcd_gcd_int @ M @ N2 )
% 5.06/5.44 = ( lattic8263393255366662781ax_int
% 5.06/5.44 @ ( collect_int
% 5.06/5.44 @ ^ [D2: int] :
% 5.06/5.44 ( ( dvd_dvd_int @ D2 @ M )
% 5.06/5.44 & ( dvd_dvd_int @ D2 @ N2 ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % gcd_is_Max_divisors_int
% 5.06/5.44 thf(fact_10137_eventually__at__right__to__0,axiom,
% 5.06/5.44 ! [P: real > $o,A: real] :
% 5.06/5.44 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 = ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( P @ ( plus_plus_real @ X2 @ A ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_at_right_to_0
% 5.06/5.44 thf(fact_10138_eventually__at__top__to__right,axiom,
% 5.06/5.44 ! [P: real > $o] :
% 5.06/5.44 ( ( eventually_real @ P @ at_top_real )
% 5.06/5.44 = ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( P @ ( inverse_inverse_real @ X2 ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_at_top_to_right
% 5.06/5.44 thf(fact_10139_eventually__at__right__to__top,axiom,
% 5.06/5.44 ! [P: real > $o] :
% 5.06/5.44 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 = ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( P @ ( inverse_inverse_real @ X2 ) )
% 5.06/5.44 @ at_top_real ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_at_right_to_top
% 5.06/5.44 thf(fact_10140_eventually__at__left__to__right,axiom,
% 5.06/5.44 ! [P: real > $o,A: real] :
% 5.06/5.44 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 = ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( P @ ( uminus_uminus_real @ X2 ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_at_left_to_right
% 5.06/5.44 thf(fact_10141_eventually__at__right__real,axiom,
% 5.06/5.44 ! [A: real,B: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ B )
% 5.06/5.44 => ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_at_right_real
% 5.06/5.44 thf(fact_10142_eventually__at__left__real,axiom,
% 5.06/5.44 ! [B: real,A: real] :
% 5.06/5.44 ( ( ord_less_real @ B @ A )
% 5.06/5.44 => ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_at_left_real
% 5.06/5.44 thf(fact_10143_lhopital__at__top__at__top,axiom,
% 5.06/5.44 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.06/5.44 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ at_top_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ at_top_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_at_top_at_top
% 5.06/5.44 thf(fact_10144_lhopital__right__at__top__at__top,axiom,
% 5.06/5.44 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ at_top_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ at_top_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_right_at_top_at_top
% 5.06/5.44 thf(fact_10145_lhopital__at__top__at__bot,axiom,
% 5.06/5.44 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.06/5.44 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ at_bot_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ at_bot_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_at_top_at_bot
% 5.06/5.44 thf(fact_10146_lhopital__left__at__top__at__top,axiom,
% 5.06/5.44 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ at_top_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ at_top_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_left_at_top_at_top
% 5.06/5.44 thf(fact_10147_lhopital,axiom,
% 5.06/5.44 ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G2 @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ F5
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ F5
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital
% 5.06/5.44 thf(fact_10148_lhopital__at__top,axiom,
% 5.06/5.44 ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y: real] :
% 5.06/5.44 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G2 @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ Y )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ Y )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_at_top
% 5.06/5.44 thf(fact_10149_lhospital__at__top__at__top,axiom,
% 5.06/5.44 ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X: real] :
% 5.06/5.44 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G2 @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ at_top_real )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ at_top_real )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ at_top_real )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ X )
% 5.06/5.44 @ at_top_real )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ X )
% 5.06/5.44 @ at_top_real ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhospital_at_top_at_top
% 5.06/5.44 thf(fact_10150_open__nat__def,axiom,
% 5.06/5.44 ( topolo4328251076210115529en_nat
% 5.06/5.44 = ( topolo1613498594424996677gy_nat @ ( sup_sup_set_set_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % open_nat_def
% 5.06/5.44 thf(fact_10151_lhopital__right__at__top__at__bot,axiom,
% 5.06/5.44 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ at_bot_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ at_bot_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_right_at_top_at_bot
% 5.06/5.44 thf(fact_10152_lhopital__left__at__top__at__bot,axiom,
% 5.06/5.44 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ at_bot_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ at_bot_real
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_left_at_top_at_bot
% 5.06/5.44 thf(fact_10153_lhopital__right,axiom,
% 5.06/5.44 ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G2 @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ F5
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ F5
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_right
% 5.06/5.44 thf(fact_10154_lhopital__right__0,axiom,
% 5.06/5.44 ! [F0: real > real,G0: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.06/5.44 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G0 @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G2 @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ F5
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F0 @ X2 ) @ ( G0 @ X2 ) )
% 5.06/5.44 @ F5
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_right_0
% 5.06/5.44 thf(fact_10155_lhopital__right__at__top,axiom,
% 5.06/5.44 ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y: real] :
% 5.06/5.44 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G2 @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ Y )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ Y )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_right_at_top
% 5.06/5.44 thf(fact_10156_lhopital__right__0__at__top,axiom,
% 5.06/5.44 ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X: real] :
% 5.06/5.44 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G2 @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ X )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ X )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_right_0_at_top
% 5.06/5.44 thf(fact_10157_lhopital__left,axiom,
% 5.06/5.44 ! [F: real > real,X: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.06/5.44 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G2 @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ F5
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ F5
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_left
% 5.06/5.44 thf(fact_10158_lhopital__left__at__top,axiom,
% 5.06/5.44 ! [G: real > real,X: real,G2: real > real,F: real > real,F4: real > real,Y: real] :
% 5.06/5.44 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] :
% 5.06/5.44 ( ( G2 @ X2 )
% 5.06/5.44 != zero_zero_real )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( ( eventually_real
% 5.06/5.44 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F4 @ X2 ) @ ( G2 @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ Y )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.06/5.44 => ( filterlim_real_real
% 5.06/5.44 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 5.06/5.44 @ ( topolo2815343760600316023s_real @ Y )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % lhopital_left_at_top
% 5.06/5.44 thf(fact_10159_GreatestI__nat,axiom,
% 5.06/5.44 ! [P: nat > $o,K: nat,B: nat] :
% 5.06/5.44 ( ( P @ K )
% 5.06/5.44 => ( ! [Y5: nat] :
% 5.06/5.44 ( ( P @ Y5 )
% 5.06/5.44 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.06/5.44 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % GreatestI_nat
% 5.06/5.44 thf(fact_10160_Greatest__le__nat,axiom,
% 5.06/5.44 ! [P: nat > $o,K: nat,B: nat] :
% 5.06/5.44 ( ( P @ K )
% 5.06/5.44 => ( ! [Y5: nat] :
% 5.06/5.44 ( ( P @ Y5 )
% 5.06/5.44 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.06/5.44 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Greatest_le_nat
% 5.06/5.44 thf(fact_10161_GreatestI__ex__nat,axiom,
% 5.06/5.44 ! [P: nat > $o,B: nat] :
% 5.06/5.44 ( ? [X_12: nat] : ( P @ X_12 )
% 5.06/5.44 => ( ! [Y5: nat] :
% 5.06/5.44 ( ( P @ Y5 )
% 5.06/5.44 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.06/5.44 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % GreatestI_ex_nat
% 5.06/5.44 thf(fact_10162_Bseq__eq__bounded,axiom,
% 5.06/5.44 ! [F: nat > real,A: real,B: real] :
% 5.06/5.44 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.06/5.44 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 5.06/5.44
% 5.06/5.44 % Bseq_eq_bounded
% 5.06/5.44 thf(fact_10163_Bseq__realpow,axiom,
% 5.06/5.44 ! [X: real] :
% 5.06/5.44 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.06/5.44 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.06/5.44 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Bseq_realpow
% 5.06/5.44 thf(fact_10164_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.06/5.44 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.06/5.44 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.06/5.44 = Y )
% 5.06/5.44 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.06/5.44 ( X
% 5.06/5.44 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.44 => ( Y
% 5.06/5.44 = ( Xa2 != one_one_nat ) ) )
% 5.06/5.44 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.44 ( ( X
% 5.06/5.44 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.44 => ( Y
% 5.06/5.44 = ( ~ ( ( Deg2 = Xa2 )
% 5.06/5.44 & ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.06/5.44 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 & ( case_o184042715313410164at_nat
% 5.06/5.44 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.06/5.44 & ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 @ ( produc6081775807080527818_nat_o
% 5.06/5.44 @ ^ [Mi3: nat,Ma3: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.06/5.44 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 & ! [I5: nat] :
% 5.06/5.44 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.06/5.44 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.06/5.44 & ( ( Mi3 = Ma3 )
% 5.06/5.44 => ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 & ( ( Mi3 != Ma3 )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.06/5.44 & ! [X2: nat] :
% 5.06/5.44 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.06/5.44 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.06/5.44 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.06/5.44 @ Mima ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % VEBT_internal.valid'.elims(1)
% 5.06/5.44 thf(fact_10165_decseq__bounded,axiom,
% 5.06/5.44 ! [X8: nat > real,B3: real] :
% 5.06/5.44 ( ( order_9091379641038594480t_real @ X8 )
% 5.06/5.44 => ( ! [I3: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I3 ) )
% 5.06/5.44 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % decseq_bounded
% 5.06/5.44 thf(fact_10166_decseq__convergent,axiom,
% 5.06/5.44 ! [X8: nat > real,B3: real] :
% 5.06/5.44 ( ( order_9091379641038594480t_real @ X8 )
% 5.06/5.44 => ( ! [I3: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I3 ) )
% 5.06/5.44 => ~ ! [L6: real] :
% 5.06/5.44 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.06/5.44 => ~ ! [I: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % decseq_convergent
% 5.06/5.44 thf(fact_10167_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.06/5.44 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.06/5.44 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 5.06/5.44 = ( ( Deg = Deg4 )
% 5.06/5.44 & ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.06/5.44 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.06/5.44 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 & ( case_o184042715313410164at_nat
% 5.06/5.44 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X4 )
% 5.06/5.44 & ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 @ ( produc6081775807080527818_nat_o
% 5.06/5.44 @ ^ [Mi3: nat,Ma3: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.06/5.44 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.06/5.44 & ! [I5: nat] :
% 5.06/5.44 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X4 ) )
% 5.06/5.44 = ( vEBT_V8194947554948674370ptions @ Summary @ I5 ) ) )
% 5.06/5.44 & ( ( Mi3 = Ma3 )
% 5.06/5.44 => ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 & ( ( Mi3 != Ma3 )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.06/5.44 & ! [X2: nat] :
% 5.06/5.44 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X2 )
% 5.06/5.44 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.06/5.44 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.06/5.44 @ Mima2 ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % VEBT_internal.valid'.simps(2)
% 5.06/5.44 thf(fact_10168_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.06/5.44 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.44 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.06/5.44 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.06/5.44 ( X
% 5.06/5.44 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.44 => ( Xa2 = one_one_nat ) )
% 5.06/5.44 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.44 ( ( X
% 5.06/5.44 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.44 => ( ( Deg2 = Xa2 )
% 5.06/5.44 & ! [X3: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.06/5.44 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 & ( case_o184042715313410164at_nat
% 5.06/5.44 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.06/5.44 & ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 @ ( produc6081775807080527818_nat_o
% 5.06/5.44 @ ^ [Mi3: nat,Ma3: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.06/5.44 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 & ! [I5: nat] :
% 5.06/5.44 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.06/5.44 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.06/5.44 & ( ( Mi3 = Ma3 )
% 5.06/5.44 => ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 & ( ( Mi3 != Ma3 )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.06/5.44 & ! [X2: nat] :
% 5.06/5.44 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.06/5.44 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.06/5.44 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.06/5.44 @ Mima ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % VEBT_internal.valid'.elims(3)
% 5.06/5.44 thf(fact_10169_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.06/5.44 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.44 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.06/5.44 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.06/5.44 ( X
% 5.06/5.44 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.44 => ( Xa2 != one_one_nat ) )
% 5.06/5.44 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.44 ( ( X
% 5.06/5.44 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.44 => ~ ( ( Deg2 = Xa2 )
% 5.06/5.44 & ! [X5: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.06/5.44 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 & ( case_o184042715313410164at_nat
% 5.06/5.44 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.06/5.44 & ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 @ ( produc6081775807080527818_nat_o
% 5.06/5.44 @ ^ [Mi3: nat,Ma3: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.06/5.44 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 & ! [I5: nat] :
% 5.06/5.44 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.06/5.44 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.06/5.44 & ( ( Mi3 = Ma3 )
% 5.06/5.44 => ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 & ( ( Mi3 != Ma3 )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.06/5.44 & ! [X2: nat] :
% 5.06/5.44 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.06/5.44 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.06/5.44 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.06/5.44 @ Mima ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % VEBT_internal.valid'.elims(2)
% 5.06/5.44 thf(fact_10170_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.06/5.44 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.44 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.06/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.44 => ( ! [Uu2: $o,Uv2: $o] :
% 5.06/5.44 ( ( X
% 5.06/5.44 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.06/5.44 => ( Xa2 = one_one_nat ) ) )
% 5.06/5.44 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.44 ( ( X
% 5.06/5.44 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.06/5.44 => ( ( Deg2 = Xa2 )
% 5.06/5.44 & ! [X3: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.06/5.44 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 & ( case_o184042715313410164at_nat
% 5.06/5.44 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.06/5.44 & ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 @ ( produc6081775807080527818_nat_o
% 5.06/5.44 @ ^ [Mi3: nat,Ma3: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.06/5.44 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 & ! [I5: nat] :
% 5.06/5.44 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.06/5.44 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.06/5.44 & ( ( Mi3 = Ma3 )
% 5.06/5.44 => ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 & ( ( Mi3 != Ma3 )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.06/5.44 & ! [X2: nat] :
% 5.06/5.44 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.06/5.44 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.06/5.44 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.06/5.44 @ Mima ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % VEBT_internal.valid'.pelims(3)
% 5.06/5.44 thf(fact_10171_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.06/5.44 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.06/5.44 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.06/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.44 => ( ! [Uu2: $o,Uv2: $o] :
% 5.06/5.44 ( ( X
% 5.06/5.44 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.06/5.44 => ( Xa2 != one_one_nat ) ) )
% 5.06/5.44 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.44 ( ( X
% 5.06/5.44 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.06/5.44 => ~ ( ( Deg2 = Xa2 )
% 5.06/5.44 & ! [X5: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.06/5.44 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 & ( case_o184042715313410164at_nat
% 5.06/5.44 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.06/5.44 & ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 @ ( produc6081775807080527818_nat_o
% 5.06/5.44 @ ^ [Mi3: nat,Ma3: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.06/5.44 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 & ! [I5: nat] :
% 5.06/5.44 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.06/5.44 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.06/5.44 & ( ( Mi3 = Ma3 )
% 5.06/5.44 => ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 & ( ( Mi3 != Ma3 )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.06/5.44 & ! [X2: nat] :
% 5.06/5.44 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.06/5.44 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.06/5.44 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.06/5.44 @ Mima ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % VEBT_internal.valid'.pelims(2)
% 5.06/5.44 thf(fact_10172_Sup__int__def,axiom,
% 5.06/5.44 ( complete_Sup_Sup_int
% 5.06/5.44 = ( ^ [X4: set_int] :
% 5.06/5.44 ( the_int
% 5.06/5.44 @ ^ [X2: int] :
% 5.06/5.44 ( ( member_int @ X2 @ X4 )
% 5.06/5.44 & ! [Y2: int] :
% 5.06/5.44 ( ( member_int @ Y2 @ X4 )
% 5.06/5.44 => ( ord_less_eq_int @ Y2 @ X2 ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Sup_int_def
% 5.06/5.44 thf(fact_10173_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.06/5.44 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.06/5.44 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.06/5.44 = Y )
% 5.06/5.44 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.06/5.44 => ( ! [Uu2: $o,Uv2: $o] :
% 5.06/5.44 ( ( X
% 5.06/5.44 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.06/5.44 => ( ( Y
% 5.06/5.44 = ( Xa2 = one_one_nat ) )
% 5.06/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.06/5.44 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.06/5.44 ( ( X
% 5.06/5.44 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.06/5.44 => ( ( Y
% 5.06/5.44 = ( ( Deg2 = Xa2 )
% 5.06/5.44 & ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.06/5.44 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.06/5.44 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 & ( case_o184042715313410164at_nat
% 5.06/5.44 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.06/5.44 & ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 @ ( produc6081775807080527818_nat_o
% 5.06/5.44 @ ^ [Mi3: nat,Ma3: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.06/5.44 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 & ! [I5: nat] :
% 5.06/5.44 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.06/5.44 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 5.06/5.44 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.06/5.44 & ( ( Mi3 = Ma3 )
% 5.06/5.44 => ! [X2: vEBT_VEBT] :
% 5.06/5.44 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.06/5.44 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X4 ) ) )
% 5.06/5.44 & ( ( Mi3 != Ma3 )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.06/5.44 & ! [X2: nat] :
% 5.06/5.44 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.06/5.44 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X2 )
% 5.06/5.44 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.06/5.44 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 5.06/5.44 @ Mima ) ) )
% 5.06/5.44 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % VEBT_internal.valid'.pelims(1)
% 5.06/5.44 thf(fact_10174_GMVT,axiom,
% 5.06/5.44 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.06/5.44 ( ( ord_less_real @ A @ B )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.06/5.44 & ( ord_less_eq_real @ X3 @ B ) )
% 5.06/5.44 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( ( ord_less_real @ A @ X3 )
% 5.06/5.44 & ( ord_less_real @ X3 @ B ) )
% 5.06/5.44 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( ( ord_less_eq_real @ A @ X3 )
% 5.06/5.44 & ( ord_less_eq_real @ X3 @ B ) )
% 5.06/5.44 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G ) )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( ( ord_less_real @ A @ X3 )
% 5.06/5.44 & ( ord_less_real @ X3 @ B ) )
% 5.06/5.44 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 5.06/5.44 => ? [G_c: real,F_c: real,C3: real] :
% 5.06/5.44 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.06/5.44 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.06/5.44 & ( ord_less_real @ A @ C3 )
% 5.06/5.44 & ( ord_less_real @ C3 @ B )
% 5.06/5.44 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.06/5.44 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % GMVT
% 5.06/5.44 thf(fact_10175_MVT,axiom,
% 5.06/5.44 ! [A: real,B: real,F: real > real] :
% 5.06/5.44 ( ( ord_less_real @ A @ B )
% 5.06/5.44 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ X3 )
% 5.06/5.44 => ( ( ord_less_real @ X3 @ B )
% 5.06/5.44 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.06/5.44 => ? [L4: real,Z4: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ Z4 )
% 5.06/5.44 & ( ord_less_real @ Z4 @ B )
% 5.06/5.44 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z4 @ top_top_set_real ) )
% 5.06/5.44 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.06/5.44 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % MVT
% 5.06/5.44 thf(fact_10176_continuous__on__arsinh_H,axiom,
% 5.06/5.44 ! [A2: set_real,F: real > real] :
% 5.06/5.44 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.06/5.44 => ( topolo5044208981011980120l_real @ A2
% 5.06/5.44 @ ^ [X2: real] : ( arsinh_real @ ( F @ X2 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % continuous_on_arsinh'
% 5.06/5.44 thf(fact_10177_continuous__on__arcosh_H,axiom,
% 5.06/5.44 ! [A2: set_real,F: real > real] :
% 5.06/5.44 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( member_real @ X3 @ A2 )
% 5.06/5.44 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 5.06/5.44 => ( topolo5044208981011980120l_real @ A2
% 5.06/5.44 @ ^ [X2: real] : ( arcosh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % continuous_on_arcosh'
% 5.06/5.44 thf(fact_10178_continuous__image__closed__interval,axiom,
% 5.06/5.44 ! [A: real,B: real,F: real > real] :
% 5.06/5.44 ( ( ord_less_eq_real @ A @ B )
% 5.06/5.44 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.06/5.44 => ? [C3: real,D4: real] :
% 5.06/5.44 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.06/5.44 = ( set_or1222579329274155063t_real @ C3 @ D4 ) )
% 5.06/5.44 & ( ord_less_eq_real @ C3 @ D4 ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % continuous_image_closed_interval
% 5.06/5.44 thf(fact_10179_continuous__on__arcosh,axiom,
% 5.06/5.44 ! [A2: set_real] :
% 5.06/5.44 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.06/5.44 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.06/5.44
% 5.06/5.44 % continuous_on_arcosh
% 5.06/5.44 thf(fact_10180_continuous__on__artanh_H,axiom,
% 5.06/5.44 ! [A2: set_real,F: real > real] :
% 5.06/5.44 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( member_real @ X3 @ A2 )
% 5.06/5.44 => ( member_real @ ( F @ X3 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.06/5.44 => ( topolo5044208981011980120l_real @ A2
% 5.06/5.44 @ ^ [X2: real] : ( artanh_real @ ( F @ X2 ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % continuous_on_artanh'
% 5.06/5.44 thf(fact_10181_mvt,axiom,
% 5.06/5.44 ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 5.06/5.44 ( ( ord_less_real @ A @ B )
% 5.06/5.44 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ X3 )
% 5.06/5.44 => ( ( ord_less_real @ X3 @ B )
% 5.06/5.44 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.06/5.44 => ~ ! [Xi: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ Xi )
% 5.06/5.44 => ( ( ord_less_real @ Xi @ B )
% 5.06/5.44 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.06/5.44 != ( F4 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % mvt
% 5.06/5.44 thf(fact_10182_continuous__on__artanh,axiom,
% 5.06/5.44 ! [A2: set_real] :
% 5.06/5.44 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.06/5.44 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.06/5.44
% 5.06/5.44 % continuous_on_artanh
% 5.06/5.44 thf(fact_10183_DERIV__isconst2,axiom,
% 5.06/5.44 ! [A: real,B: real,F: real > real,X: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ B )
% 5.06/5.44 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.06/5.44 => ( ! [X3: real] :
% 5.06/5.44 ( ( ord_less_real @ A @ X3 )
% 5.06/5.44 => ( ( ord_less_real @ X3 @ B )
% 5.06/5.44 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 5.06/5.44 => ( ( ord_less_eq_real @ A @ X )
% 5.06/5.44 => ( ( ord_less_eq_real @ X @ B )
% 5.06/5.44 => ( ( F @ X )
% 5.06/5.44 = ( F @ A ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % DERIV_isconst2
% 5.06/5.44 thf(fact_10184_uniformity__real__def,axiom,
% 5.06/5.44 ( topolo1511823702728130853y_real
% 5.06/5.44 = ( comple2936214249959783750l_real
% 5.06/5.44 @ ( image_2178119161166701260l_real
% 5.06/5.44 @ ^ [E3: real] :
% 5.06/5.44 ( princi6114159922880469582l_real
% 5.06/5.44 @ ( collec3799799289383736868l_real
% 5.06/5.44 @ ( produc5414030515140494994real_o
% 5.06/5.44 @ ^ [X2: real,Y2: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X2 @ Y2 ) @ E3 ) ) ) )
% 5.06/5.44 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % uniformity_real_def
% 5.06/5.44 thf(fact_10185_uniformity__complex__def,axiom,
% 5.06/5.44 ( topolo896644834953643431omplex
% 5.06/5.44 = ( comple8358262395181532106omplex
% 5.06/5.44 @ ( image_5971271580939081552omplex
% 5.06/5.44 @ ^ [E3: real] :
% 5.06/5.44 ( princi3496590319149328850omplex
% 5.06/5.44 @ ( collec8663557070575231912omplex
% 5.06/5.44 @ ( produc6771430404735790350plex_o
% 5.06/5.44 @ ^ [X2: complex,Y2: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X2 @ Y2 ) @ E3 ) ) ) )
% 5.06/5.44 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % uniformity_complex_def
% 5.06/5.44 thf(fact_10186_open__complex__def,axiom,
% 5.06/5.44 ( topolo4110288021797289639omplex
% 5.06/5.44 = ( ^ [U4: set_complex] :
% 5.06/5.44 ! [X2: complex] :
% 5.06/5.44 ( ( member_complex @ X2 @ U4 )
% 5.06/5.44 => ( eventu5826381225784669381omplex
% 5.06/5.44 @ ( produc6771430404735790350plex_o
% 5.06/5.44 @ ^ [X9: complex,Y2: complex] :
% 5.06/5.44 ( ( X9 = X2 )
% 5.06/5.44 => ( member_complex @ Y2 @ U4 ) ) )
% 5.06/5.44 @ topolo896644834953643431omplex ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % open_complex_def
% 5.06/5.44 thf(fact_10187_open__real__def,axiom,
% 5.06/5.44 ( topolo4860482606490270245n_real
% 5.06/5.44 = ( ^ [U4: set_real] :
% 5.06/5.44 ! [X2: real] :
% 5.06/5.44 ( ( member_real @ X2 @ U4 )
% 5.06/5.44 => ( eventu3244425730907250241l_real
% 5.06/5.44 @ ( produc5414030515140494994real_o
% 5.06/5.44 @ ^ [X9: real,Y2: real] :
% 5.06/5.44 ( ( X9 = X2 )
% 5.06/5.44 => ( member_real @ Y2 @ U4 ) ) )
% 5.06/5.44 @ topolo1511823702728130853y_real ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % open_real_def
% 5.06/5.44 thf(fact_10188_less__eq,axiom,
% 5.06/5.44 ! [M: nat,N2: nat] :
% 5.06/5.44 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.06/5.44 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.06/5.44
% 5.06/5.44 % less_eq
% 5.06/5.44 thf(fact_10189_card_Ocomp__fun__commute__on,axiom,
% 5.06/5.44 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.06/5.44 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.06/5.44
% 5.06/5.44 % card.comp_fun_commute_on
% 5.06/5.44 thf(fact_10190_eventually__prod__sequentially,axiom,
% 5.06/5.44 ! [P: product_prod_nat_nat > $o] :
% 5.06/5.44 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.06/5.44 = ( ? [N6: nat] :
% 5.06/5.44 ! [M6: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ N6 @ M6 )
% 5.06/5.44 => ! [N: nat] :
% 5.06/5.44 ( ( ord_less_eq_nat @ N6 @ N )
% 5.06/5.44 => ( P @ ( product_Pair_nat_nat @ N @ M6 ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % eventually_prod_sequentially
% 5.06/5.44 thf(fact_10191_filtermap__at__right__shift,axiom,
% 5.06/5.44 ! [D: real,A: real] :
% 5.06/5.44 ( ( filtermap_real_real
% 5.06/5.44 @ ^ [X2: real] : ( minus_minus_real @ X2 @ D )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.06/5.44 = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % filtermap_at_right_shift
% 5.06/5.44 thf(fact_10192_at__right__to__0,axiom,
% 5.06/5.44 ! [A: real] :
% 5.06/5.44 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.06/5.44 = ( filtermap_real_real
% 5.06/5.44 @ ^ [X2: real] : ( plus_plus_real @ X2 @ A )
% 5.06/5.44 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % at_right_to_0
% 5.06/5.44 thf(fact_10193_at__right__minus,axiom,
% 5.06/5.44 ! [A: real] :
% 5.06/5.44 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.06/5.44 = ( filtermap_real_real @ uminus_uminus_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A ) @ ( set_or5984915006950818249n_real @ ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % at_right_minus
% 5.06/5.44 thf(fact_10194_at__left__minus,axiom,
% 5.06/5.44 ! [A: real] :
% 5.06/5.44 ( ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) )
% 5.06/5.44 = ( filtermap_real_real @ uminus_uminus_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % at_left_minus
% 5.06/5.44 thf(fact_10195_divmod__integer__eq__cases,axiom,
% 5.06/5.44 ( code_divmod_integer
% 5.06/5.44 = ( ^ [K3: code_integer,L: code_integer] :
% 5.06/5.44 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.06/5.44 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.06/5.44 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 5.06/5.44 @ ( if_Pro6119634080678213985nteger
% 5.06/5.44 @ ( ( sgn_sgn_Code_integer @ K3 )
% 5.06/5.44 = ( sgn_sgn_Code_integer @ L ) )
% 5.06/5.44 @ ( code_divmod_abs @ K3 @ L )
% 5.06/5.44 @ ( produc6916734918728496179nteger
% 5.06/5.44 @ ^ [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 ) ) )
% 5.06/5.44 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % divmod_integer_eq_cases
% 5.06/5.44 thf(fact_10196_Gcd__int__def,axiom,
% 5.06/5.44 ( gcd_Gcd_int
% 5.06/5.44 = ( ^ [K7: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K7 ) ) ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % Gcd_int_def
% 5.06/5.44 thf(fact_10197_Code__Numeral_Onegative__def,axiom,
% 5.06/5.44 ( code_negative
% 5.06/5.44 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 5.06/5.44
% 5.06/5.44 % Code_Numeral.negative_def
% 5.06/5.44 thf(fact_10198_Code__Target__Int_Onegative__def,axiom,
% 5.06/5.44 ( code_Target_negative
% 5.06/5.44 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.06/5.44
% 5.06/5.44 % Code_Target_Int.negative_def
% 5.06/5.44 thf(fact_10199_incseq__bounded,axiom,
% 5.06/5.44 ! [X8: nat > real,B3: real] :
% 5.06/5.44 ( ( order_mono_nat_real @ X8 )
% 5.06/5.44 => ( ! [I3: nat] : ( ord_less_eq_real @ ( X8 @ I3 ) @ B3 )
% 5.06/5.44 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % incseq_bounded
% 5.06/5.44 thf(fact_10200_mono__Suc,axiom,
% 5.06/5.44 order_mono_nat_nat @ suc ).
% 5.06/5.44
% 5.06/5.44 % mono_Suc
% 5.06/5.44 thf(fact_10201_mono__times__nat,axiom,
% 5.06/5.44 ! [N2: nat] :
% 5.06/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.06/5.44 => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 5.06/5.44
% 5.06/5.44 % mono_times_nat
% 5.06/5.44
% 5.06/5.44 % Helper facts (36)
% 5.06/5.44 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.06/5.44 ! [X: int,Y: int] :
% 5.06/5.44 ( ( if_int @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.06/5.44 ! [X: int,Y: int] :
% 5.06/5.44 ( ( if_int @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.06/5.44 ! [X: nat,Y: nat] :
% 5.06/5.44 ( ( if_nat @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.06/5.44 ! [X: nat,Y: nat] :
% 5.06/5.44 ( ( if_nat @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.06/5.44 ! [X: num,Y: num] :
% 5.06/5.44 ( ( if_num @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.06/5.44 ! [X: num,Y: num] :
% 5.06/5.44 ( ( if_num @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.06/5.44 ! [X: rat,Y: rat] :
% 5.06/5.44 ( ( if_rat @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.06/5.44 ! [X: rat,Y: rat] :
% 5.06/5.44 ( ( if_rat @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.06/5.44 ! [X: real,Y: real] :
% 5.06/5.44 ( ( if_real @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.06/5.44 ! [X: real,Y: real] :
% 5.06/5.44 ( ( if_real @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.06/5.44 ! [P: real > $o] :
% 5.06/5.44 ( ( P @ ( fChoice_real @ P ) )
% 5.06/5.44 = ( ? [X4: real] : ( P @ X4 ) ) ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.06/5.44 ! [X: complex,Y: complex] :
% 5.06/5.44 ( ( if_complex @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.06/5.44 ! [X: complex,Y: complex] :
% 5.06/5.44 ( ( if_complex @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.06/5.44 ! [X: extended_enat,Y: extended_enat] :
% 5.06/5.44 ( ( if_Extended_enat @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.06/5.44 ! [X: extended_enat,Y: extended_enat] :
% 5.06/5.44 ( ( if_Extended_enat @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.06/5.44 ! [X: code_integer,Y: code_integer] :
% 5.06/5.44 ( ( if_Code_integer @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.06/5.44 ! [X: code_integer,Y: code_integer] :
% 5.06/5.44 ( ( if_Code_integer @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.06/5.44 ! [X: set_int,Y: set_int] :
% 5.06/5.44 ( ( if_set_int @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.06/5.44 ! [X: set_int,Y: set_int] :
% 5.06/5.44 ( ( if_set_int @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.06/5.44 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.06/5.44 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.06/5.44 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.06/5.44 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.06/5.44 ! [X: list_int,Y: list_int] :
% 5.06/5.44 ( ( if_list_int @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.06/5.44 ! [X: list_int,Y: list_int] :
% 5.06/5.44 ( ( if_list_int @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.06/5.44 ! [X: option_nat,Y: option_nat] :
% 5.06/5.44 ( ( if_option_nat @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.06/5.44 ! [X: option_nat,Y: option_nat] :
% 5.06/5.44 ( ( if_option_nat @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.06/5.44 ! [X: option_num,Y: option_num] :
% 5.06/5.44 ( ( if_option_num @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.06/5.44 ! [X: option_num,Y: option_num] :
% 5.06/5.44 ( ( if_option_num @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.06/5.44 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.06/5.44 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.06/5.44 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.06/5.44 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.06/5.44 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.06/5.44 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.06/5.44 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.06/5.44 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.06/5.44 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.06/5.44 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.06/5.44 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.06/5.44 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.06/5.44 ! [P: $o] :
% 5.06/5.44 ( ( P = $true )
% 5.06/5.44 | ( P = $false ) ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.06/5.44 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.06/5.44 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 5.06/5.44 = Y ) ).
% 5.06/5.44
% 5.06/5.44 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.06/5.44 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.06/5.44 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 5.06/5.44 = X ) ).
% 5.06/5.44
% 5.06/5.44 % Conjectures (1)
% 5.06/5.44 thf(conj_0,conjecture,
% 5.06/5.44 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.06/5.44 = ( vEBT_Node
% 5.06/5.44 @ ( some_P7363390416028606310at_nat
% 5.06/5.44 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.06/5.44 @ ( if_nat
% 5.06/5.44 @ ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.06/5.44 = ma )
% 5.06/5.44 @ ( if_nat
% 5.06/5.44 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
% 5.06/5.44 = none_nat )
% 5.06/5.44 @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
% 5.06/5.44 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) ) )
% 6.18/6.66 @ ma ) ) )
% 6.18/6.66 @ deg
% 6.18/6.66 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
% 6.18/6.66 @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ).
% 6.18/6.66
% 6.18/6.66 %------------------------------------------------------------------------------
% 6.18/6.66 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.V2qbXVH6W0/cvc5---1.0.5_11563.p...
% 6.18/6.66 (declare-sort $$unsorted 0)
% 6.18/6.66 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 6.18/6.66 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 6.18/6.66 (declare-sort tptp.produc1193250871479095198on_num 0)
% 6.18/6.66 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 6.18/6.66 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 6.18/6.66 (declare-sort tptp.produc3368934014287244435at_num 0)
% 6.18/6.66 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.18/6.66 (declare-sort tptp.produc7036089656553540234on_num 0)
% 6.18/6.66 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 6.18/6.66 (declare-sort tptp.set_fi4554929511873752355omplex 0)
% 6.18/6.66 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.18/6.66 (declare-sort tptp.produc3447558737645232053on_num 0)
% 6.18/6.66 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 6.18/6.66 (declare-sort tptp.produc2963631642982155120at_num 0)
% 6.18/6.66 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.18/6.66 (declare-sort tptp.set_fi7789364187291644575l_real 0)
% 6.18/6.66 (declare-sort tptp.filter6041513312241820739omplex 0)
% 6.18/6.66 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.18/6.66 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.18/6.66 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.18/6.66 (declare-sort tptp.list_P7524865323317820941T_VEBT 0)
% 6.18/6.66 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.18/6.66 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 6.18/6.66 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.18/6.66 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.18/6.66 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.18/6.66 (declare-sort tptp.filter2146258269922977983l_real 0)
% 6.18/6.66 (declare-sort tptp.list_P8526636022914148096eger_o 0)
% 6.18/6.66 (declare-sort tptp.set_Pr448751882837621926eger_o 0)
% 6.18/6.66 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.18/6.66 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 6.18/6.66 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 6.18/6.66 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 6.18/6.66 (declare-sort tptp.list_P1726324292696863441at_num 0)
% 6.18/6.66 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.18/6.66 (declare-sort tptp.list_P3521021558325789923at_int 0)
% 6.18/6.66 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 6.18/6.66 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.18/6.66 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 6.18/6.66 (declare-sort tptp.set_Pr8218934625190621173um_num 0)
% 6.18/6.66 (declare-sort tptp.set_Pr6200539531224447659at_num 0)
% 6.18/6.66 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.18/6.66 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.18/6.66 (declare-sort tptp.produc4411394909380815293omplex 0)
% 6.18/6.66 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.18/6.66 (declare-sort tptp.list_P5087981734274514673_int_o 0)
% 6.18/6.66 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.18/6.66 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 6.18/6.66 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.18/6.66 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.18/6.66 (declare-sort tptp.produc2422161461964618553l_real 0)
% 6.18/6.66 (declare-sort tptp.product_prod_num_num 0)
% 6.18/6.66 (declare-sort tptp.product_prod_nat_num 0)
% 6.18/6.66 (declare-sort tptp.product_prod_nat_nat 0)
% 6.18/6.66 (declare-sort tptp.product_prod_nat_int 0)
% 6.18/6.66 (declare-sort tptp.product_prod_int_int 0)
% 6.18/6.66 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.18/6.66 (declare-sort tptp.set_list_complex 0)
% 6.18/6.66 (declare-sort tptp.set_set_complex 0)
% 6.18/6.66 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.18/6.66 (declare-sort tptp.set_list_nat 0)
% 6.18/6.66 (declare-sort tptp.set_list_int 0)
% 6.18/6.66 (declare-sort tptp.product_prod_nat_o 0)
% 6.18/6.66 (declare-sort tptp.list_set_nat 0)
% 6.18/6.66 (declare-sort tptp.list_Code_integer 0)
% 6.18/6.66 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.18/6.66 (declare-sort tptp.set_set_nat 0)
% 6.18/6.66 (declare-sort tptp.set_set_int 0)
% 6.18/6.66 (declare-sort tptp.set_Code_integer 0)
% 6.18/6.66 (declare-sort tptp.set_Product_unit 0)
% 6.18/6.66 (declare-sort tptp.list_complex 0)
% 6.18/6.66 (declare-sort tptp.set_list_o 0)
% 6.18/6.66 (declare-sort tptp.set_complex 0)
% 6.18/6.66 (declare-sort tptp.filter_real 0)
% 6.18/6.66 (declare-sort tptp.set_set_o 0)
% 6.18/6.66 (declare-sort tptp.option_num 0)
% 6.18/6.66 (declare-sort tptp.option_nat 0)
% 6.18/6.66 (declare-sort tptp.filter_nat 0)
% 6.18/6.66 (declare-sort tptp.set_char 0)
% 6.18/6.66 (declare-sort tptp.list_real 0)
% 6.18/6.66 (declare-sort tptp.set_real 0)
% 6.18/6.66 (declare-sort tptp.list_num 0)
% 6.18/6.66 (declare-sort tptp.list_nat 0)
% 6.18/6.66 (declare-sort tptp.list_int 0)
% 6.18/6.66 (declare-sort tptp.vEBT_VEBT 0)
% 6.18/6.66 (declare-sort tptp.set_rat 0)
% 6.18/6.66 (declare-sort tptp.set_num 0)
% 6.18/6.66 (declare-sort tptp.set_nat 0)
% 6.18/6.66 (declare-sort tptp.set_int 0)
% 6.18/6.66 (declare-sort tptp.code_integer 0)
% 6.18/6.66 (declare-sort tptp.extended_enat 0)
% 6.18/6.66 (declare-sort tptp.list_o 0)
% 6.18/6.66 (declare-sort tptp.complex 0)
% 6.18/6.66 (declare-sort tptp.set_o 0)
% 6.18/6.66 (declare-sort tptp.char 0)
% 6.18/6.66 (declare-sort tptp.real 0)
% 6.18/6.66 (declare-sort tptp.rat 0)
% 6.18/6.66 (declare-sort tptp.num 0)
% 6.18/6.66 (declare-sort tptp.nat 0)
% 6.18/6.66 (declare-sort tptp.int 0)
% 6.18/6.66 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.18/6.66 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.18/6.66 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.18/6.66 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.18/6.66 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.18/6.66 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.18/6.66 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.18/6.66 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.18/6.66 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.18/6.66 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.18/6.66 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.18/6.66 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.18/6.66 (declare-fun tptp.code_negative (tptp.num) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.18/6.66 (declare-fun tptp.code_positive (tptp.num) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 6.18/6.66 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 6.18/6.66 (declare-fun tptp.comple8358262395181532106omplex (tptp.set_fi4554929511873752355omplex) tptp.filter6041513312241820739omplex)
% 6.18/6.66 (declare-fun tptp.comple2936214249959783750l_real (tptp.set_fi7789364187291644575l_real) tptp.filter2146258269922977983l_real)
% 6.18/6.66 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.18/6.66 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 6.18/6.66 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.18/6.66 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.18/6.66 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.18/6.66 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.18/6.66 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.18/6.66 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.18/6.66 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.18/6.66 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.18/6.66 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.18/6.66 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.18/6.66 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.18/6.66 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.18/6.66 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.18/6.66 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.18/6.66 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.18/6.66 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.18/6.66 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.18/6.66 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.18/6.66 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.18/6.66 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.18/6.66 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.18/6.66 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.18/6.66 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.18/6.66 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.18/6.66 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.18/6.66 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.18/6.66 (declare-fun tptp.eventu5826381225784669381omplex ((-> tptp.produc4411394909380815293omplex Bool) tptp.filter6041513312241820739omplex) Bool)
% 6.18/6.66 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 6.18/6.66 (declare-fun tptp.eventu3244425730907250241l_real ((-> tptp.produc2422161461964618553l_real Bool) tptp.filter2146258269922977983l_real) Bool)
% 6.18/6.66 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.18/6.66 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.18/6.66 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.18/6.66 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.18/6.66 (declare-fun tptp.filtermap_real_real ((-> tptp.real tptp.real) tptp.filter_real) tptp.filter_real)
% 6.18/6.66 (declare-fun tptp.princi3496590319149328850omplex (tptp.set_Pr5085853215250843933omplex) tptp.filter6041513312241820739omplex)
% 6.18/6.66 (declare-fun tptp.princi6114159922880469582l_real (tptp.set_Pr6218003697084177305l_real) tptp.filter2146258269922977983l_real)
% 6.18/6.66 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 6.18/6.66 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.18/6.66 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.18/6.66 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.18/6.66 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.18/6.66 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.18/6.66 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 6.18/6.66 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.18/6.66 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.18/6.66 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 6.18/6.66 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 6.18/6.66 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 6.18/6.66 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 6.18/6.66 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 6.18/6.66 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 6.18/6.66 (declare-fun tptp.finite2998713641127702882nt_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 6.18/6.66 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 6.18/6.66 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 6.18/6.66 (declare-fun tptp.finite6551019134538273531omplex (tptp.set_set_complex) Bool)
% 6.18/6.66 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 6.18/6.66 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 6.18/6.66 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.18/6.66 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.18/6.66 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.18/6.66 (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)
% 6.18/6.66 (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)
% 6.18/6.66 (declare-fun tptp.comp_C3531382070062128313er_num ((-> tptp.code_integer tptp.code_integer) (-> tptp.num tptp.code_integer) tptp.num) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 6.18/6.66 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 6.18/6.66 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.18/6.66 (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)
% 6.18/6.66 (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)
% 6.18/6.66 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.18/6.66 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.18/6.66 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.18/6.66 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.18/6.66 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.minus_8727706125548526216plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool) tptp.complex) Bool)
% 6.18/6.66 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 6.18/6.66 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.minus_711738161318947805_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.18/6.66 (declare-fun tptp.minus_minus_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 6.18/6.66 (declare-fun tptp.minus_6910147592129066416_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.18/6.66 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.minus_1052850069191792384nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.18/6.66 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.18/6.66 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.one_one_int () tptp.int)
% 6.18/6.66 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.18/6.66 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.18/6.66 (declare-fun tptp.one_one_real () tptp.real)
% 6.18/6.66 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.uminus1680532995456772888plex_o ((-> tptp.complex Bool) tptp.complex) Bool)
% 6.18/6.66 (declare-fun tptp.uminus_uminus_int_o ((-> tptp.int Bool) tptp.int) Bool)
% 6.18/6.66 (declare-fun tptp.uminus_uminus_nat_o ((-> tptp.nat Bool) tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.uminus7117520113953359693_int_o ((-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.18/6.66 (declare-fun tptp.uminus_uminus_real_o ((-> tptp.real Bool) tptp.real) Bool)
% 6.18/6.66 (declare-fun tptp.uminus6401447641752708672_nat_o ((-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.uminus8566677241136511917omplex (tptp.set_complex) tptp.set_complex)
% 6.18/6.66 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.uminus6221592323253981072nt_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.18/6.66 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.18/6.66 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.18/6.66 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.18/6.66 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.18/6.66 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.18/6.66 (declare-fun tptp.groups8507830703676809646_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 6.18/6.66 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.18/6.66 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.18/6.66 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.18/6.66 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.18/6.66 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.18/6.66 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.18/6.66 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.18/6.66 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.18/6.66 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.18/6.66 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.18/6.66 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.18/6.66 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.18/6.66 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.18/6.66 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.18/6.66 (declare-fun tptp.groups8255218700646806128omplex ((-> tptp.set_nat tptp.complex) tptp.set_set_nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.groups5107569545109728110t_real ((-> tptp.set_nat tptp.real) tptp.set_set_nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.18/6.66 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.18/6.66 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.18/6.66 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.18/6.66 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.18/6.66 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.18/6.66 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.18/6.66 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.18/6.66 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.18/6.66 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.18/6.66 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.18/6.66 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.18/6.66 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.18/6.66 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.18/6.66 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.18/6.66 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.18/6.66 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.18/6.66 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.sup_sup_set_set_o (tptp.set_set_o tptp.set_set_o) tptp.set_set_o)
% 6.18/6.66 (declare-fun tptp.sup_sup_set_set_int (tptp.set_set_int tptp.set_set_int) tptp.set_set_int)
% 6.18/6.66 (declare-fun tptp.sup_sup_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 6.18/6.66 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.18/6.66 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 6.18/6.66 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.18/6.66 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.18/6.66 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 6.18/6.66 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.18/6.66 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.18/6.66 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.18/6.66 (declare-fun tptp.nil_int () tptp.list_int)
% 6.18/6.66 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.18/6.66 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.18/6.66 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.18/6.66 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.18/6.66 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.18/6.66 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 6.18/6.66 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.18/6.66 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.18/6.66 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.18/6.66 (declare-fun tptp.list_update_set_nat (tptp.list_set_nat tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.18/6.66 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.18/6.66 (declare-fun tptp.nth_Pr8522763379788166057eger_o (tptp.list_P8526636022914148096eger_o tptp.nat) tptp.produc6271795597528267376eger_o)
% 6.18/6.66 (declare-fun tptp.nth_Pr112076138515278198_nat_o (tptp.list_P7333126701944960589_nat_o tptp.nat) tptp.product_prod_nat_o)
% 6.18/6.66 (declare-fun tptp.nth_Pr3440142176431000676at_int (tptp.list_P3521021558325789923at_int tptp.nat) tptp.product_prod_nat_int)
% 6.18/6.66 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 6.18/6.66 (declare-fun tptp.nth_Pr8326237132889035090at_num (tptp.list_P1726324292696863441at_num tptp.nat) tptp.product_prod_nat_num)
% 6.18/6.66 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 6.18/6.66 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 6.18/6.66 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.18/6.66 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.18/6.66 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.18/6.66 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.18/6.66 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.18/6.66 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.18/6.66 (declare-fun tptp.produc3607205314601156340eger_o (tptp.list_Code_integer tptp.list_o) tptp.list_P8526636022914148096eger_o)
% 6.18/6.66 (declare-fun tptp.product_int_o (tptp.list_int tptp.list_o) tptp.list_P5087981734274514673_int_o)
% 6.18/6.66 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 6.18/6.66 (declare-fun tptp.produc662631939642741121T_VEBT (tptp.list_int tptp.list_VEBT_VEBT) tptp.list_P7524865323317820941T_VEBT)
% 6.18/6.66 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.18/6.66 (declare-fun tptp.product_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 6.18/6.66 (declare-fun tptp.product_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 6.18/6.66 (declare-fun tptp.product_nat_num (tptp.list_nat tptp.list_num) tptp.list_P1726324292696863441at_num)
% 6.18/6.66 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.18/6.66 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 6.18/6.66 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.18/6.66 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.18/6.66 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.18/6.66 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.18/6.66 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.18/6.66 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.18/6.66 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.18/6.66 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.18/6.66 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.18/6.66 (declare-fun tptp.replicate_set_nat (tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.18/6.66 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.18/6.66 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.18/6.66 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.18/6.66 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.18/6.66 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.semiri4055485073559036834nteger ((-> tptp.code_integer tptp.code_integer) tptp.nat tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s4246224855604898693_int_o (tptp.list_P5087981734274514673_int_o) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s5157815400016825771nt_int (tptp.list_P5707943133018811711nt_int) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s6639371672096860321T_VEBT (tptp.list_P7524865323317820941T_VEBT) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.18/6.66 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.18/6.66 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.18/6.66 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.18/6.66 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.18/6.66 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.one () tptp.num)
% 6.18/6.66 (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)
% 6.18/6.66 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.18/6.66 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.18/6.66 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.18/6.66 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.18/6.66 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.18/6.66 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.18/6.66 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.18/6.66 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.18/6.66 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.none_num () tptp.option_num)
% 6.18/6.66 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.18/6.66 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.18/6.66 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.18/6.66 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.18/6.66 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.18/6.66 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.18/6.66 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.18/6.66 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.18/6.66 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 6.18/6.66 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 6.18/6.66 (declare-fun tptp.bot_bo4731626569425807221er_o_o (tptp.code_integer Bool) Bool)
% 6.18/6.66 (declare-fun tptp.bot_bot_int_int_o (tptp.int tptp.int) Bool)
% 6.18/6.66 (declare-fun tptp.bot_bot_nat_nat_o (tptp.nat tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.bot_bot_nat_num_o (tptp.nat tptp.num) Bool)
% 6.18/6.66 (declare-fun tptp.bot_bot_num_num_o (tptp.num tptp.num) Bool)
% 6.18/6.66 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.18/6.66 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.18/6.66 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.18/6.66 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.18/6.66 (declare-fun tptp.bot_bo5379713665208646970eger_o () tptp.set_Pr448751882837621926eger_o)
% 6.18/6.66 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 6.18/6.66 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.18/6.66 (declare-fun tptp.bot_bo7038385379056416535at_num () tptp.set_Pr6200539531224447659at_num)
% 6.18/6.66 (declare-fun tptp.bot_bo9056780473022590049um_num () tptp.set_Pr8218934625190621173um_num)
% 6.18/6.66 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.18/6.66 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.18/6.66 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 6.18/6.66 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.ord_less_o (Bool Bool) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_set_o (tptp.set_o tptp.set_o) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le2162486998276636481er_o_o ((-> tptp.code_integer Bool Bool) (-> tptp.code_integer Bool Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le4573692005234683329plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le6741204236512500942_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le6558929396352911974_nat_o ((-> tptp.list_nat tptp.list_nat Bool) (-> tptp.list_nat tptp.list_nat Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le1520216061033275535_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le2646555220125990790_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le3404735783095501756_num_o ((-> tptp.nat tptp.num Bool) (-> tptp.nat tptp.num Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le6124364862034508274_num_o ((-> tptp.num tptp.num Bool) (-> tptp.num tptp.num Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le1598226405681992910_int_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le8369615600986905444_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le5604493270027003598_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le704812498762024988_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le2556027599737686990_num_o ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le2239182809043710856_num_o ((-> tptp.product_prod_num_num Bool) (-> tptp.product_prod_num_num Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le3964352015994296041_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_o (Bool Bool) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le8980329558974975238eger_o (tptp.set_Pr448751882837621926eger_o tptp.set_Pr448751882837621926eger_o) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le8085105155179020875at_num (tptp.set_Pr6200539531224447659at_num tptp.set_Pr6200539531224447659at_num) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le880128212290418581um_num (tptp.set_Pr8218934625190621173um_num tptp.set_Pr8218934625190621173um_num) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.18/6.66 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.18/6.66 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.ord_max_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.18/6.66 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 6.18/6.66 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.18/6.66 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 6.18/6.66 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.18/6.66 (declare-fun tptp.top_top_set_int () tptp.set_int)
% 6.18/6.66 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.18/6.66 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.18/6.66 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.18/6.66 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 6.18/6.66 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.18/6.66 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 6.18/6.66 (declare-fun tptp.produc851828971589881931at_num ((-> tptp.nat tptp.num tptp.num) tptp.produc2963631642982155120at_num) tptp.produc3368934014287244435at_num)
% 6.18/6.66 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 6.18/6.66 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 6.18/6.66 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 6.18/6.66 (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)
% 6.18/6.66 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.18/6.66 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.18/6.66 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.18/6.66 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 6.18/6.66 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 6.18/6.66 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.18/6.66 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.18/6.66 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.18/6.66 (declare-fun tptp.produc1195630363706982562at_num (tptp.nat tptp.product_prod_nat_num) tptp.produc2963631642982155120at_num)
% 6.18/6.66 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 6.18/6.66 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.18/6.66 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 6.18/6.66 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 6.18/6.66 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 6.18/6.66 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.18/6.66 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.18/6.66 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.18/6.66 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.18/6.66 (declare-fun tptp.produc7828578312038201481er_o_o ((-> tptp.code_integer Bool Bool) tptp.produc6271795597528267376eger_o) Bool)
% 6.18/6.66 (declare-fun tptp.produc1043322548047392435omplex ((-> tptp.code_integer Bool tptp.set_complex) tptp.produc6271795597528267376eger_o) tptp.set_complex)
% 6.18/6.66 (declare-fun tptp.produc1253318751659547953et_int ((-> tptp.code_integer Bool tptp.set_int) tptp.produc6271795597528267376eger_o) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.produc5431169771168744661et_nat ((-> tptp.code_integer Bool tptp.set_nat) tptp.produc6271795597528267376eger_o) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.produc242741666403216561t_real ((-> tptp.code_integer Bool tptp.set_real) tptp.produc6271795597528267376eger_o) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.produc4188289175737317920o_char ((-> tptp.code_integer Bool tptp.char) tptp.produc6271795597528267376eger_o) tptp.char)
% 6.18/6.66 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.18/6.66 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.18/6.66 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.18/6.66 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.18/6.66 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.18/6.66 (declare-fun tptp.produc6771430404735790350plex_o ((-> tptp.complex tptp.complex Bool) tptp.produc4411394909380815293omplex) Bool)
% 6.18/6.66 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.18/6.66 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.18/6.66 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.18/6.66 (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)
% 6.18/6.66 (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)
% 6.18/6.66 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.18/6.66 (declare-fun tptp.produc1830744345554046123nteger ((-> tptp.nat tptp.nat tptp.code_integer) tptp.product_prod_nat_nat) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.18/6.66 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.produc4927758841916487424_num_o ((-> tptp.nat tptp.num Bool) tptp.product_prod_nat_num) Bool)
% 6.18/6.66 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.18/6.66 (declare-fun tptp.produc6231982587499038204omplex ((-> tptp.nat tptp.num tptp.set_complex) tptp.product_prod_nat_num) tptp.set_complex)
% 6.18/6.66 (declare-fun tptp.produc1435849484188172666t_real ((-> tptp.nat tptp.num tptp.set_real) tptp.product_prod_nat_num) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.produc5703948589228662326_num_o ((-> tptp.num tptp.num Bool) tptp.product_prod_num_num) Bool)
% 6.18/6.66 (declare-fun tptp.produc2866383454006189126omplex ((-> tptp.num tptp.num tptp.set_complex) tptp.product_prod_num_num) tptp.set_complex)
% 6.18/6.66 (declare-fun tptp.produc6406642877701697732et_int ((-> tptp.num tptp.num tptp.set_int) tptp.product_prod_num_num) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.produc1361121860356118632et_nat ((-> tptp.num tptp.num tptp.set_nat) tptp.product_prod_num_num) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.produc8296048397933160132t_real ((-> tptp.num tptp.num tptp.set_real) tptp.product_prod_num_num) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.produc5414030515140494994real_o ((-> tptp.real tptp.real Bool) tptp.produc2422161461964618553l_real) Bool)
% 6.18/6.66 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.18/6.66 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.18/6.66 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.18/6.66 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.18/6.66 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.18/6.66 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.18/6.66 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.18/6.66 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.18/6.66 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 6.18/6.66 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.18/6.66 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.18/6.66 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.18/6.66 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.18/6.66 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.18/6.66 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.18/6.66 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.18/6.66 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.18/6.66 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.18/6.66 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.18/6.66 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.18/6.66 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.18/6.66 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.18/6.66 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.18/6.66 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.18/6.66 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.18/6.66 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.18/6.66 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.18/6.66 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.18/6.66 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.18/6.66 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.18/6.66 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.18/6.66 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.18/6.66 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 6.18/6.66 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.18/6.66 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.18/6.66 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 6.18/6.66 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 6.18/6.66 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 6.18/6.66 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.18/6.66 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.18/6.66 (declare-fun tptp.collec8663557070575231912omplex ((-> tptp.produc4411394909380815293omplex Bool)) tptp.set_Pr5085853215250843933omplex)
% 6.18/6.66 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.18/6.66 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.18/6.66 (declare-fun tptp.collec3799799289383736868l_real ((-> tptp.produc2422161461964618553l_real Bool)) tptp.set_Pr6218003697084177305l_real)
% 6.18/6.66 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.18/6.66 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.collect_set_complex ((-> tptp.set_complex Bool)) tptp.set_set_complex)
% 6.18/6.66 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 6.18/6.66 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.image_o_set_o ((-> Bool tptp.set_o) tptp.set_o) tptp.set_set_o)
% 6.18/6.66 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.image_int_set_int ((-> tptp.int tptp.set_int) tptp.set_int) tptp.set_set_int)
% 6.18/6.66 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.18/6.66 (declare-fun tptp.image_5971271580939081552omplex ((-> tptp.real tptp.filter6041513312241820739omplex) tptp.set_real) tptp.set_fi4554929511873752355omplex)
% 6.18/6.66 (declare-fun tptp.image_2178119161166701260l_real ((-> tptp.real tptp.filter2146258269922977983l_real) tptp.set_real) tptp.set_fi7789364187291644575l_real)
% 6.18/6.66 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.set_fo1084959871951514735nteger ((-> tptp.nat tptp.code_integer tptp.code_integer) tptp.nat tptp.nat tptp.code_integer) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.18/6.66 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.set_fo8365102181078989356at_num ((-> tptp.nat tptp.num tptp.num) tptp.nat tptp.nat tptp.num) tptp.num)
% 6.18/6.66 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.set_fo3699595496184130361el_nat (tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat) Bool)
% 6.18/6.66 (declare-fun tptp.set_fo256927282339908995el_num (tptp.produc3368934014287244435at_num tptp.produc3368934014287244435at_num) Bool)
% 6.18/6.66 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.18/6.66 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.18/6.66 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 6.18/6.66 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.set_ord_atMost_o (Bool) tptp.set_o)
% 6.18/6.66 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.18/6.66 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 6.18/6.66 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.set_or58775011639299419et_int (tptp.set_int) tptp.set_set_int)
% 6.18/6.66 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.set_or6416164934427428222Than_o (Bool) tptp.set_o)
% 6.18/6.66 (declare-fun tptp.set_or1207661135979820486an_int (tptp.int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.set_ord_lessThan_o (Bool) tptp.set_o)
% 6.18/6.66 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.18/6.66 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.18/6.66 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.18/6.66 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.18/6.66 (declare-fun tptp.set_or890127255671739683et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.18/6.66 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.18/6.66 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.18/6.66 (declare-fun tptp.char_of_integer (tptp.code_integer) tptp.char)
% 6.18/6.66 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.18/6.66 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.18/6.66 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo4667128019001906403logy_o (tptp.set_set_o tptp.set_o) Bool)
% 6.18/6.66 (declare-fun tptp.topolo1611008123915946401gy_int (tptp.set_set_int tptp.set_int) Bool)
% 6.18/6.66 (declare-fun tptp.topolo1613498594424996677gy_nat (tptp.set_set_nat tptp.set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.topolo2919662092509805066nteger ((-> tptp.nat tptp.code_integer)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo3100542954746470799et_int ((-> tptp.nat tptp.set_int)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo9180104560040979295open_o (tptp.set_o) Bool)
% 6.18/6.66 (declare-fun tptp.topolo4110288021797289639omplex (tptp.set_complex) Bool)
% 6.18/6.66 (declare-fun tptp.topolo4325760605701065253en_int (tptp.set_int) Bool)
% 6.18/6.66 (declare-fun tptp.topolo4328251076210115529en_nat (tptp.set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.topolo4860482606490270245n_real (tptp.set_real) Bool)
% 6.18/6.66 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.18/6.66 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.18/6.66 (declare-fun tptp.topolo6517432010174082258omplex ((-> tptp.nat tptp.complex)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.18/6.66 (declare-fun tptp.topolo896644834953643431omplex () tptp.filter6041513312241820739omplex)
% 6.18/6.66 (declare-fun tptp.topolo1511823702728130853y_real () tptp.filter2146258269922977983l_real)
% 6.18/6.66 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.diffs_Code_integer ((-> tptp.nat tptp.code_integer) tptp.nat) tptp.code_integer)
% 6.18/6.66 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 6.18/6.66 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 6.18/6.66 (declare-fun tptp.diffs_rat ((-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.18/6.66 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.pi () tptp.real)
% 6.18/6.66 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.18/6.66 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.18/6.66 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.18/6.66 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.18/6.66 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_delete (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_delete_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 6.18/6.66 (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)
% 6.18/6.66 (declare-fun tptp.vEBT_V3895251965096974666el_nat (tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_V452583751252753300el_num (tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_V7235779383477046023at_nat (tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.18/6.66 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.18/6.66 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.18/6.66 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.18/6.66 (declare-fun tptp.accp_P6019419558468335806at_nat ((-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool) tptp.produc4471711990508489141at_nat) Bool)
% 6.18/6.66 (declare-fun tptp.accp_P5496254298877145759on_nat ((-> tptp.produc8306885398267862888on_nat tptp.produc8306885398267862888on_nat Bool) tptp.produc8306885398267862888on_nat) Bool)
% 6.18/6.66 (declare-fun tptp.accp_P4916641582247091100at_num ((-> tptp.produc3368934014287244435at_num tptp.produc3368934014287244435at_num Bool) tptp.produc3368934014287244435at_num) Bool)
% 6.18/6.66 (declare-fun tptp.accp_P7605991808943153877on_num ((-> tptp.produc1193250871479095198on_num tptp.produc1193250871479095198on_num Bool) tptp.produc1193250871479095198on_num) Bool)
% 6.18/6.66 (declare-fun tptp.accp_P3267385326087170368at_nat ((-> tptp.produc5542196010084753463at_nat tptp.produc5542196010084753463at_nat Bool) tptp.produc5542196010084753463at_nat) Bool)
% 6.18/6.66 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.18/6.66 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.18/6.66 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.18/6.66 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.18/6.66 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.18/6.66 (declare-fun tptp.measure_int ((-> tptp.int tptp.nat)) tptp.set_Pr958786334691620121nt_int)
% 6.18/6.66 (declare-fun tptp.measure_nat ((-> tptp.nat tptp.nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.18/6.66 (declare-fun tptp.measure_num ((-> tptp.num tptp.nat)) tptp.set_Pr8218934625190621173um_num)
% 6.18/6.66 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.18/6.66 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.18/6.66 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.18/6.66 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.18/6.66 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.18/6.66 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.18/6.66 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 6.18/6.66 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 6.18/6.66 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.18/6.66 (declare-fun tptp.member1379723562493234055eger_o (tptp.produc6271795597528267376eger_o tptp.set_Pr448751882837621926eger_o) Bool)
% 6.18/6.66 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.18/6.66 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.18/6.66 (declare-fun tptp.member9148766508732265716at_num (tptp.product_prod_nat_num tptp.set_Pr6200539531224447659at_num) Bool)
% 6.18/6.66 (declare-fun tptp.member7279096912039735102um_num (tptp.product_prod_num_num tptp.set_Pr8218934625190621173um_num) Bool)
% 6.18/6.66 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.18/6.66 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.18/6.66 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 6.18/6.66 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.18/6.66 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.18/6.66 (declare-fun tptp.deg () tptp.nat)
% 6.18/6.66 (declare-fun tptp.lx () tptp.nat)
% 6.18/6.66 (declare-fun tptp.m () tptp.nat)
% 6.18/6.66 (declare-fun tptp.ma () tptp.nat)
% 6.18/6.66 (declare-fun tptp.mi () tptp.nat)
% 6.18/6.66 (declare-fun tptp.na () tptp.nat)
% 6.18/6.66 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.summin () tptp.nat)
% 6.18/6.66 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.18/6.66 (declare-fun tptp.xa () tptp.nat)
% 6.18/6.66 (assert (= tptp.xa tptp.mi))
% 6.18/6.66 (assert (forall ((X tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D)) (@ (@ tptp.vEBT_VEBT_low X) D)) D) X)))
% 6.18/6.66 (assert (= tptp.xa tptp.mi))
% 6.18/6.66 (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)))))
% 6.18/6.66 (assert (or (not (= tptp.xa tptp.mi)) (not (= tptp.xa tptp.ma))))
% 6.18/6.66 (assert (= tptp.vEBT_VEBT_high (lambda ((X2 tptp.nat) (N tptp.nat)) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.18/6.66 (assert (= (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))
% 6.18/6.66 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L tptp.nat) (D2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D2))) L))))
% 6.18/6.66 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.18/6.66 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.18/6.66 (assert (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na)))) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) _let_3)) _let_2) _let_3)))))
% 6.18/6.66 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.18/6.66 (assert (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na)))))
% 6.18/6.66 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (= tptp.xa tptp.mi))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint tptp.summary)))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_5)))))) (=> (not _let_4) (= _let_3 tptp.xa)))))))))
% 6.18/6.66 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx)))
% 6.18/6.66 (assert (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))))))))
% 6.18/6.66 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.18/6.66 (assert (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_1 tptp.na))) tptp.lx)) (@ _let_1 tptp.deg))))
% 6.18/6.66 (assert (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))) tptp.na)))
% 6.18/6.66 (assert (and (not (= tptp.mi tptp.ma)) (@ (@ tptp.ord_less_nat tptp.xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))))
% 6.18/6.66 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 6.18/6.66 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 6.18/6.66 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 6.18/6.66 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.deg))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (assert (@ (@ tptp.vEBT_vebt_member tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na)))
% 6.18/6.66 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.18/6.66 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) N2) (= Deg N2))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.18/6.66 (assert (= (@ tptp.some_nat tptp.summin) (@ tptp.vEBT_vebt_mint tptp.summary)))
% 6.18/6.66 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.18/6.66 (assert (not (forall ((Summin tptp.nat)) (not (= (@ tptp.some_nat Summin) (@ tptp.vEBT_vebt_mint tptp.summary))))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_delete T) X)) Y) (and (not (= X Y)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) Y))))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.18/6.66 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) Xs) (@ (@ tptp.ord_less_eq_nat Y2) X2)))))))
% 6.18/6.66 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) Xs) (@ (@ tptp.ord_less_eq_nat X2) Y2)))))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.18/6.66 (assert (= tptp.na tptp.m))
% 6.18/6.66 (assert (= (@ tptp.some_nat tptp.lx) (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat Mini) X))))))
% 6.18/6.66 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.18/6.66 (assert (forall ((A tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.member5262025264175285858nt_int A) (@ tptp.collec213857154873943460nt_int P)) (@ P A))))
% 6.18/6.66 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.18/6.66 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 6.18/6.66 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.18/6.66 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.18/6.66 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A2))) A2)))
% 6.18/6.66 (assert (forall ((A2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X2) A2))) A2)))
% 6.18/6.66 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A2))) A2)))
% 6.18/6.66 (assert (forall ((A2 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) A2))) A2)))
% 6.18/6.66 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A2))) A2)))
% 6.18/6.66 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2))) A2)))
% 6.18/6.66 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 tptp.product_prod_int_int)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec213857154873943460nt_int P) (@ tptp.collec213857154873943460nt_int Q)))))
% 6.18/6.66 (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)))))
% 6.18/6.66 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_nat Q)))))
% 6.18/6.66 (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)))))
% 6.18/6.66 (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)))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat X) Maxi))))))
% 6.18/6.66 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N2)) (= M N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N2)) (= M N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N2)) (= M N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N2)) (= M N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N2)) (= M N2))))
% 6.18/6.66 (assert (forall ((X22 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X22) (@ tptp.some_P7363390416028606310at_nat Y22)) (= X22 Y22))))
% 6.18/6.66 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.some_nat X22) (@ tptp.some_nat Y22)) (= X22 Y22))))
% 6.18/6.66 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.some_num X22) (@ tptp.some_num Y22)) (= X22 Y22))))
% 6.18/6.66 (assert (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin)) X_1)))
% 6.18/6.66 (assert (not (forall ((Lx tptp.nat)) (not (= (@ tptp.some_nat Lx) (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin)))))))
% 6.18/6.66 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 6.18/6.66 (assert (forall ((X tptp.nat)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete tptp.summary) X)) tptp.m)))
% 6.18/6.66 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I)))))
% 6.18/6.66 (assert (forall ((Ma tptp.nat) (N2 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 N2) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N2)) (@ _let_1 M))))))
% 6.18/6.66 (assert (and (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.xa) (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma)))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ 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))) N2))))))
% 6.18/6.66 (assert (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.18/6.66 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin)) tptp.na))
% 6.18/6.66 (assert (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) tptp.summin)) tptp.lx))
% 6.18/6.66 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na)))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.18/6.66 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) Y)))))
% 6.18/6.66 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N2) X)))))
% 6.18/6.66 (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))))
% 6.18/6.66 (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))))
% 6.18/6.66 (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))))
% 6.18/6.66 (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))))
% 6.18/6.66 (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))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2)))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))))
% 6.18/6.66 (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))))
% 6.18/6.66 (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))))
% 6.18/6.66 (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))))
% 6.18/6.66 (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))))
% 6.18/6.66 (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))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.66 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.66 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N2) (@ tptp.bit0 N2))))
% 6.18/6.66 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (and (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary))))))
% 6.18/6.66 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y2 tptp.product_prod_nat_nat)) (not (= X (@ tptp.some_P7363390416028606310at_nat Y2)))) (= X tptp.none_P5556105721700978146at_nat))))
% 6.18/6.66 (assert (forall ((X tptp.option_nat)) (= (forall ((Y2 tptp.nat)) (not (= X (@ tptp.some_nat Y2)))) (= X tptp.none_nat))))
% 6.18/6.66 (assert (forall ((X tptp.option_num)) (= (forall ((Y2 tptp.num)) (not (= X (@ tptp.some_num Y2)))) (= X tptp.none_num))))
% 6.18/6.66 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y2 tptp.product_prod_nat_nat)) (= X (@ tptp.some_P7363390416028606310at_nat Y2))))))
% 6.18/6.66 (assert (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y2 tptp.nat)) (= X (@ tptp.some_nat Y2))))))
% 6.18/6.66 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y2 tptp.num)) (= X (@ tptp.some_num Y2))))))
% 6.18/6.66 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))))
% 6.18/6.66 (assert (@ (@ tptp.ord_less_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.18/6.66 (assert (forall ((X 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 (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))))
% 6.18/6.66 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na))) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na)))
% 6.18/6.66 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)))))
% 6.18/6.66 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((Y3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y3) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low Y3) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y3) (@ (@ tptp.ord_less_eq_nat Y3) tptp.ma)))))))))
% 6.18/6.66 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N2) (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))))))
% 6.18/6.66 (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)))))))))
% 6.18/6.66 (assert (and (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma) (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))))
% 6.18/6.66 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X 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) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 6.18/6.66 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X 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 X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi) X) (@ (@ 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 X) _let_2)))))))))))
% 6.18/6.66 (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)))))
% 6.18/6.66 (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)))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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)))))
% 6.18/6.66 (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)))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (assert (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx)) tptp.na)) (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList)))
% 6.18/6.66 (assert (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 tptp.na))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) _let_2)) tptp.lx))) (and (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na)) (@ _let_1 tptp.m)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)) _let_2))))))
% 6.18/6.66 (assert (forall ((Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_low Y) tptp.na))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Y) tptp.na))) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_3)) _let_2) (=> (@ (@ tptp.ord_less_nat _let_3) (@ _let_1 tptp.m)) (and (@ (@ tptp.ord_less_nat tptp.mi) Y) (@ (@ tptp.ord_less_eq_nat Y) tptp.ma) (@ (@ tptp.ord_less_nat _let_2) (@ _let_1 tptp.na))))))))))
% 6.18/6.66 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((Y3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y3) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low Y3) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y3) (@ (@ tptp.ord_less_eq_nat Y3) tptp.ma))))))))
% 6.18/6.66 (assert (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (=> (and (not (= I2 _let_4)) (@ (@ tptp.ord_less_nat I2) (@ _let_2 tptp.m))) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ _let_1 _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na)))) I2) (@ _let_1 I2)))))))))
% 6.18/6.66 (assert (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_1 tptp.na))) tptp.lx))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high _let_2) tptp.na))) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_3) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low _let_2) tptp.na)))) (@ _let_1 tptp.m))))))
% 6.18/6.66 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Newlist 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.product_Pair_nat_nat Mi))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_4 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_2) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H2)) L2)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) (@ (@ tptp.power_power_nat _let_1) _let_2))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H2))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))
% 6.18/6.66 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_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.power_power_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xn) _let_2))) (let ((_let_6 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_5 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_4 _let_6))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_2) L2) (=> (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_4 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H2))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))
% 6.18/6.66 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H2)) L2))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) _let_1))) (let ((_let_3 (@ tptp.nth_VEBT_VEBT _let_2))) (let ((_let_4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_5 (@ (@ tptp.divide_divide_nat Deg) _let_4))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_4) _let_5))) (let ((_let_7 (@ tptp.if_nat (= X Ma)))) (let ((_let_8 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_5))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_4) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_5) L2) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_1)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 _let_11)))))) Ma)))) Deg) _let_2) _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 H2))))) Ma)))) Deg) _let_2) Summary)))))))))))))))))))))))
% 6.18/6.66 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT) (Summary tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high X) _let_4))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_6 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_4) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H2)) L2)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat _let_3) _let_4)) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn))))))))))))))))))))
% 6.18/6.66 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= X Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 Ma))) Deg) TreeList) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_3) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H2))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))))))))
% 6.18/6.66 (assert (forall ((X 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))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_high _let_7) _let_3))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_8)) (@ (@ tptp.vEBT_VEBT_low _let_7) _let_3)))) (let ((_let_10 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_8) _let_9))) (let ((_let_11 (@ tptp.nth_VEBT_VEBT _let_10))) (let ((_let_12 (@ tptp.if_nat (= _let_7 Ma)))) (let ((_let_13 (@ tptp.product_Pair_nat_nat _let_7))) (let ((_let_14 (@ (@ tptp.vEBT_vebt_delete Summary) _let_8))) (let ((_let_15 (@ tptp.vEBT_vebt_maxt _let_14))) (let ((_let_16 (@ tptp.the_nat _let_15))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_8) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ (@ tptp.if_nat (= _let_15 tptp.none_nat)) _let_7) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_16)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_16)))))) Ma)))) Deg) _let_10) _let_14)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_8))))) Ma)))) Deg) _let_10) Summary))) _let_1)))))))))))))))))))))))
% 6.18/6.66 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_high Xn) _let_4))) (let ((_let_8 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_7 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_5)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_8))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_4) L2) (=> (@ (@ tptp.ord_less_nat _let_7) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_6 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn)))))))))))))))))))))))
% 6.18/6.66 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_3))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_13 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_12 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_3) L2) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_12 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H2))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))))))))))))))
% 6.18/6.66 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ _let_1 H2)) L2))) (let ((_let_3 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT _let_3))) (let ((_let_5 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_6 (@ (@ tptp.divide_divide_nat Deg) _let_5))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_5) _let_6))) (let ((_let_8 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_9 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_10 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ tptp.the_nat _let_11))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_6))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_5) Deg) (=> (= _let_13 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_1 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_6) L2) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_2)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ (@ tptp.if_nat (= _let_11 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_12)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 _let_12)))))) Ma)))) Deg) _let_3) _let_10)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 H2))))) Ma)))) Deg) _let_3) Summary))))))))))))))))))))))))))
% 6.18/6.66 (assert (forall ((Mi tptp.nat) (X 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))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (= X Mi))) (let ((_let_9 (@ tptp.if_nat _let_8))) (let ((_let_10 (@ (@ _let_9 _let_7) X))) (let ((_let_11 (@ (@ tptp.vEBT_VEBT_high _let_10) _let_3))) (let ((_let_12 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_11)) (@ (@ tptp.vEBT_VEBT_low _let_10) _let_3)))) (let ((_let_13 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_11) _let_12))) (let ((_let_14 (@ tptp.nth_VEBT_VEBT _let_13))) (let ((_let_15 (@ tptp.if_nat (and (=> _let_8 (= _let_7 Ma)) (=> (not _let_8) (= X Ma)))))) (let ((_let_16 (@ (@ _let_9 _let_10) Mi))) (let ((_let_17 (@ tptp.product_Pair_nat_nat _let_16))) (let ((_let_18 (@ (@ tptp.vEBT_vebt_delete Summary) _let_11))) (let ((_let_19 (@ tptp.vEBT_vebt_maxt _let_18))) (let ((_let_20 (@ tptp.the_nat _let_19))) (=> (and (@ (@ tptp.ord_less_eq_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_11) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_12)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ (@ tptp.if_nat (= _let_19 tptp.none_nat)) _let_16) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_20)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_20)))))) Ma)))) Deg) _let_13) _let_18)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_11) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_11))))) Ma)))) Deg) _let_13) Summary))) _let_1)))))))))))))))))))))))))))
% 6.18/6.66 (assert (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X5) tptp.na) (forall ((Xa tptp.nat)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete X5) Xa)) tptp.na))))))
% 6.18/6.66 (assert (=> (= tptp.mi tptp.ma) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))))
% 6.18/6.66 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N2) (@ (@ tptp.plus_plus_num N2) tptp.one))))
% 6.18/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))
% 6.18/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N2) K)))))
% 6.18/6.66 (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)))))))
% 6.18/6.66 (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)))))))
% 6.18/6.66 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I2) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) I2))))
% 6.18/6.66 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2))) M)))
% 6.18/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2)) M)))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (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))))))
% 6.18/6.66 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 6.18/6.66 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 6.18/6.66 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_num B2)) (@ (@ P X) Y)))) _let_1))))))
% 6.18/6.66 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 6.18/6.66 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 6.18/6.66 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= X (@ tptp.some_nat A3)) (=> (= Y (@ tptp.some_num B2)) (@ (@ P X) Y)))) _let_1))))))
% 6.18/6.66 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 6.18/6.66 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.nat)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 6.18/6.66 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= X (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_num B2)) (@ (@ P X) Y)))) _let_1))))))
% 6.18/6.66 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X6 tptp.option4927543243414619207at_nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P3 tptp.none_P5556105721700978146at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 6.18/6.66 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (forall ((X6 tptp.option_nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.option_nat Bool))) (and (@ P3 tptp.none_nat) (forall ((X2 tptp.nat)) (@ P3 (@ tptp.some_nat X2)))))))
% 6.18/6.66 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (forall ((X6 tptp.option_num)) (@ P2 X6))) (lambda ((P3 (-> tptp.option_num Bool))) (and (@ P3 tptp.none_num) (forall ((X2 tptp.num)) (@ P3 (@ tptp.some_num X2)))))))
% 6.18/6.66 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X6 tptp.option4927543243414619207at_nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P3 tptp.none_P5556105721700978146at_nat) (exists ((X2 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 6.18/6.66 (assert (= (lambda ((P2 (-> tptp.option_nat Bool))) (exists ((X6 tptp.option_nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.option_nat Bool))) (or (@ P3 tptp.none_nat) (exists ((X2 tptp.nat)) (@ P3 (@ tptp.some_nat X2)))))))
% 6.18/6.66 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (exists ((X6 tptp.option_num)) (@ P2 X6))) (lambda ((P3 (-> tptp.option_num Bool))) (or (@ P3 tptp.none_num) (exists ((X2 tptp.num)) (@ P3 (@ tptp.some_num X2)))))))
% 6.18/6.66 (assert (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y (@ tptp.some_P7363390416028606310at_nat X23))))))))
% 6.18/6.66 (assert (forall ((Y tptp.option_nat)) (=> (not (= Y tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y (@ tptp.some_nat X23))))))))
% 6.18/6.66 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))))
% 6.18/6.66 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.18/6.66 (assert (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))))
% 6.18/6.66 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 6.18/6.66 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 6.18/6.66 (assert (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))))
% 6.18/6.66 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 6.18/6.66 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N2) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N2)) Q2)))))
% 6.18/6.66 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X22)) X22)))
% 6.18/6.66 (assert (forall ((X22 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X22)) X22)))
% 6.18/6.66 (assert (forall ((X22 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X22)) X22)))
% 6.18/6.66 (assert (forall ((Option tptp.option_nat) (Option2 tptp.option_nat)) (let ((_let_1 (= Option2 tptp.none_nat))) (let ((_let_2 (= Option tptp.none_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_nat Option) (@ tptp.the_nat Option2)))) (= Option Option2)))))))
% 6.18/6.66 (assert (forall ((Option tptp.option4927543243414619207at_nat) (Option2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (= Option2 tptp.none_P5556105721700978146at_nat))) (let ((_let_2 (= Option tptp.none_P5556105721700978146at_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_Pr8591224930841456533at_nat Option) (@ tptp.the_Pr8591224930841456533at_nat Option2)))) (= Option Option2)))))))
% 6.18/6.66 (assert (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_num Option) (@ tptp.the_num Option2)))) (= Option Option2)))))))
% 6.18/6.66 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.18/6.66 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.18/6.66 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.18/6.66 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.18/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.18/6.66 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.18/6.66 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.18/6.66 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.18/6.66 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.18/6.66 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.18/6.66 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.18/6.66 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.18/6.67 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 6.18/6.67 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 6.18/6.67 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.18/6.67 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.18/6.67 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.18/6.67 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.18/6.67 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.18/6.67 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.18/6.67 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.18/6.67 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.18/6.67 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.18/6.67 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.18/6.67 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X2) N))) (@ (@ tptp.vEBT_VEBT_low X2) N)))))
% 6.18/6.67 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X 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) X) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ 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)) X) tptp.none_nat)))))))
% 6.18/6.67 (assert (forall ((Deg tptp.nat) (X 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 X) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ 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)) X) tptp.none_nat)))))))
% 6.18/6.67 (assert (forall ((X5 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) tptp.lx))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high _let_1) tptp.na))) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low _let_1) tptp.na))))) (@ (@ tptp.vEBT_invar_vebt X5) tptp.na))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y) (or (@ (@ tptp.vEBT_vebt_member T) Y) (= X Y)))))))))
% 6.18/6.67 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 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)) N2) (=> (= N2 (@ 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)))))))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y)) X))))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))))
% 6.18/6.67 (assert (forall ((X 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 (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))))
% 6.18/6.67 (assert (forall ((X 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 X) _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 X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X))))))))
% 6.18/6.67 (assert (forall ((Deg tptp.nat) (X 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 X) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ tptp.some_nat Mi))))))
% 6.18/6.67 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X 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) X) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ tptp.some_nat Ma))))))
% 6.18/6.67 (assert (forall ((X tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))))
% 6.18/6.67 (assert (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N2))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N2))) TreeList3) S))))))
% 6.18/6.67 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.na))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) N2))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) N2))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) (@ tptp.set_set_nat2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ P (@ (@ tptp.nth_set_nat Xs2) N2))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) N2))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N2))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (N2 tptp.nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) N2))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (N2 tptp.nat)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) N2))))))
% 6.18/6.67 (assert (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt X5) tptp.na))))
% 6.18/6.67 (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 ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))))
% 6.18/6.67 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X 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) N2) (=> (@ (@ tptp.ord_less_eq_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X) tptp.none_nat))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.18/6.67 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 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) N2))) (=> (= (@ 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) N2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N2) tptp.one_one_complex) (= N2 tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real N2) tptp.one_one_real) (= N2 tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_rat N2) tptp.one_one_rat) (= N2 tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat N2) tptp.one_one_nat) (= N2 tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int N2) tptp.one_one_int) (= N2 tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N2)) (= tptp.one N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N2)) (= tptp.one N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N2)) (= tptp.one N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N2)) (= tptp.one N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N2)) (= tptp.one N2))))
% 6.18/6.67 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X 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)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.18/6.67 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.18/6.67 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.18/6.67 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.18/6.67 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.18/6.67 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ tptp.suc (@ tptp.suc N2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N2)))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N2)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 6.18/6.67 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 6.18/6.67 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 6.18/6.67 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.18/6.67 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.18/6.67 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.18/6.67 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.18/6.67 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.18/6.67 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.18/6.67 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.18/6.67 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.18/6.67 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.18/6.67 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.18/6.67 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.18/6.67 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.18/6.67 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N2))))
% 6.18/6.67 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.18/6.67 (assert (forall ((V tptp.num) (N2 tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M) N2) Q2))))))
% 6.18/6.67 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (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.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= X Mi))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) X))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= X Ma))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (@ (@ tptp.vEBT_vebt_delete _let_2) X))) (let ((_let_24 (and _let_9 _let_16))) (let ((_let_25 (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)))) (and (=> _let_25 (= _let_23 _let_2)) (=> (not _let_25) (and (=> _let_24 (= _let_23 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary))) (=> (not _let_24) (= _let_23 (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma)))) _let_1) _let_14) Summary))) _let_2)))))))))))))))))))))))))))))))))
% 6.18/6.67 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 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) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _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 ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X3) N2))) (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)))))))))))))))
% 6.18/6.67 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 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) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _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 ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N2) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X3) N2))) (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)))))))))))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.18/6.67 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X 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 X) _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) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X) (=> (not (= X Mi)) (=> (not (= X 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 X) _let_2))) _let_4))))))))))))))))
% 6.18/6.67 (assert (forall ((I2 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 I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_nat2 Xs2))))))))
% 6.18/6.67 (assert (forall ((I2 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 I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_VEBT_VEBT2 Xs2))))))))
% 6.18/6.67 (assert (forall ((I2 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 I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_o2 Xs2))))))))
% 6.18/6.67 (assert (forall ((I2 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 I2) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I2) (@ _let_1 J))) J) (@ _let_1 I2))) (@ tptp.set_int2 Xs2))))))))
% 6.18/6.67 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 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) N2))) (=> (@ (@ 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 N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) 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))))))))))
% 6.18/6.67 (assert (forall ((B tptp.real) (X tptp.nat) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (X tptp.nat) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (X tptp.nat) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.18/6.67 (assert (forall ((B tptp.int) (X tptp.nat) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.18/6.67 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X)) I2) Y) (@ _let_1 Y)))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat Y) X) (forall ((Z2 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z2) (@ (@ tptp.ord_less_nat Z2) X)) (@ (@ tptp.ord_less_eq_nat Z2) Y)))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z2 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z2) (@ (@ tptp.ord_less_nat X) Z2)) (@ (@ tptp.ord_less_eq_nat Y) Z2)))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Px)))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Sx)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N2) tptp.one_one_rat)))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N2) tptp.one_one_nat)))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N2) tptp.one_one_real)))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N2) tptp.one_one_int)))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N2) tptp.one_one_complex)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) (@ tptp.size_size_list_o Xs2))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) (@ tptp.size_size_list_int Xs2))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) J) (@ (@ tptp.nth_nat Xs2) J)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) J) (@ (@ tptp.nth_int Xs2) J)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (not (= I2 J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) J) (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_nat) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs2) I2) (@ (@ tptp.nth_nat Xs2) I2)) Xs2)))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs2) I2) (@ (@ tptp.nth_int Xs2) I2)) Xs2)))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)) Xs2)))
% 6.18/6.67 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) I2) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_o) (I2 tptp.nat) (X Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) I2) (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_int) (I2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) I2) (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (M tptp.num) (N2 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 N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.18/6.67 (assert (forall ((B tptp.real) (X tptp.nat) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (X tptp.nat) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (X tptp.nat) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.18/6.67 (assert (forall ((B tptp.int) (X tptp.nat) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (M tptp.num) (N2 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 N2))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (M tptp.num) (N2 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 N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) I2) X))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) I2) X))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) I2) X))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) I2) X))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_complex) (B3 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) B3) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 (@ tptp.set_complex2 Xs2)) (@ _let_1 B3)))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) B3) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 (@ tptp.set_real2 Xs2)) (@ _let_1 B3)))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_set_nat) (B3 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs2)) B3) (forall ((X2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (=> (@ _let_1 (@ tptp.set_set_nat2 Xs2)) (@ _let_1 B3)))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) B3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 (@ tptp.set_nat2 Xs2)) (@ _let_1 B3)))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) B3) (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs2)) (@ _let_1 B3)))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) B3) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 (@ tptp.set_int2 Xs2)) (@ _let_1 B3)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N2))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (I4 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (X7 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs2))) (=> (not (= I2 I4)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I2) X)) I4) X7) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I4) X7)) I2) X))))))
% 6.18/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) N2))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) N2))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) N2))) (let ((_let_2 (@ tptp.times_times_rat Y))) (=> (= (@ (@ tptp.times_times_rat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N2))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N2))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A) B)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N2) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (= (@ (@ tptp.times_times_rat _let_1) A) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B)) N2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N2)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_real (@ _let_1 M)) N2)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_int (@ _let_1 M)) N2)))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N2)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_complex) (A2 tptp.set_complex) (X tptp.complex) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (=> (@ (@ tptp.member_complex X) A2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) I2) X))) A2)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_real) (A2 tptp.set_real) (X tptp.real) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) A2) (=> (@ (@ tptp.member_real X) A2) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I2) X))) A2)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_set_nat) (A2 tptp.set_set_nat) (X tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs2)) A2) (=> (@ (@ tptp.member_set_nat X) A2) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs2) I2) X))) A2)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_nat) (A2 tptp.set_nat) (X tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2) (=> (@ (@ tptp.member_nat X) A2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I2) X))) A2)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X))) A2)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_int) (A2 tptp.set_int) (X tptp.int) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2) (=> (@ (@ tptp.member_int X) A2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I2) X))) A2)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.18/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)) tptp.one_one_complex))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)) tptp.one_one_real))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.power_power_rat Y) N2)) tptp.one_one_rat))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) N2)) tptp.one_one_nat))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) tptp.one_one_int))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) A)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) A)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) A)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) A)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) A)))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat A) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_complex A) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) (@ (@ tptp.nth_nat Ys) I3)))) (= Xs2 Ys)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) (@ (@ tptp.nth_VEBT_VEBT Ys) I3)))) (= Xs2 Ys)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) (@ (@ tptp.nth_o Ys) I3)))) (= Xs2 Ys)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) (@ (@ tptp.nth_int Ys) I3)))) (= Xs2 Ys)))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.nat)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_nat Xs) I5)))))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.vEBT_VEBT)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_VEBT_VEBT Xs) I5)))))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 Bool)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_o Xs) I5)))))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.int)) (@ (@ P I5) X4)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_int Xs) I5)))))))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.list_nat) (Z3 tptp.list_nat)) (= Y4 Z3)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I5) (@ (@ tptp.nth_nat Ys3) I5))))))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.list_VEBT_VEBT) (Z3 tptp.list_VEBT_VEBT)) (= Y4 Z3)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I5) (@ (@ tptp.nth_VEBT_VEBT Ys3) I5))))))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.list_o) (Z3 tptp.list_o)) (= Y4 Z3)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I5) (@ (@ tptp.nth_o Ys3) I5))))))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.list_int) (Z3 tptp.list_int)) (= Y4 Z3)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I5) (@ (@ tptp.nth_int Ys3) I5))))))))
% 6.18/6.67 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Uu tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) Uu) _let_1))))
% 6.18/6.67 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (N2 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) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (N2 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) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (N2 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) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (N2 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) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (N2 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 N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (N2 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 N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (N2 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 N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (N2 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 N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs2) N2)) (@ tptp.set_complex2 Xs2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs2) N2)) (@ tptp.set_real2 Xs2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_set_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ (@ tptp.member_set_nat (@ (@ tptp.nth_set_nat Xs2) N2)) (@ tptp.set_set_nat2 Xs2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs2) N2)) (@ tptp.set_nat2 Xs2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N2)) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs2) N2)) (@ tptp.set_o2 Xs2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs2) N2)) (@ tptp.set_int2 Xs2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ 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) N2))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ 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) N2))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_o Xs2) N2))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ 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) N2))))))
% 6.18/6.67 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I5) X))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I5) X))))))
% 6.18/6.67 (assert (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s3254054031482475050et_nat Xs2)) (= (@ (@ tptp.nth_set_nat Xs2) I5) X))))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I5) X))))))
% 6.18/6.67 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I5) X))))))
% 6.18/6.67 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I5) X))))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I5) X))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) I3)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ P X)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) I3)))) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ P X)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (X tptp.set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ P (@ (@ tptp.nth_set_nat Xs2) I3)))) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (@ P X)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I3)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P X)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I3)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X Bool)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I3)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I3)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P X)))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I5)))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I5)))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I5)))))))
% 6.18/6.67 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (@ P X2))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I5)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) N2) X))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N2) X))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs2)) (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs2) N2) X))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N2) X))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N2) X))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N2) X))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N2) X))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ (@ tptp.list_update_nat Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_nat Xs2) I2) X)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) X)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ (@ tptp.list_update_o Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_o Xs2) I2) X)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ (@ tptp.list_update_int Xs2) I2) X) Xs2) (= (@ (@ tptp.nth_int Xs2) I2) X)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) J)))))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_o) (X Bool) (J tptp.nat)) (let ((_let_1 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I2) X)) J) (and (=> _let_1 X) (=> (not _let_1) (@ (@ tptp.nth_o Xs2) J))))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (Xs2 tptp.list_int) (J tptp.nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I2) X)) J))) (let ((_let_2 (= I2 J))) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs2) J)))))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.18/6.67 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X) X)) X)) X))))
% 6.18/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X) X)) X)) X))))
% 6.18/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X) X)) X)) X))))
% 6.18/6.67 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.power_power_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X) X)) X)) X))))
% 6.18/6.67 (assert (forall ((X tptp.int)) (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X) X)) X)) X))))
% 6.18/6.67 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.18/6.67 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.18/6.67 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.18/6.67 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.18/6.67 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.18/6.67 (assert (forall ((A tptp.nat) (N2 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) N2)) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (N2 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) N2)) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (N2 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) N2)) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1))))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (N2 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) N2)) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 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 N2) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((X tptp.complex) (Y 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 X) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y 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 X) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y 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 X) Y)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)))))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y))))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y 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 X) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (N2 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) N2))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (N2 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) N2))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (N2 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) N2))) (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat (@ _let_2 N2)) _let_1)))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (N2 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) N2))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1)))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (N2 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) N2))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1)))))))
% 6.18/6.67 (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)))))))))))
% 6.18/6.67 (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))))))))))
% 6.18/6.67 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 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) N2))) (=> (@ (@ 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 N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) 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))))))))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((Y2 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X2)) (@ tptp.some_nat Y2)))))
% 6.18/6.67 (assert (forall ((X 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 X) _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) X) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 6.18/6.67 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X 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 X) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ 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)))))))))))))
% 6.18/6.67 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N2) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M2) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))))
% 6.18/6.67 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N2))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y 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)) X)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y 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)) X)) Y)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2)))))))
% 6.18/6.67 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X 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)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList) Summary)))))
% 6.18/6.67 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N2)) (= M N2))))
% 6.18/6.67 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.18/6.67 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y22)) (= X22 Y22))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit0 N2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ tptp.suc (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N2)) K))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat I2) N2) (= (@ _let_1 (@ _let_1 I2)) I2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N2)) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 6.18/6.67 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N2)))))
% 6.18/6.67 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N2) N2)))
% 6.18/6.67 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.18/6.67 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.18/6.67 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.18/6.67 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.18/6.67 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N2)))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))))))
% 6.18/6.67 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ 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)))))))))
% 6.18/6.67 (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)))))))))
% 6.18/6.67 (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)))))))))
% 6.18/6.67 (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)))))))))
% 6.18/6.67 (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)))))))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) _let_1) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.one_one_Code_integer) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K)))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)))
% 6.18/6.67 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ tptp.suc J))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N2) M)) M) (@ (@ tptp.ord_max_nat N2) M))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N2)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N2) Q2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q2))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N2)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N2) Q2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q2))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I2 tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I2))))))
% 6.18/6.67 (assert (forall ((J tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N2)) K))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N2) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 M))))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M))))))
% 6.18/6.67 (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))))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) M)))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N2) L2)))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ _let_1 N2))))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N2) K)) (= M N2)))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.minus_minus_nat M) N2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M)) N2) M)))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) N2) M)))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N2)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N2) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N2))) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ tptp.suc M))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_nat M) N2)))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat M) N2)) M))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) J))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.minus_minus_nat J) I2) K) (= J (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2)))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))))
% 6.18/6.67 (assert (forall ((J tptp.nat) (K tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I2) K)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N2)))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I2) K))))))
% 6.18/6.67 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M) N2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.18/6.67 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.18/6.67 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.18/6.67 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.18/6.67 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P M3)))))) (@ P N2))))
% 6.18/6.67 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ P M3))) (@ P N3))) (@ P N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.18/6.67 (assert (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) M) (not (= M N2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.18/6.67 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (exists ((X3 tptp.nat)) (and (@ P X3) (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) X3)))))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= M N2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) N2)))
% 6.18/6.67 (assert (forall ((X tptp.char) (Y tptp.char)) (=> (not (= (@ tptp.size_size_char X) (@ tptp.size_size_char Y))) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X) (@ tptp.size_size_list_o Y))) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X)) _let_1)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X)) _let_1)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y) X)) _let_1)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X)) _let_1)))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N2 M))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I3 tptp.nat)) (=> (= J (@ tptp.suc I3)) (@ P I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ P (@ tptp.suc I3)) (@ P I3)))) (@ P I2))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I3 tptp.nat)) (@ (@ P I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I3))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I2) J))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N2))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) M) (exists ((M4 tptp.nat)) (and (= M (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N2) M4))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (and (@ P N2) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N2) (@ P I5)))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (or (@ _let_1 N2) (= M N2))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (or (@ P N2) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) N2) (@ P I5)))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N2)) (=> (not (@ _let_1 N2)) (= M N2))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N2) (=> (not (= _let_1 N2)) (@ (@ tptp.ord_less_nat _let_1) N2))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (=> (not (= K (@ tptp.suc I2))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.18/6.67 (assert (forall ((X tptp.complex) (Y 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 X) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y 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 X) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y 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 X) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)))))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y 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 X) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (forall ((X3 tptp.nat)) (@ (@ R X3) X3)) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y5) (=> (@ (@ R Y5) Z4) (@ _let_1 Z4))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M) N2)))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N2))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M3)) N3) (@ P M3))) (@ P N3))) (@ P N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N2) (= M _let_1)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M5) (exists ((M2 tptp.nat)) (= M5 (@ tptp.suc M2))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N2)) (= M _let_1)))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N2)))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J tptp.nat)) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (@ (@ tptp.ord_less_nat (@ F I3)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (not (= M N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N) (= M6 N)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (not (= M6 N))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) K) (@ (@ tptp.ord_less_nat I2) K))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat K) L2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) I2))))
% 6.18/6.67 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I2)) I2))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (L2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L2) (=> (= (@ (@ tptp.plus_plus_nat M) L2) (@ (@ tptp.plus_plus_nat K) N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (not (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (@ (@ tptp.ord_less_eq_nat K) N2)))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M) N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M6) K3))))))
% 6.18/6.67 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.18/6.67 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) L2))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J)) U)) K))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)))
% 6.18/6.67 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D 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) D))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) _let_2)) (@ (@ tptp.power_power_real D) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 6.18/6.67 (assert (forall ((X 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 X) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) _let_2))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_real (@ F N2)) (@ F N5))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F N5))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_num (@ F N2)) (@ F N5))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F N5))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_int (@ F N2)) (@ F N5))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_int (@ F N5)) (@ F N2))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 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 N2) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N2))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 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 N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N2))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 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 N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N2))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 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 N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N2))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_int (@ F N2)) (@ F N5))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 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 N2) N5) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F N5))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 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 N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F N5))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 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 N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N5))))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 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 N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N5))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((N tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) __flatten_var_0))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)) (= N2 M)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P J) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I2))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P I2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (exists ((K2 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (forall ((Q3 tptp.nat)) (not (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.18/6.67 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N3) (@ (@ tptp.ord_less_nat (@ F M2)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.18/6.67 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat M) N2)))))
% 6.18/6.67 (assert (= tptp.suc (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))
% 6.18/6.67 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.18/6.67 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.18/6.67 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X 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 X) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X))) (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) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X Mi) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) 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)))))))))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((Deg tptp.nat) (X 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 X) _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 X) _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 X) 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)) X) (@ (@ (@ 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) X)) (@ 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)))))))))))))))))))))
% 6.18/6.67 (assert (forall ((Deg tptp.nat) (X 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 X) _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 X) _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 X) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ 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) X)) (@ 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)))))))))))))))
% 6.18/6.67 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X 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 X) _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 X) _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) X) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ 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)))))))))))))))
% 6.18/6.67 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X 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 X) _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 X) _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) X) (=> (@ (@ 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)) X) (@ (@ (@ 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)))))))))))))))))))))
% 6.18/6.67 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 6.18/6.67 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 6.18/6.67 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (M tptp.nat) (N2 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 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.18/6.67 (assert (forall ((R2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R2)) (@ (@ tptp.divide_divide_real A) R2)))))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.18/6.67 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y2) (= X2 Y2)))))
% 6.18/6.67 (assert (forall ((S3 tptp.set_real)) (=> (exists ((X5 tptp.real)) (@ (@ tptp.member_real X5) S3)) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real X3) Z5)))) (exists ((Y5 tptp.real)) (and (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Y5))) (forall ((Z5 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real X3) Z5))) (@ (@ tptp.ord_less_eq_real Y5) Z5)))))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X) N3))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real C) D)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int C) D)))))
% 6.18/6.67 (assert (= (lambda ((X2 tptp.complex)) X2) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.18/6.67 (assert (= (lambda ((X2 tptp.real)) X2) (@ tptp.times_times_real tptp.one_one_real)))
% 6.18/6.67 (assert (= (lambda ((X2 tptp.rat)) X2) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.18/6.67 (assert (= (lambda ((X2 tptp.nat)) X2) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.18/6.67 (assert (= (lambda ((X2 tptp.int)) X2) (@ tptp.times_times_int tptp.one_one_int)))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((Uu (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv tptp.option4927543243414619207at_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uu) tptp.none_P5556105721700978146at_nat) Uv) tptp.none_P5556105721700978146at_nat)))
% 6.18/6.67 (assert (forall ((Uu (-> tptp.num tptp.num tptp.num)) (Uv tptp.option_num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uu) tptp.none_num) Uv) tptp.none_num)))
% 6.18/6.67 (assert (forall ((Uu (-> tptp.nat tptp.nat tptp.nat)) (Uv tptp.option_nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uu) tptp.none_nat) Uv) tptp.none_nat)))
% 6.18/6.67 (assert (forall ((M tptp.real) (N2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_real M) N2)))))))
% 6.18/6.67 (assert (forall ((M tptp.rat) (N2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_rat M) N2)))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))))
% 6.18/6.67 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_int M) N2)))))))
% 6.18/6.67 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.18/6.67 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N2) (@ (@ tptp.ord_less_eq_real I2) (@ (@ tptp.minus_minus_real N2) K)))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N2) (@ (@ tptp.ord_less_eq_rat I2) (@ (@ tptp.minus_minus_rat N2) K)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N2) K)))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N2) K)))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N2) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N2) K)) J)))))))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N2) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N2) K)) J)))))))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K)) J)))))))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N2) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K)) J)))))))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) A)) B))))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real X) Y)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_rat X) Y)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C) D))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D))))
% 6.18/6.67 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D))))
% 6.18/6.67 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb) Y) (=> (=> (= 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 ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A3)) (forall ((B2 tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B2)) (not (= Y (@ tptp.some_P7363390416028606310at_nat (@ (@ X A3) B2)))))))))))))))
% 6.18/6.67 (assert (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (@ tptp.some_num V2))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A3 tptp.num)) (=> (= Xa2 (@ tptp.some_num A3)) (forall ((B2 tptp.num)) (=> (= Xb (@ tptp.some_num B2)) (not (= Y (@ tptp.some_num (@ (@ X A3) B2)))))))))))))))
% 6.18/6.67 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (@ tptp.some_nat V2))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A3)) (forall ((B2 tptp.nat)) (=> (= Xb (@ tptp.some_nat B2)) (not (= Y (@ tptp.some_nat (@ (@ X A3) B2)))))))))))))))
% 6.18/6.67 (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)))
% 6.18/6.67 (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)))
% 6.18/6.67 (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)))
% 6.18/6.67 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D 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)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D 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)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D 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)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D 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)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D 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)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 6.18/6.67 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D 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)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 6.18/6.67 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D 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)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D 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)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D 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)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D 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)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D 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)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 6.18/6.67 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D 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)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 6.18/6.67 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))
% 6.18/6.67 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.18/6.67 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))
% 6.18/6.67 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 6.18/6.67 (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)))
% 6.18/6.67 (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)))
% 6.18/6.67 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X))))
% 6.18/6.67 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((X 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 X) _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 X) _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)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat X) 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))))))))))))))))))
% 6.18/6.67 (assert (forall ((Ma tptp.nat) (X 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 X) _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 X) _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)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X))) (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) X)) (@ 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))))))))))))))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat Y2) X)))) tptp.bot_bot_set_nat)))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y2) (@ (@ tptp.ord_less_nat X) Y2)))) tptp.bot_bot_set_nat)))))
% 6.18/6.67 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (= (@ (@ tptp.ord_max_Code_integer A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.18/6.67 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.ord_max_Code_integer A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.18/6.67 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (and (@ (@ tptp.ord_le6747313008572928689nteger X) Z) (@ (@ tptp.ord_le6747313008572928689nteger Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X) Y)) Z) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (and (@ (@ tptp.ord_less_rat X) Z) (@ (@ tptp.ord_less_rat Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X) Y)) Z) (and (@ (@ tptp.ord_less_num X) Z) (@ (@ tptp.ord_less_num Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (and (@ (@ tptp.ord_less_nat X) Z) (@ (@ tptp.ord_less_nat Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y)) Z) (and (@ (@ tptp.ord_less_int X) Z) (@ (@ tptp.ord_less_int Y) Z)))))
% 6.18/6.67 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= (@ (@ tptp.ord_max_Code_integer A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_max_nat A) B))) (= (@ (@ tptp.ord_max_nat _let_1) B) _let_1))))
% 6.18/6.67 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) B) _let_1))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.ord_max_int A) B))) (= (@ (@ tptp.ord_max_int _let_1) B) _let_1))))
% 6.18/6.67 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.ord_max_Code_integer A) B))) (= (@ (@ tptp.ord_max_Code_integer _let_1) B) _let_1))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.18/6.67 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.18/6.67 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_max_Code_integer A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_max_int A) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A) A) A)))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= (@ tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (and (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ (@ tptp.ord_le3102999989581377725nteger C) A)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (= (@ (@ tptp.ord_max_Code_integer A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat B))) (let ((_let_2 (@ tptp.ord_max_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.18/6.67 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat B))) (let ((_let_2 (@ tptp.ord_ma741700101516333627d_enat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_max_int B))) (let ((_let_2 (@ tptp.ord_max_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.18/6.67 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_max_Code_integer B))) (let ((_let_2 (@ tptp.ord_max_Code_integer A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.18/6.67 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_max_nat B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (@ (@ tptp.ord_ma741700101516333627d_enat B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_max_int B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_max_Code_integer (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.ord_max_Code_integer B4) A4))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A))) (= (@ (@ tptp.ord_max_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_nat B) C))))))
% 6.18/6.67 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_ma741700101516333627d_enat A))) (= (@ (@ tptp.ord_ma741700101516333627d_enat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat B) C))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A))) (= (@ (@ tptp.ord_max_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_int B) C))))))
% 6.18/6.67 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_max_Code_integer A))) (= (@ (@ tptp.ord_max_Code_integer (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_Code_integer B) C))))))
% 6.18/6.67 (assert (forall ((C tptp.real)) (= (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C)) (@ tptp.times_times_real C))))
% 6.18/6.67 (assert (forall ((C tptp.rat)) (= (lambda ((X2 tptp.rat)) (@ (@ tptp.times_times_rat X2) C)) (@ tptp.times_times_rat C))))
% 6.18/6.67 (assert (forall ((C tptp.nat)) (= (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C)) (@ tptp.times_times_nat C))))
% 6.18/6.67 (assert (forall ((C tptp.int)) (= (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int X2) C)) (@ tptp.times_times_int C))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4) B4))))
% 6.18/6.67 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A4) B4) B4))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B4) B4))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B4) B4))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B4) B4))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B4) B4))))
% 6.18/6.67 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A4) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (= (@ (@ tptp.ord_max_rat A4) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (= (@ (@ tptp.ord_max_num A4) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= (@ (@ tptp.ord_max_nat A4) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= (@ (@ tptp.ord_max_int A4) B4) A4))))
% 6.18/6.67 (assert (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.18/6.67 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.ord_max_Code_integer A) B))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.18/6.67 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.18/6.67 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.ord_max_Code_integer A) B))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.18/6.67 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4)))))
% 6.18/6.67 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (= A4 (@ (@ tptp.ord_max_Code_integer A4) B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (= A4 (@ (@ tptp.ord_max_rat A4) B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (= A4 (@ (@ tptp.ord_max_num A4) B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (= A4 (@ (@ tptp.ord_max_nat A4) B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (= A4 (@ (@ tptp.ord_max_int A4) B4)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (not (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (not (@ (@ tptp.ord_le3102999989581377725nteger C) A)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 6.18/6.67 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A (@ (@ tptp.ord_max_Code_integer A) B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.18/6.67 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))))
% 6.18/6.67 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= A (@ (@ tptp.ord_max_Code_integer A) B)))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.18/6.67 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (D tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat D) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat C) D)) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.18/6.67 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger D) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer C) D)) (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.18/6.67 (assert (forall ((C tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D)) (@ (@ tptp.ord_max_rat A) B))))))
% 6.18/6.67 (assert (forall ((C tptp.num) (A tptp.num) (D tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C) A) (=> (@ (@ tptp.ord_less_eq_num D) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C) D)) (@ (@ tptp.ord_max_num A) B))))))
% 6.18/6.67 (assert (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D)) (@ (@ tptp.ord_max_nat A) B))))))
% 6.18/6.67 (assert (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D)) (@ (@ tptp.ord_max_int A) B))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B4 tptp.extended_enat) (A4 tptp.extended_enat)) (and (= A4 (@ (@ tptp.ord_ma741700101516333627d_enat A4) B4)) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (and (= A4 (@ (@ tptp.ord_max_Code_integer A4) B4)) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (= A4 (@ (@ tptp.ord_max_real A4) B4)) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (and (= A4 (@ (@ tptp.ord_max_rat A4) B4)) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (= A4 (@ (@ tptp.ord_max_num A4) B4)) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (= A4 (@ (@ tptp.ord_max_nat A4) B4)) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (= A4 (@ (@ tptp.ord_max_int A4) B4)) (not (= A4 B4))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (not (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (not (@ (@ tptp.ord_le6747313008572928689nteger C) A)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.18/6.67 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) Xs) (@ (@ tptp.ord_less_nat X2) Y2) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) Xs) (=> (@ (@ tptp.ord_less_nat X2) Z2) (@ (@ tptp.ord_less_eq_nat Y2) Z2))))))))
% 6.18/6.67 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) Xs) (@ (@ tptp.ord_less_nat Y2) X2) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member_nat Z2) Xs) (=> (@ (@ tptp.ord_less_nat Z2) X2) (@ (@ tptp.ord_less_eq_nat Z2) Y2))))))))
% 6.18/6.67 (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)))
% 6.18/6.67 (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)))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N2)) tptp.bot_bot_set_nat)))
% 6.18/6.67 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)))
% 6.18/6.67 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)))
% 6.18/6.67 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X) tptp.bot_bot_set_real) X)))
% 6.18/6.67 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)))
% 6.18/6.67 (assert (forall ((X tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) tptp.bot_bo4199563552545308370d_enat) X)))
% 6.18/6.67 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)))
% 6.18/6.67 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)))
% 6.18/6.67 (assert (forall ((X tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X) X)))
% 6.18/6.67 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)))
% 6.18/6.67 (assert (forall ((X tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.bot_bo4199563552545308370d_enat) X) X)))
% 6.18/6.67 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 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 N2))))))
% 6.18/6.67 (assert (forall ((M tptp.nat) (N2 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 N2)))))))
% 6.18/6.67 (assert (forall ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) X)))
% 6.18/6.67 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) X)))
% 6.18/6.67 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)))
% 6.18/6.67 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 6.18/6.67 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 6.18/6.67 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.18/6.67 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_le211207098394363844omplex A2) B3))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_real A2) B3))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B3))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_nat A2) B3))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_set_int A2) B3)))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= A2 B3)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) tptp.bot_bot_set_int) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) tptp.bot_bot_set_real) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) tptp.bot_bot_set_nat) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A2) tptp.bot_bot_set_int)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real tptp.bot_bot_set_real) A2) tptp.bot_bot_set_real)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A2) tptp.bot_bot_set_nat)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) A2) tptp.bot_bot_set_int)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) A2) tptp.bot_bot_set_real)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) A2) tptp.bot_bot_set_nat)))
% 6.18/6.67 (assert (= tptp.minus_minus_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.minus_minus_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A5))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) B5)))))))
% 6.18/6.67 (assert (= tptp.minus_1052850069191792384nt_int (lambda ((A5 tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (@ (@ tptp.minus_711738161318947805_int_o (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X2) A5))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X2) B5)))))))
% 6.18/6.67 (assert (= tptp.minus_811609699411566653omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (@ tptp.collect_complex (@ (@ tptp.minus_8727706125548526216plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A5))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) B5)))))))
% 6.18/6.67 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.minus_6910147592129066416_nat_o (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) A5))) (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) B5)))))))
% 6.18/6.67 (assert (= tptp.minus_minus_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A5))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) B5)))))))
% 6.18/6.67 (assert (= tptp.minus_minus_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A5))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) B5)))))))
% 6.18/6.67 (assert (= tptp.minus_minus_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 6.18/6.67 (assert (= tptp.minus_1052850069191792384nt_int (lambda ((A5 tptp.set_Pr958786334691620121nt_int) (B5 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int X2))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 6.18/6.67 (assert (= tptp.minus_811609699411566653omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 6.18/6.67 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 6.18/6.67 (assert (= tptp.minus_minus_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 6.18/6.67 (assert (= tptp.minus_minus_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (and (@ _let_1 A5) (not (@ _let_1 B5)))))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)) (not (@ _let_1 B3))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)) (@ _let_1 A2)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A2) B3) (exists ((B2 tptp.complex)) (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B3) A2))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B3) (exists ((B2 tptp.real)) (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B3) A2))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A2) B3) (exists ((B2 tptp.set_nat)) (@ (@ tptp.member_set_nat B2) (@ (@ tptp.minus_2163939370556025621et_nat B3) A2))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (exists ((B2 tptp.int)) (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B3) A2))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (exists ((B2 tptp.nat)) (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B3) A2))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat B) A) (not (= B A))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num B) A) (not (= B A))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat B) A) (not (= B A))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (not (= B A))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.set_int) (Z3 tptp.set_int)) (= Y4 Z3)) (lambda ((X2 tptp.set_int) (Y2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y2) (@ (@ tptp.ord_less_eq_set_int Y2) X2)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.rat) (Z3 tptp.rat)) (= Y4 Z3)) (lambda ((X2 tptp.rat) (Y2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y2) (@ (@ tptp.ord_less_eq_rat Y2) X2)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.num) (Z3 tptp.num)) (= Y4 Z3)) (lambda ((X2 tptp.num) (Y2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y2) (@ (@ tptp.ord_less_eq_num Y2) X2)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.nat) (Z3 tptp.nat)) (= Y4 Z3)) (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat Y2) X2)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.int) (Z3 tptp.int)) (= Y4 Z3)) (lambda ((X2 tptp.int) (Y2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y2) (@ (@ tptp.ord_less_eq_int Y2) X2)))))
% 6.18/6.67 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ (@ tptp.ord_less_eq_set_int A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ (@ tptp.ord_less_eq_num A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))))
% 6.18/6.67 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 6.18/6.67 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 6.18/6.67 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 6.18/6.67 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.set_int) (Z3 tptp.set_int)) (= Y4 Z3)) (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B4) A4) (@ (@ tptp.ord_less_eq_set_int A4) B4)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.rat) (Z3 tptp.rat)) (= Y4 Z3)) (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A4) (@ (@ tptp.ord_less_eq_rat A4) B4)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.num) (Z3 tptp.num)) (= Y4 Z3)) (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (@ (@ tptp.ord_less_eq_num A4) B4)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.nat) (Z3 tptp.nat)) (= Y4 Z3)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (@ (@ tptp.ord_less_eq_nat A4) B4)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.int) (Z3 tptp.int)) (= Y4 Z3)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (@ (@ tptp.ord_less_eq_int A4) B4)))))
% 6.18/6.67 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= A B)))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.18/6.67 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.set_int) (Z3 tptp.set_int)) (= Y4 Z3)) (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B4) (@ (@ tptp.ord_less_eq_set_int B4) A4)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.rat) (Z3 tptp.rat)) (= Y4 Z3)) (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B4) (@ (@ tptp.ord_less_eq_rat B4) A4)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.num) (Z3 tptp.num)) (= Y4 Z3)) (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (@ (@ tptp.ord_less_eq_num B4) A4)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.nat) (Z3 tptp.nat)) (= Y4 Z3)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ tptp.ord_less_eq_nat B4) A4)))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.int) (Z3 tptp.int)) (= Y4 Z3)) (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ tptp.ord_less_eq_int B4) A4)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.18/6.67 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.ord_less_eq_set_int X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.real)) (exists ((Y5 tptp.real)) (@ (@ tptp.ord_less_real Y5) X))))
% 6.18/6.67 (assert (forall ((X tptp.rat)) (exists ((Y5 tptp.rat)) (@ (@ tptp.ord_less_rat Y5) X))))
% 6.18/6.67 (assert (forall ((X tptp.int)) (exists ((Y5 tptp.int)) (@ (@ tptp.ord_less_int Y5) X))))
% 6.18/6.67 (assert (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X) X_1))))
% 6.18/6.67 (assert (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_1))))
% 6.18/6.67 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 6.18/6.67 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real X) Z4) (@ (@ tptp.ord_less_real Z4) Y))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (exists ((Z4 tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z4) (@ (@ tptp.ord_less_rat Z4) Y))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y3) X3) (@ P Y3))) (@ P X3))) (@ P A))))
% 6.18/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X)) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.18/6.67 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.18/6.67 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.18/6.67 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.18/6.67 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N tptp.nat)) (and (@ P3 N) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (not (@ P3 M6)))))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.real)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.rat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.num)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.int)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (or (@ (@ tptp.ord_less_real Y) X) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (or (@ (@ tptp.ord_less_rat Y) X) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 6.18/6.67 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.18/6.67 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_num Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real X) X))))
% 6.18/6.67 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 6.18/6.67 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 6.18/6.67 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 6.18/6.67 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real Y) X) P))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) X) P))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y) (@ (@ tptp.ord_less_real Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y) (@ (@ tptp.ord_less_rat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= Y X)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= Y X)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat) (C2 tptp.set_nat) (D3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C2) (=> (@ (@ tptp.ord_less_eq_set_nat D3) B3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_set_nat C2) D3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (C2 tptp.set_int) (D3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C2) (=> (@ (@ tptp.ord_less_eq_set_int D3) B3) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_set_int C2) D3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B3)) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (= (@ (@ tptp.minus_minus_set_nat B3) (@ (@ tptp.minus_minus_set_nat C2) A2)) A2)))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C2) (= (@ (@ tptp.minus_minus_set_int B3) (@ (@ tptp.minus_minus_set_int C2) A2)) A2)))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int B3) A2))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (not (@ (@ tptp.ord_less_eq_set_int B3) A2)))))))
% 6.18/6.67 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.18/6.67 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (forall ((X2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (@ (@ tptp.ord_less_eq_set_int B3) A2))))
% 6.18/6.67 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (not (= A5 B5))))))
% 6.18/6.67 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (forall ((T2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.18/6.67 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (forall ((T2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 6.18/6.67 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int Q)))))
% 6.18/6.67 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X3 tptp.complex)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)))))
% 6.18/6.67 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 6.18/6.67 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 6.18/6.67 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C2) (@ _let_1 C2))))))
% 6.18/6.67 (assert (= (lambda ((Y4 tptp.set_int) (Z3 tptp.set_int)) (= Y4 Z3)) (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (@ (@ tptp.ord_less_eq_set_int B5) A5)))))
% 6.18/6.67 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int Q)) (forall ((X2 tptp.product_prod_int_int)) (=> (@ P X2) (@ Q X2))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)) (forall ((X2 tptp.complex)) (=> (@ P X2) (@ Q X2))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)) (forall ((X2 tptp.set_nat)) (=> (@ P X2) (@ Q X2))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X2 tptp.nat)) (=> (@ P X2) (@ Q X2))))))
% 6.18/6.67 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X2 tptp.int)) (=> (@ P X2) (@ Q X2))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C2) (@ _let_1 C2))))))
% 6.18/6.67 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (not (@ (@ tptp.ord_less_eq_set_int B5) A5))))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_set_int B3) C2) (@ (@ tptp.ord_less_set_int A2) C2)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A5) B5) (= A5 B5)))))
% 6.18/6.67 (assert (= tptp.bot_bo1796632182523588997nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) false))))
% 6.18/6.67 (assert (= tptp.bot_bot_set_complex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) false))))
% 6.18/6.67 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) false))))
% 6.18/6.67 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) false))))
% 6.18/6.67 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X2 tptp.int)) false))))
% 6.18/6.67 (assert (= tptp.bot_bot_set_real (@ tptp.collect_real (lambda ((X2 tptp.real)) false))))
% 6.18/6.67 (assert (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (and (@ (@ tptp.member5262025264175285858nt_int X2) A2) (@ P X2))))) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.complex Bool))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X2) A2) (@ P X2))))) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) A2)))
% 6.18/6.67 (assert (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) A2)))
% 6.18/6.67 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A5))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) B5))))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A5))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) B5))))))
% 6.18/6.67 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) A5))) (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) B5))))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A5))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) B5))))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A5))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) B5))))))
% 6.18/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (not (@ (@ tptp.ord_less_real X) Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (not (@ (@ tptp.ord_less_set_int X) Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (not (@ (@ tptp.ord_less_rat X) Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 6.18/6.67 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A) B)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A) B)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_num A) B)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (= A B)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (= A B)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X) Y)) (= (@ (@ tptp.ord_less_eq_set_int X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (not (@ (@ tptp.ord_less_set_int X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.18/6.67 (assert (forall ((Z tptp.real) (Y tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X3) (@ (@ tptp.ord_less_eq_real Y) X3))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 6.18/6.67 (assert (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X3) (@ (@ tptp.ord_less_eq_rat Y) X3))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 6.18/6.67 (assert (forall ((Y tptp.real) (Z tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y) (@ (@ tptp.ord_less_eq_real X3) Z))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 6.18/6.67 (assert (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (@ (@ tptp.ord_less_eq_rat X3) Z))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 6.18/6.67 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y2) (not (@ (@ tptp.ord_less_eq_real Y2) X2))))))
% 6.18/6.67 (assert (= tptp.ord_less_set_int (lambda ((X2 tptp.set_int) (Y2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y2) (not (@ (@ tptp.ord_less_eq_set_int Y2) X2))))))
% 6.18/6.67 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y2) (not (@ (@ tptp.ord_less_eq_rat Y2) X2))))))
% 6.18/6.67 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y2) (not (@ (@ tptp.ord_less_eq_num Y2) X2))))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y2) (not (@ (@ tptp.ord_less_eq_nat Y2) X2))))))
% 6.18/6.67 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y2) (not (@ (@ tptp.ord_less_eq_int Y2) X2))))))
% 6.18/6.67 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X)) (@ (@ tptp.ord_less_real X) Y))))
% 6.18/6.67 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.18/6.67 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))))
% 6.18/6.67 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 6.18/6.67 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A4) B4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (or (@ (@ tptp.ord_less_rat A4) B4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B4 tptp.num)) (or (@ (@ tptp.ord_less_num A4) B4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (or (@ (@ tptp.ord_less_nat A4) B4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B4) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B4) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (= A4 B4))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_set_int B) C) (@ (@ tptp.ord_less_set_int A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 6.18/6.67 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B4) (not (@ (@ tptp.ord_less_eq_real B4) A4))))))
% 6.18/6.67 (assert (= tptp.ord_less_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B4) (not (@ (@ tptp.ord_less_eq_set_int B4) A4))))))
% 6.18/6.67 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B4) (not (@ (@ tptp.ord_less_eq_rat B4) A4))))))
% 6.18/6.67 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B4) (not (@ (@ tptp.ord_less_eq_num B4) A4))))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B4) (not (@ (@ tptp.ord_less_eq_nat B4) A4))))))
% 6.18/6.67 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B4) (not (@ (@ tptp.ord_less_eq_int B4) A4))))))
% 6.18/6.67 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X) (@ (@ tptp.ord_less_eq_real Y) W2)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.18/6.67 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W2) (=> (@ (@ tptp.ord_less_rat W2) X) (@ (@ tptp.ord_less_eq_rat Y) W2)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) W2) (=> (@ (@ tptp.ord_less_real W2) Y) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W2) (=> (@ (@ tptp.ord_less_rat W2) Y) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_real (lambda ((B4 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B4) A4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_int (lambda ((B4 tptp.set_int) (A4 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B4) A4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (or (@ (@ tptp.ord_less_rat B4) A4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_num (lambda ((B4 tptp.num) (A4 tptp.num)) (or (@ (@ tptp.ord_less_num B4) A4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (or (@ (@ tptp.ord_less_nat B4) A4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_int (lambda ((B4 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B4) A4) (= A4 B4)))))
% 6.18/6.67 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_set_int (lambda ((B4 tptp.set_int) (A4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B4) A4) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A4) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (not (= A4 B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (= A4 B4))))))
% 6.18/6.67 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.18/6.67 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_real C) A)))))
% 6.18/6.67 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int C) B) (@ (@ tptp.ord_less_set_int C) A)))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_rat C) A)))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) B) (@ (@ tptp.ord_less_num C) A)))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A)))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_int C) A)))))
% 6.18/6.67 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B4) A4) (not (@ (@ tptp.ord_less_eq_real A4) B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_set_int (lambda ((B4 tptp.set_int) (A4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B4) A4) (not (@ (@ tptp.ord_less_eq_set_int A4) B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B4) A4) (not (@ (@ tptp.ord_less_eq_rat A4) B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B4) A4) (not (@ (@ tptp.ord_less_eq_num A4) B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B4) A4) (not (@ (@ tptp.ord_less_eq_nat A4) B4))))))
% 6.18/6.67 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B4) A4) (not (@ (@ tptp.ord_less_eq_int A4) B4))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.18/6.67 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.18/6.67 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.18/6.67 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (@ (@ tptp.ord_less_eq_set_int B) A))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.18/6.67 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y2) (= X2 Y2)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_set_int (lambda ((X2 tptp.set_int) (Y2 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X2) Y2) (= X2 Y2)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y2 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y2) (= X2 Y2)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_num (lambda ((X2 tptp.num) (Y2 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y2) (= X2 Y2)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y2) (= X2 Y2)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y2) (= X2 Y2)))))
% 6.18/6.67 (assert (= tptp.ord_less_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X2) Y2) (not (= X2 Y2))))))
% 6.18/6.67 (assert (= tptp.ord_less_set_int (lambda ((X2 tptp.set_int) (Y2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X2) Y2) (not (= X2 Y2))))))
% 6.18/6.67 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y2) (not (= X2 Y2))))))
% 6.18/6.67 (assert (= tptp.ord_less_num (lambda ((X2 tptp.num) (Y2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X2) Y2) (not (= X2 Y2))))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y2) (not (= X2 Y2))))))
% 6.18/6.67 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y2) (not (= X2 Y2))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_real Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.18/6.67 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_int A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ (@ tptp.ord_less_set_int A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z) (@ (@ tptp.ord_less_set_int X) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y5) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y5) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y5) (@ (@ tptp.ord_less_real (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y5) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_real Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_rat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (or (@ (@ tptp.ord_less_set_int X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 6.18/6.67 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 6.18/6.67 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.18/6.67 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.18/6.67 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.18/6.67 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.18/6.67 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.18/6.67 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.18/6.67 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.18/6.67 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.18/6.67 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.18/6.67 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.18/6.67 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.18/6.67 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.18/6.67 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4)) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_max_Code_integer (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le3102999989581377725nteger A4) B4)) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_max_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A4) B4)) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B4)) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B4)) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B4)) B4) A4))))
% 6.18/6.67 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B4)) B4) A4))))
% 6.18/6.67 (assert (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) X) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y) X))))
% 6.18/6.67 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) X) (= (@ (@ tptp.ord_max_Code_integer X) Y) X))))
% 6.18/6.67 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.ord_max_set_int X) Y) X))))
% 6.18/6.67 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_max_rat X) Y) X))))
% 6.18/6.67 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_max_num X) Y) X))))
% 6.18/6.67 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))))
% 6.18/6.67 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))))
% 6.18/6.67 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y) Y))))
% 6.18/6.67 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (= (@ (@ tptp.ord_max_Code_integer X) Y) Y))))
% 6.18/6.67 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (@ (@ tptp.ord_max_set_int X) Y) Y))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.ord_max_rat X) Y) Y))))
% 6.18/6.67 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (@ (@ tptp.ord_max_num X) Y) Y))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.18/6.67 (assert (forall ((X5 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X5) X_1))))
% 6.18/6.67 (assert (forall ((X5 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X5) X_1))))
% 6.18/6.67 (assert (forall ((X5 tptp.real)) (exists ((Y5 tptp.real)) (@ (@ tptp.ord_less_real Y5) X5))))
% 6.18/6.67 (assert (forall ((X5 tptp.rat)) (exists ((Y5 tptp.rat)) (@ (@ tptp.ord_less_rat Y5) X5))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (= tptp.times_times_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real B4) A4))))
% 6.18/6.67 (assert (= tptp.times_times_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.times_times_rat B4) A4))))
% 6.18/6.67 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.times_times_nat B4) A4))))
% 6.18/6.67 (assert (= tptp.times_times_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.times_times_int B4) A4))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_real I2) K) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_rat I2) K) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_nat I2) K) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (= K L2)) (= (@ (@ tptp.plus_plus_int I2) K) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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))))))))
% 6.18/6.67 (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))))))))
% 6.18/6.67 (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))))))))
% 6.18/6.67 (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))))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real B4) A4))))
% 6.18/6.67 (assert (= tptp.plus_plus_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat B4) A4))))
% 6.18/6.67 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A4))))
% 6.18/6.67 (assert (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int B4) A4))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 6.18/6.67 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 6.18/6.67 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 6.18/6.67 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 6.18/6.67 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 6.18/6.67 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (= A B) (= C D)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (= A B) (= C D)))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (= K L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (exists ((C4 tptp.nat)) (= B4 (@ (@ tptp.plus_plus_nat A4) C4))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (= K L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (= K L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (= K L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (= K L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real C) D)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C) D)))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D)))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.18/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex Y) W)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) W)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) W)))))
% 6.18/6.67 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W)) (@ (@ tptp.times_times_complex Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W)) (@ (@ tptp.times_times_real Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W)) (@ (@ tptp.times_times_rat Y) Z)))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z)) (@ (@ tptp.plus_plus_real Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z)) (@ (@ tptp.plus_plus_rat Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Z)) (@ (@ tptp.plus_p5714425477246183910nteger Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger X))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer Y) Z)) (@ (@ tptp.ord_max_Code_integer (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.18/6.67 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) Z)) (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X) Z)) (@ (@ tptp.minus_minus_real Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X) Z)) (@ (@ tptp.minus_minus_rat Y) Z)))))
% 6.18/6.67 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y) Z)))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.18/6.67 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.18/6.67 (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))))))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (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)))))))
% 6.18/6.67 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X 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 X) _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)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))))
% 6.18/6.67 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X 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 X) _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) S2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.18/6.67 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X 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 X) _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)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.18/6.67 (assert (forall ((L2 tptp.num) (R2 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) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R2))))))))))
% 6.18/6.67 (assert (forall ((L2 tptp.num) (R2 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) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_int L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R2))))))))))
% 6.18/6.67 (assert (forall ((L2 tptp.num) (R2 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) R2)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R2))))))))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N2)) X))))
% 6.18/6.67 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A3 Bool)) (=> (exists ((Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))))) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (=> (exists ((Va2 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va2)))) (not (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ 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)) (= X (@ (@ (@ (@ 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) (Va2 tptp.nat) (TreeList3 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 Va2)))) (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 TreeList3))) (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))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ 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)))))))))))))))))))))))))))))
% 6.18/6.67 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (forall ((Uu2 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uu2) B2)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X (@ (@ 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)) (= X (@ (@ (@ (@ 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)) (= X (@ (@ (@ (@ 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)) (= X (@ (@ (@ (@ 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) (Va2 tptp.nat) (TreeList3 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 Va2)))) (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 TreeList3))) (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))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ 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))))))))))))))))))))))))))))
% 6.18/6.67 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) __flatten_var_0))))
% 6.18/6.67 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A4) tptp.one_one_int)) __flatten_var_0))))
% 6.18/6.67 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (=> (= Xa2 tptp.zero_zero_nat) (not (= Y (@ (@ tptp.vEBT_Leaf false) B2)))))) (=> (forall ((A3 Bool)) (=> (exists ((B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (= Y (@ (@ tptp.vEBT_Leaf A3) false)))))) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_1) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc N3)))) (not (= Y _let_1)))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (=> (= X _let_1) (not (= Y _let_1))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) 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.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= Xa2 Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa2))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= Xa2 Ma2))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi2))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (and _let_9 _let_16))) (let ((_let_24 (or (@ (@ tptp.ord_less_nat Xa2) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (=> (= X _let_2) (not (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))))))))))))))))))))))))))))))))))))))))
% 6.18/6.67 (assert (= tptp.vEBT_VEBT_low (lambda ((X2 tptp.nat) (N tptp.nat)) (@ (@ tptp.modulo_modulo_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N2)) X))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.18/6.67 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A4 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A4) B4))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (=> (= N2 tptp.one_one_nat) (exists ((A3 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B2)))))))
% 6.18/6.67 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N2)) N2))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))
% 6.18/6.67 (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))))
% 6.18/6.67 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 6.18/6.67 (assert (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))))
% 6.18/6.67 (assert (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y222 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.18/6.67 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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))))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (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)))))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.18/6.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.18/6.67 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.18/6.67 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.18/6.67 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.18/6.67 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.18/6.67 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.18/6.67 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.18/6.67 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.18/6.67 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.18/6.67 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.18/6.67 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.18/6.67 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.18/6.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.18/6.67 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.18/6.67 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.18/6.67 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.18/6.68 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.18/6.68 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N2) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N2) K)) (or (= M N2) (= K tptp.zero_zero_nat)))))
% 6.18/6.68 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= M N2) (= K tptp.zero_zero_nat))))))
% 6.18/6.68 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat M) N2) M))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.18/6.68 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.18/6.68 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.18/6.68 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.18/6.68 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.18/6.68 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.18/6.68 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.18/6.68 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N2)) tptp.zero_zero_rat)))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N2)) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N2)) tptp.zero_zero_real)))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N2)) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N2)) tptp.zero_zero_complex)))
% 6.18/6.68 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.18/6.68 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.18/6.68 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.18/6.68 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.18/6.68 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.zero_z3403309356797280102nteger) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) _let_1) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.18/6.68 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (@ _let_1 M) (@ _let_1 N2))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (= M _let_1) (= N2 _let_1))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N2) _let_1) (and (= M _let_1) (= N2 _let_1))))))
% 6.18/6.68 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.18/6.68 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.18/6.68 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N2) _let_1))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M) _let_1) (or (= M tptp.zero_zero_nat) (= X _let_1))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))))
% 6.18/6.68 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)))) (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) N2)))))))))
% 6.18/6.68 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N2) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.18/6.68 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.18/6.68 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) M)) N2) M))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N2)) N2) M))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) K)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.18/6.68 (assert (forall ((K tptp.nat) (N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N2)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N2) K)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((B tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.18/6.68 (assert (forall ((B tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.18/6.68 (assert (forall ((B tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.18/6.68 (assert (forall ((B tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 6.18/6.68 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.18/6.68 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.18/6.68 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.18/6.68 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.18/6.68 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.18/6.68 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))))
% 6.18/6.68 (assert (forall ((K tptp.num) (N2 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) N2))) _let_1) tptp.one_one_nat)))))
% 6.18/6.68 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.18/6.68 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.18/6.68 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.18/6.68 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y 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 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X Y))))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y 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 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X Y))))))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (Y 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 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X Y))))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y 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 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X Y))))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((B tptp.real) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.18/6.68 (assert (forall ((B tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.18/6.68 (assert (forall ((B tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.18/6.68 (assert (forall ((B tptp.int) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (let ((_let_3 (= _let_1 N2))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))))
% 6.18/6.68 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.18/6.68 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 6.18/6.68 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q3))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.68 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D4)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) Deg3))))))))
% 6.18/6.68 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.18/6.68 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) B))))
% 6.18/6.68 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) X3)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S)) X3)))))))))
% 6.18/6.68 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((X 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 (= X (@ (@ 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 (= X (@ (@ 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)) (A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A3)) (@ tptp.some_P7363390416028606310at_nat B2)))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B2 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A3)) (@ tptp.some_nat B2)))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc1193250871479095198on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A3 tptp.num) (B2 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A3)) (@ tptp.some_num B2)))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ 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 (= X (@ (@ 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) (Y5 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X3)) (@ tptp.some_P7363390416028606310at_nat Y5)))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc2233624965454879586on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat Bool)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat Bool)) (V2 tptp.nat)) (not (= X (@ (@ 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) (Y5 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X3)) (@ tptp.some_nat Y5)))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc7036089656553540234on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num Bool)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num Bool)) (V2 tptp.num)) (not (= X (@ (@ 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) (Y5 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X3)) (@ tptp.some_num Y5)))))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))))
% 6.18/6.68 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.18/6.68 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (= (@ (@ tptp.vEBT_vebt_delete (@ _let_1 B)) (@ tptp.suc tptp.zero_zero_nat)) (@ _let_1 false)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N2) tptp.zero_zero_rat))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N2) tptp.zero_zero_real))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N2) tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2) tptp.zero_zero_complex))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (C tptp.nat) (A6 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A6) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A6) B6)) C))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A6) B6)) C))))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A6 tptp.code_integer) (B tptp.code_integer) (B6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A6) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B6) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A6) B6)) C))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (C tptp.nat) (A6 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A6) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A6) B6)) C))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A6) B6)) C))))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A6 tptp.code_integer) (B tptp.code_integer) (B6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A6) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B6) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A6) B6)) C))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A6) B6)) C))))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A6 tptp.code_integer) (B tptp.code_integer) (B6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A6) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B6) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A6) B6)) C))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N2)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N2)) B))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N2)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N2)) B))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N2)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) B))))
% 6.18/6.68 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N2))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.18/6.68 (assert (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) M)))
% 6.18/6.68 (assert (forall ((X 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) X))) (let ((_let_4 (= X tptp.one_one_nat))) (let ((_let_5 (= X 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))))))))))))
% 6.18/6.68 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.18/6.68 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N2)))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N2)))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N2)))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N2)))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N2)))))
% 6.18/6.68 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))))
% 6.18/6.68 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))))
% 6.18/6.68 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))))
% 6.18/6.68 (assert (forall ((M tptp.num) (N2 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 N2)) _let_1)))))
% 6.18/6.68 (assert (forall ((M tptp.num) (N2 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 N2)) _let_1)))))
% 6.18/6.68 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger tptp.one))) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.18/6.68 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.18/6.68 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.18/6.68 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.18/6.68 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.18/6.68 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.18/6.68 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.18/6.68 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (= (lambda ((Y4 tptp.complex) (Z3 tptp.complex)) (= Y4 Z3)) (lambda ((A4 tptp.complex) (B4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A4) B4) tptp.zero_zero_complex))))
% 6.18/6.68 (assert (= (lambda ((Y4 tptp.real) (Z3 tptp.real)) (= Y4 Z3)) (lambda ((A4 tptp.real) (B4 tptp.real)) (= (@ (@ tptp.minus_minus_real A4) B4) tptp.zero_zero_real))))
% 6.18/6.68 (assert (= (lambda ((Y4 tptp.rat) (Z3 tptp.rat)) (= Y4 Z3)) (lambda ((A4 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A4) B4) tptp.zero_zero_rat))))
% 6.18/6.68 (assert (= (lambda ((Y4 tptp.int) (Z3 tptp.int)) (= Y4 Z3)) (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.minus_minus_int A4) B4) tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N2) tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat)))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int)))))
% 6.18/6.68 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex)))))
% 6.18/6.68 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.18/6.68 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 6.18/6.68 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 6.18/6.68 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.18/6.68 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va2 tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va2))))))))))
% 6.18/6.68 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 6.18/6.68 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.18/6.68 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 6.18/6.68 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N2)))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y5 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y5))) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ P X3) Y5) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y5)))) (@ (@ P M) N2))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.18/6.68 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M2 tptp.nat)) (= N2 (@ tptp.suc M2))))))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P M3))))))) (@ P N2)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)))
% 6.18/6.68 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (= M N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N2) M) tptp.zero_zero_nat) (= M N2)))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N2)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I5)) J3)) (@ P J3))))))))))
% 6.18/6.68 (assert (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (= A B))))))))
% 6.18/6.68 (assert (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N2) (@ (@ tptp.power_power_rat B) N2)) (= A B))))))))
% 6.18/6.68 (assert (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (= A B))))))))
% 6.18/6.68 (assert (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (= A B))))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N2) (@ (@ tptp.power_power_rat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.18/6.68 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.18/6.68 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.18/6.68 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.18/6.68 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.18/6.68 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2)) X3)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2)) X3)))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) X3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ 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 (= X (@ (@ 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 (= X (@ (@ 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) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X3)))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (B2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B2 Bool) (N3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) (@ tptp.suc (@ tptp.suc N3)))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) Uu2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry)) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X3)))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S)) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S)) X3)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2)) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X3)))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B2)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw2 Bool) (N3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N3))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2)) Va3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve tptp.nat)) (not (= X (@ (@ 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 (= X (@ (@ 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) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X3))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A3 Bool) (Uw2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 Bool) (B2 Bool) (Va2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) (@ tptp.suc (@ tptp.suc Va2)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3)) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (not (= X (@ (@ 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 (= X (@ (@ 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) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X3)))))))))))))
% 6.18/6.68 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X 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)) X) (or (= X Mi) (= X Ma)))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (assert (forall ((Q2 tptp.num) (N2 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 N2))) _let_1))))))
% 6.18/6.68 (assert (forall ((Q2 tptp.num) (N2 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 N2))) _let_1))))))
% 6.18/6.68 (assert (forall ((Q2 tptp.num) (N2 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 N2))) _let_1))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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 ((D4 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D4)))))))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D4 tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D4)))))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N2))) M) tptp.one_one_nat))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (P4 tptp.nat) (M tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat N2) P4) (=> (@ (@ tptp.ord_less_nat M) P4) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P4) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P4))))) (@ P M)))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N2))) N2)))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (N2 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) N2) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (N2 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) N2) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q3 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q3))))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (forall ((S tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S))))))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (forall ((S tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q2) S))))))))))
% 6.18/6.68 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N)) N)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 6.18/6.68 (assert (forall ((A Bool) (B Bool) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) (@ tptp.suc (@ tptp.suc N2))) _let_1))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D 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) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D 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) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D 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) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D 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) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D 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) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D 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) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D 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) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D 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) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.18/6.68 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.18/6.68 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C3 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.18/6.68 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.18/6.68 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A4) B4)) tptp.zero_zero_real))))
% 6.18/6.68 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A4) B4)) tptp.zero_zero_rat))))
% 6.18/6.68 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A4) B4)) tptp.zero_zero_int))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A4) B4)) tptp.zero_zero_real))))
% 6.18/6.68 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A4) B4)) tptp.zero_zero_rat))))
% 6.18/6.68 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A4) B4)) tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (N2 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) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2)) (@ (@ tptp.power_power_nat B) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (N2 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) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X) Z) (@ (@ tptp.times_times_complex W) Y)))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X) Z) (@ (@ tptp.times_times_real W) Y)))))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X) Z) (@ (@ tptp.times_times_rat W) Y)))))))
% 6.18/6.68 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.18/6.68 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N2)))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M2 tptp.nat)) (= N2 (@ tptp.suc M2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (and (@ P tptp.zero_zero_nat) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N2) (@ P (@ tptp.suc I5))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M6 tptp.nat)) (= N2 (@ tptp.suc M6))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (or (@ P tptp.zero_zero_nat) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) N2) (@ P (@ tptp.suc I5))))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N2) _let_1) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))))
% 6.18/6.68 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))))
% 6.18/6.68 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I2) K2) J))))))
% 6.18/6.68 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.18/6.68 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.18/6.68 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K))))))
% 6.18/6.68 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.18/6.68 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.18/6.68 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) M))))))
% 6.18/6.68 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N2) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.68 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N2)) (or (= N2 tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 6.18/6.68 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (assert (forall ((M tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X))) (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) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (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) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.18/6.68 (assert (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (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) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N2))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N2)) Q2))) (@ _let_1 N2)))))))
% 6.18/6.68 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N)) N)))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2)))))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))))
% 6.18/6.68 (assert (forall ((Uv Bool) (Uw Bool) (N2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N2)) tptp.none_nat)))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D 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) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D 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) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D 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) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D 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) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ 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) D))))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y) E2)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat Y) E2)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (X tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ 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 X) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (X tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ 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 X) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W)))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X)) X)))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X)) X)))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y)) X)))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y)) X)))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z)))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))))))))
% 6.18/6.68 (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))))))))))))
% 6.18/6.68 (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))))))))))))
% 6.18/6.68 (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))))))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 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) N2)) tptp.one_one_real)))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 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) N2)) tptp.one_one_rat)))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 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) N2)) tptp.one_one_nat)))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 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) N2)) tptp.one_one_int)))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.18/6.68 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.18/6.68 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.18/6.68 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) Y)) Z)))))
% 6.18/6.68 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))))
% 6.18/6.68 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 6.18/6.68 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.18/6.68 (assert (forall ((Y tptp.complex) (X tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.18/6.68 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.18/6.68 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.18/6.68 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.18/6.68 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) Y)) Z)))))
% 6.18/6.68 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))))
% 6.18/6.68 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 6.18/6.68 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.18/6.68 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat M) N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat N2) M))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I2))) N2))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ 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 N2))))))
% 6.18/6.68 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs2)))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))))
% 6.18/6.68 (assert (forall ((X tptp.set_nat) (Xs2 tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs2)))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 6.18/6.68 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N2) K)))))
% 6.18/6.68 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.68 (assert (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N2))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 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) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M)))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N2)) (and (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2))))))
% 6.18/6.68 (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 ((D2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D2)) (@ P D2)))))))
% 6.18/6.68 (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 ((D2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D2)) (not (@ P D2)))))))))
% 6.18/6.68 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N2) Q2))))))
% 6.18/6.68 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.divide_divide_nat M) N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N2) M) (= N2 tptp.one_one_nat)))))
% 6.18/6.68 (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))))))))))
% 6.18/6.68 (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))))))))))
% 6.18/6.68 (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))))))))))
% 6.18/6.68 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 6.18/6.68 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A3) B2)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ 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 (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y) (=> (=> (exists ((Uu2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) true))) Y) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Mi2)))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Ma2)))))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z4) (=> (@ (@ tptp.ord_less_real Z4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z4) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z4) (=> (@ (@ tptp.ord_less_rat Z4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z4) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z)))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))))))
% 6.18/6.68 (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))))))))))))
% 6.18/6.68 (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)))))))))))
% 6.18/6.68 (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)))))))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (A tptp.real) (Y 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 X) A) (=> (@ (@ tptp.ord_less_eq_real Y) 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) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (A tptp.rat) (Y 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 X) A) (=> (@ (@ tptp.ord_less_eq_rat Y) 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) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (A tptp.int) (Y 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 X) A) (=> (@ (@ tptp.ord_less_eq_int Y) 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) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.18/6.68 (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)))))))))))))
% 6.18/6.68 (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)))))))))))))
% 6.18/6.68 (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)))))))))))))
% 6.18/6.68 (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)))))))))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.18/6.68 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ 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))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (=> (@ (@ 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))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ 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))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ 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))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 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 N2))) A)))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 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 N2))) A)))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 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 N2))) A)))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 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 N2))) A)))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 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 N2))) tptp.one_one_real)))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 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 N2))) tptp.one_one_rat)))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 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 N2))) tptp.one_one_nat)))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 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 N2))) tptp.one_one_int)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) 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 N2))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) 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 N2))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) 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 N2))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) 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 N2))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) 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 N2))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) 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 N2))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) 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 N2))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) 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 N2))))))))
% 6.18/6.68 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.18/6.68 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.18/6.68 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.18/6.68 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.18/6.68 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N2))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2)))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_rat A) N2)))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_nat A) N2)))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_int A) N2)))))))
% 6.18/6.68 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.18/6.68 (assert (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.18/6.68 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N)) N))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= N2 (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.18/6.68 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N2) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N2)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2)))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I5)) J3)) (@ P I5))))))))))
% 6.18/6.68 (assert (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 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 TreeList3)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 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 TreeList3)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 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 TreeList3)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.18/6.68 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N))))))
% 6.18/6.68 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))))
% 6.18/6.68 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) TrLst2) Smry2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 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 TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList3 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 TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 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 TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList3 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 TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.18/6.68 (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)))))))))))))
% 6.18/6.68 (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)))))))))))))
% 6.18/6.68 (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))))))))))))
% 6.18/6.68 (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))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y) 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) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A) (=> (@ (@ tptp.ord_less_rat Y) 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) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) 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) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (assert (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S2))) V))))))
% 6.18/6.68 (assert (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U))) S2))) V))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y 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 X) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y 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 X) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (Y 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 X) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y 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 X) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 N2) tptp.zero_zero_nat))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 N2) tptp.zero_zero_int))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_nat))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_int))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 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 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 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 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (N2 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 N2))))))
% 6.18/6.68 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.68 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.68 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.68 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.68 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (or (and (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (N2 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 N2))) (= (@ (@ 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 N2) M)))) _let_2))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 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 N2))) (= (@ (@ 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 N2) M)))) _let_2))))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 6.18/6.68 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 6.18/6.68 (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)))
% 6.18/6.68 (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)))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X) Y))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y 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 X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y 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 X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y 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 X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y 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 X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y 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 X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y 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 X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y 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 X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y 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 X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y 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 X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 6.18/6.68 (assert (forall ((X tptp.real) (Y 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 X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 6.18/6.68 (assert (forall ((X tptp.rat) (Y 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 X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))))
% 6.18/6.68 (assert (forall ((X tptp.int) (Y 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 X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 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))) N2)))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 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))) N2)))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 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))) N2)))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (N2 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 N2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 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) N2) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 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) N2) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.18/6.68 (assert (forall ((M tptp.nat) (N2 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) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 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))) N2)))) (@ _let_1 A)))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 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))) N2)))) (@ _let_1 A)))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 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))) N2)))) (@ _let_1 A)))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 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))) N2)))) tptp.zero_zero_real))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (N2 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))) N2)))) tptp.zero_zero_rat))))
% 6.18/6.68 (assert (forall ((A tptp.int) (N2 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))) N2)))) tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (N2 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 X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (=> (@ _let_2 N2) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N2)) (@ _let_1 M)))))))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (N2 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 X) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (=> (@ _let_2 N2) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N2)) (@ _let_1 N2)))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ 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 TreeList3)))) (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)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) 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 TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ 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 TreeList3)))) (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)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2))) (= Y (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 TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ 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 (= X (@ (@ (@ (@ 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 (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ 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 TreeList3)))) (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)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) 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 TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 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 TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList3 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 TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 6.18/6.68 (assert (forall ((U tptp.real) (X tptp.real) (Y 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 X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.18/6.68 (assert (forall ((U tptp.rat) (X tptp.rat) (Y 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 X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.18/6.68 (assert (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A4 Bool) (B4 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A4) B4))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= A22 (@ (@ tptp.plus_plus_nat N) N)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N) _let_1)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N 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) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 N)) (= A22 (@ (@ tptp.plus_plus_nat N) N)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I5)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) (@ (@ tptp.vEBT_VEBT_low Ma3) N))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) (@ (@ tptp.vEBT_VEBT_low X2) N))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N 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 N))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList2) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X2) N))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N) _let_3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I5)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) (@ (@ tptp.vEBT_VEBT_low Ma3) N))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) (@ (@ tptp.vEBT_VEBT_low X2) N))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))))
% 6.18/6.68 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M2)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M2)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 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) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M2)) (=> (= M2 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M2)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X5) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 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) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X5) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M2)) (=> (= M2 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M2)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X5) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2)))))))))))))))))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B2))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) 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 TreeList3) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (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 TreeList3) _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))))))))))))))))))))
% 6.18/6.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N2))))))
% 6.18/6.68 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ (@ 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))) N2)) tptp.one_one_nat))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y 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)) (=> (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= Xa2 _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y 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) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) 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 TreeList3))) (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))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ 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))))))))))))))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) Uw2))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (=> (= Xa2 _let_1) (=> (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) (=> (= X _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y 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) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) 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 TreeList3))) (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))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ 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)))))))))))))))))))))))))))))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y (@ (@ tptp.vEBT_Leaf false) B2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.vEBT_Leaf A3))) (let ((_let_3 (@ _let_2 B2))) (=> (= X _let_3) (=> (= Xa2 _let_1) (=> (= Y (@ _let_2 false)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) _let_1)))))))))) (=> (forall ((A3 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A3) B2)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= Xa2 _let_1) (=> (= Y _let_2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1)))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst) Smry))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) 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.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= Xa2 Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa2))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= Xa2 Ma2))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi2))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (and _let_9 _let_16))) (let ((_let_24 (or (@ (@ tptp.ord_less_nat Xa2) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (=> (= X _let_2) (=> (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))))))))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N2)) N2)) (@ (@ tptp.modulo_modulo_nat A2) N2)))))
% 6.18/6.68 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y22)) (= X22 Y22))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N2) tptp.zero_z5237406670263579293d_enat) N2)))
% 6.18/6.68 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N2) tptp.zero_z5237406670263579293d_enat)))
% 6.18/6.68 (assert (forall ((X tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X) X))) (= X tptp.zero_zero_real))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N2)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N2) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N2))))))
% 6.18/6.68 (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))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((K tptp.int) (I2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I2) K)) (@ (@ tptp.ord_less_eq_int K) I2))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K)) (@ (@ tptp.modulo_modulo_int N2) K)) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ (@ P I5) J3)))))))
% 6.18/6.68 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K)) (@ (@ tptp.modulo_modulo_int N2) K)) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ (@ P I5) J3)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B6 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) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B6)) (@ _let_1 B))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (A6 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A6) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A6) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.18/6.68 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I2) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I2))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B6 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) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B6))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (A6 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A6) B))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N2) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P I5)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P I5))))))))
% 6.18/6.68 (assert (forall ((A2 tptp.int) (N2 tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N2)) N2)) (@ (@ tptp.modulo_modulo_int A2) N2)))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.18/6.68 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.18/6.68 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N2) tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))))
% 6.18/6.68 (assert (forall ((N2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N2)))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.18/6.68 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.18/6.68 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.18/6.68 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.18/6.68 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.18/6.68 (assert (forall ((A tptp.real) (N2 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 N2)) A))))))
% 6.18/6.68 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N3)) Y))))))
% 6.18/6.68 (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)))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ 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) N2) A)))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ 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) N2) A) (forall ((Y3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (= (@ (@ tptp.power_power_real Y3) N2) A)) (= Y3 X3)))))))))
% 6.18/6.68 (assert (forall ((B6 tptp.real) (A6 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B6) A6)) (@ (@ tptp.ord_less_real A6) B6))))
% 6.18/6.68 (assert (forall ((B6 tptp.rat) (A6 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B6) A6)) (@ (@ tptp.ord_less_rat A6) B6))))
% 6.18/6.68 (assert (forall ((B6 tptp.num) (A6 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B6) A6)) (@ (@ tptp.ord_less_num A6) B6))))
% 6.18/6.68 (assert (forall ((B6 tptp.nat) (A6 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B6) A6)) (@ (@ tptp.ord_less_nat A6) B6))))
% 6.18/6.68 (assert (forall ((B6 tptp.int) (A6 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B6) A6)) (@ (@ tptp.ord_less_int A6) B6))))
% 6.18/6.68 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.18/6.68 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.18/6.68 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.18/6.68 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.18/6.68 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.18/6.68 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 6.18/6.68 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A4 tptp.extended_enat) (B4 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A4) B4)) B4) A4))))
% 6.18/6.68 (assert (= tptp.ord_max_Code_integer (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le3102999989581377725nteger A4) B4)) B4) A4))))
% 6.18/6.68 (assert (= tptp.ord_max_set_int (lambda ((A4 tptp.set_int) (B4 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A4) B4)) B4) A4))))
% 6.18/6.68 (assert (= tptp.ord_max_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A4) B4)) B4) A4))))
% 6.18/6.68 (assert (= tptp.ord_max_num (lambda ((A4 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A4) B4)) B4) A4))))
% 6.18/6.68 (assert (= tptp.ord_max_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A4) B4)) B4) A4))))
% 6.18/6.68 (assert (= tptp.ord_max_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A4) B4)) B4) A4))))
% 6.18/6.68 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ tptp.divide_divide_nat B3) N2))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A3))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B2))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _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) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S))) (=> (= X _let_1) (=> (= Y _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) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList3 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) TreeList3) Summary2))) (=> (= X _let_2) (=> (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList3) 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) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) 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 TreeList3) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (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 TreeList3) _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))))))))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _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))) (=> (= X _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))) (=> (= X _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))) (=> (= X _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) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (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 TreeList3)))) (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) TreeList3) Summary2))) (=> (= X _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 TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B2) _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))) (=> (= X _let_1) (=> (not Y) (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))) (=> (= X _let_1) (=> (not Y) (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))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) 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 TreeList3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X _let_2) (=> (= Y (=> (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 TreeList3) _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))))))))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _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))) (=> (= X _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) (TreeList3 tptp.list_VEBT_VEBT) (S 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 TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S))) (=> (= X _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 TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S 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 TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S))) (=> (= X _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 TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B2) _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))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S))) (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 TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _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))))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (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 TreeList3)))) (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) TreeList3) Summary2))) (=> (= X _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 TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _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))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 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) Va3) Vb2))) (=> (= X _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) (TreeList3 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 TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _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 TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _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 TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 6.18/6.68 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 6.18/6.68 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) (@ _let_1 K)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) (@ _let_1 K)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I2) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.18/6.68 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 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)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 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)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int R2) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))
% 6.18/6.68 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B6 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B6) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 6.18/6.68 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I2) K) I2) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I2))))))
% 6.18/6.68 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B6 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 B6) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B6) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((B6 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 B6) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B6) (@ _let_1 Q5)))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N2) K)) (and (=> (= K tptp.zero_zero_int) (@ P N2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P J3))))))))
% 6.18/6.68 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.18/6.68 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N2) tptp.one_one_int) (and (= M tptp.one_one_int) (= N2 tptp.one_one_int))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I2) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L2) L2)))
% 6.18/6.68 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 6.18/6.68 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((M tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q4 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q4))))))
% 6.18/6.68 (assert (forall ((M tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q3))))))
% 6.18/6.68 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L2) tptp.zero_zero_int)))
% 6.18/6.68 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.18/6.68 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 6.18/6.68 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.18/6.68 (assert (forall ((K tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N2) K))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) K)))
% 6.18/6.68 (assert (forall ((A tptp.int) (X tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X) (= A X) (@ (@ tptp.ord_less_eq_int X) A))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.18/6.68 (assert (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I2 tptp.int)) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 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) Va3) Vb2))) (=> (= X _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) (TreeList3 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 TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _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 TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 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 TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _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 TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 6.18/6.68 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (not Y) (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))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 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) Va3) Vb2))) (=> (= X _let_1) (=> (= Y (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) (TreeList3 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) TreeList3) 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 TreeList3)))) (=> (= X _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _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) (TreeList3 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) TreeList3) 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 TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _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))))))))))))))))))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_eq_set_int B) D))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D))))))
% 6.18/6.68 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B) D))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B) D))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B) D))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B) D))))))
% 6.18/6.68 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A) B) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K) D))))))))))
% 6.18/6.68 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) (@ (@ tptp.times_times_int K) D))))))))))
% 6.18/6.68 (assert (forall ((L2 tptp.set_int) (H2 tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L2) H2) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L2) H2)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (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)))))))
% 6.18/6.68 (assert (forall ((I2 tptp.set_nat) (L2 tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ (@ tptp.set_or4548717258645045905et_nat L2) U)) (and (@ (@ tptp.ord_less_eq_set_nat L2) I2) (@ (@ tptp.ord_less_eq_set_nat I2) U)))))
% 6.18/6.68 (assert (forall ((I2 tptp.set_int) (L2 tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ (@ tptp.set_or370866239135849197et_int L2) U)) (and (@ (@ tptp.ord_less_eq_set_int L2) I2) (@ (@ tptp.ord_less_eq_set_int I2) U)))))
% 6.18/6.68 (assert (forall ((I2 tptp.rat) (L2 tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ (@ tptp.set_or633870826150836451st_rat L2) U)) (and (@ (@ tptp.ord_less_eq_rat L2) I2) (@ (@ tptp.ord_less_eq_rat I2) U)))))
% 6.18/6.68 (assert (forall ((I2 tptp.num) (L2 tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I2) (@ (@ tptp.set_or7049704709247886629st_num L2) U)) (and (@ (@ tptp.ord_less_eq_num L2) I2) (@ (@ tptp.ord_less_eq_num I2) U)))))
% 6.18/6.68 (assert (forall ((I2 tptp.nat) (L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (and (@ (@ tptp.ord_less_eq_nat L2) I2) (@ (@ tptp.ord_less_eq_nat I2) U)))))
% 6.18/6.68 (assert (forall ((I2 tptp.int) (L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I2) (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (and (@ (@ tptp.ord_less_eq_int L2) I2) (@ (@ tptp.ord_less_eq_int I2) U)))))
% 6.18/6.68 (assert (forall ((I2 tptp.real) (L2 tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I2) (@ (@ tptp.set_or1222579329274155063t_real L2) U)) (and (@ (@ tptp.ord_less_eq_real L2) I2) (@ (@ tptp.ord_less_eq_real I2) U)))))
% 6.18/6.68 (assert (forall ((D3 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) D3)) (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) D3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (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) D3))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X5) D3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.18/6.68 (assert (forall ((D3 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) D3)) (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) D3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (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) D3))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X5) D3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.18/6.68 (assert (forall ((D3 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) D3)) (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) D3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (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) D3))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) D3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.18/6.68 (assert (forall ((D3 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) D3)) (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) D3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (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) D3))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) D3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (not (@ (@ tptp.ord_less_real X5) T)))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (not (@ (@ tptp.ord_less_rat X5) T)))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (not (@ (@ tptp.ord_less_num X5) T)))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (not (@ (@ tptp.ord_less_nat X5) T)))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (not (@ (@ tptp.ord_less_int X5) T)))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (@ (@ tptp.ord_less_real T) X5))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (@ (@ tptp.ord_less_rat T) X5))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (@ (@ tptp.ord_less_num T) X5))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (@ (@ tptp.ord_less_nat T) X5))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (@ (@ tptp.ord_less_int T) X5))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (and (@ P X5) (@ Q X5)) (and (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ Q X3) (@ Q6 X3))))) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (or (@ P X5) (@ Q X5)) (or (@ P6 X5) (@ Q6 X5))))))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (not (= X5 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X5))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X5))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X5))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X5))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X5))) (=> (@ _let_1 Z4) (@ _let_1 T)))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (not (@ (@ tptp.ord_less_real T) X5)))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (not (@ (@ tptp.ord_less_rat T) X5)))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (not (@ (@ tptp.ord_less_num T) X5)))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (not (@ (@ tptp.ord_less_nat T) X5)))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (not (@ (@ tptp.ord_less_int T) X5)))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M7 tptp.nat)) (=> (@ P X) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M7))) (not (forall ((M2 tptp.nat)) (=> (@ P M2) (not (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M2)))))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.num)) (not (= X (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A3) (@ (@ tptp.product_Pair_nat_num B2) Acc)))))))))
% 6.18/6.68 (assert (forall ((X tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.nat)) (not (= X (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A3) (@ (@ tptp.product_Pair_nat_nat B2) Acc)))))))))
% 6.18/6.68 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X4 tptp.int)) (@ P X4)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X2))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X5 T) (= (@ (@ tptp.minus_minus_int X5) D3) T))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T) B3) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.minus_minus_int X5) D3) T)))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X5) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X5) D3)) T)))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T) B3) (forall ((X5 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) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D3))))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X5 T) (= (@ (@ tptp.plus_plus_int X5) D3) T))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.plus_plus_int X5) D3) T)))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X5) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X5) D3)) T))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X5 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) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.plus_plus_int X5) D3)))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X5) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X5) D3)) T)))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X5 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) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D3))))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X5) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X5) D3)) T))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X5 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) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.plus_plus_int X5) D3)))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) 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) D3)) (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) D3))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (= (exists ((X4 tptp.int)) (@ P X4)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (@ P6 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (exists ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) A2) (@ P (@ (@ tptp.minus_minus_int Y2) X2))))))))))))))
% 6.18/6.68 (assert (forall ((D3 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (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) D3))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (= (exists ((X4 tptp.int)) (@ P X4)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (@ P6 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (exists ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ P (@ (@ tptp.plus_plus_int Y2) X2))))))))))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (not (@ (@ tptp.ord_less_eq_real X5) T)))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (not (@ (@ tptp.ord_less_eq_rat X5) T)))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (not (@ (@ tptp.ord_less_eq_num X5) T)))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (not (@ (@ tptp.ord_less_eq_nat X5) T)))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (not (@ (@ tptp.ord_less_eq_int X5) T)))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (@ (@ tptp.ord_less_eq_real T) X5))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (@ (@ tptp.ord_less_eq_rat T) X5))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (@ (@ tptp.ord_less_eq_num T) X5))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (@ (@ tptp.ord_less_eq_nat T) X5))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (@ (@ tptp.ord_less_eq_int T) X5))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (@ (@ tptp.ord_less_eq_real X5) T))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (@ (@ tptp.ord_less_eq_rat X5) T))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (@ (@ tptp.ord_less_eq_num X5) T))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (@ (@ tptp.ord_less_eq_nat X5) T))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (@ (@ tptp.ord_less_eq_int X5) T))))))
% 6.18/6.68 (assert (forall ((T tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (not (@ (@ tptp.ord_less_eq_real T) X5)))))))
% 6.18/6.68 (assert (forall ((T tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (not (@ (@ tptp.ord_less_eq_rat T) X5)))))))
% 6.18/6.68 (assert (forall ((T tptp.num)) (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (not (@ (@ tptp.ord_less_eq_num T) X5)))))))
% 6.18/6.68 (assert (forall ((T tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (not (@ (@ tptp.ord_less_eq_nat T) X5)))))))
% 6.18/6.68 (assert (forall ((T tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (not (@ (@ tptp.ord_less_eq_int T) X5)))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.real Bool)) (D3 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D3))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D3))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.rat Bool)) (D3 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D3))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D3))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.int Bool)) (D3 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.real Bool)) (D3 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D3))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D3))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.rat Bool)) (D3 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D3))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D3))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.18/6.68 (assert (forall ((P (-> tptp.int Bool)) (D3 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (X7 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X X7) (=> (=> _let_2 (= P P6)) (= (and (@ _let_1 X) P) (and _let_2 P6))))))))
% 6.18/6.68 (assert (forall ((X tptp.int) (X7 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X X7) (=> (=> _let_2 (= P P6)) (= (=> (@ _let_1 X) P) (=> _let_2 P6))))))))
% 6.18/6.68 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (= (@ (@ tptp.ord_less_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_int B) D) (or (@ (@ tptp.ord_less_set_int C) A) (@ (@ tptp.ord_less_set_int B) D)))) (@ _let_1 D))))))
% 6.18/6.68 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D 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) D)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D)))) (@ _let_1 D))))))
% 6.18/6.68 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D 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) D)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D)))) (@ _let_1 D))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D 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) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D)))) (@ _let_1 D))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D 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) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D)))) (@ _let_1 D))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D 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) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) D) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B) D)))) (@ _let_1 D))))))
% 6.18/6.68 (assert (forall ((D tptp.int) (P6 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((X_12 tptp.int)) (@ P6 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.18/6.68 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.18/6.68 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A3 tptp.real) (B2 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B2) (=> (@ (@ P B2) C3) (=> (@ (@ tptp.ord_less_eq_real A3) B2) (=> (@ (@ tptp.ord_less_eq_real B2) C3) (@ _let_1 C3))))))) (=> (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 ((A3 tptp.real) (B2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A3) X3) (@ (@ tptp.ord_less_eq_real X3) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B2) A3)) D5)) (@ (@ P A3) B2)))))))) (@ (@ P A) B))))))
% 6.18/6.68 (assert (forall ((Z tptp.real) (X tptp.real) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.18/6.68 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 6.18/6.68 (assert (forall ((Z tptp.int) (X tptp.int) (Y 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 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.18/6.68 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X) Y)))))
% 6.18/6.68 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 6.18/6.68 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 6.18/6.68 (assert (forall ((Q2 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R2)) (= R2 tptp.zero_zero_nat))))
% 6.18/6.68 (assert (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R2)) (= R2 tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) (@ _let_1 K)))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.18/6.68 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X) Y)))))
% 6.18/6.68 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X) Y)))))
% 6.18/6.68 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))))
% 6.18/6.68 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 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 R2)) (@ (@ (@ 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 R2)) tptp.one_one_int)))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs2) Ys)) N2) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr8326237132889035090at_num (@ (@ tptp.product_nat_num Xs2) Ys)) N2) (@ (@ tptp.product_Pair_nat_num (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.product_nat_nat Xs2) Ys)) N2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) N2) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.product_nat_o Xs2) Ys)) N2) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_Code_integer) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs2) Ys)) N2) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_nat) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.product_nat_int Xs2) Ys)) N2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) N2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) N2) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.18/6.68 (assert (forall ((N2 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) N2) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.18/6.68 (assert (forall ((Z tptp.nat) (X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X) (=> (@ (@ 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) X) X_1)))))))
% 6.18/6.68 (assert (forall ((X tptp.nat) (Z tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X) 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) X) X_1))))))))
% 6.18/6.68 (assert (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N2) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.18/6.68 (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 ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) Xs2) (@ (@ tptp.ord_less_nat A) X5))))))))
% 6.18/6.68 (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 ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) Xs2) (@ (@ tptp.ord_less_nat X5) A))))))))
% 6.18/6.68 (assert (forall ((X1 tptp.code_integer) (X22 Bool) (Y1 tptp.code_integer) (Y22 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o X1) X22) (@ (@ tptp.produc6677183202524767010eger_o Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.18/6.68 (assert (forall ((X1 tptp.num) (X22 tptp.num) (Y1 tptp.num) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num X1) X22) (@ (@ tptp.product_Pair_num_num Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.18/6.68 (assert (forall ((X1 tptp.nat) (X22 tptp.num) (Y1 tptp.nat) (Y22 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num X1) X22) (@ (@ tptp.product_Pair_nat_num Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.18/6.68 (assert (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y22 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.18/6.68 (assert (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (B Bool) (A6 tptp.code_integer) (B6 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A6) B6)) (and (= A A6) (= B B6)))))
% 6.18/6.68 (assert (forall ((A tptp.num) (B tptp.num) (A6 tptp.num) (B6 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A6) B6)) (and (= A A6) (= B B6)))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.num) (A6 tptp.nat) (B6 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A6) B6)) (and (= A A6) (= B B6)))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (A6 tptp.nat) (B6 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A6) B6)) (and (= A A6) (= B B6)))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (A6 tptp.int) (B6 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A6) B6)) (and (= A A6) (= B B6)))))
% 6.18/6.68 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))))
% 6.18/6.68 (assert (forall ((Xs2 tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs2))))
% 6.18/6.68 (assert (forall ((Xs2 tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs2))))
% 6.18/6.68 (assert (forall ((Xs2 tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs2))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (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)))))
% 6.18/6.68 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6639371672096860321T_VEBT (@ (@ tptp.produc662631939642741121T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.18/6.68 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_o)) (= (@ tptp.size_s4246224855604898693_int_o (@ (@ tptp.product_int_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs2)) (@ tptp.size_size_list_o Ys)))))
% 6.18/6.68 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.size_s5157815400016825771nt_int (@ (@ tptp.product_int_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs2)) (@ tptp.size_size_list_int Ys)))))
% 6.18/6.68 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_nat X2) M6)))))))
% 6.18/6.68 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N4) (@ (@ tptp.ord_less_nat X3) N2))) (@ tptp.finite_finite_nat N4))))
% 6.18/6.68 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N6) (@ (@ tptp.ord_less_eq_nat X2) M6)))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A2)))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A2)))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A2)))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A2)))))
% 6.18/6.68 (assert (forall ((P (-> tptp.nat Bool)) (I2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I2)))))))
% 6.18/6.68 (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 ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) U)))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_nat) (N2 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) N2))))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_complex) (N2 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) N2))))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N2 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) N2))))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_o) (N2 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) N2))))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_int) (N2 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) N2))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_nat) (N2 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)) N2))))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_complex) (N2 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)) N2))))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N2 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)) N2))))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_o) (N2 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)) N2))))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_int) (N2 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)) N2))))))))
% 6.18/6.68 (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))))))
% 6.18/6.68 (assert (forall ((Y tptp.produc6271795597528267376eger_o)) (not (forall ((A3 tptp.code_integer) (B2 Bool)) (not (= Y (@ (@ tptp.produc6677183202524767010eger_o A3) B2)))))))
% 6.18/6.68 (assert (forall ((Y tptp.product_prod_num_num)) (not (forall ((A3 tptp.num) (B2 tptp.num)) (not (= Y (@ (@ tptp.product_Pair_num_num A3) B2)))))))
% 6.18/6.68 (assert (forall ((Y tptp.product_prod_nat_num)) (not (forall ((A3 tptp.nat) (B2 tptp.num)) (not (= Y (@ (@ tptp.product_Pair_nat_num A3) B2)))))))
% 6.18/6.68 (assert (forall ((Y tptp.product_prod_nat_nat)) (not (forall ((A3 tptp.nat) (B2 tptp.nat)) (not (= Y (@ (@ tptp.product_Pair_nat_nat A3) B2)))))))
% 6.18/6.68 (assert (forall ((Y tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B2 tptp.int)) (not (= Y (@ (@ tptp.product_Pair_int_int A3) B2)))))))
% 6.18/6.68 (assert (forall ((P4 tptp.produc6271795597528267376eger_o)) (exists ((X3 tptp.code_integer) (Y5 Bool)) (= P4 (@ (@ tptp.produc6677183202524767010eger_o X3) Y5)))))
% 6.18/6.68 (assert (forall ((P4 tptp.product_prod_num_num)) (exists ((X3 tptp.num) (Y5 tptp.num)) (= P4 (@ (@ tptp.product_Pair_num_num X3) Y5)))))
% 6.18/6.68 (assert (forall ((P4 tptp.product_prod_nat_num)) (exists ((X3 tptp.nat) (Y5 tptp.num)) (= P4 (@ (@ tptp.product_Pair_nat_num X3) Y5)))))
% 6.18/6.68 (assert (forall ((P4 tptp.product_prod_nat_nat)) (exists ((X3 tptp.nat) (Y5 tptp.nat)) (= P4 (@ (@ tptp.product_Pair_nat_nat X3) Y5)))))
% 6.18/6.68 (assert (forall ((P4 tptp.product_prod_int_int)) (exists ((X3 tptp.int) (Y5 tptp.int)) (= P4 (@ (@ tptp.product_Pair_int_int X3) Y5)))))
% 6.18/6.68 (assert (forall ((P (-> tptp.produc6271795597528267376eger_o Bool)) (P4 tptp.produc6271795597528267376eger_o)) (=> (forall ((A3 tptp.code_integer) (B2 Bool)) (@ P (@ (@ tptp.produc6677183202524767010eger_o A3) B2))) (@ P P4))))
% 6.18/6.68 (assert (forall ((P (-> tptp.product_prod_num_num Bool)) (P4 tptp.product_prod_num_num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (@ P (@ (@ tptp.product_Pair_num_num A3) B2))) (@ P P4))))
% 6.18/6.68 (assert (forall ((P (-> tptp.product_prod_nat_num Bool)) (P4 tptp.product_prod_nat_num)) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (@ P (@ (@ tptp.product_Pair_nat_num A3) B2))) (@ P P4))))
% 6.18/6.68 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P4 tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A3) B2))) (@ P P4))))
% 6.18/6.68 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P4 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A3) B2))) (@ P P4))))
% 6.18/6.68 (assert (forall ((A tptp.code_integer) (B Bool) (A6 tptp.code_integer) (B6 Bool)) (=> (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A6) B6)) (not (=> (= A A6) (= B (not B6)))))))
% 6.18/6.68 (assert (forall ((A tptp.num) (B tptp.num) (A6 tptp.num) (B6 tptp.num)) (=> (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A6) B6)) (not (=> (= A A6) (not (= B B6)))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.num) (A6 tptp.nat) (B6 tptp.num)) (=> (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A6) B6)) (not (=> (= A A6) (not (= B B6)))))))
% 6.18/6.68 (assert (forall ((A tptp.nat) (B tptp.nat) (A6 tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A6) B6)) (not (=> (= A A6) (not (= B B6)))))))
% 6.18/6.68 (assert (forall ((A tptp.int) (B tptp.int) (A6 tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A6) B6)) (not (=> (= A A6) (not (= B B6)))))))
% 6.18/6.68 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N4))))
% 6.18/6.68 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R2 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) R2)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L2) Q2)) R2)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (@ (@ tptp.ord_less_int R2) L2))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R2) (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))))
% 6.18/6.68 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 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 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 6.18/6.68 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K))))))
% 6.18/6.68 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) K))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B5 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B5) A2)))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B5 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B5) A2)))))))
% 6.18/6.68 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B5 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B5) A2)))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z2 tptp.real)) (= (@ (@ tptp.power_power_real Z2) N2) tptp.one_one_real)))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N2) tptp.one_one_complex)))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B3) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B3)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int Q))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (or (@ P X2) (@ Q X2))))) (and (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (or (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int Q))) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (and (@ P X2) (@ Q X2))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (or (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (and (@ P X2) (@ Q X2))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ P X2) (@ Q X2))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ P X2) (@ Q X2))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (or (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P)) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex Q))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ P X2) (@ Q X2))))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I5) (@ (@ tptp.ord_less_eq_int I5) B)))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_int A) I5) (@ (@ tptp.ord_less_int I5) B)))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I5) (@ (@ tptp.ord_less_int I5) B)))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_int A) I5) (@ (@ tptp.ord_less_eq_int I5) B)))))))
% 6.18/6.69 (assert (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M7) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X5)) N3)))))))
% 6.18/6.69 (assert (forall ((M7 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M7) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_o)) (=> (@ (@ tptp.member_list_o X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X5)) N3)))))))
% 6.18/6.69 (assert (forall ((M7 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M7) (exists ((N3 tptp.nat)) (forall ((X5 tptp.list_int)) (=> (@ (@ tptp.member_list_int X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X5)) N3)))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (=> (not (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P))) (exists ((X_1 tptp.product_prod_int_int)) (@ P X_1)))))
% 6.18/6.69 (assert (forall ((P (-> tptp.set_nat Bool))) (=> (not (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P))) (exists ((X_1 tptp.set_nat)) (@ P X_1)))))
% 6.18/6.69 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P))) (exists ((X_1 tptp.nat)) (@ P X_1)))))
% 6.18/6.69 (assert (forall ((P (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P))) (exists ((X_1 tptp.int)) (@ P X_1)))))
% 6.18/6.69 (assert (forall ((P (-> tptp.complex Bool))) (=> (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex P))) (exists ((X_1 tptp.complex)) (@ P X_1)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (R (-> tptp.real tptp.nat Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A2) (@ (@ R A4) X3)))))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_int) (R (-> tptp.real tptp.int Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B3) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A2) (@ (@ R A4) X3)))))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_complex) (R (-> tptp.real tptp.complex Bool))) (=> (not (@ tptp.finite_finite_real A2)) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) B3) (not (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((A4 tptp.real)) (and (@ (@ tptp.member_real A4) A2) (@ (@ R A4) X3)))))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A2) (@ (@ R A4) X3)))))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_int) (R (-> tptp.nat tptp.int Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A2) (@ (@ R A4) X3)))))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_complex) (R (-> tptp.nat tptp.complex Bool))) (=> (not (@ tptp.finite_finite_nat A2)) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) B3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A4 tptp.nat)) (and (@ (@ tptp.member_nat A4) A2) (@ (@ R A4) X3)))))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_nat) (R (-> tptp.int tptp.nat Bool))) (=> (not (@ tptp.finite_finite_int A2)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A4 tptp.int)) (and (@ (@ tptp.member_int A4) A2) (@ (@ R A4) X3)))))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A2)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A4 tptp.int)) (and (@ (@ tptp.member_int A4) A2) (@ (@ R A4) X3)))))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_complex) (R (-> tptp.int tptp.complex Bool))) (=> (not (@ tptp.finite_finite_int A2)) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A4 tptp.int)) (and (@ (@ tptp.member_int A4) A2) (@ (@ R A4) X3)))))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_nat) (R (-> tptp.complex tptp.nat Bool))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) B3) (@ (@ R X3) Xa))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((A4 tptp.complex)) (and (@ (@ tptp.member_complex A4) A2) (@ (@ R A4) X3)))))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A2) (@ (@ tptp.ord_less_eq_set_int X3) A) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X3) (= X3 Xa))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A2) (@ (@ tptp.ord_less_eq_set_int A) X3) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X3) Xa) (= X3 Xa))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ tptp.finite_finite_nat B3) (@ tptp.finite_finite_nat A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ tptp.finite3207457112153483333omplex B3) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ tptp.finite_finite_int B3) (@ tptp.finite_finite_int A2)))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_nat) (T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (not (@ tptp.finite_finite_nat S3)) (not (@ tptp.finite_finite_nat T3))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_complex) (T3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (not (@ tptp.finite3207457112153483333omplex S3)) (not (@ tptp.finite3207457112153483333omplex T3))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_int) (T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S3) T3) (=> (not (@ tptp.finite_finite_int S3)) (not (@ tptp.finite_finite_int T3))))))
% 6.18/6.69 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (@ tptp.finite_finite_nat A2)))))
% 6.18/6.69 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.18/6.69 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ tptp.finite_finite_int A2)))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_int) (S3 tptp.set_int)) (=> (@ tptp.finite_finite_int T3) (=> (not (@ tptp.finite_finite_int S3)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S3) T3)))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (not (@ tptp.finite3207457112153483333omplex S3)) (not (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex S3) T3)))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat T3) (=> (not (@ tptp.finite_finite_nat S3)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S3) T3)))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X3) Xa) (= X3 Xa))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X3) (= X3 Xa))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N2) C)))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_one_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_times_rat (@ X I5)) (@ Y I5)) tptp.one_one_rat))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.one_one_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.times_times_rat (@ X I5)) (@ Y I5)) tptp.one_one_rat))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_plus_rat (@ X I5)) (@ Y I5)) tptp.zero_zero_rat))))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.plus_plus_rat (@ X I5)) (@ Y I5)) tptp.zero_zero_rat))))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (@ (@ P M2) tptp.zero_zero_nat)) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M2) N3)) (@ (@ P M2) N3)))) (@ (@ P M) N2)))))
% 6.18/6.69 (assert (forall ((N2 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 N2)) K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N2) (@ (@ tptp.divide_divide_int K) _let_1)) L2)))))))
% 6.18/6.69 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.18/6.69 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.18/6.69 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.18/6.69 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (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) N2) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (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) N2) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (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) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 6.18/6.69 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.18/6.69 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.18/6.69 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.18/6.69 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.18/6.69 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.18/6.69 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.69 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 6.18/6.69 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.18/6.69 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.18/6.69 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.18/6.69 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.18/6.69 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.18/6.69 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.18/6.69 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L2) L2)))
% 6.18/6.69 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.18/6.69 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.18/6.69 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.18/6.69 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.69 (assert (forall ((N2 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 N2) K) L2)) (@ _let_1 L2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N2) K) L2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))
% 6.18/6.69 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.18/6.69 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.18/6.69 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.18/6.69 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N2))) (@ _let_1 N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N2)) (not (@ _let_1 N2))))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N2) _let_1)))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (assert (forall ((N2 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) N2)) tptp.one_one_Code_integer)) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((N2 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) N2)) tptp.one_one_nat)) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((N2 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) N2)) tptp.one_one_int)) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.18/6.69 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B7 tptp.nat) (C5 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B7) C5)) (@ (@ tptp.dvd_dvd_nat B7) B) (@ (@ tptp.dvd_dvd_nat C5) C))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B7 tptp.int) (C5 tptp.int)) (and (= A (@ (@ tptp.times_times_int B7) C5)) (@ (@ tptp.dvd_dvd_int B7) B) (@ (@ tptp.dvd_dvd_int C5) C))))))
% 6.18/6.69 (assert (forall ((P4 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P4) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (= P4 (@ (@ tptp.times_times_nat X3) Y5)) (=> (@ (@ tptp.dvd_dvd_nat X3) A) (not (@ (@ tptp.dvd_dvd_nat Y5) B)))))))))
% 6.18/6.69 (assert (forall ((P4 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P4) (@ (@ tptp.times_times_int A) B)) (not (forall ((X3 tptp.int) (Y5 tptp.int)) (=> (= P4 (@ (@ tptp.times_times_int X3) Y5)) (=> (@ (@ tptp.dvd_dvd_int X3) A) (not (@ (@ tptp.dvd_dvd_int Y5) B)))))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.18/6.69 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.18/6.69 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.18/6.69 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.18/6.69 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.18/6.69 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D))))))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C) D) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B4 tptp.code_integer) (A4 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A4 (@ (@ tptp.times_3573771949741848930nteger B4) K3))))))
% 6.18/6.69 (assert (= tptp.dvd_dvd_real (lambda ((B4 tptp.real) (A4 tptp.real)) (exists ((K3 tptp.real)) (= A4 (@ (@ tptp.times_times_real B4) K3))))))
% 6.18/6.69 (assert (= tptp.dvd_dvd_rat (lambda ((B4 tptp.rat) (A4 tptp.rat)) (exists ((K3 tptp.rat)) (= A4 (@ (@ tptp.times_times_rat B4) K3))))))
% 6.18/6.69 (assert (= tptp.dvd_dvd_nat (lambda ((B4 tptp.nat) (A4 tptp.nat)) (exists ((K3 tptp.nat)) (= A4 (@ (@ tptp.times_times_nat B4) K3))))))
% 6.18/6.69 (assert (= tptp.dvd_dvd_int (lambda ((B4 tptp.int) (A4 tptp.int)) (exists ((K3 tptp.int)) (= A4 (@ (@ tptp.times_times_int B4) K3))))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K2))))))))
% 6.18/6.69 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K2 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K2))))))))
% 6.18/6.69 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K2 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K2))))))))
% 6.18/6.69 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K2))))))))
% 6.18/6.69 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K2 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K2))))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.18/6.69 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.18/6.69 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.18/6.69 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.18/6.69 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.18/6.69 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))))
% 6.18/6.69 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z)))))))
% 6.18/6.69 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z)))))))
% 6.18/6.69 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z)))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((D tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer D) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 D)) (@ (@ tptp.divide6298287555418463151nteger B) D)) (@ _let_1 B)))))))
% 6.18/6.69 (assert (forall ((D tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B) D)) (@ _let_1 B)))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B) D)) (@ _let_1 B)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) N2)))))
% 6.18/6.69 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) N2)))))
% 6.18/6.69 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)))))
% 6.18/6.69 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)))))
% 6.18/6.69 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N2)))))))
% 6.18/6.69 (assert (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N2)))))))
% 6.18/6.69 (assert (forall ((K tptp.code_integer) (M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N2)))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))))))
% 6.18/6.69 (assert (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M) N2)) (=> (@ _let_1 N2) (@ _let_1 M))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (@ _let_1 M))))))
% 6.18/6.69 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y 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 D))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D))) (exists ((X3 tptp.nat) (Y5 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 D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_3 Y5)) D)) (= (@ _let_3 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y5)) D)))))))))))))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D4 tptp.nat) (X3 tptp.nat) (Y5 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 D4))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y5)) D4)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y5)) D4))))))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D4 tptp.nat) (X3 tptp.nat) (Y5 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 D4))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X3)) (@ _let_2 Y5)) D4) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X3)) (@ _let_1 Y5)) D4)))))))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) A)))) (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) B)))) (@ (@ tptp.dvd_dvd_complex A) B))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) A)))) (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C4 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C4) A)))) (@ tptp.collect_Code_integer (lambda ((C4 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C4) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) A)))) (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (K tptp.int) (M tptp.nat) (L2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N2) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L2) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 L2)) R2)))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) A)))) (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) B)))) (and (@ (@ tptp.dvd_dvd_complex A) B) (not (@ (@ tptp.dvd_dvd_complex B) A))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) A)))) (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) A)))) (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C4 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C4) A)))) (@ tptp.collect_Code_integer (lambda ((C4 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C4) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))))
% 6.18/6.69 (assert (forall ((I2 tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D2 tptp.int)) (@ (@ tptp.dvd_dvd_int D2) I2)))))))
% 6.18/6.69 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.18/6.69 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.18/6.69 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.18/6.69 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X5) Z4) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S2))))) (=> (@ (@ tptp.ord_less_real X5) Z4) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S2))))) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S2))))) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S2))))) (=> (@ (@ tptp.ord_less_int X5) Z4) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X5) Z4) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S2)))) (=> (@ (@ tptp.ord_less_real X5) Z4) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S2)))) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S2)))) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S2)))) (=> (@ (@ tptp.ord_less_int X5) Z4) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X5) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S2))))) (=> (@ (@ tptp.ord_less_real Z4) X5) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S2))))) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S2))))) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S2))))) (=> (@ (@ tptp.ord_less_int Z4) X5) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z4 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z4) X5) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S2)))) (=> (@ (@ tptp.ord_less_real Z4) X5) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S2)))) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S2)))) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= _let_1 _let_1)))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S2)))) (=> (@ (@ tptp.ord_less_int Z4) X5) (= _let_1 _let_1)))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D)))))))
% 6.18/6.69 (assert (forall ((B tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))
% 6.18/6.69 (assert (forall ((B tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N2) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))))
% 6.18/6.69 (assert (forall ((B tptp.nat) (A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2))))))
% 6.18/6.69 (assert (forall ((B tptp.int) (A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N2) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.18/6.69 (assert (= tptp.dvd_dvd_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B4) A4) tptp.zero_zero_nat))))
% 6.18/6.69 (assert (= tptp.dvd_dvd_int (lambda ((A4 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B4) A4) tptp.zero_zero_int))))
% 6.18/6.69 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B4) A4) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.18/6.69 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))))
% 6.18/6.69 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) M))))))
% 6.18/6.69 (assert (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) M))))))
% 6.18/6.69 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) M))))))
% 6.18/6.69 (assert (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) M))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 6.18/6.69 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (N2 tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.69 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.18/6.69 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (not (@ (@ tptp.dvd_dvd_nat N2) M))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D4 tptp.nat) (X3 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D4))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y5)) D4))))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (or (@ (@ tptp.ord_less_nat N2) M) (@ _let_1 N2))))))
% 6.18/6.69 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_int M) N2) (=> (@ (@ tptp.dvd_dvd_int N2) M) (= M N2))))))))
% 6.18/6.69 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 M)))))))
% 6.18/6.69 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2)))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))))))
% 6.18/6.69 (assert (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M) N2))))))
% 6.18/6.69 (assert (forall ((K tptp.int) (M tptp.int) (T tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 T)))))))
% 6.18/6.69 (assert (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))))
% 6.18/6.69 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat X2) X2))))
% 6.18/6.69 (assert (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))))
% 6.18/6.69 (assert (forall ((K tptp.int) (N2 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N2) (@ (@ tptp.times_times_int K) M))) (@ _let_1 N2)))))
% 6.18/6.69 (assert (forall ((A tptp.int) (D tptp.int) (X tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))))
% 6.18/6.69 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M)))))))
% 6.18/6.69 (assert (forall ((X tptp.nat) (Y 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 X) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y)) (= X Y)))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.code_integer Bool)) (L2 tptp.code_integer)) (= (exists ((X2 tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L2) X2))) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L2) (@ (@ tptp.plus_p5714425477246183910nteger X2) tptp.zero_z3403309356797280102nteger)) (@ P X2))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.complex Bool)) (L2 tptp.complex)) (= (exists ((X2 tptp.complex)) (@ P (@ (@ tptp.times_times_complex L2) X2))) (exists ((X2 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L2) (@ (@ tptp.plus_plus_complex X2) tptp.zero_zero_complex)) (@ P X2))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.real Bool)) (L2 tptp.real)) (= (exists ((X2 tptp.real)) (@ P (@ (@ tptp.times_times_real L2) X2))) (exists ((X2 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L2) (@ (@ tptp.plus_plus_real X2) tptp.zero_zero_real)) (@ P X2))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.rat Bool)) (L2 tptp.rat)) (= (exists ((X2 tptp.rat)) (@ P (@ (@ tptp.times_times_rat L2) X2))) (exists ((X2 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L2) (@ (@ tptp.plus_plus_rat X2) tptp.zero_zero_rat)) (@ P X2))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.nat Bool)) (L2 tptp.nat)) (= (exists ((X2 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L2) X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L2) (@ (@ tptp.plus_plus_nat X2) tptp.zero_zero_nat)) (@ P X2))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.int Bool)) (L2 tptp.int)) (= (exists ((X2 tptp.int)) (@ P (@ (@ tptp.times_times_int L2) X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L2) (@ (@ tptp.plus_plus_int X2) tptp.zero_zero_int)) (@ P X2))))))
% 6.18/6.69 (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 ((C3 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C3)))))))))
% 6.18/6.69 (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 ((C3 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C3)))))))))
% 6.18/6.69 (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 ((C3 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C3)))))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D 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) D) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D)))))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D 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) D) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D)))))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D 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) D) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D)))))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((D tptp.code_integer) (D3 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D3) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X5) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X5) (@ (@ tptp.times_3573771949741848930nteger K4) D3))) T))))))))
% 6.18/6.69 (assert (forall ((D tptp.real) (D3 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D3) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3))) T))))))))
% 6.18/6.69 (assert (forall ((D tptp.rat) (D3 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D3) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3))) T))))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (D3 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3))) T))))))))
% 6.18/6.69 (assert (forall ((D tptp.code_integer) (D3 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D3) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X5) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X5) (@ (@ tptp.times_3573771949741848930nteger K4) D3))) T)))))))))
% 6.18/6.69 (assert (forall ((D tptp.real) (D3 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D3) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3))) T)))))))))
% 6.18/6.69 (assert (forall ((D tptp.rat) (D3 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D3) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3))) T)))))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (D3 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3))) T)))))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat K) N2)))))
% 6.18/6.69 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.18/6.69 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.18/6.69 (assert (forall ((Z tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int Z) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N2)) (not (@ (@ tptp.dvd_dvd_nat N2) M)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.18/6.69 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M2 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K2) M2)))))))
% 6.18/6.69 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.18/6.69 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.18/6.69 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2))))))))
% 6.18/6.69 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2))))))))
% 6.18/6.69 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2))))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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 ((B2 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B2 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B2) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B2)))))))))))))))
% 6.18/6.69 (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 ((B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_times_nat A) B2) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B2)))))))))))))))
% 6.18/6.69 (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 ((B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_times_int A) B2) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B2)))))))))))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.18/6.69 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.18/6.69 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.18/6.69 (assert (= (lambda ((Y4 tptp.code_integer) (Z3 tptp.code_integer)) (= Y4 Z3)) (lambda ((A4 tptp.code_integer) (B4 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 A4) (@ _let_2 B4)) (= (@ (@ tptp.divide6298287555418463151nteger A4) _let_1) (@ (@ tptp.divide6298287555418463151nteger B4) _let_1))))))))
% 6.18/6.69 (assert (= (lambda ((Y4 tptp.nat) (Z3 tptp.nat)) (= Y4 Z3)) (lambda ((A4 tptp.nat) (B4 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 A4) (@ _let_2 B4)) (= (@ (@ tptp.divide_divide_nat A4) _let_1) (@ (@ tptp.divide_divide_nat B4) _let_1))))))))
% 6.18/6.69 (assert (= (lambda ((Y4 tptp.int) (Z3 tptp.int)) (= Y4 Z3)) (lambda ((A4 tptp.int) (B4 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 A4) (@ _let_2 B4)) (= (@ (@ tptp.divide_divide_int A4) _let_1) (@ (@ tptp.divide_divide_int B4) _let_1))))))))
% 6.18/6.69 (assert (forall ((X tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.18/6.69 (assert (forall ((X tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.18/6.69 (assert (forall ((X tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (X tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X) (@ (@ tptp.power_power_rat X) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X) (@ (@ tptp.power_power_real X) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (X tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X) (@ (@ tptp.power_power_complex X) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N2) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N2)) M) (= N2 tptp.one_one_nat)))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N2) M)) M) (= N2 tptp.one_one_nat)))))
% 6.18/6.69 (assert (forall ((Q2 tptp.nat) (N2 tptp.nat) (R2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N2) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N2) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))))
% 6.18/6.69 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.69 (assert (forall ((R2 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N2) (=> (@ (@ tptp.ord_less_eq_nat R2) M) (=> (@ (@ tptp.dvd_dvd_nat N2) (@ (@ tptp.minus_minus_nat M) R2)) (= (@ (@ tptp.modulo_modulo_nat M) N2) R2))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (D3 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) D3)) T)))))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (D3 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) D3)) T))))))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (D3 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X5))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D3)) T))))))))))
% 6.18/6.69 (assert (forall ((D tptp.int) (D3 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X5))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D3)) T)))))))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.18/6.69 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_Code_integer))))))))
% 6.18/6.69 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_nat))))))))
% 6.18/6.69 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_int))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N2)))))
% 6.18/6.69 (assert (forall ((N2 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))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (@ _let_1 A))))))
% 6.18/6.69 (assert (forall ((N2 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))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (@ _let_1 A))))))
% 6.18/6.69 (assert (forall ((N2 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))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (@ _let_1 A))))))
% 6.18/6.69 (assert (forall ((A tptp.real) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.18/6.69 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X (@ tptp.suc N3))))))))
% 6.18/6.69 (assert (forall ((A tptp.real) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ P A3) B2) (@ (@ P B2) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B2))))) (@ (@ P A) B))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.18/6.69 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 6.18/6.69 (assert (forall ((N2 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 N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) _let_3)) _let_2))))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ 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) N2))))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2))) (= (@ (@ 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) N2))))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2))) (= (@ (@ 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) N2))))))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 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 N2))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.18/6.69 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.18/6.69 (assert (forall ((A tptp.int) (M tptp.nat) (N2 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 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.18/6.69 (assert (forall ((X8 tptp.set_real)) (=> (not (= X8 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) X8) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X8) (@ (@ tptp.ord_less_real X3) Xa))))) (not (@ tptp.finite_finite_real X8))))))
% 6.18/6.69 (assert (forall ((X8 tptp.set_rat)) (=> (not (= X8 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) X8) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X8) (@ (@ tptp.ord_less_rat X3) Xa))))) (not (@ tptp.finite_finite_rat X8))))))
% 6.18/6.69 (assert (forall ((X8 tptp.set_num)) (=> (not (= X8 tptp.bot_bot_set_num)) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) X8) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X8) (@ (@ tptp.ord_less_num X3) Xa))))) (not (@ tptp.finite_finite_num X8))))))
% 6.18/6.69 (assert (forall ((X8 tptp.set_nat)) (=> (not (= X8 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X8) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X8) (@ (@ tptp.ord_less_nat X3) Xa))))) (not (@ tptp.finite_finite_nat X8))))))
% 6.18/6.69 (assert (forall ((X8 tptp.set_int)) (=> (not (= X8 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X8) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X8) (@ (@ tptp.ord_less_int X3) Xa))))) (not (@ tptp.finite_finite_int X8))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_real)) (=> (@ tptp.finite_finite_real S3) (=> (not (= S3 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) S3) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S3) (@ (@ tptp.ord_less_real Xa) X3))))))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat S3) (=> (not (= S3 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) S3) (not (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) S3) (@ (@ tptp.ord_less_rat Xa) X3))))))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_num)) (=> (@ tptp.finite_finite_num S3) (=> (not (= S3 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) S3) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S3) (@ (@ tptp.ord_less_num Xa) X3))))))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) S3) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S3) (@ (@ tptp.ord_less_nat Xa) X3))))))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_int)) (=> (@ tptp.finite_finite_int S3) (=> (not (= S3 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) S3) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S3) (@ (@ tptp.ord_less_int Xa) X3))))))))))
% 6.18/6.69 (assert (= tptp.nat_triangle (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.18/6.69 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (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))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((X (-> tptp.nat tptp.nat)) (X22 tptp.nat)) (= (@ (@ tptp.size_option_nat X) (@ tptp.some_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((X (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N2)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N2) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.69 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y))))
% 6.18/6.69 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.18/6.69 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.18/6.69 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I2))))))
% 6.18/6.69 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I2))))))
% 6.18/6.69 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I2))))))
% 6.18/6.69 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.18/6.69 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.18/6.69 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.18/6.69 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.18/6.69 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 6.18/6.69 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.18/6.69 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.18/6.69 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.18/6.69 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.18/6.69 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 6.18/6.69 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.18/6.69 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.18/6.69 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.18/6.69 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.18/6.69 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.18/6.69 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.18/6.69 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.18/6.69 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.18/6.69 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.18/6.69 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.18/6.69 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.18/6.69 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.18/6.69 (assert (forall ((M tptp.nat) (X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X) (@ (@ tptp.replicate_VEBT_VEBT N2) Y)) (and (= M N2) (=> (not (= M tptp.zero_zero_nat)) (= X Y))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) N2)))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N2) X)) N2)))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N2) X)) N2)))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.18/6.69 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N2) (@ tptp.zero_n2687167440665602831ol_nat (not (= N2 _let_1)))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 6.18/6.69 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.18/6.69 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.18/6.69 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.18/6.69 (assert (forall ((X tptp.set_nat) (N2 tptp.nat) (Y tptp.set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ tptp.replicate_set_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.18/6.69 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.18/6.69 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.18/6.69 (assert (forall ((X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X2))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X2))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X2))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X2))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X)) I2) X))))
% 6.18/6.69 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X)) I2) X))))
% 6.18/6.69 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X)) I2) X))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N2)) _let_1)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.18/6.69 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P4))) P4)))
% 6.18/6.69 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P4))) P4)))
% 6.18/6.69 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P4))) P4)))
% 6.18/6.69 (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)))
% 6.18/6.69 (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)))
% 6.18/6.69 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.69 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M) (= M N2)))))
% 6.18/6.69 (assert (forall ((P4 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P4) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P4 Q2))))
% 6.18/6.69 (assert (forall ((P4 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P4) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P4 Q2))))
% 6.18/6.69 (assert (forall ((P4 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P4) (@ tptp.zero_n356916108424825756nteger Q2)) (= P4 Q2))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.18/6.69 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.18/6.69 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.18/6.69 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.18/6.69 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.18/6.69 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.18/6.69 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.18/6.69 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.18/6.69 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.18/6.69 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.18/6.69 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.18/6.69 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P5 Bool)) (@ (@ (@ tptp.if_complex P5) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.18/6.69 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P5 Bool)) (@ (@ (@ tptp.if_real P5) tptp.one_one_real) tptp.zero_zero_real))))
% 6.18/6.69 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_rat P5) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.18/6.69 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_nat P5) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.18/6.69 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P5 Bool)) (@ (@ (@ tptp.if_int P5) tptp.one_one_int) tptp.zero_zero_int))))
% 6.18/6.69 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P5 Bool)) (@ (@ (@ tptp.if_Code_integer P5) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.69 (assert (forall ((P (-> tptp.complex Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P4)) (and (=> P4 (@ P tptp.one_one_complex)) (=> (not P4) (@ P tptp.zero_zero_complex))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.real Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P4)) (and (=> P4 (@ P tptp.one_one_real)) (=> (not P4) (@ P tptp.zero_zero_real))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.rat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P4)) (and (=> P4 (@ P tptp.one_one_rat)) (=> (not P4) (@ P tptp.zero_zero_rat))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.nat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P4)) (and (=> P4 (@ P tptp.one_one_nat)) (=> (not P4) (@ P tptp.zero_zero_nat))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.int Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P4)) (and (=> P4 (@ P tptp.one_one_int)) (=> (not P4) (@ P tptp.zero_zero_int))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.code_integer Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P4)) (and (=> P4 (@ P tptp.one_one_Code_integer)) (=> (not P4) (@ P tptp.zero_z3403309356797280102nteger))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.complex Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P4)) (not (or (and P4 (not (@ P tptp.one_one_complex))) (and (not P4) (not (@ P tptp.zero_zero_complex))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.real Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P4)) (not (or (and P4 (not (@ P tptp.one_one_real))) (and (not P4) (not (@ P tptp.zero_zero_real))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.rat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P4)) (not (or (and P4 (not (@ P tptp.one_one_rat))) (and (not P4) (not (@ P tptp.zero_zero_rat))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.nat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P4)) (not (or (and P4 (not (@ P tptp.one_one_nat))) (and (not P4) (not (@ P tptp.zero_zero_nat))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.int Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P4)) (not (or (and P4 (not (@ P tptp.one_one_int))) (and (not P4) (not (@ P tptp.zero_zero_int))))))))
% 6.18/6.69 (assert (forall ((P (-> tptp.code_integer Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P4)) (not (or (and P4 (not (@ P tptp.one_one_Code_integer))) (and (not P4) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 6.18/6.69 (assert (forall ((Xs2 tptp.list_complex) (N2 tptp.nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) N2) (=> (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) (@ tptp.set_complex2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_complex N2) X))))))
% 6.18/6.69 (assert (forall ((Xs2 tptp.list_real) (N2 tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N2) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.member_real Y5) (@ tptp.set_real2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_real N2) X))))))
% 6.18/6.69 (assert (forall ((Xs2 tptp.list_set_nat) (N2 tptp.nat) (X tptp.set_nat)) (=> (= (@ tptp.size_s3254054031482475050et_nat Xs2) N2) (=> (forall ((Y5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y5) (@ tptp.set_set_nat2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_set_nat N2) X))))))
% 6.18/6.69 (assert (forall ((Xs2 tptp.list_nat) (N2 tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N2) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) (@ tptp.set_nat2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_nat N2) X))))))
% 6.18/6.69 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N2) (=> (forall ((Y5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y5) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N2) X))))))
% 6.18/6.69 (assert (forall ((Xs2 tptp.list_o) (N2 tptp.nat) (X Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N2) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) (@ tptp.set_o2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_o N2) X))))))
% 6.18/6.69 (assert (forall ((Xs2 tptp.list_int) (N2 tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N2) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) (@ tptp.set_int2 Xs2)) (= Y5 X))) (= Xs2 (@ (@ tptp.replicate_int N2) X))))))
% 6.18/6.69 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs2)) X) Xs2))))
% 6.18/6.69 (assert (forall ((Xs2 tptp.list_o) (X Bool)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs2)) X) Xs2))))
% 6.18/6.69 (assert (forall ((Xs2 tptp.list_int) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs2)) X) Xs2))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.nat) (B2 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) (@ (@ tptp.times_times_nat _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.18/6.69 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.int) (B2 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B2)) (@ (@ tptp.times_times_int _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.18/6.69 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A3 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.code_integer) (B2 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B2)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))))
% 6.18/6.69 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.18/6.69 (assert (forall ((N2 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 N2)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N2))))))))
% 6.18/6.69 (assert (forall ((X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.18/6.69 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.18/6.69 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.18/6.69 (assert (= tptp.nat_set_decode (lambda ((X2 tptp.nat)) (@ tptp.collect_nat (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat _let_1) N))))))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.18/6.69 (assert (forall ((M tptp.nat) (N2 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 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.18/6.69 (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))))))))))))))))
% 6.18/6.69 (assert (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R2)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R2 tptp.zero_zero_int)))))))
% 6.18/6.69 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A4) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N 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 N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))))))))))
% 6.18/6.69 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A4) _let_1))) (@ (@ (@ tptp.if_int (= N 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 N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))))))))))
% 6.18/6.69 (assert (forall ((X tptp.nat) (Y 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 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (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))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _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)))))))))))))))))))))))
% 6.18/6.69 (assert (forall ((R2 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D)))))))))
% 6.18/6.69 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))))
% 6.18/6.69 (assert (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))))
% 6.18/6.69 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))))
% 6.18/6.69 (assert (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))))
% 6.18/6.69 (assert (= tptp.artanh_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.18/6.69 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int M) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N2) (@ (@ tptp.plus_plus_int N2) 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)))))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B3)) (@ tptp.uminus1532241313380277803et_int A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ tptp.uminus1532241313380277803et_int B3)) (@ (@ tptp.ord_less_eq_set_int B3) A2))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) (@ tptp.uminus1532241313380277803et_int Y)) (@ (@ tptp.ord_less_eq_set_int Y) X))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= M N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= M N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= M N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (= M N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= M N2))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.18/6.69 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X)) Y) (@ (@ tptp.dvd_dvd_real X) Y))))
% 6.18/6.69 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.dvd_dvd_int X) Y))))
% 6.18/6.69 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X)) Y) (@ (@ tptp.dvd_dvd_complex X) Y))))
% 6.18/6.69 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X)) Y) (@ (@ tptp.dvd_dvd_rat X) Y))))
% 6.18/6.69 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X)) Y) (@ (@ tptp.dvd_dvd_Code_integer X) Y))))
% 6.18/6.69 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))))
% 6.18/6.69 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 6.18/6.69 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))))
% 6.18/6.69 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y)) (@ _let_1 Y)))))
% 6.18/6.69 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y)) (@ _let_1 Y)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.18/6.69 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A2) tptp.zero_zero_int)))
% 6.18/6.69 (assert (forall ((A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((Uu3 tptp.complex)) tptp.zero_zero_complex)) A2) tptp.zero_zero_complex)))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A2) tptp.zero_zero_nat)))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A2) tptp.zero_zero_real)))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.18/6.69 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.18/6.69 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.18/6.69 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.18/6.69 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.18/6.69 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.18/6.69 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.18/6.69 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.69 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.18/6.69 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.18/6.69 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.18/6.69 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.69 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.18/6.69 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.18/6.69 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.18/6.69 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.18/6.69 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 6.18/6.69 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 6.18/6.69 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.18/6.69 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (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)))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (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)))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (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)))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (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)))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (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)))))))
% 6.18/6.69 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.18/6.69 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.18/6.69 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.18/6.69 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.18/6.69 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.18/6.69 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.18/6.69 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.18/6.69 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.18/6.69 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.18/6.69 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.18/6.69 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.18/6.69 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 6.18/6.69 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 6.18/6.69 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.divide_divide_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.18/6.69 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 6.18/6.69 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N2) _let_1) _let_1))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) _let_1) _let_1))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= A K3)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (= K3 A)) (@ B K3)) tptp.zero_zero_complex))) S3) tptp.zero_zero_complex)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.zero_zero_real))) S3) tptp.zero_zero_real)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S3) tptp.zero_zero_rat)))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.18/6.69 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.18/6.69 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.18/6.69 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.18/6.69 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.18/6.69 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.18/6.69 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.18/6.69 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.18/6.69 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.18/6.69 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.18/6.69 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.18/6.69 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.18/6.69 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.18/6.69 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.18/6.69 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N2 tptp.one))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N2 tptp.one))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N2 tptp.one))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N2 tptp.one))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N2 tptp.one))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= N2 tptp.one))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= N2 tptp.one))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= N2 tptp.one))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (= N2 tptp.one))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= N2 tptp.one))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 6.18/6.69 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.18/6.69 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y 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))) Y)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y))))
% 6.18/6.69 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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))))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.18/6.69 (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)))
% 6.18/6.69 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.18/6.69 (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))
% 6.18/6.69 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.18/6.69 (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))
% 6.18/6.69 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.18/6.69 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.power_power_real A) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.power_power_int A) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.power_power_complex A) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ (@ tptp.power_power_rat A) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N2))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.18/6.69 (assert (forall ((N2 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))) N2)) tptp.one_one_real)))
% 6.18/6.69 (assert (forall ((N2 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))) N2)) tptp.one_one_int)))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_complex)))
% 6.18/6.69 (assert (forall ((N2 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))) N2)) tptp.one_one_rat)))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_Code_integer)))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2) tptp.one_one_real))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2) tptp.one_one_int))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2) tptp.one_one_complex))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2) tptp.one_one_rat))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2) tptp.one_one_Code_integer))))
% 6.18/6.69 (assert (forall ((N2 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))) N2)) (= (@ (@ tptp.power_power_real _let_1) N2) _let_1)))))
% 6.18/6.69 (assert (forall ((N2 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))) N2)) (= (@ (@ tptp.power_power_int _let_1) N2) _let_1)))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex _let_1) N2) _let_1)))))
% 6.18/6.69 (assert (forall ((N2 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))) N2)) (= (@ (@ tptp.power_power_rat _let_1) N2) _let_1)))))
% 6.18/6.69 (assert (forall ((N2 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))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N2) _let_1)))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.uminus_uminus_int (@ F X2)))) A2) (@ tptp.uminus_uminus_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)))))
% 6.18/6.69 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ tptp.uminus1482373934393186551omplex (@ F X2)))) A2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)))))
% 6.18/6.69 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ tptp.uminus_uminus_real (@ F X2)))) A2) (@ tptp.uminus_uminus_real (@ (@ tptp.groups6591440286371151544t_real F) A2)))))
% 6.18/6.69 (assert (forall ((G (-> tptp.int tptp.int tptp.int)) (B3 tptp.set_int) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (@ G I5)) B3))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ G I5) J3))) A2))) B3))))
% 6.18/6.69 (assert (forall ((G (-> tptp.complex tptp.complex tptp.complex)) (B3 tptp.set_complex) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((I5 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (@ G I5)) B3))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I5 tptp.complex)) (@ (@ G I5) J3))) A2))) B3))))
% 6.18/6.69 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (B3 tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G I5)) B3))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) J3))) A2))) B3))))
% 6.18/6.69 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (B3 tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ G I5)) B3))) A2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ G I5) J3))) A2))) B3))))
% 6.18/6.69 (assert (forall ((H2 (-> Bool Bool)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.18/6.69 (assert (forall ((H2 (-> Bool tptp.int)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.18/6.69 (assert (forall ((H2 (-> tptp.int Bool)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.18/6.69 (assert (forall ((H2 (-> tptp.int tptp.int)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.18/6.69 (assert (forall ((H2 (-> tptp.product_prod_int_int Bool)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.18/6.69 (assert (forall ((H2 (-> tptp.product_prod_int_int tptp.int)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.18/6.69 (assert (forall ((H2 (-> Bool tptp.product_prod_int_int)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.18/6.69 (assert (forall ((H2 (-> tptp.int tptp.product_prod_int_int)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.18/6.69 (assert (forall ((H2 (-> tptp.product_prod_int_int tptp.product_prod_int_int)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.18/6.69 (assert (forall ((H2 (-> (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat Bool)) (F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Prod tptp.product_prod_nat_nat)) (= (@ H2 (@ (@ tptp.produc8739625826339149834_nat_o F) Prod)) (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X15 tptp.nat) (X24 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ H2 (@ (@ F X15) X24)) __flatten_var_0))) Prod))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) X) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) Y))))
% 6.18/6.69 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) (@ tptp.uminus1532241313380277803et_int X)) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y)))))
% 6.18/6.69 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) (@ tptp.uminus1532241313380277803et_int X)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.18/6.69 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.18/6.69 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.18/6.69 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.18/6.69 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.18/6.69 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.int Bool)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int) (A6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A6) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A6)) B)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A6) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A6)) B)))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G) K5)))))
% 6.18/6.69 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K5)) (@ (@ tptp.groups1300246762558778688al_rat G) K5)))))
% 6.18/6.69 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))))
% 6.18/6.69 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))))
% 6.18/6.69 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G) K5)))))
% 6.18/6.69 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))))
% 6.18/6.69 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))))
% 6.18/6.69 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) K5)) (@ (@ tptp.groups5690904116761175830ex_int G) K5)))))
% 6.18/6.69 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))))
% 6.18/6.69 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))))
% 6.18/6.69 (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 ((I5 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I5)) (@ G J3)))) B3))) A2))))
% 6.18/6.69 (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 ((I5 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I5)) (@ G J3)))) B3))) A2))))
% 6.18/6.69 (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 ((I5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I5)) (@ G J3)))) B3))) A2))))
% 6.18/6.69 (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 ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I5)) (@ G J3)))) B3))) A2))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (R2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) R2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N tptp.int)) (@ (@ tptp.times_times_int (@ F N)) R2))) A2))))
% 6.18/6.69 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.times_times_complex (@ F N)) R2))) A2))))
% 6.18/6.69 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (R2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) R2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat (@ F N)) R2))) A2))))
% 6.18/6.69 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) R2))) A2))))
% 6.18/6.69 (assert (forall ((R2 tptp.int) (F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.times_times_int R2) (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N tptp.int)) (@ (@ tptp.times_times_int R2) (@ F N)))) A2))))
% 6.18/6.69 (assert (forall ((R2 tptp.complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R2) (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.times_times_complex R2) (@ F N)))) A2))))
% 6.18/6.69 (assert (forall ((R2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R2) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat R2) (@ F N)))) A2))))
% 6.18/6.69 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_real R2) (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real R2) (@ F N)))) A2))))
% 6.18/6.69 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H2) A2)))))
% 6.18/6.69 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H2) A2)))))
% 6.18/6.69 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H2) A2)))))
% 6.18/6.69 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ H2 X2)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H2) A2)))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))
% 6.18/6.69 (assert (forall ((F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) A2)))))
% 6.18/6.69 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) A2)))))
% 6.18/6.69 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) R2))) A2))))
% 6.18/6.69 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) R2))) A2))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_int) (G (-> tptp.real tptp.int tptp.int)) (R (-> tptp.real tptp.int Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups1932886352136224148al_int (lambda ((X2 tptp.real)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X2)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups1932886352136224148al_int (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_int) (G (-> tptp.nat tptp.int tptp.int)) (R (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X2)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X2 tptp.nat)) (@ (@ G X2) Y2))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_int) (G (-> tptp.complex tptp.int tptp.int)) (R (-> tptp.complex tptp.int Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((X2 tptp.complex)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X2)) (@ tptp.collect_int (lambda ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y2 tptp.int)) (@ (@ tptp.groups5690904116761175830ex_int (lambda ((X2 tptp.complex)) (@ (@ G X2) Y2))) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_complex) (G (-> tptp.real tptp.complex tptp.complex)) (R (-> tptp.real tptp.complex Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite3207457112153483333omplex B3) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((X2 tptp.real)) (@ (@ tptp.groups7754918857620584856omplex (@ G X2)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_complex) (G (-> tptp.nat tptp.complex tptp.complex)) (R (-> tptp.nat tptp.complex Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite3207457112153483333omplex B3) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (@ G X2)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ (@ G X2) Y2))) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_complex) (G (-> tptp.int tptp.complex tptp.complex)) (R (-> tptp.int tptp.complex Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite3207457112153483333omplex B3) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((X2 tptp.int)) (@ (@ tptp.groups7754918857620584856omplex (@ G X2)) (@ tptp.collect_complex (lambda ((Y2 tptp.complex)) (and (@ (@ tptp.member_complex Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((Y2 tptp.complex)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X2 tptp.int)) (@ (@ G X2) Y2))) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (G (-> tptp.real tptp.nat tptp.nat)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ G X2) Y2))) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_nat) (G (-> tptp.complex tptp.nat tptp.nat)) (R (-> tptp.complex tptp.nat Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X2 tptp.complex)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X2 tptp.complex)) (@ (@ G X2) Y2))) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (G (-> tptp.real tptp.nat tptp.real)) (R (-> tptp.real tptp.nat Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((X2 tptp.real)) (@ (@ tptp.groups6591440286371151544t_real (@ G X2)) (@ tptp.collect_nat (lambda ((Y2 tptp.nat)) (and (@ (@ tptp.member_nat Y2) B3) (@ (@ R X2) Y2))))))) A2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Y2 tptp.nat)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X2 tptp.real)) (@ (@ G X2) Y2))) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ (@ R X2) Y2))))))) B3))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))))
% 6.18/6.69 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))))
% 6.18/6.69 (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) (Y5 tptp.nat)) (= (@ (@ F X3) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y5)))) (= (@ tptp.produc27273713700761075at_nat F) G))))
% 6.18/6.69 (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) (Y5 tptp.nat)) (= (@ (@ F X3) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y5)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))))
% 6.18/6.69 (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) (Y5 tptp.int)) (= (@ (@ F X3) Y5) (@ G (@ (@ tptp.product_Pair_int_int X3) Y5)))) (= (@ tptp.produc4245557441103728435nt_int F) G))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.int Bool)) (G (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (= (@ (@ F X3) Y5) (@ G (@ (@ tptp.product_Pair_int_int X3) Y5)))) (= (@ tptp.produc4947309494688390418_int_o F) G))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (G (-> tptp.product_prod_int_int tptp.int))) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (= (@ (@ F X3) Y5) (@ G (@ (@ tptp.product_Pair_int_int X3) Y5)))) (= (@ tptp.produc8211389475949308722nt_int F) G))))
% 6.18/6.69 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y2)) __flatten_var_0))) F)))
% 6.18/6.69 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X2) Y2)) __flatten_var_0))) F)))
% 6.18/6.69 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y2)))) F)))
% 6.18/6.69 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y2)))) F)))
% 6.18/6.69 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X2) Y2)))) F)))
% 6.18/6.69 (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) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X3) Y5)) (not (@ Q (@ (@ P X3) Y5)))))))))
% 6.18/6.69 (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) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X3) Y5)) (not (@ Q (@ (@ P X3) Y5)))))))))
% 6.18/6.69 (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) (Y5 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y5)) (not (@ Q (@ (@ P X3) Y5)))))))))
% 6.18/6.69 (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) (Y5 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y5)) (not (@ Q (@ (@ P X3) Y5)))))))))
% 6.18/6.69 (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) (Y5 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y5)) (not (@ Q (@ (@ P X3) Y5)))))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.18/6.69 (assert (forall ((F (-> tptp.real tptp.rat)) (I6 tptp.set_real) (G (-> tptp.real tptp.rat)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) I6) (@ (@ tptp.groups1300246762558778688al_rat G) I6)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_real I2) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I2) (@ G I2))))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.nat tptp.rat)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I6) (@ (@ tptp.groups2906978787729119204at_rat G) I6)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I2) (@ G I2))))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.rat)) (I6 tptp.set_int) (G (-> tptp.int tptp.rat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I6) (@ (@ tptp.groups3906332499630173760nt_rat G) I6)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_int I2) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I2) (@ G I2))))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.complex tptp.rat)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) I6) (@ (@ tptp.groups5058264527183730370ex_rat G) I6)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I2) (@ G I2))))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.real tptp.nat)) (I6 tptp.set_real) (G (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I6) (@ (@ tptp.groups1935376822645274424al_nat G) I6)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_real I2) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I2) (@ G I2))))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.int tptp.nat)) (I6 tptp.set_int) (G (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I6) (@ (@ tptp.groups4541462559716669496nt_nat G) I6)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_int I2) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I2) (@ G I2))))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.complex tptp.nat)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I6) (@ (@ tptp.groups5693394587270226106ex_nat G) I6)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I2) (@ G I2))))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.real tptp.int)) (I6 tptp.set_real) (G (-> tptp.real tptp.int)) (I2 tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) I6) (@ (@ tptp.groups1932886352136224148al_int G) I6)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_real I2) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I2) (@ G I2))))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.nat tptp.int)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.int)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) I6) (@ (@ tptp.groups3539618377306564664at_int G) I6)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I2) (@ G I2))))))))
% 6.18/6.69 (assert (forall ((F (-> tptp.complex tptp.int)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.int)) (I2 tptp.complex)) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F) I6) (@ (@ tptp.groups5690904116761175830ex_int G) I6)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I2) (@ G I2))))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.18/6.69 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.18/6.69 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.18/6.69 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.18/6.69 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.18/6.69 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.18/6.69 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.18/6.69 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.69 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.18/6.69 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.69 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.18/6.69 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.18/6.69 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.18/6.69 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.18/6.69 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.18/6.69 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.18/6.69 (assert (forall ((W tptp.num) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real X) (@ tptp.uminus_uminus_real _let_1))))))
% 6.18/6.69 (assert (forall ((W tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))))
% 6.18/6.69 (assert (forall ((W tptp.num) (X tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex X) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.18/6.69 (assert (forall ((W tptp.num) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat X) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.18/6.69 (assert (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real N2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_rat N2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.18/6.69 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.18/6.69 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.18/6.69 (assert (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.18/6.69 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.18/6.69 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B4)))))
% 6.18/6.69 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B4)))))
% 6.18/6.69 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B4)))))
% 6.18/6.69 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B4)))))
% 6.18/6.69 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B4)))))
% 6.18/6.69 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B4)))))
% 6.18/6.69 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B4)))))
% 6.18/6.69 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B4)))))
% 6.18/6.69 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B4)))))
% 6.18/6.69 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B4)))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))))
% 6.18/6.69 (assert (forall ((U tptp.real) (X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X) X))))
% 6.18/6.69 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M) N2) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N2 tptp.one_one_int)) (and (= M _let_1) (= N2 _let_1)))))))
% 6.18/6.69 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (= (@ (@ tptp.times_times_int M) N2) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.18/6.69 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L2) (@ tptp.uminus_uminus_int L2))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups5754745047067104278omplex G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.zero_zero_complex))) A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.zero_zero_complex))) A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups3049146728041665814omplex G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_complex (@ P X2)) (@ G X2)) tptp.zero_zero_complex))) A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups8097168146408367636l_real G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.zero_zero_real))) A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups8778361861064173332t_real G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.zero_zero_real))) A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5808333547571424918x_real G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.zero_zero_real))) A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.rat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1300246762558778688al_rat G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.zero_zero_rat))) A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.zero_zero_rat))) A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups3906332499630173760nt_rat G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.zero_zero_rat))) A2)))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5058264527183730370ex_rat G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_rat (@ P X2)) (@ G X2)) tptp.zero_zero_rat))) A2)))))
% 6.18/6.69 (assert (= tptp.minus_minus_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real Y2)))))
% 6.18/6.69 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X))) (@ tptp.uminus_uminus_real X))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I2 (-> tptp.int tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ 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) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S2)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I2 (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S2) (=> (@ 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) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S2)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I2 (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ 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) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S2)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I2 (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ 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) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S2)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I2 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ 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) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_nat) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I2 (-> tptp.int tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ 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) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I2 (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ 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) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I2 (-> tptp.nat tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ 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) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I2 (-> tptp.int tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ 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) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I2 (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ 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) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I2 Xa) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.18/6.69 (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 ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.18/6.69 (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 ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.18/6.69 (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 ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_real))))))))
% 6.18/6.69 (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 ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.18/6.69 (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 ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.18/6.69 (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 ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.18/6.69 (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 ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_rat))))))))
% 6.18/6.69 (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 ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.18/6.69 (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 ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.18/6.69 (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 ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_nat))))))))
% 6.18/6.69 (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 ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.18/6.69 (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 ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_real (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.18/6.69 (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 ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.18/6.69 (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 ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.18/6.69 (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 ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_rat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.18/6.69 (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 ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.18/6.69 (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 ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_nat (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.18/6.69 (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 ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_int (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups3539618377306564664at_int G) A2)))))))
% 6.18/6.69 (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 ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (@ (@ tptp.ord_less_int (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups5690904116761175830ex_int G) A2)))))))
% 6.18/6.69 (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 ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (@ (@ tptp.ord_less_int (@ F X5)) (@ G X5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))))
% 6.18/6.69 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X16 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_complex X16) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups2073611262835488442omplex H2) S3)) (@ (@ tptp.groups2073611262835488442omplex G) S3))))))))
% 6.18/6.69 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X16 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_complex X16) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3049146728041665814omplex H2) S3)) (@ (@ tptp.groups3049146728041665814omplex G) S3))))))))
% 6.18/6.69 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X16 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_real X16) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups8778361861064173332t_real H2) S3)) (@ (@ tptp.groups8778361861064173332t_real G) S3))))))))
% 6.18/6.69 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X16 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_real X16) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups5808333547571424918x_real H2) S3)) (@ (@ tptp.groups5808333547571424918x_real G) S3))))))))
% 6.18/6.69 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X16) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups2906978787729119204at_rat H2) S3)) (@ (@ tptp.groups2906978787729119204at_rat G) S3))))))))
% 6.18/6.69 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X16) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3906332499630173760nt_rat H2) S3)) (@ (@ tptp.groups3906332499630173760nt_rat G) S3))))))))
% 6.18/6.69 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X16) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups5058264527183730370ex_rat H2) S3)) (@ (@ tptp.groups5058264527183730370ex_rat G) S3))))))))
% 6.18/6.69 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X16 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_nat X16) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups4541462559716669496nt_nat H2) S3)) (@ (@ tptp.groups4541462559716669496nt_nat G) S3))))))))
% 6.18/6.69 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X16 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_nat X16) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups5693394587270226106ex_nat H2) S3)) (@ (@ tptp.groups5693394587270226106ex_nat G) S3))))))))
% 6.18/6.69 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X16 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_int X16) Y15)) (@ (@ tptp.plus_plus_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3539618377306564664at_int H2) S3)) (@ (@ tptp.groups3539618377306564664at_int G) S3))))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) X))))
% 6.18/6.69 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.18/6.69 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_real) (S3 tptp.set_real) (I2 (-> 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 ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_real (@ I2 B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S4) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T4) (= (@ H2 B2) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S3) (@ (@ tptp.groups5754745047067104278omplex H2) T3)))))))))))))
% 6.18/6.69 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_int) (S3 tptp.set_real) (I2 (-> 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 ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_real (@ I2 B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S4) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T4) (= (@ H2 B2) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S3) (@ (@ tptp.groups3049146728041665814omplex H2) T3)))))))))))))
% 6.18/6.69 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_real) (S3 tptp.set_int) (I2 (-> 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 ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S3) S4)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S4) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T4) (= (@ H2 B2) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S3) (@ (@ tptp.groups5754745047067104278omplex H2) T3)))))))))))))
% 6.18/6.69 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_int) (S3 tptp.set_int) (I2 (-> 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 ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S3) S4)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S4) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T4) (= (@ H2 B2) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S3) (@ (@ tptp.groups3049146728041665814omplex H2) T3)))))))))))))
% 6.18/6.69 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_real) (S3 tptp.set_real) (I2 (-> 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 ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_real (@ I2 B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S4) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T4) (= (@ H2 B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S3) (@ (@ tptp.groups8097168146408367636l_real H2) T3)))))))))))))
% 6.18/6.69 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_int) (S3 tptp.set_real) (I2 (-> 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 ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_real (@ I2 B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S4) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T4) (= (@ H2 B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S3) (@ (@ tptp.groups8778361861064173332t_real H2) T3)))))))))))))
% 6.18/6.69 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_complex) (S3 tptp.set_real) (I2 (-> 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 ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T3) T4)))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (@ (@ tptp.member_real (@ I2 B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S4) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) T4) (= (@ H2 B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S3) (@ (@ tptp.groups5808333547571424918x_real H2) T3)))))))))))))
% 6.18/6.69 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_real) (S3 tptp.set_int) (I2 (-> 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 ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (@ (@ tptp.member_real (@ J A3)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S3) S4)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S4) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T4) (= (@ H2 B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S3) (@ (@ tptp.groups8097168146408367636l_real H2) T3)))))))))))))
% 6.18/6.69 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_int) (S3 tptp.set_int) (I2 (-> 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 ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (@ (@ tptp.member_int (@ J A3)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S3) S4)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S4) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T4) (= (@ H2 B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S3) (@ (@ tptp.groups8778361861064173332t_real H2) T3)))))))))))))
% 6.18/6.69 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_complex) (S3 tptp.set_int) (I2 (-> 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 ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (= (@ I2 (@ J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) (@ (@ tptp.minus_minus_set_int S3) S4)) (@ (@ tptp.member_complex (@ J A3)) (@ (@ tptp.minus_811609699411566653omplex T3) T4)))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S3) S4)))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S4) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) T4) (= (@ H2 B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.int)) (=> (@ (@ tptp.member_int A3) S3) (= (@ H2 (@ J A3)) (@ G A3)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S3) (@ (@ tptp.groups5808333547571424918x_real H2) T3)))))))))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.18/6.69 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.18/6.69 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.18/6.69 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.18/6.69 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.18/6.69 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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)))))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.18/6.69 (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))))
% 6.18/6.69 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (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))))))
% 6.18/6.69 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.18/6.69 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.18/6.69 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.18/6.69 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.18/6.69 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.18/6.69 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.power_power_real A) N2)))))
% 6.18/6.69 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ (@ tptp.power_power_int A) N2)))))
% 6.18/6.69 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ (@ tptp.power_power_complex A) N2)))))
% 6.18/6.69 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ (@ tptp.power_power_rat A) N2)))))
% 6.18/6.69 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.18/6.69 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.18/6.69 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ (@ tptp.power_power_int X) _let_1)))))
% 6.18/6.69 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ (@ tptp.power_power_complex X) _let_1)))))
% 6.18/6.69 (assert (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) _let_1) (@ (@ tptp.power_power_rat X) _let_1)))))
% 6.18/6.69 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X) _let_1)))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.real)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_real I2) S2) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.real)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S2) tptp.zero_zero_real) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F I2) tptp.zero_zero_real)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.nat)) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.real)) (B3 tptp.real) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real F) S2) B3) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_real (@ F I2)) B3)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.real)) (B3 tptp.real) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real F) S2) B3) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_real (@ F I2)) B3)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (B3 tptp.real) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real F) S2) B3) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_real (@ F I2)) B3)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (B3 tptp.rat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S2) B3) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B3)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B3 tptp.rat) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) B3) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B3)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (B3 tptp.rat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) B3) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B3)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (B3 tptp.rat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S2) B3) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B3)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.nat)) (B3 tptp.nat) (I2 tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S2) B3) (=> (@ (@ tptp.member_real I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B3)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat)) (B3 tptp.nat) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) B3) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B3)))))))
% 6.18/6.69 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (B3 tptp.nat) (I2 tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S2) B3) (=> (@ (@ tptp.member_complex I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B3)))))))
% 6.18/6.69 (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 ((X2 tptp.int)) (= (@ G X2) tptp.zero_zero_complex))))) (@ _let_1 A2))))))
% 6.18/6.69 (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 ((X2 tptp.int)) (= (@ G X2) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 6.18/6.69 (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 ((X2 tptp.complex)) (= (@ G X2) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 6.18/6.69 (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 ((X2 tptp.int)) (= (@ G X2) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.18/6.69 (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 ((X2 tptp.complex)) (= (@ G X2) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.18/6.69 (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 ((X2 tptp.int)) (= (@ G X2) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.zero_zero_int))))) (@ _let_1 A2))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (= (@ G X2) tptp.zero_zero_complex))))) (@ _let_1 A2))))))
% 6.18/6.69 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (= (@ G X2) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.18/6.69 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y))))
% 6.18/6.69 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X)))))
% 6.18/6.69 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X)))))
% 6.18/6.69 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y))))
% 6.18/6.69 (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))))))))))
% 6.18/6.69 (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)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups8097168146408367636l_real F) I6)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups8778361861064173332t_real F) I6)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F) I6)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I6)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I6)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F) I6)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (I2 tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) I6)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I2) I6) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F) I6)))))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I6)))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I6)))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) I6)))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I6)))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) I6)))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) I6)))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I6)))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I6)))))))
% 6.18/6.69 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))))
% 6.18/6.69 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) T3) (@ (@ tptp.groups5754745047067104278omplex H2) S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G) T3) (@ (@ tptp.groups8097168146408367636l_real H2) S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G) T3) (@ (@ tptp.groups5808333547571424918x_real H2) S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G) T3) (@ (@ tptp.groups1300246762558778688al_rat H2) S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G) T3) (@ (@ tptp.groups5058264527183730370ex_rat H2) S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) T3) (@ (@ tptp.groups1935376822645274424al_nat H2) S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) T3) (@ (@ tptp.groups5693394587270226106ex_nat H2) S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1932886352136224148al_int G) T3) (@ (@ tptp.groups1932886352136224148al_int H2) S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) T3) (@ (@ tptp.groups5690904116761175830ex_int H2) S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups2073611262835488442omplex G) T3) (@ (@ tptp.groups2073611262835488442omplex H2) S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S3) (@ (@ tptp.groups5754745047067104278omplex H2) T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S3) (@ (@ tptp.groups8097168146408367636l_real H2) T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5808333547571424918x_real G) S3) (@ (@ tptp.groups5808333547571424918x_real H2) T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1300246762558778688al_rat G) S3) (@ (@ tptp.groups1300246762558778688al_rat H2) T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G) S3) (@ (@ tptp.groups5058264527183730370ex_rat H2) T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) S3) (@ (@ tptp.groups1935376822645274424al_nat H2) T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S3) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S3) T3) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T3) S3)) (= (@ H2 X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1932886352136224148al_int G) S3) (@ (@ tptp.groups1932886352136224148al_int H2) T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ H2 X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) S3) (@ (@ tptp.groups5690904116761175830ex_int H2) T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ H2 X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups2073611262835488442omplex G) S3) (@ (@ tptp.groups2073611262835488442omplex H2) T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_nat) (S3 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 S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_nat) (S3 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 S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_int) (S3 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 S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_int) (S3 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 S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_int) (S3 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 S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_nat) (S3 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 S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_nat) (S3 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 S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T3) S3)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_int) (S3 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 S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_complex))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_int) (S3 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 S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_real))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.18/6.69 (assert (forall ((T3 tptp.set_int) (S3 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 S3) T3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T3) S3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S3) (@ _let_1 T3))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_less_eq_set_real A2) C2) (=> (@ (@ tptp.ord_less_eq_set_real B3) C2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C2) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C2) B3)) (= (@ H2 B2) tptp.zero_zero_complex))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_less_eq_set_real A2) C2) (=> (@ (@ tptp.ord_less_eq_set_real B3) C2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C2) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C2) B3)) (= (@ H2 B2) tptp.zero_zero_real))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C2) B3)) (= (@ H2 B2) tptp.zero_zero_real))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_less_eq_set_real A2) C2) (=> (@ (@ tptp.ord_less_eq_set_real B3) C2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C2) A2)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C2) B3)) (= (@ H2 B2) tptp.zero_zero_rat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C2) B3)) (= (@ H2 B2) tptp.zero_zero_rat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_less_eq_set_real A2) C2) (=> (@ (@ tptp.ord_less_eq_set_real B3) C2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C2) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C2) B3)) (= (@ H2 B2) tptp.zero_zero_nat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.18/6.69 (assert (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C2) B3)) (= (@ H2 B2) tptp.zero_zero_nat))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.18/6.69 (assert (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int H2))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real C2) (=> (@ (@ tptp.ord_less_eq_set_real A2) C2) (=> (@ (@ tptp.ord_less_eq_set_real B3) C2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C2) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C2) B3)) (= (@ H2 B2) tptp.zero_zero_int))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.18/6.69 (assert (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C2) B3)) (= (@ H2 B2) tptp.zero_zero_int))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.18/6.69 (assert (forall ((C2 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex H2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat C2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C2) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat C2) B3)) (= (@ H2 B2) tptp.zero_zero_complex))) (=> (= (@ _let_2 C2) (@ _let_1 C2)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_less_eq_set_real A2) C2) (=> (@ (@ tptp.ord_less_eq_set_real B3) C2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C2) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C2) B3)) (= (@ H2 B2) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_less_eq_set_real A2) C2) (=> (@ (@ tptp.ord_less_eq_set_real B3) C2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C2) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C2) B3)) (= (@ H2 B2) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C2) B3)) (= (@ H2 B2) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_less_eq_set_real A2) C2) (=> (@ (@ tptp.ord_less_eq_set_real B3) C2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C2) A2)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C2) B3)) (= (@ H2 B2) tptp.zero_zero_rat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 6.18/6.69 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C2) B3)) (= (@ H2 B2) tptp.zero_zero_rat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 6.18/6.70 (assert (forall ((C2 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 C2) (=> (@ (@ tptp.ord_less_eq_set_real A2) C2) (=> (@ (@ tptp.ord_less_eq_set_real B3) C2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C2) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C2) B3)) (= (@ H2 B2) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 6.18/6.70 (assert (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (H2 (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat H2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C2) B3)) (= (@ H2 B2) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 6.18/6.70 (assert (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.int)) (H2 (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int H2))) (let ((_let_2 (@ tptp.groups1932886352136224148al_int G))) (=> (@ tptp.finite_finite_real C2) (=> (@ (@ tptp.ord_less_eq_set_real A2) C2) (=> (@ (@ tptp.ord_less_eq_set_real B3) C2) (=> (forall ((A3 tptp.real)) (=> (@ (@ tptp.member_real A3) (@ (@ tptp.minus_minus_set_real C2) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C2) B3)) (= (@ H2 B2) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 6.18/6.70 (assert (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.int)) (H2 (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int H2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex C2) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C2) (=> (forall ((A3 tptp.complex)) (=> (@ (@ tptp.member_complex A3) (@ (@ tptp.minus_811609699411566653omplex C2) A2)) (= (@ G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C2) B3)) (= (@ H2 B2) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 6.18/6.70 (assert (forall ((C2 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex H2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat C2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C2) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) (@ (@ tptp.minus_minus_set_nat C2) A2)) (= (@ G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat C2) B3)) (= (@ H2 B2) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C2) (@ _let_1 C2))))))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real 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_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (= (@ tptp.ln_ln_real X) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.18/6.70 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.18/6.70 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.18/6.70 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.18/6.70 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y)))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y)))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1482373934393186551omplex Y)))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_rat Y)))))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1351360451143612070nteger Y)))))))
% 6.18/6.70 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B3) N2)) (@ (@ tptp.divide_divide_int A2) N2))))))
% 6.18/6.70 (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 ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (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 ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B2)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (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 ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (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 ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B2)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (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 ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (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 ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (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 ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B2)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B2)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B3) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B2)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) Y)) Y)))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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))))))))))))
% 6.18/6.70 (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))))))))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.18/6.70 (assert (forall ((U tptp.real) (X 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 X) _let_1)))))
% 6.18/6.70 (assert (forall ((X 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) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) K))))
% 6.18/6.70 (assert (forall ((N2 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))) N2))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))
% 6.18/6.70 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B3) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) B3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.18/6.70 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B3) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (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)))))))))))
% 6.18/6.70 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R2 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (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) R2))))))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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)))))))))))))
% 6.18/6.70 (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))))))))))))
% 6.18/6.70 (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))))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.18/6.70 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.18/6.70 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.18/6.70 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (= (@ (@ 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))) N2))))))
% 6.18/6.70 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (= (@ (@ 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))) N2))))))
% 6.18/6.70 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (= (@ (@ 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))) N2))))))
% 6.18/6.70 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2))) (= (@ (@ 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))) N2))))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 6.18/6.70 (assert (forall ((N2 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))) N2)) _let_1))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.18/6.70 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.18/6.70 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.18/6.70 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_rat (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.18/6.70 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.18/6.70 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.18/6.70 (assert (forall ((W tptp.real) (Y tptp.real) (X tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.18/6.70 (assert (forall ((W tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.18/6.70 (assert (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.18/6.70 (assert (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.18/6.70 (assert (forall ((N2 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))) N2))) _let_1))))
% 6.18/6.70 (assert (forall ((N2 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))) N2))) _let_1))))
% 6.18/6.70 (assert (forall ((N2 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))) N2))) _let_1))))
% 6.18/6.70 (assert (forall ((N2 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))) N2))) _let_1))))
% 6.18/6.70 (assert (forall ((N2 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))) N2))) _let_1))))
% 6.18/6.70 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)))))))
% 6.18/6.70 (assert (forall ((K tptp.int) (N2 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 N2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.18/6.70 (assert (forall ((X 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))) X) (=> (@ (@ tptp.ord_less_eq_real X) 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) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ 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) N2)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ 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) N2)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ 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) N2)))))
% 6.18/6.70 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ 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 M6) N)) N))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ 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))))
% 6.18/6.70 (assert (forall ((X 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 X)) (@ (@ 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) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N2)) (= M N2))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((P4 tptp.produc6271795597528267376eger_o) (C (-> tptp.code_integer Bool Bool))) (=> (forall ((A3 tptp.code_integer) (B2 Bool)) (=> (= P4 (@ (@ tptp.produc6677183202524767010eger_o A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc7828578312038201481er_o_o C) P4))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_num_num) (C (-> tptp.num tptp.num Bool))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_num_num A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc5703948589228662326_num_o C) P4))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_nat_num) (C (-> tptp.nat tptp.num Bool))) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_nat_num A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc4927758841916487424_num_o C) P4))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat Bool))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= P4 (@ (@ tptp.product_Pair_nat_nat A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc6081775807080527818_nat_o C) P4))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int A3) B2)) (@ (@ C A3) B2))) (@ (@ tptp.produc4947309494688390418_int_o C) P4))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (assert (forall ((P4 tptp.produc6271795597528267376eger_o) (Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex))) (=> (forall ((A3 tptp.code_integer) (B2 Bool)) (=> (= P4 (@ (@ tptp.produc6677183202524767010eger_o A3) B2)) (@ (@ tptp.member_complex Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P4)))))
% 6.18/6.70 (assert (forall ((P4 tptp.produc6271795597528267376eger_o) (Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real))) (=> (forall ((A3 tptp.code_integer) (B2 Bool)) (=> (= P4 (@ (@ tptp.produc6677183202524767010eger_o A3) B2)) (@ (@ tptp.member_real Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P4)))))
% 6.18/6.70 (assert (forall ((P4 tptp.produc6271795597528267376eger_o) (Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat))) (=> (forall ((A3 tptp.code_integer) (B2 Bool)) (=> (= P4 (@ (@ tptp.produc6677183202524767010eger_o A3) B2)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P4)))))
% 6.18/6.70 (assert (forall ((P4 tptp.produc6271795597528267376eger_o) (Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int))) (=> (forall ((A3 tptp.code_integer) (B2 Bool)) (=> (= P4 (@ (@ tptp.produc6677183202524767010eger_o A3) B2)) (@ (@ tptp.member_int Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P4)))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_num_num) (Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_num_num A3) B2)) (@ (@ tptp.member_complex Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P4)))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_num_num) (Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_num_num A3) B2)) (@ (@ tptp.member_real Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P4)))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_num_num) (Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_num_num A3) B2)) (@ (@ tptp.member_nat Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P4)))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_num_num) (Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_num_num A3) B2)) (@ (@ tptp.member_int Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P4)))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_nat_num) (Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex))) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_nat_num A3) B2)) (@ (@ tptp.member_complex Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc6231982587499038204omplex C) P4)))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_nat_num) (Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real))) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_nat_num A3) B2)) (@ (@ tptp.member_real Z) (@ (@ C A3) B2)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P4)))))
% 6.18/6.70 (assert (forall ((P4 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A3) B2) P4) (@ (@ (@ C A3) B2) X))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P4) X))))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N2)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N2)))))
% 6.18/6.70 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit1 N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.18/6.70 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.18/6.70 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 6.18/6.70 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 6.18/6.70 (assert (forall ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.18/6.70 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((A4 tptp.int)) (@ tptp.abs_abs_int (@ F A4)))) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((A4 tptp.int)) (@ tptp.abs_abs_int (@ F A4)))) A2))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((A4 tptp.nat)) (@ tptp.abs_abs_real (@ F A4)))) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((A4 tptp.nat)) (@ tptp.abs_abs_real (@ F A4)))) A2))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.18/6.70 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)))))
% 6.18/6.70 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)))))
% 6.18/6.70 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N2)))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N2)) (@ tptp.bit0 (@ _let_1 N2))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N2))))
% 6.18/6.70 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.18/6.70 (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 ((I5 tptp.int)) (@ tptp.abs_abs_int (@ F I5)))) A2))))
% 6.18/6.70 (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 ((I5 tptp.nat)) (@ tptp.abs_abs_real (@ F I5)))) A2))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) tptp.one)))))
% 6.18/6.70 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.18/6.70 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.bit1 N2))))
% 6.18/6.70 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ tptp.abs_abs_int (@ F I5)))) A2))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.abs_abs_real (@ F I5)))) A2))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2)))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N2))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N2))))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) (or (not (= A tptp.zero_zero_real)) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2)) (or (not (= A tptp.zero_zero_rat)) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2)) (or (not (= A tptp.zero_zero_int)) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N2) M)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N2) M)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N2) M)))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.70 (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 ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5)))) A2) tptp.zero_zero_complex))))))
% 6.18/6.70 (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 ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I5)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I5)))) A2) tptp.zero_zero_rat))))))
% 6.18/6.70 (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 ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5)))) A2) tptp.zero_zero_real))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> 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 ((I5 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5))) (@ D I5)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5))) (@ D I5)))) A2) tptp.zero_zero_complex))))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat)) (D (-> 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 ((I5 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I5))) (@ D I5)))) A2) (@ (@ tptp.divide_divide_rat (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I5))) (@ D I5)))) A2) tptp.zero_zero_rat))))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> 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 ((I5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5))) (@ D I5)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5))) (@ D I5)))) A2) tptp.zero_zero_real))))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (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) N2))) (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)))))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ 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) N2)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ 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) N2)))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ 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) N2)))))
% 6.18/6.70 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (= (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (not (@ P X2)))) (@ tptp.uminus6221592323253981072nt_int (@ tptp.collec213857154873943460nt_int P)))))
% 6.18/6.70 (assert (forall ((P (-> tptp.complex Bool))) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (not (@ P X2)))) (@ tptp.uminus8566677241136511917omplex (@ tptp.collect_complex P)))))
% 6.18/6.70 (assert (forall ((P (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (not (@ P X2)))) (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P)))))
% 6.18/6.70 (assert (forall ((P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (not (@ P X2)))) (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P)))))
% 6.18/6.70 (assert (forall ((P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (not (@ P X2)))) (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P)))))
% 6.18/6.70 (assert (= tptp.uminus612125837232591019t_real (lambda ((A5 tptp.set_real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (not (@ (@ tptp.member_real X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus6221592323253981072nt_int (lambda ((A5 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X2 tptp.product_prod_int_int)) (not (@ (@ tptp.member5262025264175285858nt_int X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus8566677241136511917omplex (lambda ((A5 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (not (@ (@ tptp.member_complex X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A5 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A5 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (not (@ (@ tptp.member_nat X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A5 tptp.set_int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (not (@ (@ tptp.member_int X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus612125837232591019t_real (lambda ((A5 tptp.set_real)) (@ tptp.collect_real (@ tptp.uminus_uminus_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus6221592323253981072nt_int (lambda ((A5 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (@ tptp.uminus7117520113953359693_int_o (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus8566677241136511917omplex (lambda ((A5 tptp.set_complex)) (@ tptp.collect_complex (@ tptp.uminus1680532995456772888plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A5 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ tptp.uminus6401447641752708672_nat_o (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A5 tptp.set_nat)) (@ tptp.collect_nat (@ tptp.uminus_uminus_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A5)))))))
% 6.18/6.70 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A5 tptp.set_int)) (@ tptp.collect_int (@ tptp.uminus_uminus_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A5)))))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.18/6.70 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.18/6.70 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X) (@ tptp.abs_abs_int Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X) (@ tptp.abs_abs_rat Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_rat Y))))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X) (@ tptp.abs_abs_Code_integer Y)) (or (= X Y) (= X (@ tptp.uminus1351360451143612070nteger Y))))))
% 6.18/6.70 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2))))
% 6.18/6.70 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))))
% 6.18/6.70 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))))
% 6.18/6.70 (assert (forall ((L2 tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L2) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L2) K))))
% 6.18/6.70 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L2) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L2) K))))
% 6.18/6.70 (assert (forall ((L2 tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L2) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L2) K))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex)) (P4 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P4)) (not (forall ((X3 tptp.code_integer) (Y5 Bool)) (=> (= P4 (@ (@ tptp.produc6677183202524767010eger_o X3) Y5)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y5)))))))))
% 6.18/6.70 (assert (forall ((Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real)) (P4 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P4)) (not (forall ((X3 tptp.code_integer) (Y5 Bool)) (=> (= P4 (@ (@ tptp.produc6677183202524767010eger_o X3) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y5)))))))))
% 6.18/6.70 (assert (forall ((Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat)) (P4 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P4)) (not (forall ((X3 tptp.code_integer) (Y5 Bool)) (=> (= P4 (@ (@ tptp.produc6677183202524767010eger_o X3) Y5)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y5)))))))))
% 6.18/6.70 (assert (forall ((Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int)) (P4 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P4)) (not (forall ((X3 tptp.code_integer) (Y5 Bool)) (=> (= P4 (@ (@ tptp.produc6677183202524767010eger_o X3) Y5)) (not (@ (@ tptp.member_int Z) (@ (@ C X3) Y5)))))))))
% 6.18/6.70 (assert (forall ((Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex)) (P4 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P4)) (not (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_num_num X3) Y5)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y5)))))))))
% 6.18/6.70 (assert (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (P4 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P4)) (not (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_num_num X3) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y5)))))))))
% 6.18/6.70 (assert (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (P4 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P4)) (not (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_num_num X3) Y5)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y5)))))))))
% 6.18/6.70 (assert (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (P4 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P4)) (not (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_num_num X3) Y5)) (not (@ (@ tptp.member_int Z) (@ (@ C X3) Y5)))))))))
% 6.18/6.70 (assert (forall ((Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex)) (P4 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc6231982587499038204omplex C) P4)) (not (forall ((X3 tptp.nat) (Y5 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_nat_num X3) Y5)) (not (@ (@ tptp.member_complex Z) (@ (@ C X3) Y5)))))))))
% 6.18/6.70 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (P4 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P4)) (not (forall ((X3 tptp.nat) (Y5 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_nat_num X3) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X3) Y5)))))))))
% 6.18/6.70 (assert (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))))
% 6.18/6.70 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((C (-> tptp.code_integer Bool Bool)) (P4 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.produc7828578312038201481er_o_o C) P4) (not (forall ((X3 tptp.code_integer) (Y5 Bool)) (=> (= P4 (@ (@ tptp.produc6677183202524767010eger_o X3) Y5)) (not (@ (@ C X3) Y5))))))))
% 6.18/6.70 (assert (forall ((C (-> tptp.num tptp.num Bool)) (P4 tptp.product_prod_num_num)) (=> (@ (@ tptp.produc5703948589228662326_num_o C) P4) (not (forall ((X3 tptp.num) (Y5 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_num_num X3) Y5)) (not (@ (@ C X3) Y5))))))))
% 6.18/6.70 (assert (forall ((C (-> tptp.nat tptp.num Bool)) (P4 tptp.product_prod_nat_num)) (=> (@ (@ tptp.produc4927758841916487424_num_o C) P4) (not (forall ((X3 tptp.nat) (Y5 tptp.num)) (=> (= P4 (@ (@ tptp.product_Pair_nat_num X3) Y5)) (not (@ (@ C X3) Y5))))))))
% 6.18/6.70 (assert (forall ((C (-> tptp.nat tptp.nat Bool)) (P4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o C) P4) (not (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (= P4 (@ (@ tptp.product_Pair_nat_nat X3) Y5)) (not (@ (@ C X3) Y5))))))))
% 6.18/6.70 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P4 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P4) (not (forall ((X3 tptp.int) (Y5 tptp.int)) (=> (= P4 (@ (@ tptp.product_Pair_int_int X3) Y5)) (not (@ (@ C X3) Y5))))))))
% 6.18/6.70 (assert (forall ((R (-> 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 R) (@ (@ tptp.product_Pair_nat_nat A) B)) C) (@ (@ (@ R A) B) C))))
% 6.18/6.70 (assert (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P4 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P4) Z) (not (forall ((X3 tptp.nat) (Y5 tptp.nat)) (=> (= P4 (@ (@ tptp.product_Pair_nat_nat X3) Y5)) (not (@ (@ (@ C X3) Y5) Z))))))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D 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) D) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D))))))))
% 6.18/6.70 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D 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) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D))))))))
% 6.18/6.70 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D 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) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D))))))))
% 6.18/6.70 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D 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) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D))))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.18/6.70 (assert (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y (@ tptp.bit0 X23)))) (not (forall ((X33 tptp.num)) (not (= Y (@ tptp.bit1 X33)))))))))
% 6.18/6.70 (assert (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M2)) tptp.one)))) (=> (forall ((M2 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M2)) (@ tptp.bit0 N3))))) (=> (forall ((M2 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M2)) (@ tptp.bit1 N3))))) (=> (forall ((M2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M2)) tptp.one)))) (=> (forall ((M2 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M2)) (@ tptp.bit0 N3))))) (not (forall ((M2 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M2)) (@ tptp.bit1 N3))))))))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y) (=> (@ (@ 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 X) U)) Y))) V)))))
% 6.18/6.70 (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 ((X2 tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2))))))
% 6.18/6.70 (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 ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_set_nat) (G (-> tptp.set_nat tptp.nat)) (F (-> tptp.set_nat tptp.nat))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A2) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A2)) (@ (@ tptp.groups8294997508430121362at_nat G) A2))))))
% 6.18/6.70 (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 ((X2 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))))
% 6.18/6.70 (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 ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X2)) (@ G X2)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E2))) (= X tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((X tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) E2))) (= X tptp.zero_zero_rat))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.18/6.70 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y))))))
% 6.18/6.70 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2))))
% 6.18/6.70 (assert (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))))
% 6.18/6.70 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2))))
% 6.18/6.70 (assert (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))))
% 6.18/6.70 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.18/6.70 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 6.18/6.70 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 6.18/6.70 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 6.18/6.70 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.18/6.70 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.18/6.70 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.18/6.70 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 6.18/6.70 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 6.18/6.70 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 6.18/6.70 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D))))))
% 6.18/6.70 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D 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) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D))))))
% 6.18/6.70 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D 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) D)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D))))))
% 6.18/6.70 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D 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) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R2) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X) (@ (@ tptp.ord_le3102999989581377725nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R2)) X) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R2) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X) (@ (@ tptp.ord_le6747313008572928689nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R2)) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.18/6.70 (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 ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.18/6.70 (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 ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.18/6.70 (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 ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))))))
% 6.18/6.70 (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 ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.one_one_nat) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.18/6.70 (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 ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.one_one_nat) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) A2) (=> (not (= X2 Y2)) (= (@ F Y2) tptp.zero_zero_nat))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_1))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_1))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_1))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_1))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_1))))))
% 6.18/6.70 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1))))))
% 6.18/6.70 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D4) (and (@ (@ tptp.ord_less_real A) Y3) (@ (@ tptp.ord_less_real Y3) B))))))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I6))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I6))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I6))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I6))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N2) C)))) tptp.zero_zero_complex))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N2) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))))
% 6.18/6.70 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X)))))
% 6.18/6.70 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))))
% 6.18/6.70 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))
% 6.18/6.70 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D4) (and (@ (@ tptp.ord_less_eq_real A) Y3) (@ (@ tptp.ord_less_eq_real Y3) B))))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) (@ tptp.abs_abs_Code_integer Y)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) (@ tptp.abs_abs_rat Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X) tptp.one_one_Code_integer))))
% 6.18/6.70 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X) tptp.one_one_rat))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X) tptp.one_one_real))))
% 6.18/6.70 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 6.18/6.70 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2) (@ (@ tptp.power_power_rat A) N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2) (@ (@ tptp.power_power_real A) N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2) (@ (@ tptp.power_power_int A) N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P4))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P4))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P4))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P4))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((Q2 tptp.num) (N2 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 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((Q2 tptp.num) (N2 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 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.18/6.70 (assert (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))))
% 6.18/6.70 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X 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 X)) (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.18/6.70 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X 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 X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.18/6.70 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X 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 X)) (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.18/6.70 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X 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 X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.18/6.70 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) Y))))))
% 6.18/6.70 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y))))))
% 6.18/6.70 (assert (forall ((Y tptp.rat) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) Y))))))
% 6.18/6.70 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y))))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.18/6.70 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.18/6.70 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.18/6.70 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.18/6.70 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.18/6.70 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.18/6.70 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.18/6.70 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.18/6.70 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.18/6.70 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ 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) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ 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) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ 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) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X) I6) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I5 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X) I6) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I5 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X) I6) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X) I6) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I5 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X) I6) tptp.one_one_real) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I6) tptp.one_one_real) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I3)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I6) tptp.one_one_real) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.rat)) (A (-> tptp.complex tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat X) I6) tptp.one_one_rat) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((I5 tptp.complex)) (@ (@ tptp.times_times_rat (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X) I6) tptp.one_one_rat) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I5 tptp.real)) (@ (@ tptp.times_times_rat (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X) I6) tptp.one_one_rat) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F M))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F M))))))
% 6.18/6.70 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N)) (@ (@ tptp.modulo_modulo_nat M6) N)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 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 N2)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 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 N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 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 N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 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 N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (= X (@ (@ tptp.minus_minus_real Y) Z)) (= Y (@ (@ tptp.plus_plus_real X) Z)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) 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) X))) X))) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.70 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I5) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N2) D)))) _let_1)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.plus_plus_nat N2) 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))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ 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 N2) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 6.18/6.70 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N)))))))
% 6.18/6.70 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N)))))))
% 6.18/6.70 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N)))))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((X 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 X)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.18/6.70 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.18/6.70 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.18/6.70 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.18/6.70 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) 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 N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) 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 N2) 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 N2)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) 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 N2) 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 N2)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N2)) (= M N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N2)) (= M N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N2)) (= M N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) (@ tptp.semiri4939895301339042750nteger N2)) (= M N2))))
% 6.18/6.70 (assert (forall ((P Bool) (Q (-> tptp.int tptp.int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (B4 tptp.int)) (and P (@ (@ Q A4) B4)))) (lambda ((Ab tptp.product_prod_int_int)) (and P (@ (@ tptp.produc4947309494688390418_int_o Q) Ab))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.18/6.70 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.18/6.70 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.18/6.70 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N2)) (= tptp.zero_zero_nat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N2)) (= tptp.zero_zero_nat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N2)) (= tptp.zero_zero_nat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.semiri4939895301339042750nteger N2)) (= tptp.zero_zero_nat N2))))
% 6.18/6.70 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.18/6.70 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.18/6.70 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.18/6.70 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.18/6.70 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.18/6.70 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera6690914467698888265omplex N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_rat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_real N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera6620942414471956472nteger N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.18/6.70 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.18/6.70 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.18/6.70 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.18/6.70 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.18/6.70 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N2)) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N2)) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N2)) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_Code_integer (@ tptp.semiri4939895301339042750nteger N2)) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N2) tptp.one_one_complex) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N2) tptp.one_one_rat) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N2) tptp.one_one_real) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger N2) tptp.one_one_Code_integer) (= N2 tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger X) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W) (@ tptp.semiri4939895301339042750nteger X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger M)) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.18/6.70 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N2) (@ tptp.numeral_numeral_nat K)) (= N2 (@ tptp.pred_numeral K)))))
% 6.18/6.70 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N2)) (= (@ tptp.pred_numeral K) N2))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.18/6.70 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.18/6.70 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.18/6.70 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.18/6.70 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.18/6.70 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.18/6.70 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.18/6.70 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.18/6.70 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.18/6.70 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.18/6.70 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.18/6.70 (assert (forall ((F (-> tptp.complex tptp.nat)) (A2 tptp.set_complex)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ tptp.semiri8010041392384452111omplex (@ F X2)))) A2))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((X2 tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ F X2)))) A2))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X2)))) A2))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X2)))) A2))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc M)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.semiri4939895301339042750nteger M)))))
% 6.18/6.70 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat W)))))
% 6.18/6.70 (assert (forall ((N2 tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) M))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N2) (@ tptp.pred_numeral K)))))
% 6.18/6.70 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N2))))
% 6.18/6.70 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.pred_numeral K)))))
% 6.18/6.70 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N2))))
% 6.18/6.70 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.pred_numeral K)))))
% 6.18/6.70 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) (@ tptp.pred_numeral K))))))
% 6.18/6.70 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.18/6.70 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.18/6.70 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.18/6.70 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.18/6.70 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.18/6.70 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.18/6.70 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.18/6.70 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.18/6.70 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.18/6.70 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))))
% 6.18/6.70 (assert (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)))))
% 6.18/6.70 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N2) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.18/6.70 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2) (@ tptp.semiri681578069525770553at_rat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.18/6.70 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.18/6.70 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N2) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.18/6.70 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))))
% 6.18/6.70 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N2) (@ tptp.semiri4939895301339042750nteger Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) Y))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.18/6.70 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((A2 (-> tptp.int tptp.int Bool)) (B3 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_le6741204236512500942_int_o A2) B3) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o A2))) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o B3))))))
% 6.18/6.70 (assert (forall ((Prod tptp.product_prod_int_int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((Uu3 tptp.int) (Uv3 tptp.int)) true)) Prod)))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger X))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ (@ tptp.times_3573771949741848930nteger Y) _let_1)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.18/6.70 (assert (forall ((Z tptp.int)) (not (forall ((M2 tptp.nat) (N3 tptp.nat)) (not (= Z (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2)) tptp.zero_zero_complex))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)) tptp.zero_zero_rat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)) tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc N2)) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.70 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (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)))))))
% 6.18/6.70 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (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)))))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_3 (@ tptp.divide6298287555418463151nteger A))) (= (@ _let_3 (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_3 _let_2)) _let_1)))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I2)) (@ tptp.semiri5074537144036343181t_real J)))))
% 6.18/6.70 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger I2)) (@ tptp.semiri4939895301339042750nteger J)))))
% 6.18/6.70 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I2)) (@ tptp.semiri681578069525770553at_rat J)))))
% 6.18/6.70 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 6.18/6.70 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.18/6.70 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N2)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.18/6.70 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 6.18/6.70 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.18/6.70 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2))) Z))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.18/6.70 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z2 tptp.int)) (exists ((N tptp.nat)) (= Z2 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N)))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X2 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X2)))) A2))))
% 6.18/6.70 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X)) (@ tptp.semiri4216267220026989637d_enat Y)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_Code_integer (@ tptp.semiri4939895301339042750nteger X)) (@ tptp.semiri4939895301339042750nteger Y)))))
% 6.18/6.70 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 6.18/6.70 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y3 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X)))))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X)))))
% 6.18/6.70 (assert (forall ((I2 tptp.int) (D tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I2))))))
% 6.18/6.70 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))
% 6.18/6.70 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z2 tptp.int)) (exists ((N tptp.nat)) (= Z2 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N2 tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((D tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real D))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_int)))
% 6.18/6.70 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3)))))))))
% 6.18/6.70 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.18/6.70 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N2))) (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)))))))))
% 6.18/6.70 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N2))) (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)))))))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N2))) (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)))))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri8010041392384452111omplex N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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)))))))))
% 6.18/6.70 (assert (= tptp.ord_less_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))))
% 6.18/6.70 (assert (= tptp.ord_less_eq_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))))
% 6.18/6.70 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.18/6.70 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N2)) M) (= (@ tptp.abs_abs_int N2) tptp.one_one_int)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) tptp.zero_zero_int)))
% 6.18/6.70 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 6.18/6.70 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.18/6.70 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.18/6.70 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.18/6.70 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.18/6.70 (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))))))))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X) D))) _let_1))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N2))))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 C) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) X)) C))) (= X tptp.zero_zero_real)))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X)))) tptp.one_one_real)))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ln_ln_real X))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_nat I3) N2)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ F I3) K)))))))))
% 6.18/6.70 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 6.18/6.70 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 6.18/6.70 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 6.18/6.70 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 6.18/6.70 (assert (forall ((D tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ 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)) D))) Z)))))
% 6.18/6.70 (assert (forall ((D tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) N2)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 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)) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ F I3) K))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ F I3) K))))))))
% 6.18/6.70 (assert (forall ((A tptp.complex) (D tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ 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) D))))))))
% 6.18/6.70 (assert (forall ((A tptp.rat) (D tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ 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) D))))))))
% 6.18/6.70 (assert (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ 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) D))))))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (D tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 A)) (@ (@ tptp.times_3573771949741848930nteger _let_1) D))))))))
% 6.18/6.70 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ 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) D))))))))
% 6.18/6.70 (assert (forall ((A tptp.real) (D tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ 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) D))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y)))))))))
% 6.18/6.70 (assert (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ 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) D)))) _let_1))))))
% 6.18/6.70 (assert (forall ((A tptp.code_integer) (D tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) A)) (@ (@ tptp.times_3573771949741848930nteger _let_2) D)))) _let_1))))))
% 6.18/6.70 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ 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) D)))) _let_1))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ 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)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ 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)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (X 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))) N2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N2))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) 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 N2))))) (@ _let_1 X)))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) 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 N2))))) (@ _let_1 X)))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ 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)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ 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)))))))
% 6.18/6.70 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (= N tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M6)))) (@ (@ (@ tptp.if_complex (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.70 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_rat (= N tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M6)))) (@ (@ (@ tptp.if_rat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.70 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M6)))) (@ (@ (@ tptp.if_int (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.70 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M6)))) (@ (@ (@ tptp.if_real (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.70 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M6)))) (@ (@ (@ tptp.if_nat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.70 (assert (= tptp.semiri4939895301339042750nteger (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= N tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.produc1830744345554046123nteger (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.semiri4939895301339042750nteger M6)))) (@ (@ (@ tptp.if_Code_integer (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.divmod_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ 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 X) _let_1))))))))
% 6.18/6.70 (assert (forall ((H2 tptp.real) (Z tptp.real) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)))) (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) N2)) (@ _let_4 N2))) 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)))))))))))))
% 6.18/6.70 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (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) N2)) (@ _let_3 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N))))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) (@ F tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) (@ F tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.18/6.70 (assert (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.18/6.70 (assert (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ 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)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 6.18/6.70 (assert (= (@ tptp.suminf_real (lambda ((N tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 6.18/6.70 (assert (= (@ tptp.suminf_nat (lambda ((N tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 6.18/6.70 (assert (= (@ tptp.suminf_int (lambda ((N tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 6.18/6.70 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.18/6.70 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.18/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((S3 tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S3))) (@ (@ tptp.groups8097168146408367636l_real G) S3)))))
% 6.18/6.70 (assert (forall ((S3 tptp.set_set_nat) (F (-> tptp.set_nat tptp.complex)) (G (-> tptp.set_nat tptp.real))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups8255218700646806128omplex F) S3))) (@ (@ tptp.groups5107569545109728110t_real G) S3)))))
% 6.18/6.70 (assert (forall ((S3 tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S3))) (@ (@ tptp.groups8778361861064173332t_real G) S3)))))
% 6.18/6.70 (assert (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S3))) (@ (@ tptp.groups6591440286371151544t_real G) S3)))))
% 6.18/6.70 (assert (forall ((S3 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X3))) (@ G X3)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S3))) (@ (@ tptp.groups5808333547571424918x_real G) S3)))))
% 6.18/6.70 (assert (forall ((S3 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ 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) S3))) (@ (@ tptp.groups6591440286371151544t_real G) S3)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N2))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N2))))
% 6.18/6.70 (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 ((I5 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I5)))) A2))))
% 6.18/6.70 (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 ((I5 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I5)))) A2))))
% 6.18/6.70 (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 ((I5 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I5)))) A2))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((W tptp.real) (N2 tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N2) (@ (@ tptp.power_power_real Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 6.18/6.70 (assert (forall ((W tptp.complex) (N2 tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N2) (@ (@ tptp.power_power_complex Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (R2 tptp.real) (Y tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real R2) S2))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (R2 tptp.real) (Y tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real R2) S2))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E))))
% 6.18/6.70 (assert (forall ((X tptp.real) (R2 tptp.real) (Y tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (R2 tptp.real) (Y tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N2))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N2))))
% 6.18/6.70 (assert (forall ((A tptp.real) (R2 tptp.real) (B tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.18/6.70 (assert (forall ((A tptp.complex) (R2 tptp.real) (B tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))))))
% 6.18/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))) E))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))) E))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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.minus_minus_real A) B)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((N4 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N4) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N4)) (= (@ F N3) tptp.zero_zero_complex))) (= (@ tptp.suminf_complex F) (@ (@ tptp.groups2073611262835488442omplex F) N4))))))
% 6.18/6.70 (assert (forall ((N4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N4) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N4)) (= (@ F N3) tptp.zero_zero_int))) (= (@ tptp.suminf_int F) (@ (@ tptp.groups3539618377306564664at_int F) N4))))))
% 6.18/6.70 (assert (forall ((N4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N4) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N4)) (= (@ F N3) tptp.zero_zero_nat))) (= (@ tptp.suminf_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N4))))))
% 6.18/6.70 (assert (forall ((N4 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N4) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N4)) (= (@ F N3) tptp.zero_zero_real))) (= (@ tptp.suminf_real F) (@ (@ tptp.groups6591440286371151544t_real F) N4))))))
% 6.18/6.70 (assert (forall ((W tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N2) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((W tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N2) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D 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) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D))))))
% 6.18/6.70 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D 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) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D))))))
% 6.18/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X) tptp.one_one_real))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X) tptp.one_one_real))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (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))))))))
% 6.18/6.70 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ 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)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _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 N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.18/6.70 (assert (forall ((H2 tptp.rat) (Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ 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)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ _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 N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.18/6.70 (assert (forall ((H2 tptp.real) (Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ 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)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _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 N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ 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)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 6.18/6.70 (assert (forall ((R tptp.set_Pr448751882837621926eger_o) (S3 tptp.set_Pr448751882837621926eger_o)) (= (@ (@ tptp.ord_le2162486998276636481er_o_o (lambda ((X2 tptp.code_integer) (Y2 Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X2) Y2)) R))) (lambda ((X2 tptp.code_integer) (Y2 Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X2) Y2)) S3))) (@ (@ tptp.ord_le8980329558974975238eger_o R) S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_Pr8218934625190621173um_num) (S3 tptp.set_Pr8218934625190621173um_num)) (= (@ (@ tptp.ord_le6124364862034508274_num_o (lambda ((X2 tptp.num) (Y2 tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X2) Y2)) R))) (lambda ((X2 tptp.num) (Y2 tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X2) Y2)) S3))) (@ (@ tptp.ord_le880128212290418581um_num R) S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_Pr6200539531224447659at_num) (S3 tptp.set_Pr6200539531224447659at_num)) (= (@ (@ tptp.ord_le3404735783095501756_num_o (lambda ((X2 tptp.nat) (Y2 tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X2) Y2)) R))) (lambda ((X2 tptp.nat) (Y2 tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X2) Y2)) S3))) (@ (@ tptp.ord_le8085105155179020875at_num R) S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le2646555220125990790_nat_o (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y2)) R))) (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y2)) S3))) (@ (@ tptp.ord_le3146513528884898305at_nat R) S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.ord_le6741204236512500942_int_o (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y2)) R))) (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y2)) S3))) (@ (@ tptp.ord_le2843351958646193337nt_int R) S3))))
% 6.18/6.70 (assert (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M6 tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_eq_int M6) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S3)))))))
% 6.18/6.70 (assert (forall ((R1 (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)) (R22 (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool))) (=> (@ (@ tptp.ord_le2556027599737686990_num_o R1) R22) (@ (@ tptp.ord_le2239182809043710856_num_o (@ tptp.accp_P3113834385874906142um_num R22)) (@ tptp.accp_P3113834385874906142um_num R1)))))
% 6.18/6.70 (assert (forall ((R1 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (R22 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le5604493270027003598_nat_o R1) R22) (@ (@ tptp.ord_le704812498762024988_nat_o (@ tptp.accp_P4275260045618599050at_nat R22)) (@ tptp.accp_P4275260045618599050at_nat R1)))))
% 6.18/6.70 (assert (forall ((R1 (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) (R22 (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le1598226405681992910_int_o R1) R22) (@ (@ tptp.ord_le8369615600986905444_int_o (@ tptp.accp_P1096762738010456898nt_int R22)) (@ tptp.accp_P1096762738010456898nt_int R1)))))
% 6.18/6.70 (assert (forall ((R1 (-> tptp.list_nat tptp.list_nat Bool)) (R22 (-> tptp.list_nat tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le6558929396352911974_nat_o R1) R22) (@ (@ tptp.ord_le1520216061033275535_nat_o (@ tptp.accp_list_nat R22)) (@ tptp.accp_list_nat R1)))))
% 6.18/6.70 (assert (forall ((R1 (-> tptp.nat tptp.nat Bool)) (R22 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_le2646555220125990790_nat_o R1) R22) (@ (@ tptp.ord_less_eq_nat_o (@ tptp.accp_nat R22)) (@ tptp.accp_nat R1)))))
% 6.18/6.70 (assert (forall ((I2 tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or890127255671739683et_nat K)) (@ (@ tptp.ord_less_set_nat I2) K))))
% 6.18/6.70 (assert (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I2) K))))
% 6.18/6.70 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I2) K))))
% 6.18/6.70 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I2) K))))
% 6.18/6.70 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I2) K))))
% 6.18/6.70 (assert (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I2) K))))
% 6.18/6.70 (assert (forall ((I2 Bool) (K Bool)) (= (@ (@ tptp.member_o I2) (@ tptp.set_ord_lessThan_o K)) (@ (@ tptp.ord_less_o I2) K))))
% 6.18/6.70 (assert (forall ((I2 tptp.nat) (F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (= R5 I2)) (@ F R5)) tptp.zero_zero_complex)))))
% 6.18/6.70 (assert (forall ((I2 tptp.nat) (F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (= R5 I2)) (@ F R5)) tptp.zero_zero_real)))))
% 6.18/6.70 (assert (forall ((I2 tptp.nat) (F (-> tptp.nat tptp.nat))) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (= R5 I2)) (@ F R5)) tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((I2 tptp.nat) (F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (= R5 I2)) (@ F R5)) tptp.zero_zero_int)))))
% 6.18/6.70 (assert (@ tptp.summable_complex (lambda ((N tptp.nat)) tptp.zero_zero_complex)))
% 6.18/6.70 (assert (@ tptp.summable_real (lambda ((N tptp.nat)) tptp.zero_zero_real)))
% 6.18/6.70 (assert (@ tptp.summable_nat (lambda ((N tptp.nat)) tptp.zero_zero_nat)))
% 6.18/6.70 (assert (@ tptp.summable_int (lambda ((N tptp.nat)) tptp.zero_zero_int)))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ tptp.summable_real F))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ tptp.summable_complex F))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X)) (@ tptp.set_ord_lessThan_rat Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.18/6.70 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.18/6.70 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.18/6.70 (assert (forall ((X Bool) (Y Bool)) (= (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_ord_lessThan_o X)) (@ tptp.set_ord_lessThan_o Y)) (@ (@ tptp.ord_less_eq_o X) Y))))
% 6.18/6.70 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.18/6.70 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.18/6.70 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P R5)) (@ F R5)) tptp.zero_zero_complex))))))
% 6.18/6.70 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ P R5)) (@ F R5)) tptp.zero_zero_real))))))
% 6.18/6.70 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P R5)) (@ F R5)) tptp.zero_zero_nat))))))
% 6.18/6.70 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ P R5)) (@ F R5)) tptp.zero_zero_int))))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_complex))))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_real))))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_nat))))))
% 6.18/6.70 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_int))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.18/6.70 (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))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N)))) (@ tptp.summable_real F))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N)))) (@ tptp.summable_complex F))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_complex))))
% 6.18/6.70 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N)) (@ G N))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N)) (@ G N))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ tptp.summable_real F))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ tptp.summable_complex F))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ F N)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ F N)))) (@ tptp.summable_real F))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N)))) (@ tptp.summable_complex F))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.real))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ tptp.summable_real (@ F I3)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ (@ F I5) N))) I6))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat tptp.real))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ tptp.summable_real (@ F I3)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ (@ F I5) N))) I6))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.real))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ tptp.summable_real (@ F I3)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ (@ F I5) N))) I6))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat tptp.complex))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ tptp.summable_complex (@ F I3)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((I5 tptp.real)) (@ (@ F I5) N))) I6))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.complex))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ tptp.summable_complex (@ F I3)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ F I5) N))) I6))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.complex))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ tptp.summable_complex (@ F I3)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((I5 tptp.int)) (@ (@ F I5) N))) I6))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.int))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ tptp.summable_int (@ F I3)))) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ F I5) N))) I6))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.complex))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ tptp.summable_complex (@ F I3)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I5 tptp.complex)) (@ (@ F I5) N))) I6))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.nat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ tptp.summable_nat (@ F I3)))) (@ tptp.summable_nat (lambda ((N tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ F I5) N))) I6))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.real))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ tptp.summable_real (@ F I3)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ F I5) N))) I6))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (X 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))) X)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (X 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))) X)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (X 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))) X)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N)))) (@ tptp.summable_real F))))
% 6.18/6.70 (assert (= tptp.set_or890127255671739683et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X2) U2))))))
% 6.18/6.70 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat X2) U2))))))
% 6.18/6.70 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_num X2) U2))))))
% 6.18/6.70 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) U2))))))
% 6.18/6.70 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_int X2) U2))))))
% 6.18/6.70 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.ord_less_real X2) U2))))))
% 6.18/6.70 (assert (= tptp.set_ord_lessThan_o (lambda ((U2 Bool)) (@ tptp.collect_o (lambda ((X2 Bool)) (@ (@ tptp.ord_less_o X2) U2))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (X 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))) X)) (@ tptp.summable_int F)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (X 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))) X)) (@ tptp.summable_nat F)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (X 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))) X)) (@ tptp.summable_real F)))))
% 6.18/6.70 (assert (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_lessThan_nat K3))))))
% 6.18/6.70 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S3) (@ tptp.set_ord_lessThan_nat K2))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex F) (@ (@ tptp.plus_plus_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K))))) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.18/6.70 (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 ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.18/6.70 (assert (forall ((M tptp.rat) (N2 tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N2)) (@ (@ tptp.ord_less_rat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N2)) (@ (@ tptp.ord_less_int M) N2))))
% 6.18/6.70 (assert (forall ((M tptp.real) (N2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N2)) (@ (@ tptp.ord_less_real M) N2))))
% 6.18/6.70 (assert (forall ((M Bool) (N2 Bool)) (= (@ (@ tptp.ord_less_set_o (@ tptp.set_ord_lessThan_o M)) (@ tptp.set_ord_lessThan_o N2)) (@ (@ tptp.ord_less_o M) N2))))
% 6.18/6.70 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))))
% 6.18/6.70 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 6.18/6.70 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.18/6.70 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.18/6.70 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.18/6.70 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M2)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M2)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M2)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex F)) C) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C)))))))
% 6.18/6.70 (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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) (@ tptp.suminf_complex F))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) (@ tptp.suminf_real F))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (= (@ (@ tptp.plus_plus_complex (@ tptp.suminf_complex F)) (@ tptp.suminf_complex G)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N)) (@ G N)))))))))
% 6.18/6.70 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))))))))
% 6.18/6.70 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))))))))
% 6.18/6.70 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (=> (@ tptp.summable_complex G) (= (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ tptp.suminf_complex G)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N)) (@ G N)))))))))
% 6.18/6.70 (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 ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ F N)))) (@ tptp.uminus_uminus_real (@ tptp.suminf_real F))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N)))) (@ tptp.uminus1482373934393186551omplex (@ tptp.suminf_complex F))))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.real))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ tptp.summable_real (@ F I3)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ tptp.suminf_real (@ F I5)))) I6)))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat tptp.real))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ tptp.summable_real (@ F I3)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ tptp.suminf_real (@ F I5)))) I6)))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.real))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ tptp.summable_real (@ F I3)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ tptp.suminf_real (@ F I5)))) I6)))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat tptp.complex))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ tptp.summable_complex (@ F I3)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((I5 tptp.real)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups5754745047067104278omplex (lambda ((I5 tptp.real)) (@ tptp.suminf_complex (@ F I5)))) I6)))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.complex))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ tptp.summable_complex (@ F I3)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ tptp.suminf_complex (@ F I5)))) I6)))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.complex))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ tptp.summable_complex (@ F I3)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((I5 tptp.int)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups3049146728041665814omplex (lambda ((I5 tptp.int)) (@ tptp.suminf_complex (@ F I5)))) I6)))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.int))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ tptp.summable_int (@ F I3)))) (= (@ tptp.suminf_int (lambda ((N tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ tptp.suminf_int (@ F I5)))) I6)))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.complex))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ tptp.summable_complex (@ F I3)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I5 tptp.complex)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I5 tptp.complex)) (@ tptp.suminf_complex (@ F I5)))) I6)))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.nat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ tptp.summable_nat (@ F I3)))) (= (@ tptp.suminf_nat (lambda ((N tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ tptp.suminf_nat (@ F I5)))) I6)))))
% 6.18/6.70 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.real))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ tptp.summable_real (@ F I3)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.suminf_real (@ F I5)))) I6)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M2)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I2)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M2)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M2)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))))
% 6.18/6.70 (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 ((N tptp.nat)) (= (@ F N) tptp.zero_zero_real)))))))
% 6.18/6.70 (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 ((N tptp.nat)) (= (@ F N) tptp.zero_zero_nat)))))))
% 6.18/6.70 (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 ((N tptp.nat)) (= (@ F N) tptp.zero_zero_int)))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ F N)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))))
% 6.18/6.70 (assert (forall ((Q (-> tptp.int tptp.nat)) (P (-> tptp.int tptp.nat)) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_int N2))) (=> (forall ((X3 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat P) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat Q) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.18/6.70 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N2 tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N2))) (=> (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 ((X2 tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.18/6.70 (assert (forall ((Q (-> Bool tptp.nat)) (P (-> Bool tptp.nat)) (N2 Bool)) (let ((_let_1 (@ tptp.set_ord_lessThan_o N2))) (=> (forall ((X3 Bool)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8507830703676809646_o_nat P) _let_1)) (@ (@ tptp.groups8507830703676809646_o_nat Q) _let_1)) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X2 Bool)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.18/6.70 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (=> (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 ((X2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X2)) (@ Q X2)))) _let_1))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (I2 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 I2)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 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 I2)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 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 I2)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 6.18/6.70 (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 ((I5 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I5))))))))
% 6.18/6.70 (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 ((I5 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I5))))))))
% 6.18/6.70 (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 ((I5 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I5))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (X tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (X tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex X) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X)))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex F)) (@ F tptp.zero_zero_nat))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 6.18/6.70 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.18/6.70 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D4))) (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))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (R2 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) R2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I5)) R2))) _let_1)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (R2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) R2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I5)) R2))) _let_1)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (N2 tptp.nat) (R2 tptp.code_integer)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger F) _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N2)) R2)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger (@ F I5)) R2))) _let_1)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (R2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) R2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I5)) R2))) _let_1)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.18/6.70 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (I6 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I6)) (@ tptp.suminf_int F)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (I6 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I6)) (@ tptp.suminf_nat F)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (I6 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I6) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I6)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I6)) (@ tptp.suminf_real F)))))))
% 6.18/6.70 (assert (forall ((R tptp.set_Pr448751882837621926eger_o) (S3 tptp.set_Pr448751882837621926eger_o)) (= (= (lambda ((X2 tptp.code_integer) (Y2 Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X2) Y2)) R)) (lambda ((X2 tptp.code_integer) (Y2 Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X2) Y2)) S3))) (= R S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_Pr8218934625190621173um_num) (S3 tptp.set_Pr8218934625190621173um_num)) (= (= (lambda ((X2 tptp.num) (Y2 tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X2) Y2)) R)) (lambda ((X2 tptp.num) (Y2 tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X2) Y2)) S3))) (= R S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_Pr6200539531224447659at_num) (S3 tptp.set_Pr6200539531224447659at_num)) (= (= (lambda ((X2 tptp.nat) (Y2 tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X2) Y2)) R)) (lambda ((X2 tptp.nat) (Y2 tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X2) Y2)) S3))) (= R S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (= (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y2)) R)) (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y2)) S3))) (= R S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (= (= (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y2)) R)) (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y2)) S3))) (= R S3))))
% 6.18/6.70 (assert (= tptp.bot_bo4731626569425807221er_o_o (lambda ((X2 tptp.code_integer) (Y2 Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X2) Y2)) tptp.bot_bo5379713665208646970eger_o))))
% 6.18/6.70 (assert (= tptp.bot_bot_num_num_o (lambda ((X2 tptp.num) (Y2 tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X2) Y2)) tptp.bot_bo9056780473022590049um_num))))
% 6.18/6.70 (assert (= tptp.bot_bot_nat_num_o (lambda ((X2 tptp.nat) (Y2 tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X2) Y2)) tptp.bot_bo7038385379056416535at_num))))
% 6.18/6.70 (assert (= tptp.bot_bot_nat_nat_o (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y2)) tptp.bot_bo2099793752762293965at_nat))))
% 6.18/6.70 (assert (= tptp.bot_bot_int_int_o (lambda ((X2 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y2)) tptp.bot_bo1796632182523588997nt_int))))
% 6.18/6.70 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.18/6.70 (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)))
% 6.18/6.70 (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)))
% 6.18/6.70 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_rat (@ _let_2 X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (not (= X tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N))))) Z))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N))))) Z))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N))))) (@ F tptp.zero_zero_nat))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N))))) (@ F tptp.zero_zero_nat))))))
% 6.18/6.70 (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 ((N8 tptp.nat)) (not (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M3) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M3) N9)))) E)))))))))))
% 6.18/6.70 (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 ((N8 tptp.nat)) (not (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M3) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M3) N9)))) E)))))))))))
% 6.18/6.70 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N8 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N9) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N9)))))) R2))))))))
% 6.18/6.70 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N8 tptp.nat)) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N9) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N9)))))) R2))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I3)) tptp.one_one_real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ F I5)) (@ (@ tptp.power_power_real Z) I5))))))))))
% 6.18/6.70 (assert (forall ((R2 tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_real R2) 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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N))) (@ (@ tptp.power_power_real R2) N)))))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex Y) N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_complex X) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.power_power_rat Y) N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_rat X) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_int X) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.power_power_real Y) N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_real X) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P5)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) P5)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P5)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P5)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.18/6.70 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.18/6.70 (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))
% 6.18/6.70 (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)))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((Y tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.18/6.70 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.code_integer)) (K5 tptp.code_integer) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F P7)) K5))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) K5) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N2)) K5))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) K5))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) K5))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) K5))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) K5))))))
% 6.18/6.70 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.times_times_complex (@ _let_1 X)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.70 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.times_times_rat (@ _let_1 X)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.70 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.times_times_int (@ _let_1 X)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.70 (assert (forall ((R2 tptp.set_Pr448751882837621926eger_o) (S2 tptp.set_Pr448751882837621926eger_o)) (=> (forall ((X3 tptp.code_integer) (Y5 Bool)) (let ((_let_1 (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X3) Y5)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le8980329558974975238eger_o R2) S2))))
% 6.18/6.70 (assert (forall ((R2 tptp.set_Pr8218934625190621173um_num) (S2 tptp.set_Pr8218934625190621173um_num)) (=> (forall ((X3 tptp.num) (Y5 tptp.num)) (let ((_let_1 (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X3) Y5)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le880128212290418581um_num R2) S2))))
% 6.18/6.70 (assert (forall ((R2 tptp.set_Pr6200539531224447659at_num) (S2 tptp.set_Pr6200539531224447659at_num)) (=> (forall ((X3 tptp.nat) (Y5 tptp.num)) (let ((_let_1 (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X3) Y5)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le8085105155179020875at_num R2) S2))))
% 6.18/6.70 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y5)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le3146513528884898305at_nat R2) S2))))
% 6.18/6.70 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y5 tptp.int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y5)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le2843351958646193337nt_int R2) S2))))
% 6.18/6.70 (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))
% 6.18/6.70 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 6.18/6.70 (assert (forall ((Y 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 Y))))
% 6.18/6.70 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ (@ tptp.member_nat N) S3)))))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M2) (exists ((N9 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N9) (@ (@ tptp.member_nat N9) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 6.18/6.70 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.member_nat N) S3)))))))
% 6.18/6.70 (assert (forall ((D3 (-> tptp.product_prod_num_num Bool)) (R (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)) (X tptp.product_prod_num_num) (P (-> tptp.product_prod_num_num Bool))) (=> (@ (@ tptp.ord_le2239182809043710856_num_o D3) (@ tptp.accp_P3113834385874906142um_num R)) (=> (forall ((X3 tptp.product_prod_num_num) (Z4 tptp.product_prod_num_num)) (=> (@ D3 X3) (=> (@ (@ R Z4) X3) (@ D3 Z4)))) (=> (@ D3 X) (=> (forall ((X3 tptp.product_prod_num_num)) (=> (@ D3 X3) (=> (forall ((Z5 tptp.product_prod_num_num)) (=> (@ (@ R Z5) X3) (@ P Z5))) (@ P X3)))) (@ P X)))))))
% 6.18/6.70 (assert (forall ((D3 (-> tptp.product_prod_nat_nat Bool)) (R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le704812498762024988_nat_o D3) (@ tptp.accp_P4275260045618599050at_nat R)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Z4 tptp.product_prod_nat_nat)) (=> (@ D3 X3) (=> (@ (@ R Z4) X3) (@ D3 Z4)))) (=> (@ D3 X) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ D3 X3) (=> (forall ((Z5 tptp.product_prod_nat_nat)) (=> (@ (@ R Z5) X3) (@ P Z5))) (@ P X3)))) (@ P X)))))))
% 6.18/6.70 (assert (forall ((D3 (-> tptp.product_prod_int_int Bool)) (R (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) (X tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o D3) (@ tptp.accp_P1096762738010456898nt_int R)) (=> (forall ((X3 tptp.product_prod_int_int) (Z4 tptp.product_prod_int_int)) (=> (@ D3 X3) (=> (@ (@ R Z4) X3) (@ D3 Z4)))) (=> (@ D3 X) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (@ D3 X3) (=> (forall ((Z5 tptp.product_prod_int_int)) (=> (@ (@ R Z5) X3) (@ P Z5))) (@ P X3)))) (@ P X)))))))
% 6.18/6.70 (assert (forall ((D3 (-> tptp.list_nat Bool)) (R (-> tptp.list_nat tptp.list_nat Bool)) (X tptp.list_nat) (P (-> tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le1520216061033275535_nat_o D3) (@ tptp.accp_list_nat R)) (=> (forall ((X3 tptp.list_nat) (Z4 tptp.list_nat)) (=> (@ D3 X3) (=> (@ (@ R Z4) X3) (@ D3 Z4)))) (=> (@ D3 X) (=> (forall ((X3 tptp.list_nat)) (=> (@ D3 X3) (=> (forall ((Z5 tptp.list_nat)) (=> (@ (@ R Z5) X3) (@ P Z5))) (@ P X3)))) (@ P X)))))))
% 6.18/6.70 (assert (forall ((D3 (-> tptp.nat Bool)) (R (-> tptp.nat tptp.nat Bool)) (X tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o D3) (@ tptp.accp_nat R)) (=> (forall ((X3 tptp.nat) (Z4 tptp.nat)) (=> (@ D3 X3) (=> (@ (@ R Z4) X3) (@ D3 Z4)))) (=> (@ D3 X) (=> (forall ((X3 tptp.nat)) (=> (@ D3 X3) (=> (forall ((Z5 tptp.nat)) (=> (@ (@ R Z5) X3) (@ P Z5))) (@ P X3)))) (@ P X)))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ F I5)) (@ G I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) tptp.one_one_nat)))) _let_1))))))
% 6.18/6.70 (assert (forall ((R tptp.set_complex) (S3 tptp.set_complex)) (= (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) R))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) S3))) (@ (@ tptp.ord_le211207098394363844omplex R) S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_real) (S3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) R))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) S3))) (@ (@ tptp.ord_less_eq_set_real R) S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_set_nat) (S3 tptp.set_set_nat)) (= (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) R))) (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) S3))) (@ (@ tptp.ord_le6893508408891458716et_nat R) S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_nat) (S3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) R))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) S3))) (@ (@ tptp.ord_less_eq_set_nat R) S3))))
% 6.18/6.70 (assert (forall ((R tptp.set_int) (S3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) R))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) S3))) (@ (@ tptp.ord_less_eq_set_int R) S3))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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))))))))))))))))
% 6.18/6.70 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_1) (=> (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (= Y 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))) (=> (= X _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 6.18/6.70 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X _let_1) (=> (and (=> A3 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A3) (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y 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))) (=> (= X _let_1) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.18/6.70 (assert (forall ((A0 (-> tptp.nat tptp.num tptp.num)) (A12 tptp.nat) (A23 tptp.nat) (A32 tptp.num) (P (-> (-> tptp.nat tptp.num tptp.num) tptp.nat tptp.nat tptp.num Bool))) (=> (@ (@ tptp.accp_P4916641582247091100at_num tptp.set_fo256927282339908995el_num) (@ (@ tptp.produc851828971589881931at_num A0) (@ (@ tptp.produc1195630363706982562at_num A12) (@ (@ tptp.product_Pair_nat_num A23) A32)))) (=> (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.num)) (let ((_let_1 (@ P F2))) (=> (@ (@ tptp.accp_P4916641582247091100at_num tptp.set_fo256927282339908995el_num) (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A3) (@ (@ tptp.product_Pair_nat_num B2) Acc)))) (=> (=> (not (@ (@ tptp.ord_less_nat B2) A3)) (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) B2) (@ (@ F2 A3) Acc))) (@ (@ (@ _let_1 A3) B2) Acc))))) (@ (@ (@ (@ P A0) A12) A23) A32)))))
% 6.18/6.70 (assert (forall ((A0 (-> tptp.nat tptp.nat tptp.nat)) (A12 tptp.nat) (A23 tptp.nat) (A32 tptp.nat) (P (-> (-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat A0) (@ (@ tptp.produc487386426758144856at_nat A12) (@ (@ tptp.product_Pair_nat_nat A23) A32)))) (=> (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.nat)) (let ((_let_1 (@ P F2))) (=> (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A3) (@ (@ tptp.product_Pair_nat_nat B2) Acc)))) (=> (=> (not (@ (@ tptp.ord_less_nat B2) A3)) (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) B2) (@ (@ F2 A3) Acc))) (@ (@ (@ _let_1 A3) B2) Acc))))) (@ (@ (@ (@ P A0) A12) A23) A32)))))
% 6.18/6.70 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ tptp.produc2899441246263362727at_nat X))) (let ((_let_2 (@ tptp.accp_P3267385326087170368at_nat tptp.vEBT_V7235779383477046023at_nat))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb) Y) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.produc488173922507101015at_nat Xa2) Xb))) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) (=> (= Y tptp.none_P5556105721700978146at_nat) (not (@ _let_2 (@ _let_1 (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Xb)))))) (=> (forall ((V2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xa2 _let_1) (=> (= Xb tptp.none_P5556105721700978146at_nat) (=> (= Y tptp.none_P5556105721700978146at_nat) (not (@ (@ tptp.accp_P3267385326087170368at_nat tptp.vEBT_V7235779383477046023at_nat) (@ (@ tptp.produc2899441246263362727at_nat X) (@ (@ tptp.produc488173922507101015at_nat _let_1) tptp.none_P5556105721700978146at_nat))))))))) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A3)) (forall ((B2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.some_P7363390416028606310at_nat B2))) (=> (= Xb _let_1) (=> (= Y (@ tptp.some_P7363390416028606310at_nat (@ (@ X A3) B2))) (not (@ (@ tptp.accp_P3267385326087170368at_nat tptp.vEBT_V7235779383477046023at_nat) (@ (@ tptp.produc2899441246263362727at_nat X) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A3)) _let_1)))))))))))))))))))
% 6.18/6.70 (assert (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (@ tptp.produc5778274026573060048on_num X))) (let ((_let_2 (@ tptp.accp_P7605991808943153877on_num tptp.vEBT_V452583751252753300el_num))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb) Y) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.produc8585076106096196333on_num Xa2) Xb))) (=> (=> (= Xa2 tptp.none_num) (=> (= Y tptp.none_num) (not (@ _let_2 (@ _let_1 (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Xb)))))) (=> (forall ((V2 tptp.num)) (let ((_let_1 (@ tptp.some_num V2))) (=> (= Xa2 _let_1) (=> (= Xb tptp.none_num) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P7605991808943153877on_num tptp.vEBT_V452583751252753300el_num) (@ (@ tptp.produc5778274026573060048on_num X) (@ (@ tptp.produc8585076106096196333on_num _let_1) tptp.none_num))))))))) (not (forall ((A3 tptp.num)) (=> (= Xa2 (@ tptp.some_num A3)) (forall ((B2 tptp.num)) (let ((_let_1 (@ tptp.some_num B2))) (=> (= Xb _let_1) (=> (= Y (@ tptp.some_num (@ (@ X A3) B2))) (not (@ (@ tptp.accp_P7605991808943153877on_num tptp.vEBT_V452583751252753300el_num) (@ (@ tptp.produc5778274026573060048on_num X) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A3)) _let_1)))))))))))))))))))
% 6.18/6.70 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (@ tptp.produc8929957630744042906on_nat X))) (let ((_let_2 (@ tptp.accp_P5496254298877145759on_nat tptp.vEBT_V3895251965096974666el_nat))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb) Y) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.produc5098337634421038937on_nat Xa2) Xb))) (=> (=> (= Xa2 tptp.none_nat) (=> (= Y tptp.none_nat) (not (@ _let_2 (@ _let_1 (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Xb)))))) (=> (forall ((V2 tptp.nat)) (let ((_let_1 (@ tptp.some_nat V2))) (=> (= Xa2 _let_1) (=> (= Xb tptp.none_nat) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P5496254298877145759on_nat tptp.vEBT_V3895251965096974666el_nat) (@ (@ tptp.produc8929957630744042906on_nat X) (@ (@ tptp.produc5098337634421038937on_nat _let_1) tptp.none_nat))))))))) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A3)) (forall ((B2 tptp.nat)) (let ((_let_1 (@ tptp.some_nat B2))) (=> (= Xb _let_1) (=> (= Y (@ tptp.some_nat (@ (@ X A3) B2))) (not (@ (@ tptp.accp_P5496254298877145759on_nat tptp.vEBT_V3895251965096974666el_nat) (@ (@ tptp.produc8929957630744042906on_nat X) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A3)) _let_1)))))))))))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) tptp.one_one_real)))
% 6.18/6.70 (assert (forall ((X (-> tptp.nat tptp.num tptp.num)) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.num) (Y tptp.num)) (let ((_let_1 (@ (@ tptp.accp_P4916641582247091100at_num tptp.set_fo256927282339908995el_num) (@ (@ tptp.produc851828971589881931at_num X) (@ (@ tptp.produc1195630363706982562at_num Xa2) (@ (@ tptp.product_Pair_nat_num Xb) Xc)))))) (let ((_let_2 (@ tptp.set_fo8365102181078989356at_num X))) (let ((_let_3 (@ (@ tptp.ord_less_nat Xb) Xa2))) (=> (= (@ (@ (@ _let_2 Xa2) Xb) Xc) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y Xc)) (=> (not _let_3) (= Y (@ (@ (@ _let_2 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X Xa2) Xc))))) (not _let_1))))))))))
% 6.18/6.70 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat X) (@ (@ tptp.produc487386426758144856at_nat Xa2) (@ (@ tptp.product_Pair_nat_nat Xb) Xc)))))) (let ((_let_2 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_3 (@ (@ tptp.ord_less_nat Xb) Xa2))) (=> (= (@ (@ (@ _let_2 Xa2) Xb) Xc) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y Xc)) (=> (not _let_3) (= Y (@ (@ (@ _let_2 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X Xa2) Xc))))) (not _let_1))))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.num tptp.num)) (A tptp.nat) (B tptp.nat) (Acc2 tptp.num)) (let ((_let_1 (@ tptp.set_fo8365102181078989356at_num F))) (let ((_let_2 (@ (@ (@ _let_1 A) B) Acc2))) (let ((_let_3 (@ (@ tptp.ord_less_nat B) A))) (=> (@ (@ tptp.accp_P4916641582247091100at_num tptp.set_fo256927282339908995el_num) (@ (@ tptp.produc851828971589881931at_num F) (@ (@ tptp.produc1195630363706982562at_num A) (@ (@ tptp.product_Pair_nat_num B) Acc2)))) (and (=> _let_3 (= _let_2 Acc2)) (=> (not _let_3) (= _let_2 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) B) (@ (@ F A) Acc2)))))))))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat) (Acc2 tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat F))) (let ((_let_2 (@ (@ (@ _let_1 A) B) Acc2))) (let ((_let_3 (@ (@ tptp.ord_less_nat B) A))) (=> (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat F) (@ (@ tptp.produc487386426758144856at_nat A) (@ (@ tptp.product_Pair_nat_nat B) Acc2)))) (and (=> _let_3 (= _let_2 Acc2)) (=> (not _let_3) (= _let_2 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) B) (@ (@ F A) Acc2)))))))))))
% 6.18/6.70 (assert (forall ((N2 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)) N2)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))))
% 6.18/6.70 (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))))
% 6.18/6.70 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.18/6.70 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real tptp.pi) X)) (@ tptp.sin_real X))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X))) (let ((_let_2 (@ tptp.cos_complex X))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (let ((_let_2 (@ tptp.cos_real X))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) tptp.zero_zero_real)))
% 6.18/6.70 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.18/6.70 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.18/6.70 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.cos_real X))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) tptp.one_one_real))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) tptp.one_one_complex))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) tptp.one_one_real))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) tptp.one_one_complex))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.zero_zero_real)))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.one_one_real)))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.18/6.70 (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))
% 6.18/6.70 (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)))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (exists ((R3 tptp.real) (A3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X (@ _let_1 (@ tptp.cos_real A3))) (= Y (@ _let_1 (@ tptp.sin_real A3))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X))) (@ tptp.cos_complex X))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X))) (@ tptp.cos_real X))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (exists ((Y5 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y5) (@ (@ tptp.ord_less_eq_real Y5) tptp.pi) (= (@ tptp.sin_real Y5) (@ tptp.sin_real X)) (= (@ tptp.cos_real Y5) (@ tptp.cos_real X))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) X))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 6.18/6.70 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 6.18/6.70 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) (@ tptp.abs_abs_real X))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))))) tptp.one_one_real)))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) (@ tptp.sin_real X)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X) (@ tptp.cos_real Y)) (= X Y)))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ _let_1 X))))))))))
% 6.18/6.70 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 6.18/6.70 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((X 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)) X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_2)))))))
% 6.18/6.70 (assert (forall ((X 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)) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_2)))))))
% 6.18/6.70 (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)))))))))
% 6.18/6.70 (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)))))))))
% 6.18/6.70 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X)))))))))
% 6.18/6.70 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 6.18/6.70 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 6.18/6.70 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _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) (= X (@ tptp.cos_real T5)) (= Y (@ tptp.sin_real T5)))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ 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))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ 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)))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.18/6.70 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.18/6.70 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.18/6.70 (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 ((Y3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_eq_real Y3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y3) tptp.zero_zero_real)) (= Y3 X3))))))
% 6.18/6.70 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B4 tptp.nat) (Acc3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B4) A4)) Acc3) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) B4) (@ (@ F3 A4) Acc3))))))
% 6.18/6.70 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (@ (@ X Xa2) Xc))))))))))
% 6.18/6.70 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 6.18/6.70 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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) Y) (forall ((Y3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.cos_real Y3) Y)) (= Y3 X3)))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y 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 X) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _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)))) (= X (@ tptp.cos_real T5)) (= Y (@ tptp.sin_real T5)))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _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)) (= X (@ tptp.cos_real T5)) (= Y (@ tptp.sin_real T5))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _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)) (=> (= X (@ tptp.cos_real T5)) (not (= Y (@ tptp.sin_real T5))))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X))) tptp.one_one_real))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X)))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y 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 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y)) (= X Y))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (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 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))))
% 6.18/6.70 (assert (forall ((Y tptp.real) (X 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)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 6.18/6.70 (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)))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_complex))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_rat))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_int))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A4)) __flatten_var_0))) A) B) tptp.zero_zero_real))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X)) (@ (@ 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))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.cos_real X))) (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 X)) (@ (@ 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))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.18/6.70 (assert (forall ((X tptp.real) (Y 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 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X) Y))))))))))
% 6.18/6.70 (assert (forall ((Y tptp.real) (X 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)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 6.18/6.70 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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) Y) (forall ((Y3 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)) Y3) (@ (@ tptp.ord_less_eq_real Y3) _let_1) (= (@ tptp.sin_real Y3) Y)) (= Y3 X3)))))))))))
% 6.18/6.70 (assert (forall ((X 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)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.18/6.70 (assert (forall ((X 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)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (or (exists ((X2 tptp.nat)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X2 tptp.nat)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) 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) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) 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)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (or (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_real T5) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real X) T5) (@ (@ tptp.ord_less_real T5) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))
% 6.18/6.70 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_complex X) 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)))))))))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_real X) 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)))))))))))))
% 6.18/6.70 (assert (forall ((X tptp.num) (Y tptp.num) (F (-> tptp.num tptp.nat))) (= (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y)) (@ tptp.measure_num F)) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))))
% 6.18/6.70 (assert (forall ((X tptp.nat) (Y tptp.nat) (F (-> tptp.nat tptp.nat))) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.measure_nat F)) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))))
% 6.18/6.70 (assert (forall ((X tptp.int) (Y tptp.int) (F (-> tptp.int tptp.nat))) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.measure_int F)) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.tan_real X))))
% 6.18/6.70 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.18/6.70 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.18/6.70 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.18/6.70 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.18/6.70 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.18/6.70 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.18/6.70 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.18/6.70 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.18/6.70 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.18/6.70 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.18/6.70 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.18/6.70 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.18/6.70 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri3624122377584611663nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger _let_1)) (@ tptp.semiri3624122377584611663nteger N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N2)) tptp.pi))) (@ tptp.tan_real X))))
% 6.18/6.70 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi))) (@ tptp.tan_real X))))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.18/6.70 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.18/6.70 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N2)) tptp.zero_zero_rat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N2)) tptp.zero_zero_real))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real M)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N2))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2))))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N2))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat N2))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N2))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N2))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N2))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.70 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat N2) N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N2) N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N2) N2)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.18/6.70 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex X2)))))
% 6.18/6.70 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X2)) (@ tptp.cos_real X2)))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri3624122377584611663nteger N2)))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.18/6.70 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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))))))
% 6.18/6.70 (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)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ 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))) N2))))))
% 6.18/6.70 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.18/6.70 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M6)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M6)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (= tptp.semiri3624122377584611663nteger (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M6 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M6)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M6)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M6)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.18/6.70 (assert (= tptp.semiri3624122377584611663nteger (lambda ((N tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.18/6.70 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.18/6.70 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri773545260158071498ct_rat N2) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1406184849735516958ct_int N2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri3624122377584611663nteger N2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N2)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri2265585572941072030t_real N2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1408675320244567234ct_nat N2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.18/6.70 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.18/6.70 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (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 Y) (@ tptp.tan_real X3)))))))
% 6.18/6.70 (assert (forall ((Y 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) Y) (forall ((Y3 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)) Y3) (@ (@ tptp.ord_less_real Y3) _let_1) (= (@ tptp.tan_real Y3) Y)) (= Y3 X3)))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real) (X 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)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y))) (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 Y) (=> (@ _let_1 _let_2) (=> (@ _let_3 X) (=> (@ (@ tptp.ord_less_real X) _let_2) (= (@ _let_1 X) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (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 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ _let_1 Y)))))))))))
% 6.18/6.71 (assert (forall ((Y 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) Y))))))
% 6.18/6.71 (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)))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y)))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (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) Y))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y 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 X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y 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)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ 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 X))) tptp.one_one_real))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arctan Y))) (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) Y))))))
% 6.18/6.71 (assert (forall ((X 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)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X)) X))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y 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)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (= (@ tptp.tan_real X) Y) (= (@ tptp.arctan Y) X)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.18/6.71 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B8 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N2)) (@ tptp.semiri2265585572941072030t_real N2)))))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (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 X)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X))) (=> (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 X)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X) Y))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) 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))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_real X) Y))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) 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))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X) Y))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) 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))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.plus_plus_real X) Y))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) 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))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z4 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)) Z4) (@ (@ tptp.ord_less_real Z4) _let_1) (= (@ tptp.tan_real Z4) X)))))))
% 6.18/6.71 (assert (= tptp.tan_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 6.18/6.71 (assert (= tptp.tan_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 6.18/6.71 (assert (= tptp.cos_coeff (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ tptp.semiri2265585572941072030t_real N))) tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_real T5) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T5 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))
% 6.18/6.71 (assert (= tptp.sin_coeff (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) 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 N) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N2))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N2)))))))))
% 6.18/6.71 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) R2)))) (@ (@ tptp.power_power_nat N2) R2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N2)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N2))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X) (@ (@ 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)))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X) (@ (@ 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 X)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.18/6.71 (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)))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (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 X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.sqrt X) (@ tptp.sqrt Y)) (= X Y))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.18/6.71 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.18/6.71 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.18/6.71 (assert (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 6.18/6.71 (assert (@ (@ tptp.sums_real (lambda ((N tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 6.18/6.71 (assert (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 6.18/6.71 (assert (@ (@ tptp.sums_int (lambda ((N tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 6.18/6.71 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.18/6.71 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.18/6.71 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))))
% 6.18/6.71 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.complex)) (X tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.real)) (X tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) X) (= (@ A tptp.zero_zero_nat) X))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y 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 X) _let_1)) (@ (@ tptp.power_power_real Y) _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)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S2 tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S2) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S2) T))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S2 tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S2) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S2) T))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S2 tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S2) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S2) T))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X)))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X)) K))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D)))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (F (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (= R5 I2)) (@ F R5)) tptp.zero_zero_complex))) (@ F I2))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (F (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (= R5 I2)) (@ F R5)) tptp.zero_zero_real))) (@ F I2))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (F (-> tptp.nat tptp.nat))) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (= R5 I2)) (@ F R5)) tptp.zero_zero_nat))) (@ F I2))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (F (-> tptp.nat tptp.int))) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (= R5 I2)) (@ F R5)) tptp.zero_zero_int))) (@ F I2))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) A)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) A)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))) (@ (@ tptp.times_times_complex A) C)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))) (@ (@ tptp.times_times_real A) C)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (G (-> tptp.nat tptp.complex)) (B tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (=> (@ (@ tptp.sums_complex G) B) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_complex (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_complex A) B))))))
% 6.18/6.71 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_real A) B))))))
% 6.18/6.71 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_nat A) B))))))
% 6.18/6.71 (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 ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_int A) B))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (G (-> tptp.nat tptp.complex)) (B tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (=> (@ (@ tptp.sums_complex G) B) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N)) (@ G N)))) (@ (@ tptp.minus_minus_complex A) B))))))
% 6.18/6.71 (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 ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))) (@ (@ tptp.minus_minus_real A) B))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (@ (@ tptp.divide_divide_real A) C)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ F N)))) (@ tptp.uminus_uminus_real A)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N)))) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.18/6.71 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.real)) (X (-> tptp.complex tptp.real))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.sums_real (@ F I3)) (@ X I3)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups5808333547571424918x_real X) I6)))))
% 6.18/6.71 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat tptp.real)) (X (-> tptp.real tptp.real))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.sums_real (@ F I3)) (@ X I3)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups8097168146408367636l_real X) I6)))))
% 6.18/6.71 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.real)) (X (-> tptp.int tptp.real))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.sums_real (@ F I3)) (@ X I3)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups8778361861064173332t_real X) I6)))))
% 6.18/6.71 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat tptp.complex)) (X (-> tptp.real tptp.complex))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.sums_complex (@ F I3)) (@ X I3)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups5754745047067104278omplex (lambda ((I5 tptp.real)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups5754745047067104278omplex X) I6)))))
% 6.18/6.71 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.complex)) (X (-> tptp.nat tptp.complex))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.sums_complex (@ F I3)) (@ X I3)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups2073611262835488442omplex X) I6)))))
% 6.18/6.71 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.complex)) (X (-> tptp.int tptp.complex))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.sums_complex (@ F I3)) (@ X I3)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups3049146728041665814omplex (lambda ((I5 tptp.int)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups3049146728041665814omplex X) I6)))))
% 6.18/6.71 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat tptp.int)) (X (-> tptp.int tptp.int))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.sums_int (@ F I3)) (@ X I3)))) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups4538972089207619220nt_int X) I6)))))
% 6.18/6.71 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat tptp.complex)) (X (-> tptp.complex tptp.complex))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.sums_complex (@ F I3)) (@ X I3)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I5 tptp.complex)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups7754918857620584856omplex X) I6)))))
% 6.18/6.71 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.nat)) (X (-> tptp.nat tptp.nat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.sums_nat (@ F I3)) (@ X I3)))) (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups3542108847815614940at_nat X) I6)))))
% 6.18/6.71 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.nat tptp.real)) (X (-> tptp.nat tptp.real))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.sums_real (@ F I3)) (@ X I3)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ F I5) N))) I6))) (@ (@ tptp.groups6591440286371151544t_real X) I6)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ (@ tptp.times_times_complex Y) X)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X) Y) (@ (@ tptp.times_times_real Y) X)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)))))
% 6.18/6.71 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))))
% 6.18/6.71 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))))
% 6.18/6.71 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))))
% 6.18/6.71 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real X) _let_1) _let_1)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X)) (@ tptp.sqrt Y))))))))
% 6.18/6.71 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))))
% 6.18/6.71 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S2) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex S2) (@ F tptp.zero_zero_nat))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ F tptp.zero_zero_nat))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (L2 tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex L2) (@ F tptp.zero_zero_nat))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L2) (@ F tptp.zero_zero_nat))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (L2 tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L2) (@ F tptp.zero_zero_nat))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.int)) (L2 tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L2) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L2) (@ F tptp.zero_zero_nat))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (= (@ F I3) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (= (@ F I3) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))) tptp.one_one_real)))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) X)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N2))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N2))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N2))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F) A2)))))
% 6.18/6.71 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) A2)))))
% 6.18/6.71 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) A2)))))
% 6.18/6.71 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat R5) A2)) (@ F R5)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) A2)))))
% 6.18/6.71 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P R5)) (@ F R5)) tptp.zero_zero_complex))) (@ (@ tptp.groups2073611262835488442omplex F) _let_1))))))
% 6.18/6.71 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (@ P R5)) (@ F R5)) tptp.zero_zero_int))) (@ (@ tptp.groups3539618377306564664at_int F) _let_1))))))
% 6.18/6.71 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P R5)) (@ F R5)) tptp.zero_zero_nat))) (@ (@ tptp.groups3542108847815614940at_nat F) _let_1))))))
% 6.18/6.71 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.collect_nat P))) (=> (@ tptp.finite_finite_nat _let_1) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (@ P R5)) (@ F R5)) tptp.zero_zero_real))) (@ (@ tptp.groups6591440286371151544t_real F) _let_1))))))
% 6.18/6.71 (assert (forall ((N4 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat N4) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N4)) (= (@ F N3) tptp.zero_zero_complex))) (@ (@ tptp.sums_complex F) (@ (@ tptp.groups2073611262835488442omplex F) N4))))))
% 6.18/6.71 (assert (forall ((N4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat N4) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N4)) (= (@ F N3) tptp.zero_zero_int))) (@ (@ tptp.sums_int F) (@ (@ tptp.groups3539618377306564664at_int F) N4))))))
% 6.18/6.71 (assert (forall ((N4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat N4) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N4)) (= (@ F N3) tptp.zero_zero_nat))) (@ (@ tptp.sums_nat F) (@ (@ tptp.groups3542108847815614940at_nat F) N4))))))
% 6.18/6.71 (assert (forall ((N4 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat N4) (=> (forall ((N3 tptp.nat)) (=> (not (@ (@ tptp.member_nat N3) N4)) (= (@ F N3) tptp.zero_zero_real))) (@ (@ tptp.sums_real F) (@ (@ tptp.groups6591440286371151544t_real F) N4))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D 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) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_2 C)) (@ _let_1 D))) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.power_power_complex Z) M))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.power_power_real Z) M))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N)))) (@ (@ tptp.power_power_int Z) M))))
% 6.18/6.71 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) (@ A tptp.zero_zero_nat))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) (@ A tptp.zero_zero_nat))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X)))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y) (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 Y) tptp.one_one_real)) (= (@ tptp.exp_real X3) Y))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (S2 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S2) (@ (@ tptp.sums_complex F) (@ (@ tptp.plus_plus_complex S2) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (S2 tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.sums_complex F) S2) (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_complex S2) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.sums_real F) S2) (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (N2 tptp.nat) (S2 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_complex S2) (@ (@ tptp.groups2073611262835488442omplex F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_complex F) S2))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_real F) S2))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.complex)) (S3 tptp.complex) (A2 tptp.set_nat) (S4 tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.sums_complex G) S3) (=> (@ tptp.finite_finite_nat A2) (=> (= S4 (@ (@ tptp.plus_plus_complex S3) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F N)) (@ G N)))) A2))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.member_nat N) A2)) (@ F N)) (@ G N)))) S4))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.real)) (S3 tptp.real) (A2 tptp.set_nat) (S4 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S3) (=> (@ tptp.finite_finite_nat A2) (=> (= S4 (@ (@ tptp.plus_plus_real S3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))) A2))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N) A2)) (@ F N)) (@ G N)))) S4))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.set_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((X2 tptp.nat)) (@ (@ tptp.complex2 (@ F X2)) tptp.zero_zero_real))) S2) (@ (@ tptp.complex2 (@ (@ tptp.groups6591440286371151544t_real F) S2)) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((F (-> tptp.complex tptp.real)) (S2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.complex2 (@ F X2)) tptp.zero_zero_real))) S2) (@ (@ tptp.complex2 (@ (@ tptp.groups5808333547571424918x_real F) S2)) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X) (@ tptp.sqrt Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.18/6.71 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.semiri8010041392384452111omplex N2)))) N2) (@ tptp.exp_complex X)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N2)))) N2) (@ tptp.exp_real X)))))
% 6.18/6.71 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))) (let ((_let_2 (@ tptp.exp_real X2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.18/6.71 (assert (= tptp.tanh_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))) (let ((_let_2 (@ tptp.exp_complex X2))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.18/6.71 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X) Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y)))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X) (= Y tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D 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) D)) _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 D) _let_1))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.18/6.71 (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)))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) Y)))))))
% 6.18/6.71 (assert (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N)))) tptp.one_one_real))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y 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 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X) Y))))))))
% 6.18/6.71 (assert (forall ((N2 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) N2) (= (@ tptp.sqrt (@ _let_3 N2)) (@ _let_3 (@ (@ tptp.divide_divide_nat N2) _let_2)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.18/6.71 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y 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 X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.sqrt X)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ (@ tptp.sums_real G) X) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_1)))))) X))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) (@ F (@ (@ tptp.divide_divide_nat N) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X) Y))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) N2) (@ (@ tptp.power_power_real X) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y 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 X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y 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 X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))))
% 6.18/6.71 (assert (forall ((X tptp.real) (U tptp.real) (Y 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 X)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (= (@ tptp.arcosh_real X) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real X)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (U tptp.real) (Y 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 X) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (=> (@ (@ 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 X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.18/6.71 (assert (= tptp.arctan (lambda ((X2 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 X2) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.18/6.71 (assert (= tptp.tanh_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.cos_real X))))
% 6.18/6.71 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))) (@ (@ 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))))))))
% 6.18/6.71 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ 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))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ C N))) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ C N))) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N))))))))
% 6.18/6.71 (assert (= tptp.arsinh_real (lambda ((X2 tptp.real)) (@ tptp.ln_ln_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)))))))
% 6.18/6.71 (assert (= tptp.binomial (lambda ((N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) K3))) (let ((_let_2 (@ tptp.ord_less_nat N))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_1) N2) _let_1))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) N2) tptp.one_one_nat)))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) (@ tptp.suc tptp.zero_zero_nat)) N2)))
% 6.18/6.71 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N2) K))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N2))) (= (@ (@ tptp.binomial (@ tptp.suc N2)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y)))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y)) Y)))))
% 6.18/6.71 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.18/6.71 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.one_one_nat) N2)))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2) K)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (R2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R2))) (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)))))))))
% 6.18/6.71 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) R2)) (@ (@ tptp.power_power_nat N2) R2)))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real))) (= (@ tptp.diffs_real (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ C N)))) (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ (@ tptp.diffs_real C) N))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.int))) (= (@ tptp.diffs_int (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_int (@ C N)))) (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_int (@ (@ tptp.diffs_int C) N))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex))) (= (@ tptp.diffs_complex (lambda ((N tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ C N)))) (lambda ((N tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.diffs_complex C) N))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.rat))) (= (@ tptp.diffs_rat (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_rat (@ C N)))) (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_rat (@ (@ tptp.diffs_rat C) N))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.code_integer))) (= (@ tptp.diffs_Code_integer (lambda ((N tptp.nat)) (@ tptp.uminus1351360451143612070nteger (@ C N)))) (lambda ((N tptp.nat)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.diffs_Code_integer C) N))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K))) _let_1))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y)) (= X Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y)) (= X Y))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) K))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.binomial N2) K)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.18/6.71 (assert (= tptp.diffs_rat (lambda ((C4 (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C4 _let_1))))))
% 6.18/6.71 (assert (= tptp.diffs_int (lambda ((C4 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C4 _let_1))))))
% 6.18/6.71 (assert (= tptp.diffs_real (lambda ((C4 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C4 _let_1))))))
% 6.18/6.71 (assert (= tptp.diffs_Code_integer (lambda ((C4 (-> tptp.nat tptp.code_integer)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger _let_1)) (@ C4 _let_1))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real K))) K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.semiri681578069525770553at_rat K))) K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ 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)) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N2) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) tptp.pi)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X)) X)))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((X3 tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ C N)) (@ (@ tptp.power_power_complex X3) N))))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N)))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((X3 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ C N)) (@ (@ tptp.power_power_real X3) N))))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N2) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N2) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N2) _let_1))) (let ((_let_3 (@ tptp.binomial N2))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.binomial N2) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N2)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X) (= (@ tptp.arccos (@ tptp.cos_real X)) (@ tptp.uminus_uminus_real X))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) _let_1)))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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) Y)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) K5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X3)) K5) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ C N)) (@ (@ tptp.power_power_real X3) N)))))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X) N))))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) K5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X3)) K5) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ C N)) (@ (@ tptp.power_power_complex X3) N)))))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X) N))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) 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))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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 Y))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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))))))))
% 6.18/6.71 (assert (forall ((X 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)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X)) X))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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) Y)))))))
% 6.18/6.71 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (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)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) 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) Y))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) N2)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_complex _let_1) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I5))) tptp.zero_z3403309356797280102nteger))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_real _let_1) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_complex _let_1) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I5))) tptp.zero_z3403309356797280102nteger))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_real _let_1) N2))))))
% 6.18/6.71 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_real (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_real (@ X4 N)) (@ X4 M6))))))))
% 6.18/6.71 (assert (= tptp.topolo3100542954746470799et_int (lambda ((X4 (-> tptp.nat tptp.set_int))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_int (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_int (@ X4 N)) (@ X4 M6))))))))
% 6.18/6.71 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X4 (-> tptp.nat tptp.rat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_rat (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_rat (@ X4 N)) (@ X4 M6))))))))
% 6.18/6.71 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_num (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_num (@ X4 N)) (@ X4 M6))))))))
% 6.18/6.71 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_nat (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_nat (@ X4 N)) (@ X4 M6))))))))
% 6.18/6.71 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_int (@ X4 M6)) (@ X4 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_int (@ X4 N)) (@ X4 M6))))))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_real (@ X8 N3)) (@ X8 M2)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_set_int (@ X8 N3)) (@ X8 M2)))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ X8 M2)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_num (@ X8 N3)) (@ X8 M2)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_nat (@ X8 N3)) (@ X8 M2)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_int (@ X8 N3)) (@ X8 M2)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_real (@ X8 M2)) (@ X8 N3)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_set_int (@ X8 M2)) (@ X8 N3)))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 M2)) (@ X8 N3)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_num (@ X8 M2)) (@ X8 N3)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_nat (@ X8 M2)) (@ X8 N3)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (@ (@ tptp.ord_less_eq_int (@ X8 M2)) (@ X8 N3)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.18/6.71 (assert (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I2) K))))
% 6.18/6.71 (assert (forall ((I2 tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or4236626031148496127et_nat K)) (@ (@ tptp.ord_less_eq_set_nat I2) K))))
% 6.18/6.71 (assert (forall ((I2 tptp.set_int) (K tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ tptp.set_or58775011639299419et_int K)) (@ (@ tptp.ord_less_eq_set_int I2) K))))
% 6.18/6.71 (assert (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_atMost_rat K)) (@ (@ tptp.ord_less_eq_rat I2) K))))
% 6.18/6.71 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_atMost_num K)) (@ (@ tptp.ord_less_eq_num I2) K))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I2) K))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I2) K))))
% 6.18/6.71 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ tptp.set_or58775011639299419et_int X)) (@ tptp.set_or58775011639299419et_int Y)) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.18/6.71 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X)) (@ tptp.set_ord_atMost_rat Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.18/6.71 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X)) (@ tptp.set_ord_atMost_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.18/6.71 (assert (forall ((L2 tptp.set_int) (H2 tptp.set_int) (H3 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L2) H2)) (@ tptp.set_or58775011639299419et_int H3)) (or (not (@ (@ tptp.ord_less_eq_set_int L2) H2)) (@ (@ tptp.ord_less_eq_set_int H2) H3)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.18/6.71 (assert (= tptp.set_or4236626031148496127et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X2) U2))))))
% 6.18/6.71 (assert (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X2) U2))))))
% 6.18/6.71 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) U2))))))
% 6.18/6.71 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) U2))))))
% 6.18/6.71 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) U2))))))
% 6.18/6.71 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) U2))))))
% 6.18/6.71 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.18/6.71 (assert (forall ((H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H2)) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)))))
% 6.18/6.71 (assert (forall ((H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H2)) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)))))
% 6.18/6.71 (assert (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_atMost_nat K3))))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat A)) (@ tptp.set_ord_lessThan_rat B)) (@ (@ tptp.ord_less_rat A) B))))
% 6.18/6.71 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num A)) (@ tptp.set_ord_lessThan_num B)) (@ (@ tptp.ord_less_num A) B))))
% 6.18/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A)) (@ tptp.set_ord_lessThan_nat B)) (@ (@ tptp.ord_less_nat A) B))))
% 6.18/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A)) (@ tptp.set_ord_lessThan_int B)) (@ (@ tptp.ord_less_int A) B))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A)) (@ tptp.set_or5984915006950818249n_real B)) (@ (@ tptp.ord_less_real A) B))))
% 6.18/6.71 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_ord_atMost_o A)) (@ tptp.set_ord_lessThan_o B)) (@ (@ tptp.ord_less_o A) B))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc N2)) (@ tptp.suc M)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I5)) (@ F (@ tptp.suc I5))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I5)) (@ F (@ tptp.suc I5))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I5)) (@ F (@ tptp.suc I5))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X2) I5)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I5)) (@ (@ tptp.power_power_complex X2) I5)))) _let_1)))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) (@ D I5)))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X2) I5)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ D I5)) (@ (@ tptp.power_power_real X2) I5)))) _let_1)))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) (@ D I5)))))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.int)) (B3 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int A) (@ tptp.set_ord_atMost_nat N3))) B3)) (@ tptp.summable_int A)))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.nat)) (B3 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat A) (@ tptp.set_ord_atMost_nat N3))) B3)) (@ tptp.summable_nat A)))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real A) (@ tptp.set_ord_atMost_nat N3))) B3)) (@ tptp.summable_real A)))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I5)) (@ tptp.set_ord_lessThan_nat I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ A I5) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A I5)) (@ tptp.set_ord_lessThan_nat I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ A I5) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.18/6.71 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K3)) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N2))) N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N2) M)) tptp.one_one_nat)) M))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ 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))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) tptp.zero_zero_complex))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) tptp.zero_zero_real))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex W2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_complex)))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real W2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N2)) M)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R2) K3))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N2)) R2))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.18/6.71 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ (@ tptp.times_times_rat (@ _let_2 X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.18/6.71 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I5) N2) (not (= (@ C I5) tptp.zero_zero_complex)))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I5) N2) (not (= (@ C I5) tptp.zero_zero_real)))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex)) (K tptp.nat) (N2 tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex Z2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real)) (K tptp.nat) (N2 tptp.nat)) (=> (not (= (@ C K) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real Z2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex)) (A tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex) (not (forall ((B2 (-> tptp.nat tptp.complex))) (not (forall ((Z5 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex Z5) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 I5)) (@ (@ tptp.power_power_complex Z5) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.rat)) (A tptp.rat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat) (not (forall ((B2 (-> tptp.nat tptp.rat))) (not (forall ((Z5 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat Z5) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ B2 I5)) (@ (@ tptp.power_power_rat Z5) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.int)) (A tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int) (not (forall ((B2 (-> tptp.nat tptp.int))) (not (forall ((Z5 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int Z5) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 I5)) (@ (@ tptp.power_power_int Z5) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real)) (A tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real) (not (forall ((B2 (-> tptp.nat tptp.real))) (not (forall ((Z5 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real Z5) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 I5)) (@ (@ tptp.power_power_real Z5) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (A tptp.complex)) (exists ((B2 (-> tptp.nat tptp.complex))) (forall ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex Z5) I5)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z5) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ B2 I5)) (@ (@ tptp.power_power_complex Z5) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex A) I5)))) _let_1))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.rat)) (N2 tptp.nat) (A tptp.rat)) (exists ((B2 (-> tptp.nat tptp.rat))) (forall ((Z5 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat Z5) I5)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z5) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ B2 I5)) (@ (@ tptp.power_power_rat Z5) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat A) I5)))) _let_1))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.int)) (N2 tptp.nat) (A tptp.int)) (exists ((B2 (-> tptp.nat tptp.int))) (forall ((Z5 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int Z5) I5)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z5) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ B2 I5)) (@ (@ tptp.power_power_int Z5) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int A) I5)))) _let_1))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (A tptp.real)) (exists ((B2 (-> tptp.nat tptp.real))) (forall ((Z5 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real Z5) I5)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z5) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ B2 I5)) (@ (@ tptp.power_power_real Z5) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real A) I5)))) _let_1))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N2)) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ tptp.summable_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)) (@ tptp.suminf_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.18/6.71 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.complex)) (N2 tptp.nat) (B (-> tptp.nat tptp.complex)) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) tptp.zero_zero_complex))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex X) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B J3)) (@ (@ tptp.power_power_complex X) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_complex X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.rat)) (N2 tptp.nat) (B (-> tptp.nat tptp.rat)) (X tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) tptp.zero_zero_rat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_rat))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I5)) (@ (@ tptp.power_power_rat X) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B J3)) (@ (@ tptp.power_power_rat X) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_rat X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.int)) (N2 tptp.nat) (B (-> tptp.nat tptp.int)) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) tptp.zero_zero_int))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int X) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ B J3)) (@ (@ tptp.power_power_int X) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_int X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.real)) (N2 tptp.nat) (B (-> tptp.nat tptp.real)) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) tptp.zero_zero_real))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real X) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ B J3)) (@ (@ tptp.power_power_real X) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_real X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.complex)) (= (forall ((X2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X2) tptp.zero_zero_complex)))))))
% 6.18/6.71 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.real)) (= (forall ((X2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X2) I5)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X2) tptp.zero_zero_real)))))))
% 6.18/6.71 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_complex A) K3))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_rat A) K3))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) N2) (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_8256067586552552935nteger A) K3))) (@ (@ tptp.power_8256067586552552935nteger B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_real A) K3))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N2 tptp.nat) (B (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I5)) (@ (@ tptp.power_power_nat X) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N2) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) N2))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ (@ tptp.sums_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)))))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ (@ tptp.sums_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3)))) (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)))))))
% 6.18/6.71 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_complex (= J3 K)) tptp.zero_zero_complex) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.18/6.71 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.zero_zero_rat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.18/6.71 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.zero_zero_int) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.18/6.71 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.zero_zero_nat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.18/6.71 (assert (forall ((P4 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P4) (=> (@ (@ tptp.ord_less_eq_nat K) P4) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_real (= J3 K)) tptp.zero_zero_real) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P4) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Z tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_int Z) N2) A) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= I5 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int A)) (@ (@ (@ tptp.if_int (= I5 N2)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.power_power_int Z) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Z tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_complex Z) N2) A) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= I5 tptp.zero_zero_nat)) (@ tptp.uminus1482373934393186551omplex A)) (@ (@ (@ tptp.if_complex (= I5 N2)) tptp.one_one_complex) tptp.zero_zero_complex))) (@ (@ tptp.power_power_complex Z) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Z tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_rat Z) N2) A) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ (@ tptp.if_rat (= I5 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_rat A)) (@ (@ (@ tptp.if_rat (= I5 N2)) tptp.one_one_rat) tptp.zero_zero_rat))) (@ (@ tptp.power_power_rat Z) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Z tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_8256067586552552935nteger Z) N2) A) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ (@ tptp.if_Code_integer (= I5 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ (@ tptp.if_Code_integer (= I5 N2)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.power_8256067586552552935nteger Z) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Z tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_real Z) N2) A) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= I5 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_real A)) (@ (@ (@ tptp.if_real (= I5 N2)) tptp.one_one_real) tptp.zero_zero_real))) (@ (@ tptp.power_power_real Z) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X)))))))))))
% 6.18/6.71 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X)))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X)))))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I5)) (@ tptp.semiri8010041392384452111omplex I5))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I5)) (@ tptp.semiri681578069525770553at_rat I5))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I5)) (@ tptp.semiri1314217659103216013at_int I5))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I5)) (@ tptp.semiri4939895301339042750nteger I5))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ tptp.semiri5074537144036343181t_real I5))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex X) I5)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex Y) I5)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_complex Y) K3))) (@ (@ tptp.power_power_complex X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I5)) (@ (@ tptp.power_power_rat X) I5)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I5)) (@ (@ tptp.power_power_rat Y) I5)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_rat Y) K3))) (@ (@ tptp.power_power_rat X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int X) I5)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int Y) I5)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_int Y) K3))) (@ (@ tptp.power_power_int X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real X) I5)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real Y) I5)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ A (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat J3) K3)) tptp.one_one_nat))) (@ (@ tptp.power_power_real Y) K3))) (@ (@ tptp.power_power_real X) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.int))) (=> (@ tptp.topolo4899668324122417113eq_int A) (@ tptp.topolo4899668324122417113eq_int (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_int (@ A N)))))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.rat))) (=> (@ tptp.topolo4267028734544971653eq_rat A) (@ tptp.topolo4267028734544971653eq_rat (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_rat (@ A N)))))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.code_integer))) (=> (@ tptp.topolo2919662092509805066nteger A) (@ tptp.topolo2919662092509805066nteger (lambda ((N tptp.nat)) (@ tptp.uminus1351360451143612070nteger (@ A N)))))))
% 6.18/6.71 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.topolo6980174941875973593q_real (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ A N)))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat I5) (@ (@ tptp.binomial N2) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) I5)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I5)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I5)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I5)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I5))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((E tptp.real) (C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z5))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex Z5) I5)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))))
% 6.18/6.71 (assert (forall ((E tptp.real) (C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M8 tptp.real)) (forall ((Z5 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z5))) (=> (@ (@ tptp.ord_less_eq_real M8) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real Z5) I5)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex X) I5)))) _let_1)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex Y) I5)))) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I5) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2))) (@ (@ tptp.power_power_complex X) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I5)) (@ (@ tptp.power_power_rat X) I5)))) _let_1)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I5)) (@ (@ tptp.power_power_rat Y) I5)))) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I5)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I5) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2))) (@ (@ tptp.power_power_rat X) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int X) I5)))) _let_1)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int Y) I5)))) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I5) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2))) (@ (@ tptp.power_power_int X) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real X) I5)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real Y) I5)))) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat I5) J3)) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2))) (@ (@ tptp.power_power_real X) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.18/6.71 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.18/6.71 (assert (= tptp.topolo3100542954746470799et_int (lambda ((X4 (-> tptp.nat tptp.set_int))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.18/6.71 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X4 (-> tptp.nat tptp.rat))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.18/6.71 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.18/6.71 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.18/6.71 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 N)) (@ X4 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 (@ tptp.suc N))) (@ X4 N)))))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.set_int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo3100542954746470799et_int X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.18/6.71 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ 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))))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ 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))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ 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))))))
% 6.18/6.71 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (= (@ (@ tptp.groups2073611262835488442omplex (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) (@ tptp.semiri8010041392384452111omplex M))) tptp.one_one_complex))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_complex _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.18/6.71 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat _let_2) (@ tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.18/6.71 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ (@ tptp.groups6591440286371151544t_real (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) (@ tptp.semiri5074537144036343181t_real M))) tptp.one_one_real))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.18/6.71 (assert (forall ((Z tptp.complex) (N2 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) N2))) (= (@ (@ 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) N2))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N2)))))))))
% 6.18/6.71 (assert (forall ((Z tptp.rat) (N2 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) N2))) (= (@ (@ 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) N2))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N2)))))))))
% 6.18/6.71 (assert (forall ((Z tptp.real) (N2 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) N2))) (= (@ (@ 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) N2))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N2)))))))))
% 6.18/6.71 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I5 tptp.complex)) (@ (@ tptp.plus_plus_complex I5) tptp.one_one_complex))) N) tptp.zero_zero_complex))))
% 6.18/6.71 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I5 tptp.rat)) (@ (@ tptp.plus_plus_rat I5) tptp.one_one_rat))) N) tptp.zero_zero_rat))))
% 6.18/6.71 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I5 tptp.int)) (@ (@ tptp.plus_plus_int I5) tptp.one_one_int))) N) tptp.zero_zero_int))))
% 6.18/6.71 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I5 tptp.real)) (@ (@ tptp.plus_plus_real I5) tptp.one_one_real))) N) tptp.zero_zero_real))))
% 6.18/6.71 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat I5) tptp.one_one_nat))) N) tptp.zero_zero_nat))))
% 6.18/6.71 (assert (= tptp.semiri4939895301339042750nteger (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri4055485073559036834nteger (lambda ((I5 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger I5) tptp.one_one_Code_integer))) N) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.71 (assert (forall ((R2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R2) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ 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 R2) _let_1))))))
% 6.18/6.71 (assert (forall ((R2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R2) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ (@ 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 R2) _let_1))))))
% 6.18/6.71 (assert (forall ((R2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R2) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ 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 R2) _let_1))))))
% 6.18/6.71 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) N)))
% 6.18/6.71 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 6.18/6.71 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.18/6.71 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 6.18/6.71 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.18/6.71 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.18/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.18/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.18/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.18/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.18/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.18/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.18/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.18/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.18/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.18/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N2))))))
% 6.18/6.71 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X) N2))))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N2))))))
% 6.18/6.71 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N2))))))
% 6.18/6.71 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_complex)))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_real)))))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_rat)))))))
% 6.18/6.71 (assert (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N2) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_complex))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_real))))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_rat))))))
% 6.18/6.71 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.18/6.71 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 6.18/6.71 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.18/6.71 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.18/6.71 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.18/6.71 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A4)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.18/6.71 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A4)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.18/6.71 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A4)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.18/6.71 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex K3))) tptp.one_one_complex)) K3)) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.18/6.71 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A4) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.18/6.71 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real K3))) tptp.one_one_real)) K3)) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N2)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N2)))))
% 6.18/6.71 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X) N2)))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N2)))))
% 6.18/6.71 (assert (forall ((X tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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)))))))))
% 6.18/6.71 (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)))))))))
% 6.18/6.71 (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)))))))))
% 6.18/6.71 (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)))))))))
% 6.18/6.71 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N2)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N2)))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N2)))))
% 6.18/6.71 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N2)))))
% 6.18/6.71 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N2)))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N2)))))))
% 6.18/6.71 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.18/6.71 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N2)))))))
% 6.18/6.71 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N2)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger N2)))))))
% 6.18/6.71 (assert (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N2))) (@ _let_1 N2))))))
% 6.18/6.71 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) (@ _let_1 N2))))))
% 6.18/6.71 (assert (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) (@ _let_1 N2))))))
% 6.18/6.71 (assert (forall ((Z tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) (@ _let_1 N2))))))
% 6.18/6.71 (assert (forall ((Z tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N2))) (@ _let_1 N2))))))
% 6.18/6.71 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N2) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N2) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N2) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N2) K))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N2) K))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N2) K))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N2) K))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N2) K))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex)))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat)))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int)))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger)))))
% 6.18/6.71 (assert (forall ((Z tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N2))) M))))))
% 6.18/6.71 (assert (forall ((Z tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) M))))))
% 6.18/6.71 (assert (forall ((Z tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) M))))))
% 6.18/6.71 (assert (forall ((Z tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) M))))))
% 6.18/6.71 (assert (forall ((Z tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N2))) M))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.18/6.71 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N2))) tptp.one_one_complex)) N2))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) N2))))
% 6.18/6.71 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2))) tptp.one_one_real)) N2))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 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 N2))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N2))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 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 N2))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N2))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 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 N2))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N2))))))
% 6.18/6.71 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K3)) A4)) tptp.one_one_complex)) K3)))))
% 6.18/6.71 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K3)) A4)) tptp.one_one_rat)) K3)))))
% 6.18/6.71 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K3)) A4)) tptp.one_one_real)) K3)))))
% 6.18/6.71 (assert (forall ((R2 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R2) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R2) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 6.18/6.71 (assert (forall ((R2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R2) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R2) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 6.18/6.71 (assert (forall ((R2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R2) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R2) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 6.18/6.71 (assert (forall ((R2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 6.18/6.71 (assert (forall ((R2 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R2) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R2) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ tptp.semiri5044797733671781792omplex N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ tptp.semiri3624122377584611663nteger N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) M)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) M)))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) M)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) M)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) M)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) M)))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) B)) N2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat A) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) N2) (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s8582702949713902594nteger A) K3))) (@ (@ tptp.comm_s8582702949713902594nteger B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s7457072308508201937r_real A) K3))) (@ (@ tptp.comm_s7457072308508201937r_real B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) A)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) A)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 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) N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (N2 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) N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N tptp.nat)) (@ (@ (@ tptp.if_complex (= N 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 A4) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.18/6.71 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N tptp.nat)) (@ (@ (@ tptp.if_rat (= N 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 A4) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.18/6.71 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N tptp.nat)) (@ (@ (@ tptp.if_int (= N 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 A4) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.18/6.71 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N tptp.nat)) (@ (@ (@ tptp.if_real (= N 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 A4) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.18/6.71 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A4 tptp.code_integer) (N tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= N tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((O tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.semiri4939895301339042750nteger O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_Code_integer)))))
% 6.18/6.71 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N 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 A4) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.18/6.71 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) M))))
% 6.18/6.71 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) M))))
% 6.18/6.71 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) M))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) A)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex K3)) A)) tptp.one_one_complex)) K3)) (@ (@ tptp.power_power_complex X) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat K3)) A)) tptp.one_one_rat)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) A)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real K3)) A)) tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.18/6.71 (assert (forall ((N2 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)) N2))) (= (@ 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)) N2))) (@ tptp.semiri5044797733671781792omplex N2))))))))
% 6.18/6.71 (assert (forall ((N2 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)) N2))) (= (@ 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)) N2))) (@ tptp.semiri773545260158071498ct_rat N2))))))))
% 6.18/6.71 (assert (forall ((N2 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)) N2))) (= (@ 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)) N2))) (@ tptp.semiri2265585572941072030t_real N2))))))))
% 6.18/6.71 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K3 tptp.nat)) (@ (@ (@ tptp.if_complex (= K3 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 A4) (@ tptp.semiri8010041392384452111omplex L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K3))))))
% 6.18/6.71 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 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 A4) (@ tptp.semiri681578069525770553at_rat L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))))
% 6.18/6.71 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 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 A4) (@ tptp.semiri5074537144036343181t_real L))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))))
% 6.18/6.71 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ 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 ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ 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)) N2)) tptp.one_one_nat))))))))
% 6.18/6.71 (assert (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ 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 ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ 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)) N2)) tptp.one_one_nat))))))))
% 6.18/6.71 (assert (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ 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 ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ 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)) N2)) tptp.one_one_nat))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P5) (not (@ _let_2 N)))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5)))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P5) (not (@ _let_2 N)))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5)))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X)) (@ tptp.sin_complex Y)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X)) N2)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) P5)) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_real)))) (@ tptp.set_ord_atMost_nat P5)))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat _let_1) P5)) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_complex)))) (@ tptp.set_ord_atMost_nat P5)))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.18/6.71 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (@ _let_2 X) (=> (=> (= X _let_1) (=> Y (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (=> (not Y) (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))) (=> (= X _let_1) (=> Y (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ _let_2 Y)) (@ _let_2 (@ _let_1 Y)))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (A tptp.real) (Y tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (let ((_let_2 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ _let_2 Y)) (@ _let_2 (@ _let_1 Y)))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) Y))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_complex X) Y))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)))))
% 6.18/6.71 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex B)))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (= (@ tptp.inverse_inverse_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X) tptp.one_one_complex) (= X tptp.one_one_complex))))
% 6.18/6.71 (assert (forall ((X tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X) tptp.one_one_rat) (= X tptp.one_one_rat))))
% 6.18/6.71 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 6.18/6.71 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.18/6.71 (assert (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real B) A))))
% 6.18/6.71 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex B) A))))
% 6.18/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat B) A))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real A) (@ (@ tptp.real_V1485227260804924795R_real B) X)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.times_times_real A) B)) X))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex A) (@ (@ tptp.real_V2046097035970521341omplex B) X)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.times_times_real A) B)) X))))
% 6.18/6.71 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.18/6.71 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.18/6.71 (assert (forall ((N2 tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N2))) tptp.zero_zero_real)))
% 6.18/6.71 (assert (forall ((X tptp.real) (I2 tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))) (@ tptp.tan_real X))))
% 6.18/6.71 (assert (forall ((N2 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 N2))) tptp.zero_zero_real)))
% 6.18/6.71 (assert (forall ((N2 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 N2))) tptp.one_one_real)))
% 6.18/6.71 (assert (forall ((N2 tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N2))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 6.18/6.71 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))))
% 6.18/6.71 (assert (= tptp.divide_divide_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.times_times_real X2) (@ tptp.inverse_inverse_real Y2)))))
% 6.18/6.71 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.real_V2046097035970521341omplex R2) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))))
% 6.18/6.71 (assert (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X)))))
% 6.18/6.71 (assert (forall ((D tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N2) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real D))))))
% 6.18/6.71 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D4 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D4) E2) (=> (@ P D4) (@ 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))))))
% 6.18/6.71 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D4 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D4) E2) (=> (@ P D4) (@ 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))))))
% 6.18/6.71 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N)))) (and (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 6.18/6.71 (assert (= tptp.ord_less_eq_int (lambda ((N tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real _let_1) X) (@ tptp.inverse_inverse_real _let_1))))))
% 6.18/6.71 (assert (= tptp.ord_less_int (lambda ((N tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) tptp.pi))))))
% 6.18/6.71 (assert (forall ((X tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X) D))) _let_1))))))
% 6.18/6.71 (assert (forall ((N2 tptp.int) (X 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 N2)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X))))))
% 6.18/6.71 (assert (forall ((N2 tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X)))) tptp.one_one_real)))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ 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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (exists ((X2 tptp.int)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ 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))))))))
% 6.18/6.71 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 6.18/6.71 (assert (forall ((Theta tptp.real)) (not (forall ((K2 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 K2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 6.18/6.71 (assert (forall ((X 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 X) (=> (@ _let_2 X) (=> (=> (= X _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))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I5)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I5) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.18/6.71 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.times_times_complex X2) (@ tptp.invers8013647133539491842omplex Y2)))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J))))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.18/6.71 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 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 (= K3 _let_2) (= L _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X)) tptp.zero_zero_real)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 6.18/6.71 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y)))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ _let_1 X)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N2)) (@ tptp.bit1 (@ tptp.bitM N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 N2)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X) Y)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.arcosh_real (@ tptp.cosh_real X)) X))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N2)) tptp.one) (@ tptp.bit0 N2))))
% 6.18/6.71 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) _let_1)))))))
% 6.18/6.71 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 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 K3)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.cot_real X))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))))
% 6.18/6.71 (assert (forall ((X 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) X) (= (@ (@ tptp.log _let_1) X) (@ (@ 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 X)))))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X)) (@ tptp.uminus1482373934393186551omplex X)))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))))
% 6.18/6.71 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real) (Y 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 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) A))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real A) X))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))))
% 6.18/6.71 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.18/6.71 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.18/6.71 (assert (forall ((Z tptp.complex) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ (@ 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)))))
% 6.18/6.71 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.18/6.71 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))))
% 6.18/6.71 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.18/6.71 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.18/6.71 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.numera6690914467698888265omplex W)))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.18/6.71 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) tptp.one) tptp.one)))
% 6.18/6.71 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.18/6.71 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (= (@ _let_1 W) Z) (= W (@ tptp.uminus1482373934393186551omplex (@ _let_1 Z)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.18/6.71 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.18/6.71 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))))))
% 6.18/6.71 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) tptp.imaginary_unit) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 6.18/6.71 (assert (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log B) _let_1)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real) (Y 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 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y)))))))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real) (Y 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 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X)) (@ _let_1 Y)))))))))))
% 6.18/6.71 (assert (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N2)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) (@ tptp.semiri5074537144036343181t_real N2))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.power_power_real X) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_1 X)))))))
% 6.18/6.71 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M2 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M2)) (not (= Y (@ tptp.bit1 M2)))))) (=> (=> _let_3 (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.bit1 M2))) (=> (= Xa2 _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N3 tptp.num)) (= X (@ tptp.bit0 N3))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M2 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M2)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M2)))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M2 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M2)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M2)))))))) (=> (=> (exists ((N3 tptp.num)) (= X (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M2 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M2)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M2)))))))) (not (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M2 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M2)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M2)))))))))))))))))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ 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 N2))))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (X 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 X) (= (@ (@ tptp.log A) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X)))))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ 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 N2))))))))
% 6.18/6.71 (assert (forall ((N2 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)) N2)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.18/6.71 (assert (forall ((N2 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)) N2)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.18/6.71 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N 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 M6)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ 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 N2)))))))
% 6.18/6.71 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 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)) N2)) (=> (@ (@ 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 N2)))))))
% 6.18/6.71 (assert (forall ((X 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) X) (= (@ _let_1 X) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X)))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((B tptp.nat) (K tptp.nat) (N2 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 N2)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 6.18/6.71 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.18/6.71 (assert (forall ((N2 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) N2) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) 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 N2)) tptp.one_one_int))))))))
% 6.18/6.71 (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)))
% 6.18/6.71 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X) (@ (@ tptp.ord_less_eq_real X) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.18/6.71 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.bit0 M2))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bit1 M2)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.bit1 M2))) (=> (= Xa2 _let_1) (=> (= Y _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))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ 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)) (=> (= X (@ tptp.bit0 N3)) (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.bit0 M2))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.bit1 M2))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M2))) (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))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.bit0 M2))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))) (not (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.bit1 M2))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))))))))))))))))))
% 6.18/6.71 (assert (forall ((B tptp.nat) (K tptp.nat) (N2 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 N2)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.18/6.71 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N2))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N2))))))
% 6.18/6.71 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.minus_minus_real A) B)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A)))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) tptp.one_one_real)))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y 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) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) B))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X) A)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.18/6.71 (assert (forall ((Y tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y) A))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ tptp.ln_ln_real X))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X)))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X) (@ (@ tptp.ord_less_real X) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X) N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N2))))))
% 6.18/6.71 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_real R2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2))) tptp.one_one_real))))
% 6.18/6.71 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real R2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2))) tptp.one_one_real))))
% 6.18/6.71 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2)))))
% 6.18/6.71 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2)))))
% 6.18/6.71 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N2) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real X) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))))
% 6.18/6.71 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X))))))
% 6.18/6.71 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)))))))
% 6.18/6.71 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y))))))
% 6.18/6.71 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N2))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) A))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X))))))
% 6.18/6.71 (assert (forall ((B tptp.real) (X tptp.real) (Y 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 X) (= (@ (@ tptp.plus_plus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) Y)))))))))))
% 6.18/6.71 (assert (forall ((B tptp.real) (X tptp.real) (Y 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 X) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X))))))))))
% 6.18/6.71 (assert (forall ((B tptp.real) (X tptp.real) (Y 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 X) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X))))))))))
% 6.18/6.71 (assert (forall ((B tptp.real) (X tptp.real) (Y 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 X) (= (@ (@ tptp.minus_minus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N2)))))))
% 6.18/6.71 (assert (forall ((N2 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) N2) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) _let_2))))) tptp.one_one_int))))))))
% 6.18/6.71 (assert (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) 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 N2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 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 K3))) (@ tptp.semiri5074537144036343181t_real N2))))) (@ tptp.set_ord_lessThan_nat N2)) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N2) tptp.one_one_complex)))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ tptp.real_V4546457046886955230omplex (@ F N)))) (@ tptp.summable_real F))))
% 6.18/6.71 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.18/6.71 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.18/6.71 (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))
% 6.18/6.71 (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))
% 6.18/6.71 (assert (forall ((Z tptp.complex)) (exists ((A3 tptp.complex) (R3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ tptp.exp_complex A3))))))
% 6.18/6.71 (assert (forall ((R2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ _let_1 X)) (@ _let_1 Y))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X) R2)) (@ (@ tptp.times_times_real Y) R2)))))
% 6.18/6.71 (assert (forall ((R2 tptp.real) (X tptp.real) (Y tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R2) X)) Y))))
% 6.18/6.71 (assert (forall ((X tptp.real) (Y tptp.real) (R2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X) R2)) Y))))
% 6.18/6.71 (assert (= tptp.cis (lambda ((B4 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B4))))))
% 6.18/6.71 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.18/6.71 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.18/6.71 (assert (= tptp.complex2 (lambda ((A4 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A4)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B4))))))
% 6.18/6.71 (assert (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A3))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A3)))))))))
% 6.18/6.71 (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)))
% 6.18/6.71 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ 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.abs_abs_real R2))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z2) (@ (@ tptp.ord_less_int Z6) Z2))))))))
% 6.18/6.71 (assert (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z6) (@ (@ tptp.ord_less_int Z6) Z2))))))))
% 6.18/6.71 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I3 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I3) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I3) J2) (@ (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2)) (@ (@ P I3) J2)))) (@ (@ P A0) A12)))))
% 6.18/6.71 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X))))))
% 6.18/6.71 (assert (forall ((C tptp.complex) (N2 tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N2) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N2)))))) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N2) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N2) C))))))))
% 6.18/6.71 (assert (= tptp.arctan (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X2 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)) X2) (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.tan_real X2) Y2))))))))
% 6.18/6.71 (assert (= tptp.arcsin (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X2 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)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.sin_real X2) Y2))))))))
% 6.18/6.71 (assert (forall ((L2 tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)))) (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 N2))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N2 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 N2) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M)))))) _let_1)))))))))))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.root N2) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X) tptp.one_one_real) (= X tptp.one_one_real)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.root N2) tptp.one_one_real) tptp.one_one_real))))
% 6.18/6.71 (assert (forall ((R2 tptp.int) (L2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) L2)) K) (and (@ (@ tptp.dvd_dvd_int L2) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.18/6.71 (assert (forall ((L2 tptp.int) (R2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L2) (@ tptp.sgn_sgn_int R2))) K) (and (@ (@ tptp.dvd_dvd_int L2) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.18/6.71 (assert (forall ((L2 tptp.int) (R2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) K)) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 6.18/6.71 (assert (forall ((L2 tptp.int) (K tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L2))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R2))) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N2)) X) (@ (@ tptp.root M) (@ (@ tptp.root N2) X)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ _let_1 Y))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N2))) (= (@ _let_1 (@ _let_2 X)) (@ _let_2 (@ _let_1 X)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 Y))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ _let_1 X))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N2) X))))))
% 6.18/6.71 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat) (L4 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L4)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.18/6.71 (assert (= tptp.ln_ln_real (lambda ((X2 tptp.real)) (@ tptp.the_real (lambda ((U2 tptp.real)) (= (@ tptp.exp_real U2) X2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X) (@ tptp.the_real (lambda ((X2 tptp.real)) false))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N2) X)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N4) X)) (@ (@ tptp.root N2) X)))))))
% 6.18/6.71 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.abs_abs_real (@ (@ tptp.root N2) (@ (@ tptp.power_power_real Y) N2))) (@ tptp.abs_abs_real Y)))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N2) X))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X)) (@ (@ tptp.root N4) X))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N4) X)) (@ (@ tptp.root N2) X)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X) N2)) X))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (= (@ (@ tptp.power_power_real Y) N2) X) (= (@ (@ tptp.root N2) X) Y)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X)) N2) X))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N2) X) (= (@ (@ tptp.root N2) X) Y))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X) N2)) X)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X)) (@ (@ tptp.root N4) X))))))))
% 6.18/6.71 (assert (= tptp.arccos (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.cos_real X2) Y2)))))))
% 6.18/6.71 (assert (forall ((R2 tptp.int) (L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int L2)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int L2)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L2)) R2)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R2)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N2) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N2) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (B tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N2) B)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) X)))))))
% 6.18/6.71 (assert (forall ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A32) (=> (=> (= A23 tptp.zero_zero_int) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q3 tptp.int)) (=> (= A32 (@ (@ 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)) (=> (= A32 (@ (@ 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)))))))))))))
% 6.18/6.71 (assert (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 tptp.zero_zero_int) (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A1 K3) (= A22 L) (= A33 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q4) L)))) (exists ((R5 tptp.int) (L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A1 K3) (= A22 L) (= A33 (@ (@ 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)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L)) R5))))))))
% 6.18/6.71 (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)))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N2) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.18/6.71 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real))))))
% 6.18/6.71 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X2) tptp.zero_zero_real)))))))
% 6.18/6.71 (assert (forall ((L2 tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N2))) (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 N2))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N2 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 N2) M)))))))))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X)) (@ _let_1 X)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N2) X)) (@ tptp.sgn_sgn_real X)))))
% 6.18/6.71 (assert (= tptp.sgn_sgn_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (= A4 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (N2 tptp.nat) (X tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) X) (=> (= X (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N2) X))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N2)) X)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.root N2) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N2))) Y))))
% 6.18/6.71 (assert (forall ((Z tptp.complex) (X tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arg Z) X))))))
% 6.18/6.71 (assert (forall ((P (-> tptp.real Bool)) (N2 tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N2) X)) (and (=> (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (forall ((Y2 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N2)) X) (@ P Y2))))))))
% 6.18/6.71 (assert (= tptp.archim6058952711729229775r_real (lambda ((X2 tptp.real)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X))))))
% 6.18/6.71 (assert (= tptp.modulo_modulo_int (lambda ((K3 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 K3))) (@ 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)) K3) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) _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) K3))))) _let_2)))))))))))
% 6.18/6.71 (assert (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ 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 K3) (@ 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) K3))))))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ _let_1 N2)))))
% 6.18/6.71 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.18/6.71 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.18/6.71 (assert (forall ((I2 tptp.int)) (= (= (@ tptp.nat2 I2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int))))
% 6.18/6.71 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 6.18/6.71 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2) Y))))
% 6.18/6.71 (assert (forall ((Y tptp.int) (X tptp.num) (N2 tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.18/6.71 (assert (forall ((X tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))) A) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.18/6.71 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.18/6.71 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.18/6.71 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.18/6.71 (assert (= tptp.numeral_numeral_nat (lambda ((I5 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I5)))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y)))))
% 6.18/6.71 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((X2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P3 (@ tptp.nat2 X2)))))))
% 6.18/6.71 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (forall ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P3 (@ tptp.nat2 X2)))))))
% 6.18/6.71 (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 Z) (@ tptp.nat2 Z7)) (= Z Z7)))))))
% 6.18/6.71 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.18/6.71 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N2)) tptp.zero_zero_int))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((X tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N2) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.18/6.71 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M) Z) (and (= M (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) M)) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 6.18/6.71 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 6.18/6.71 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.18/6.71 (assert (= tptp.minus_minus_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 6.18/6.71 (assert (= tptp.divide_divide_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 6.18/6.71 (assert (= tptp.modulo_modulo_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat2 W) M) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M (@ tptp.nat2 W)) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) K)))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (= tptp.suc (lambda ((A4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) tptp.one_one_int)))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.18/6.71 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N2)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N2)))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) A) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.18/6.71 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N2)))))
% 6.18/6.71 (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)))))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.71 (assert (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.18/6.71 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))
% 6.18/6.71 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (N2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N2)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N2)))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (I2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real I2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I2)))))))))))))
% 6.18/6.71 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X2 tptp.rat)) (@ tptp.the_int (lambda ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))))
% 6.18/6.71 (assert (= tptp.arg (lambda ((Z2 tptp.complex)) (@ (@ (@ tptp.if_real (= Z2 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z2) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))))
% 6.18/6.71 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K))))))
% 6.18/6.71 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (not (forall ((S tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S) (forall ((T5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T5) (not (= R2 (@ (@ tptp.plus_plus_rat S) T5)))))))))))
% 6.18/6.71 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y2 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y2) (= X2 Y2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M)))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) Q2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N2))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) B)) (@ _let_1 B)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int) (L2 tptp.int) (R2 tptp.int) (S2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ tptp.bit_concat_bit N2))) (= (= (@ (@ _let_2 K) L2) (@ (@ _let_2 R2) S2)) (and (= (@ _let_1 K) (@ _let_1 R2)) (= L2 S2)))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ _let_1 tptp.zero_zero_int)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) tptp.zero_zero_int))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N2)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (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)))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.18/6.71 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.71 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.18/6.71 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) M))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) 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))) N2))))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 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))) N2)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (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))) N2)) 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)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) (@ tptp.bit_se2000444600071755411sk_int N2)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 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))) N2))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.18/6.71 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 6.18/6.71 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.18/6.71 (assert (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R5)))))
% 6.18/6.71 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X3 tptp.num)) (=> (@ P X3) (@ P (@ tptp.inc X3)))) (@ P X)))))
% 6.18/6.71 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 6.18/6.71 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.18/6.71 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 6.18/6.71 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 6.18/6.71 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ tptp.inc (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.inc N2)) (@ tptp.bit1 N2))))
% 6.18/6.71 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.18/6.71 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ 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 K3) N))))))))
% 6.18/6.71 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 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 (= K3 tptp.zero_zero_int) (= L tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L) (@ (@ (@ tptp.if_int (= L _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N2))))
% 6.18/6.71 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N2))))
% 6.18/6.71 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int)))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int) tptp.one_one_int)))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.zero_zero_int)))
% 6.18/6.71 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N2)))))
% 6.18/6.71 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2))))))
% 6.18/6.71 (assert (forall ((K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) N2)))))
% 6.18/6.71 (assert (forall ((K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) N2)))))
% 6.18/6.71 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 6.18/6.71 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 6.18/6.71 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Y))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) X))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y))))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) (@ (@ tptp.plus_plus_int X) Y))))
% 6.18/6.71 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 6.18/6.71 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L2)) N2) (or (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) (@ (@ tptp.minus_minus_nat N2) M)))))))
% 6.18/6.71 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))))))
% 6.18/6.71 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N3) M3) (= (@ _let_1 M3) (@ _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)))))))))))
% 6.18/6.71 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N))))))))
% 6.18/6.71 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 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 K3)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.18/6.71 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 6.18/6.71 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y 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 X)) (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 X) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 6.18/6.71 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 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 K3)) (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 K3) _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 K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) 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 X)) (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 X) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 6.18/6.71 (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))))))))))))))))
% 6.18/6.71 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.18/6.71 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.18/6.71 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.18/6.71 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (= N2 tptp.zero_zero_nat))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N2)))))
% 6.18/6.71 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.18/6.71 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N2))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N2))))))))
% 6.18/6.71 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I5)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I5) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3))))))
% 6.18/6.71 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N))))))))
% 6.18/6.71 (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 ((K2 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 K2) L4)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K2) L4)))))) (@ (@ P A0) A12)))))
% 6.18/6.71 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.18/6.71 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N 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 M6)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) 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)) N2)) tptp.one_one_complex))))
% 6.18/6.71 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A4 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A4)) B4)) (@ tptp.abs_abs_int A4))))) (@ tptp.quotient_of P4)))))
% 6.18/6.71 (assert (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N2) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N2) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.nat_set_encode A2)))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))
% 6.18/6.71 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2)))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N2) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.18/6.71 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.abs_abs_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.abs_abs_int A4)) __flatten_var_0))) (@ tptp.quotient_of P4)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.18/6.71 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A4)) __flatten_var_0))) (@ tptp.quotient_of P4)))))
% 6.18/6.71 (assert (= tptp.ord_less_rat (lambda ((P5 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B4 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A4) D2)) (@ (@ tptp.times_times_int C4) B4)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P5)))))
% 6.18/6.71 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P5 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P5)))))
% 6.18/6.71 (assert (= tptp.ord_less_eq_rat (lambda ((P5 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B4 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A4) D2)) (@ (@ tptp.times_times_int C4) B4)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P5)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N2) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) Z)) (@ (@ tptp.insert_nat N2) _let_1))))))
% 6.18/6.71 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) 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)) N2)) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) 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)) N2)) tptp.one_one_real))))
% 6.18/6.71 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A4) D2)) (@ (@ tptp.times_times_int B4) C4))) (@ (@ tptp.times_times_int C4) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 6.18/6.71 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A4) D2)) (@ (@ tptp.times_times_int B4) C4))) (@ (@ tptp.times_times_int C4) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 6.18/6.71 (assert (forall ((Q2 tptp.int) (S2 tptp.int) (P4 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S2))) (= (@ (@ tptp.times_times_int P4) S2) (@ (@ tptp.times_times_int R2) Q2)))))))
% 6.18/6.71 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A4) B4)) (@ (@ tptp.times_times_int C4) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 6.18/6.71 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B4 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A4) D2)) (@ (@ tptp.times_times_int C4) B4))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.18/6.71 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 6.18/6.71 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.18/6.71 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))))
% 6.18/6.71 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))
% 6.18/6.71 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N 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 M6)) (not (@ _let_2 N)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ _let_1 K)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) tptp.zero_zero_int) L2) (@ (@ tptp.bit_se545348938243370406it_int N2) L2))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.18/6.71 (assert (forall ((K tptp.int) (L2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) N2) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L2) N2))))))
% 6.18/6.71 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N2) K)))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X) Y)))))))
% 6.18/6.71 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.18/6.71 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.18/6.71 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.18/6.71 (assert (= tptp.bit_concat_bit (lambda ((N tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.bit_se545348938243370406it_int N) L)))))
% 6.18/6.71 (assert (= tptp.bit_concat_bit (lambda ((N tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.bit_se545348938243370406it_int N) L)))))
% 6.18/6.71 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))))
% 6.18/6.71 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.18/6.71 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.18/6.71 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y)) _let_1)))))))
% 6.18/6.71 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 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 K3)) (not (@ _let_2 L)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.18/6.71 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 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 (= K3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L)) (@ (@ (@ tptp.if_int (= L _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))))))
% 6.18/6.71 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X4 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M6) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X4 M6)) (@ X4 N)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (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))))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (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))))))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.18/6.71 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L))))))
% 6.18/6.71 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 6.18/6.71 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.18/6.71 (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)))
% 6.18/6.71 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int))))))
% 6.18/6.71 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int)))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N2) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N2))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N2)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N2) M))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N2))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ 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 N2)))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.zero_zero_int)))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ 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 N2)))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ 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 N2)))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ 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 N2)))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ 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 N2))))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ 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 N2))))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ 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 N2))))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ 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 N2))))))))
% 6.18/6.71 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 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) K3))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K3) _let_1))))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) 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))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X2))))))
% 6.18/6.71 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L2) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat N2) (@ _let_1 N2))))))
% 6.18/6.71 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N4))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N2) (@ _let_1 N2)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.18/6.71 (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)))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) N2) (@ (@ tptp.ord_less_eq_nat (@ A I3)) (@ A J2))))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) N2) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I3))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I5)) (@ B I5)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.18/6.71 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L2) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L2) U))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.18/6.71 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.18/6.71 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.18/6.71 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 6.18/6.71 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.18/6.71 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex X8) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ tptp.re (@ X8 N)))) (@ tptp.re A)))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.complex))) (=> (@ tptp.topolo6517432010174082258omplex X8) (@ tptp.topolo4055970368930404560y_real (lambda ((N tptp.nat)) (@ tptp.re (@ X8 N)))))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X)) (@ tptp.real_V1022390504157884413omplex X))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y)))))
% 6.18/6.71 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.re X)))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.re X)) (@ tptp.re Y)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (@ tptp.summable_real (lambda ((X2 tptp.nat)) (@ tptp.re (@ F X2)))))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.18/6.71 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N2)))))
% 6.18/6.71 (assert (= tptp.csqrt (lambda ((Z2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z2))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z2))) (let ((_let_4 (@ tptp.im Z2))) (@ (@ 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)))))))))))
% 6.18/6.71 (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)))))))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.power_power_complex X) N2)) tptp.zero_zero_real))))
% 6.18/6.71 (assert (forall ((V tptp.num)) (= (@ tptp.im (@ tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)))
% 6.18/6.71 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.re Z))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_real (@ tptp.re X)) N2)))))
% 6.18/6.71 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.im X))) (=> (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 X)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X)))))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex X8) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ tptp.im (@ X8 N)))) (@ tptp.im A)))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.complex))) (=> (@ tptp.topolo6517432010174082258omplex X8) (@ tptp.topolo4055970368930404560y_real (lambda ((N tptp.nat)) (@ tptp.im (@ X8 N)))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y)))))
% 6.18/6.71 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.im X)))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.im X)) (@ tptp.im Y)))))
% 6.18/6.71 (assert (= tptp.sums_complex (lambda ((F3 (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (and (@ (@ tptp.sums_real (lambda ((Y2 tptp.nat)) (@ tptp.re (@ F3 Y2)))) (@ tptp.re X2)) (@ (@ tptp.sums_real (lambda ((Y2 tptp.nat)) (@ tptp.im (@ F3 Y2)))) (@ tptp.im X2))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex F) (@ tptp.summable_real (lambda ((X2 tptp.nat)) (@ tptp.im (@ F X2)))))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.18/6.71 (assert (= tptp.summable_complex (lambda ((F3 (-> tptp.nat tptp.complex))) (and (@ tptp.summable_real (lambda ((X2 tptp.nat)) (@ tptp.re (@ F3 X2)))) (@ tptp.summable_real (lambda ((X2 tptp.nat)) (@ tptp.im (@ F3 X2))))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.im Y))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.re Y))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.im X) (@ tptp.im Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.abs_abs_real (@ tptp.re Y)))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.re X) (@ tptp.re Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.abs_abs_real (@ tptp.im Y)))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.re Y))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.im Y))))))
% 6.18/6.71 (assert (= tptp.plus_plus_complex (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X2)) (@ tptp.re Y2))) (@ (@ tptp.plus_plus_real (@ tptp.im X2)) (@ tptp.im Y2))))))
% 6.18/6.71 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X2))) (@ _let_1 (@ tptp.im X2)))))))
% 6.18/6.71 (assert (= tptp.minus_minus_complex (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ tptp.re X2)) (@ tptp.re Y2))) (@ (@ tptp.minus_minus_real (@ tptp.im X2)) (@ tptp.im Y2))))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N2)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((A tptp.complex)) (= A (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.re A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.im A)))))))
% 6.18/6.71 (assert (= tptp.times_times_complex (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.re Y2))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X2)))) (let ((_let_3 (@ tptp.im Y2))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X2)))) (@ (@ 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))))))))))
% 6.18/6.71 (assert (= tptp.exp_complex (lambda ((Z2 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z2)))) (@ tptp.cis (@ tptp.im Z2))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X))) (@ tptp.im X))))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z2 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 Z2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z2)) _let_1)))))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((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))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.18/6.71 (assert (forall ((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))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (= tptp.invers8013647133539491842omplex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (let ((_let_3 (@ tptp.re X2))) (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)))))))))
% 6.18/6.71 (assert (= tptp.divide1717551699836669952omplex (lambda ((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))) (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 X2)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X2)))) (@ (@ 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)))))))))))
% 6.18/6.71 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R2))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.71 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R2)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.71 (assert (forall ((Y tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y) X) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 6.18/6.71 (assert (forall ((Y tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= X (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y)) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.times_times_complex (@ tptp.cnj X)) (@ tptp.cnj Y)))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (N2 tptp.nat)) (= (@ tptp.cnj (@ (@ tptp.power_power_complex X) N2)) (@ (@ tptp.power_power_complex (@ tptp.cnj X)) N2))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.cnj X)) (@ tptp.cnj Y)))))
% 6.18/6.71 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.cnj _let_1) _let_1))))
% 6.18/6.71 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ tptp.cnj X)) (@ tptp.cnj Y)))))
% 6.18/6.71 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.cnj _let_1) _let_1))))
% 6.18/6.71 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 6.18/6.71 (assert (forall ((F (-> tptp.nat tptp.complex)) (L2 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((X2 tptp.nat)) (@ tptp.cnj (@ F X2)))) (@ tptp.cnj L2)) (@ (@ tptp.sums_complex F) L2))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z2 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z2) (@ tptp.cnj Z2)))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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)))))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A4) (@ tptp.cnj B4))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.ord_less_nat I5) N2)))) N2)))
% 6.18/6.71 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.18/6.71 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I5) N2)))) (@ tptp.suc N2))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) L2) (@ tptp.uminus1351360451143612070nteger L2))))
% 6.18/6.71 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.18/6.71 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.18/6.71 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.71 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L2) tptp.zero_z3403309356797280102nteger)))
% 6.18/6.71 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.18/6.71 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.18/6.71 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L2) L2)))
% 6.18/6.71 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.18/6.71 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.18/6.71 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2)))))) tptp.zero_zero_nat)))))
% 6.18/6.71 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I2)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.18/6.71 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I2))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N2))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M4) N2)))) M)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) M4)))) M)))))
% 6.18/6.71 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N4)) N2))))
% 6.18/6.71 (assert (forall ((S3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) S3))))
% 6.18/6.71 (assert (forall ((C tptp.complex) (N2 tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N2) C)))) N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z2 tptp.complex)) (= (@ (@ tptp.power_power_complex Z2) N2) tptp.one_one_complex)))) N2))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N2))))))
% 6.18/6.71 (assert (= tptp.code_integer_of_int (lambda ((K3 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 K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.18/6.71 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int Xa2) X)))))
% 6.18/6.71 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa2) X)))))
% 6.18/6.71 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ (@ tptp.ord_less_eq_int Xa2) X))))
% 6.18/6.71 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.minus_minus_int Xa2) X)))))
% 6.18/6.71 (assert (= tptp.code_positive tptp.numera6620942414471956472nteger))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N2))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 6.18/6.71 (assert (= tptp.code_integer_of_num tptp.numera6620942414471956472nteger))
% 6.18/6.71 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N2))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 6.18/6.71 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.18/6.71 (assert (= tptp.code_int_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K3)))) (@ (@ (@ tptp.if_int (= K3 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 K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.18/6.71 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K3) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K3)))))))
% 6.18/6.71 (assert (= tptp.code_num_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K3) 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 K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.18/6.71 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.ord_max_Code_integer K) L2)) (@ (@ tptp.ord_max_int (@ tptp.code_int_of_integer K)) (@ tptp.code_int_of_integer L2)))))
% 6.18/6.71 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 6.18/6.71 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Xa2)) (@ (@ tptp.plus_plus_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.18/6.71 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X) Xa2)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.18/6.71 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.minus_8373710615458151222nteger X) Xa2)) (@ (@ tptp.minus_minus_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.18/6.71 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X2 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa4)))))
% 6.18/6.71 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L)))))
% 6.18/6.71 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 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) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S6))) (= S6 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.18/6.71 (assert (= tptp.code_nat_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K3) 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 K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.18/6.71 (assert (forall ((K tptp.code_integer)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.code_nat_of_integer K)) (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) K))))
% 6.18/6.71 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 6.18/6.71 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.18/6.71 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.18/6.71 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.18/6.71 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _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 K3)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K3) 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))))))))))))
% 6.18/6.71 (assert (= tptp.binomial (lambda ((N tptp.nat) (K3 tptp.nat)) (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((K7 tptp.set_nat)) (and (@ (@ tptp.member_set_nat K7) (@ tptp.pow_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (= (@ tptp.finite_card_nat K7) K3))))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M6 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M6) K3)) (@ (@ tptp.product_Pair_nat_nat M6) (@ (@ tptp.minus_minus_nat K3) M6))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M6) _let_1)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) (@ _let_1 K)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N2) _let_1) _let_1))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N2) M)) K)))))
% 6.18/6.71 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S3))) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N9) (@ tptp.finite_card_nat S3)) (@ (@ tptp.member_nat (@ R3 N9)) S3))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N2)) (@ (@ tptp.divide_divide_nat M) N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)))))
% 6.18/6.71 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ 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) N2))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ 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) N2)))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ 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) N2))))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ 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) N2)))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ 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) Xa2))))))))))))))
% 6.18/6.71 (assert (= tptp.bezw (lambda ((X2 tptp.nat) (Y2 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.if_Pro3027730157355071871nt_int (= Y2 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 X2) Y2)))))))))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ 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 X) Xa2)))))))) (not _let_1)))))))))))
% 6.18/6.71 (assert (forall ((Y tptp.nat) (X 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.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X) Y) (@ (@ 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)))))))))))
% 6.18/6.71 (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)))))))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X) (@ (@ tptp.gcd_gcd_int _let_1) X)))))
% 6.18/6.71 (assert (forall ((X tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.gcd_gcd_int X))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X) Y))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int)) (exists ((U3 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U3) X)) (@ (@ tptp.times_times_int V2) Y)) (@ (@ tptp.gcd_gcd_int X) Y)))))
% 6.18/6.71 (assert (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int K)) (@ (@ tptp.gcd_gcd_int M) N2)) (@ (@ tptp.gcd_gcd_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X))) (let ((_let_2 (@ P (@ _let_1 Y)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y))) (let ((_let_9 (@ _let_7 X))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 6.18/6.71 (assert (forall ((D tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D) (@ _let_1 A) (@ _let_1 B) (forall ((E3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int E3))) (=> (and (@ _let_1 A) (@ _let_1 B)) (@ _let_1 D))))) (= D (@ (@ tptp.gcd_gcd_int A) B))))))
% 6.18/6.71 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 6.18/6.71 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N2)) (or (not (= M tptp.zero_zero_nat)) (not (= N2 tptp.zero_zero_nat))))))
% 6.18/6.71 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M) N2)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N2)) N2) (@ (@ tptp.gcd_gcd_nat M) N2)))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N2) M)) N2) (@ (@ tptp.gcd_gcd_nat M) N2)))))
% 6.18/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y5 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y5)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.18/6.71 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X3 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y5))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X3))) (let ((_let_6 (@ _let_4 Y5))) (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)))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X) Y))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X) Y)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I) (@ P I))) (@ P K2)))) (@ P M)))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2))))) (not _let_1)))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L2) U))))
% 6.18/6.71 (assert (forall ((K tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)) K)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N2)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.compow_nat_nat N2) tptp.suc) (@ tptp.plus_plus_nat N2))))
% 6.18/6.71 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y2) X2))) (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_nat Y2) X2))))
% 6.18/6.71 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M6 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M6) N) (not (= M6 N))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 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 Y2))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ 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) X)))))
% 6.18/6.71 (assert (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y5 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X3) Y5))))))))
% 6.18/6.71 (assert (forall ((N4 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N4) (= (@ tptp.gcd_Gcd_nat N4) tptp.one_one_nat))))
% 6.18/6.71 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X))))
% 6.18/6.71 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.18/6.71 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N) tptp.zero_zero_nat)))))
% 6.18/6.71 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y2) X2))) X)))))
% 6.18/6.71 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.18/6.71 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y2 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 X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0))) Xa2) X))))
% 6.18/6.71 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X2 tptp.nat) (Y2 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 X2) V4)) (@ (@ tptp.plus_plus_nat U2) Y2)))) __flatten_var_0))) Xa2) X))))
% 6.18/6.71 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 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 X2) U2)) (@ (@ tptp.plus_plus_nat Y2) V4)))) __flatten_var_0))) Xa2) X)))))
% 6.18/6.71 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y2 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 X2) V4)) (@ (@ tptp.plus_plus_nat Y2) U2)))) __flatten_var_0))) Xa2) X)))))
% 6.18/6.71 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 6.18/6.71 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y2 tptp.nat) (Z2 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 Y2) V4)) (@ (@ tptp.plus_plus_nat U2) Z2)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 6.18/6.71 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y2 tptp.nat) (Z2 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 Y2) V4)) (@ (@ tptp.plus_plus_nat U2) Z2)))) __flatten_var_0))) (@ tptp.rep_Integ X2)) (@ tptp.rep_Integ Xa4)))))
% 6.18/6.71 (assert (= tptp.nat2 (lambda ((X2 tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X2)))))
% 6.18/6.71 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N))) M6)))))
% 6.18/6.71 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y2) X2))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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 ((X2 tptp.nat) (Y2 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 Y2))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ 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))))))
% 6.18/6.71 (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 ((X2 tptp.nat) (Y2 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 X2) V4)) (@ (@ tptp.plus_plus_nat Y2) U2)))) __flatten_var_0))))))
% 6.18/6.71 (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 ((X2 tptp.nat) (Y2 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 X2) U2)) (@ (@ tptp.plus_plus_nat Y2) V4)))) __flatten_var_0))))))
% 6.18/6.71 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N tptp.nat)) (= N (@ tptp.suc M6)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N2)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N2)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 6.18/6.71 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.18/6.71 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N2)) N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) tptp.one_one_nat) (= (@ tptp.num_of_nat N2) tptp.one))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N2) N2)) (@ tptp.bit0 (@ tptp.num_of_nat N2))))))
% 6.18/6.71 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N2))))))))
% 6.18/6.71 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X)))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N2))))))
% 6.18/6.71 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.18/6.71 (assert (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))))
% 6.18/6.71 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 6.18/6.71 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N2)) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))))
% 6.18/6.71 (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))))))))
% 6.18/6.71 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.18/6.71 (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))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I2) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I2)) (@ tptp.suc J)))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I2) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I2)) (@ tptp.suc J)))))
% 6.18/6.71 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))
% 6.18/6.71 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int B) C)))))
% 6.18/6.71 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))))
% 6.18/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.fract A) B)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B))))))
% 6.18/6.71 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.18/6.71 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.18/6.71 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.18/6.71 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.18/6.71 (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.fract (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.fract A) B))))))
% 6.18/6.71 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (@ (@ tptp.fract A) B) (@ (@ tptp.fract C) D)) (= (@ (@ tptp.times_times_int A) D) (@ (@ tptp.times_times_int C) B)))))))
% 6.18/6.71 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.18/6.71 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 6.18/6.71 (assert (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))
% 6.18/6.71 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N2)))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N2)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N2)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N2))))))
% 6.18/6.71 (assert (forall ((N2 tptp.int) (M tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ (@ tptp.plus_plus_int M) N2)) N2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract M) N2)) tptp.one_one_rat)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((K5 tptp.set_int)) (= (@ tptp.gcd_Gcd_int (@ (@ tptp.image_int_int tptp.abs_abs_int) K5)) (@ tptp.gcd_Gcd_int K5))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((N4 tptp.set_nat)) (= (@ tptp.gcd_Gcd_int (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) N4)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat N4)))))
% 6.18/6.71 (assert (forall ((K5 tptp.set_int)) (= (@ tptp.gcd_Gcd_nat (@ (@ tptp.image_int_nat (lambda ((K3 tptp.int)) (@ tptp.nat2 (@ tptp.abs_abs_int K3)))) K5)) (@ tptp.nat2 (@ tptp.gcd_Gcd_int K5)))))
% 6.18/6.71 (assert (= tptp.comple4887499456419720421f_real (lambda ((X4 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X4))))))
% 6.18/6.71 (assert (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_atMost_int K3))))))
% 6.18/6.71 (assert (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_lessThan_int K3))))))
% 6.18/6.71 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L2) U))))
% 6.18/6.71 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) L2))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L2))) (@ (@ tptp.set_or4662586982721622107an_int L2) U))))
% 6.18/6.71 (assert (forall ((U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) U) (= (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U) (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ tptp.set_ord_lessThan_nat (@ tptp.nat2 U)))))))
% 6.18/6.71 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X8 I3))) (= (@ tptp.suminf_real X8) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X8) (@ tptp.set_ord_lessThan_nat I5)))) tptp.top_top_set_nat)))))))
% 6.18/6.71 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.18/6.71 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.18/6.71 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N2))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 6.18/6.71 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.18/6.71 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (= tptp.root (lambda ((N tptp.nat) (X2 tptp.real)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N)))) X2)))))
% 6.18/6.71 (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)))))))))))
% 6.18/6.71 (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)))))))))))))
% 6.18/6.71 (assert (forall ((X1 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X22) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.18/6.71 (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))))))))))))
% 6.18/6.71 (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))))))))))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (= tptp.char_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q0 tptp.code_integer) (B02 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q1 tptp.code_integer) (B12 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q22 tptp.code_integer) (B23 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q32 tptp.code_integer) (B33 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q42 tptp.code_integer) (B43 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q52 tptp.code_integer) (B53 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Q62 tptp.code_integer) (B63 Bool)) (@ (@ tptp.produc4188289175737317920o_char (lambda ((Uu3 tptp.code_integer) (__flatten_var_0 Bool)) (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B02) B12) B23) B33) B43) B53) B63) __flatten_var_0))) (@ tptp.code_bit_cut_integer Q62)))) (@ tptp.code_bit_cut_integer Q52)))) (@ tptp.code_bit_cut_integer Q42)))) (@ tptp.code_bit_cut_integer Q32)))) (@ tptp.code_bit_cut_integer Q22)))) (@ tptp.code_bit_cut_integer Q1)))) (@ tptp.code_bit_cut_integer Q0)))) (@ tptp.code_bit_cut_integer K3)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 6.18/6.71 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X3) Xs3)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X3) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.18/6.71 (assert (= tptp.upto_aux (lambda ((I5 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I5)) Js) (@ (@ (@ tptp.upto_aux I5) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.18/6.71 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.18/6.71 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.18/6.71 (assert (= tptp.sup_sup_int tptp.ord_max_int))
% 6.18/6.71 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 6.18/6.71 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs2)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs2)))))))
% 6.18/6.71 (assert (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y 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))) (=> (= X _let_1) (=> (= Y (@ 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)))))))))))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I2) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 6.18/6.71 (assert (forall ((J tptp.int) (I2 tptp.int)) (=> (@ (@ tptp.ord_less_int J) I2) (= (@ (@ tptp.upto I2) J) tptp.nil_int))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I2) J)) (@ (@ tptp.ord_less_int J) I2))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I2) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I2))))
% 6.18/6.71 (assert (forall ((I2 tptp.int)) (= (@ (@ tptp.upto I2) I2) (@ (@ tptp.cons_int I2) tptp.nil_int))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I2) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I2) J)) K) _let_1)))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I2) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I2)) tptp.one_one_int)))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (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)))))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (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)))))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (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)))))))))
% 6.18/6.71 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (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)))))))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I2) J))))
% 6.18/6.71 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I5) J3)))))
% 6.18/6.71 (assert (= tptp.upto (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I5) J3) tptp.nil_int))))
% 6.18/6.71 (assert (= tptp.upto_aux (lambda ((I5 tptp.int) (J3 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I5) J3)) __flatten_var_0))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) 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))))))))
% 6.18/6.71 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I5) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.18/6.71 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3)))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ (@ tptp.upto I2) J) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J))))))
% 6.18/6.71 (assert (= tptp.upto (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I5) J3)) (@ (@ tptp.cons_int I5) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.18/6.71 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) 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)))))))
% 6.18/6.71 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.18/6.71 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) 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)))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real) (D3 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D3 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D3 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D3) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (Y tptp.real) (X tptp.real)) (= (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y) (@ (@ tptp.topolo2177554685111907308n_real (@ tptp.uminus_uminus_real X)) tptp.top_top_set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ F (@ tptp.uminus_uminus_real X2)))) (@ tptp.uminus_uminus_real Y)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.18/6.71 (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))))))
% 6.18/6.71 (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)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D4) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D4) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D4) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S3)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D4) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D) (= (@ F X) (@ F Y5)))) (= L2 tptp.zero_zero_real))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D4) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X) H4))) (@ F X)))))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D4) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.minus_minus_real X) H4))))))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D4) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X) H4))) (@ F X)))))))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D4) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.plus_plus_real X) H4))))))))))))
% 6.18/6.71 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> 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) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z4) (@ (@ tptp.ord_less_real Z4) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F4 Z4)))))))))
% 6.18/6.71 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 6.18/6.71 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 6.18/6.71 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 6.18/6.71 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y3) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (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)))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D) (@ (@ tptp.ord_less_eq_real (@ F Y5)) (@ F X)))) (= L2 tptp.zero_zero_real))))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D) (@ (@ tptp.ord_less_eq_real (@ F X)) (@ F Y5)))) (= L2 tptp.zero_zero_real))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real) (S2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real X2) N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S2))))
% 6.18/6.71 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ G X2)) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ G X)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) M)) _let_1)))))
% 6.18/6.71 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z2 tptp.real)) (@ (@ tptp.powr_real Z2) R2))) (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 6.18/6.71 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F4 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F4 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ F X2) N3))) (@ (@ F4 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) (Y5 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X3) _let_1) (=> (@ (@ tptp.member_real Y5) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X3) N3)) (@ (@ F Y5) N3)))) (@ (@ tptp.times_times_real (@ L5 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y5)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (@ F X2)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.18/6.71 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) R2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 6.18/6.71 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (F (-> tptp.real tptp.real)) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (let ((_let_3 (@ F X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R2) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.powr_real (@ G X2)) (@ F X2)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R2) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) 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 X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))
% 6.18/6.71 (assert (forall ((X 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 X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2))))
% 6.18/6.71 (assert (forall ((X tptp.real) (D3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))) (=> (not (= X tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= D3 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D3 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D3) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))
% 6.18/6.71 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ 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 X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.18/6.71 (assert (forall ((R 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 R)) R)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) (@ (@ tptp.power_power_real X3) N)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X2) (@ tptp.suc N))))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) (@ (@ tptp.power_power_real X0) N))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) 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 X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.18/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) 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 X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.18/6.71 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N2 tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) 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 X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.18/6.71 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N2 tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M2 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) 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 X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))
% 6.18/6.71 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (not (= X tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.18/6.71 (assert (forall ((H2 tptp.real) (N2 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) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real H2) T5) (@ (@ tptp.ord_less_eq_real T5) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) 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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2))))))))))))
% 6.18/6.71 (assert (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) 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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2)))))))))))
% 6.18/6.71 (assert (forall ((H2 tptp.real) (N2 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) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) 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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2))))))))))))
% 6.18/6.71 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M2 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) 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 X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2)))))))))))))
% 6.18/6.71 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T5)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) 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 X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X) N2))))))))))
% 6.18/6.71 (assert (forall ((N2 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) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real A) T5) (@ (@ tptp.ord_less_eq_real T5) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) 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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N2)))))))))))))
% 6.18/6.72 (assert (forall ((N2 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) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real A) T5) (@ (@ tptp.ord_less_eq_real T5) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) 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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N2)))))))))))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real A) T5) (@ (@ tptp.ord_less_eq_real T5) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) T5)) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) B) (=> (not (= X C)) (exists ((T5 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T5))) (let ((_let_2 (@ tptp.ord_less_real X))) (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 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T5)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N2))))))))))))))))))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B3 tptp.real)) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T5) (@ (@ tptp.ord_less_eq_real T5) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) T5)) (@ (@ tptp.topolo2177554685111907308n_real T5) tptp.top_top_set_real)))) (=> (= N2 (@ tptp.suc K)) (forall ((M3 tptp.nat) (T6 tptp.real)) (let ((_let_1 (@ tptp.suc M3))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N2) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) M3))) (@ (@ tptp.minus_minus_real (@ (@ Diff M3) 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 M3) 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) T6)) (@ (@ 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 M3)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T6) P5)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B3) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T6) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real))))))))))
% 6.18/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ 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)) K3)) (@ (@ 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 ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_real X) 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 N2))) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))))
% 6.18/6.72 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ 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) N2))))))
% 6.18/6.72 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N2))))))
% 6.18/6.72 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.18/6.72 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.18/6.72 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ 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 N2) M)))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))))
% 6.18/6.72 (assert (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ 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 R2)) M)))))
% 6.18/6.72 (assert (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M))))))
% 6.18/6.72 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ 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 N2))))))
% 6.18/6.72 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N2))))))
% 6.18/6.72 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ 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 N2))))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N2) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N) M)))) N2))))
% 6.18/6.72 (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)))))
% 6.18/6.72 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num tptp.one))))
% 6.18/6.72 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N2)) tptp.none_num)))
% 6.18/6.72 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.18/6.72 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N2) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ tptp.some_num tptp.one))) N2))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N2) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))) N2))))
% 6.18/6.72 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.18/6.72 (assert (forall ((M tptp.num) (N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) (@ tptp.some_num Q2)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int Q2)))))
% 6.18/6.72 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ (@ 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) N2)))))
% 6.18/6.72 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int))))
% 6.18/6.72 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N2) M)))))
% 6.18/6.72 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.18/6.72 (assert (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.18/6.72 (assert (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M6 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A4 tptp.nat) (X2 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))))) X2))) A4))) (@ (@ tptp.product_Pair_nat_num N) M6)))))
% 6.18/6.72 (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) (M8 tptp.real)) (and (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M8))))) (forall ((Y3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y3) (@ (@ tptp.ord_less_eq_real Y3) M8)) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B) (= (@ F X3) Y3)))))))))))
% 6.18/6.72 (assert (forall ((X tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.sqrt)))
% 6.18/6.72 (assert (forall ((X tptp.real) (N2 tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (@ tptp.root N2))))
% 6.18/6.72 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B) (= (@ G (@ F Z4)) Z4)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G)))))))
% 6.18/6.72 (assert (forall ((B tptp.real) (X tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real B) X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X)))))))
% 6.18/6.72 (assert (forall ((D tptp.real) (X tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z4) X))) D) (= (@ G (@ F Z4)) Z4))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z4) X))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G))))))
% 6.18/6.72 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) F)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z4) (=> (@ (@ tptp.ord_less_eq_real Z4) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) G)))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z4) (=> (@ (@ tptp.ord_less_real Z4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z4)) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real))))) (=> (forall ((Z4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z4) (=> (@ (@ tptp.ord_less_real Z4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 Z4)) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F4 C3))))))))))))
% 6.18/6.72 (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 ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X5))))))))))
% 6.18/6.72 (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 ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (not (= (@ F X5) tptp.zero_zero_real))))))))))
% 6.18/6.72 (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 ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (@ (@ tptp.ord_less_real (@ F X5)) tptp.zero_zero_real)))))))))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X2)) (@ tptp.sin_real X2)))) (@ 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)))
% 6.18/6.72 (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 ((N9 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.18/6.72 (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 ((N9 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.18/6.72 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.18/6.72 (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))))
% 6.18/6.72 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X8 I3))) B3)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.root N) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 6.18/6.72 (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 ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N9)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N9))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.18/6.72 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_real R3) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.18/6.72 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.root N) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.18/6.72 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.18/6.72 (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 ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.plus_plus_real (@ F N9)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L2)) tptp.at_top_nat))))))
% 6.18/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.18/6.72 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X) N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.18/6.72 (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)))))
% 6.18/6.72 (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))))
% 6.18/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X) N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.18/6.72 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.18/6.72 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N)))) N))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_nat)))
% 6.18/6.72 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.18/6.72 (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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ A N))))))))
% 6.18/6.72 (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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ A N)))))))))
% 6.18/6.72 (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 ((K2 (-> 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 (@ K2 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 6.18/6.72 (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 ((K2 (-> 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 (@ K2 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)))))
% 6.18/6.72 (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 ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat)))))
% 6.18/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ 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 X) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.18/6.72 (assert (forall ((A (-> tptp.nat tptp.real)) (N2 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 ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))))))))
% 6.18/6.72 (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 ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat))))))
% 6.18/6.72 (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 ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) _let_1) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ 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))))) _let_1) tptp.at_top_nat)))))))))
% 6.18/6.72 (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 ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ 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))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat)))))
% 6.18/6.72 (assert (forall ((A (-> tptp.nat tptp.real)) (N2 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 ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ 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)))))))))
% 6.18/6.72 (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 ((N tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ 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))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat))))))
% 6.18/6.72 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C4 tptp.real)) (= F3 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C4)))))))
% 6.18/6.72 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y2 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y2)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.18/6.72 (assert (= tptp.real_V975177566351809787t_real (lambda ((X2 tptp.real) (Y2 tptp.real)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y2)))))
% 6.18/6.72 (assert (= tptp.real_V3694042436643373181omplex (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y2)))))
% 6.18/6.72 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 6.18/6.72 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.18/6.72 (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))))))
% 6.18/6.72 (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)))))
% 6.18/6.72 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.18/6.72 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.18/6.72 (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)))))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real tptp.ln_ln_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5984915006950818249n_real tptp.zero_zero_real))))
% 6.18/6.72 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N2))) tptp.at_bot_real) F5))))))
% 6.18/6.72 (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))
% 6.18/6.72 (assert (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (=> (not (= M7 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M6 tptp.nat)) (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M6))))) M7)))))))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) N2)))) N2))))
% 6.18/6.72 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real tptp.ln_ln_real) tptp.at_top_real) tptp.at_top_real))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real tptp.exp_real) tptp.at_top_real) tptp.at_top_real))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_nat_real tptp.semiri5074537144036343181t_real) tptp.at_top_real) tptp.at_top_nat))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_top_real) tptp.at_bot_real))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_bot_real) tptp.at_top_real))
% 6.18/6.72 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S3)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S3))))))
% 6.18/6.72 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N)) M6))))))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.gcd_gcd_nat M) N2) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_1 M) (@ _let_1 N2))))))))))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) X2))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))
% 6.18/6.72 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) tptp.at_top_real))
% 6.18/6.72 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) K)) (@ tptp.exp_real X2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 6.18/6.72 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y2 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) Y2))) Y2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_real)))
% 6.18/6.72 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.18/6.72 (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))
% 6.18/6.72 (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)))))
% 6.18/6.72 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N2))) tptp.at_top_real) F5))))))
% 6.18/6.72 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I5 tptp.nat)) (@ P (@ tptp.suc I5)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.18/6.72 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.18/6.72 (assert (forall ((N2 tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D2 tptp.int)) (@ (@ tptp.dvd_dvd_int D2) N2)))) (@ tptp.abs_abs_int N2)))))
% 6.18/6.72 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I5 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I5) K)))) tptp.at_top_nat))))
% 6.18/6.72 (assert (not (@ (@ tptp.eventually_nat (lambda ((N tptp.nat)) false)) tptp.at_top_nat)))
% 6.18/6.72 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 6.18/6.72 (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)))))
% 6.18/6.72 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ P N)))))))
% 6.18/6.72 (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))))
% 6.18/6.72 (assert (= tptp.topolo9180104560040979295open_o (@ tptp.topolo4667128019001906403logy_o (@ (@ tptp.sup_sup_set_set_o (@ (@ tptp.image_o_set_o tptp.set_ord_lessThan_o) tptp.top_top_set_o)) (@ (@ tptp.image_o_set_o tptp.set_or6416164934427428222Than_o) tptp.top_top_set_o)))))
% 6.18/6.72 (assert (= tptp.topolo4325760605701065253en_int (@ tptp.topolo1611008123915946401gy_int (@ (@ tptp.sup_sup_set_set_int (@ (@ tptp.image_int_set_int tptp.set_ord_lessThan_int) tptp.top_top_set_int)) (@ (@ tptp.image_int_set_int tptp.set_or1207661135979820486an_int) tptp.top_top_set_int)))))
% 6.18/6.72 (assert (forall ((N2 tptp.int) (M tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (@ (@ tptp.gcd_gcd_int M) N2) (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (and (@ _let_1 M) (@ _let_1 N2))))))))))
% 6.18/6.72 (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 ((X2 tptp.real)) (@ P (@ (@ tptp.plus_plus_real X2) A)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.18/6.72 (assert (forall ((P (-> tptp.real Bool))) (= (@ (@ tptp.eventually_real P) tptp.at_top_real) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ P (@ tptp.inverse_inverse_real X2)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.18/6.72 (assert (forall ((P (-> tptp.real Bool))) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ P (@ tptp.inverse_inverse_real X2)))) tptp.at_top_real))))
% 6.18/6.72 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A))) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ P (@ tptp.uminus_uminus_real X2)))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))))
% 6.18/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) (@ (@ tptp.set_or1633881224788618240n_real A) B)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))))))
% 6.18/6.72 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) (@ (@ tptp.set_or1633881224788618240n_real B) A)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))))))
% 6.18/6.72 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.18/6.72 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.18/6.72 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.18/6.72 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_top_real) _let_1)))))))))
% 6.18/6.72 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) 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 ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F5) _let_1))))))))))))
% 6.18/6.72 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.18/6.72 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) _let_1) tptp.at_top_real) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_1) tptp.at_top_real)))))))))
% 6.18/6.72 (assert (= tptp.topolo4328251076210115529en_nat (@ tptp.topolo1613498594424996677gy_nat (@ (@ tptp.sup_sup_set_set_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)))))
% 6.18/6.72 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.18/6.72 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> 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 ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) tptp.at_bot_real) _let_1)))))))))
% 6.18/6.72 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (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 ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F5) _let_1))))))))))))
% 6.18/6.72 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> 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 ((X2 tptp.real)) (not (= (@ G0 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F0) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G0) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X2)) (@ G0 X2)))) F5) _let_1))))))))))))
% 6.18/6.72 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.18/6.72 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (X 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 X))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.18/6.72 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (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 ((X2 tptp.real)) (not (= (@ G X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F5) _let_1))))))))))))
% 6.18/6.72 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (not (= (@ G2 X2) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X2)) (@ G2 X2)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) _let_2) _let_1))))))))))
% 6.18/6.72 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.18/6.72 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.18/6.72 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.18/6.72 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.image_nat_real F) tptp.top_top_set_nat)) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat))))
% 6.18/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X)) tptp.at_top_nat)))))
% 6.18/6.72 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 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)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (= Y (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))
% 6.18/6.72 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ X8 I3))) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.18/6.72 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ X8 I3))) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I tptp.nat)) (@ (@ tptp.ord_less_eq_real L6) (@ X8 I)))))))))))
% 6.18/6.72 (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 ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ 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 ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima2)))))))
% 6.18/6.72 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 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)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ 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 TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))
% 6.18/6.72 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 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)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) (not (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))
% 6.18/6.72 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _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) (TreeList3 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) TreeList3) Summary2))) (=> (= X _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 TreeList3)) (@ (@ 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 TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))))
% 6.18/6.72 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _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) (TreeList3 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) TreeList3) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))))
% 6.18/6.72 (assert (= tptp.complete_Sup_Sup_int (lambda ((X4 tptp.set_int)) (@ tptp.the_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) X4) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) X4) (@ (@ tptp.ord_less_eq_int Y2) X2)))))))))
% 6.18/6.72 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Y (= 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) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) 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)))) (=> (= X _let_1) (=> (= Y (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4))))))) (@ 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 ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X2) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 6.18/6.72 (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) (C3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C3) 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) C3) (@ (@ tptp.ord_less_real C3) 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))))))))))))
% 6.18/6.72 (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) (Z4 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z4) (@ (@ tptp.ord_less_real Z4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z4) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.18/6.72 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (@ _let_1 (lambda ((X2 tptp.real)) (@ tptp.arsinh_real (@ F X2))))))))
% 6.18/6.72 (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 ((X2 tptp.real)) (@ tptp.arcosh_real (@ F X2)))))))))
% 6.18/6.72 (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 ((C3 tptp.real) (D4 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C3) D4)) (@ (@ tptp.ord_less_eq_real C3) D4)))))))
% 6.18/6.72 (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))))
% 6.18/6.72 (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 ((X2 tptp.real)) (@ tptp.artanh_real (@ F X2)))))))))
% 6.18/6.72 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> 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) (@ F4 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)) (@ (@ F4 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 6.18/6.72 (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))))
% 6.18/6.72 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X 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) X) (=> (@ (@ tptp.ord_less_eq_real X) B) (= (@ F X) (@ F A)))))))))
% 6.18/6.72 (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 ((X2 tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X2) Y2)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.18/6.72 (assert (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X2 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X2) Y2)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.18/6.72 (assert (= tptp.topolo4110288021797289639omplex (lambda ((U4 tptp.set_complex)) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) U4) (@ (@ tptp.eventu5826381225784669381omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X9 tptp.complex) (Y2 tptp.complex)) (=> (= X9 X2) (@ (@ tptp.member_complex Y2) U4))))) tptp.topolo896644834953643431omplex))))))
% 6.18/6.72 (assert (= tptp.topolo4860482606490270245n_real (lambda ((U4 tptp.set_real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) U4) (@ (@ tptp.eventu3244425730907250241l_real (@ tptp.produc5414030515140494994real_o (lambda ((X9 tptp.real) (Y2 tptp.real)) (=> (= X9 X2) (@ (@ tptp.member_real Y2) U4))))) tptp.topolo1511823702728130853y_real))))))
% 6.18/6.72 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N2)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.18/6.72 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.18/6.72 (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 ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) M6) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ P (@ (@ tptp.product_Pair_nat_nat N) M6))))))))))
% 6.18/6.72 (assert (forall ((D tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) D))) (= (@ (@ tptp.filtermap_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real X2) D))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1))))))
% 6.18/6.72 (assert (forall ((A tptp.real)) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) A))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.18/6.72 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A))) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real tptp.uminus_uminus_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5984915006950818249n_real _let_1)))))))
% 6.18/6.72 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A))) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)) (@ (@ tptp.filtermap_real_real tptp.uminus_uminus_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))))
% 6.18/6.72 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ (@ (@ 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 K3) (@ 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))))))))))
% 6.18/6.72 (assert (= tptp.gcd_Gcd_int (lambda ((K7 tptp.set_int)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat (@ (@ tptp.image_int_nat (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) K7))))))
% 6.18/6.72 (assert (= tptp.code_negative (@ (@ tptp.comp_C3531382070062128313er_num tptp.uminus1351360451143612070nteger) tptp.numera6620942414471956472nteger)))
% 6.18/6.72 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 6.18/6.72 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I3)) B3)) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.18/6.72 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.18/6.72 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N2)))))
% 6.18/6.72 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 6.18/6.72 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 6.18/6.72 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 6.18/6.72 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 6.18/6.72 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 6.18/6.72 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 6.18/6.72 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 6.18/6.72 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 6.18/6.72 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)))
% 6.18/6.72 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)))
% 6.18/6.72 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X4 tptp.real)) (@ P X4)))))
% 6.18/6.72 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y) Y)))
% 6.18/6.72 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y) X)))
% 6.18/6.72 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y) Y)))
% 6.18/6.72 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y) X)))
% 6.33/6.73 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 6.33/6.73 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 6.33/6.73 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)))
% 6.33/6.73 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)))
% 6.33/6.73 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y) Y)))
% 6.33/6.73 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y) X)))
% 6.33/6.73 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 6.33/6.73 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 6.33/6.73 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X) Y) Y)))
% 6.33/6.73 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X) Y) X)))
% 6.33/6.73 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y) Y)))
% 6.33/6.73 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y) X)))
% 6.33/6.73 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 6.33/6.73 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)))
% 6.33/6.73 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)))
% 6.33/6.73 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)))
% 6.33/6.73 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y) Y)))
% 6.33/6.73 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y) X)))
% 6.33/6.73 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 6.33/6.73 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y) Y)))
% 6.33/6.73 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y) X)))
% 6.33/6.73 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat tptp.summin) (@ _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_delete tptp.summary) _let_4))) (let ((_let_6 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_4) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_4)) (@ (@ tptp.vEBT_VEBT_low _let_3) tptp.na))))) (let ((_let_7 (@ tptp.vEBT_vebt_maxt _let_5))) (let ((_let_8 (@ tptp.the_nat _let_7))) (not (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ 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.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat _let_3) (@ (@ (@ tptp.if_nat (= _let_3 tptp.ma)) (@ (@ (@ tptp.if_nat (= _let_7 tptp.none_nat)) _let_3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ _let_2 (@ (@ tptp.divide_divide_nat tptp.deg) _let_1))) _let_8)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT _let_6) _let_8)))))) tptp.ma)))) tptp.deg) _let_6) _let_5))))))))))))
% 6.33/6.73 (set-info :filename cvc5---1.0.5_11563)
% 6.33/6.73 (check-sat-assuming ( true ))
% 6.33/6.73 ------- get file name : TPTP file name is ITP263^3
% 6.33/6.73 ------- cvc5-thf : /export/starexec/sandbox2//export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 13923 Alarm clock ( read result; case "$result" in
% 299.74/300.17 unsat)
% 299.74/300.17 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.74/300.17 ;;
% 299.74/300.17 sat)
% 299.74/300.17 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.74/300.17 ;;
% 299.74/300.17 esac; exit 1 )
% 299.74/300.18 Alarm clock
% 299.74/300.18 % cvc5---1.0.5 exiting
% 299.74/300.18 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------