TSTP Solution File: ITP231^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP231^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 03:22:48 EDT 2023
% Result : Timeout 300.17s 290.86s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.64 % Problem : ITP231^3 : TPTP v8.1.2. Released v8.1.0.
% 0.13/0.65 % Command : do_cvc5 %s %d
% 0.67/0.86 % Computer : n018.cluster.edu
% 0.67/0.86 % Model : x86_64 x86_64
% 0.67/0.86 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.67/0.86 % Memory : 8042.1875MB
% 0.67/0.86 % OS : Linux 3.10.0-693.el7.x86_64
% 0.67/0.86 % CPULimit : 300
% 0.67/0.86 % WCLimit : 300
% 0.67/0.86 % DateTime : Sun Aug 27 12:03:46 EDT 2023
% 0.67/0.87 % CPUTime :
% 1.27/1.55 %----Proving TH0
% 1.40/1.56 %------------------------------------------------------------------------------
% 1.40/1.56 % File : ITP231^3 : TPTP v8.1.2. Released v8.1.0.
% 1.40/1.56 % Domain : Interactive Theorem Proving
% 1.40/1.56 % Problem : Sledgehammer problem VEBT_InsertCorrectness 00200_011877
% 1.40/1.56 % Version : [Des22] axioms.
% 1.40/1.56 % English :
% 1.40/1.56
% 1.40/1.56 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 1.40/1.56 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 1.40/1.56 % Source : [Des22]
% 1.40/1.56 % Names : 0067_VEBT_InsertCorrectness_00200_011877 [Des22]
% 1.40/1.56
% 1.40/1.56 % Status : Theorem
% 1.40/1.56 % Rating : 1.00 v8.1.0
% 1.40/1.56 % Syntax : Number of formulae : 3723 (1790 unt; 614 typ; 0 def)
% 1.40/1.56 % Number of atoms : 8818 (4018 equ; 0 cnn)
% 1.40/1.56 % Maximal formula atoms : 71 ( 2 avg)
% 1.40/1.56 % Number of connectives : 39778 ( 936 ~; 148 |; 688 &;34349 @)
% 1.40/1.56 % ( 0 <=>;3657 =>; 0 <=; 0 <~>)
% 1.40/1.56 % Maximal formula depth : 39 ( 6 avg)
% 1.40/1.56 % Number of types : 43 ( 42 usr)
% 1.40/1.56 % Number of type conns : 1439 (1439 >; 0 *; 0 +; 0 <<)
% 1.40/1.56 % Number of symbols : 575 ( 572 usr; 54 con; 0-8 aty)
% 1.40/1.56 % Number of variables : 7833 ( 651 ^;6820 !; 362 ?;7833 :)
% 1.40/1.56 % SPC : TH0_THM_EQU_NAR
% 1.40/1.56
% 1.40/1.56 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 1.40/1.56 % from the van Emde Boas Trees session in the Archive of Formal
% 1.40/1.56 % proofs -
% 1.40/1.56 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 1.40/1.56 % 2022-02-17 20:37:12.152
% 1.40/1.56 %------------------------------------------------------------------------------
% 1.40/1.56 % Could-be-implicit typings (42)
% 1.40/1.56 thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 1.40/1.56 produc8923325533196201883nteger: $tType ).
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% 1.40/1.56 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 1.40/1.56 thf(ty_n_t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
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% 1.40/1.56 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
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% 1.40/1.56 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 1.40/1.56 thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
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% 1.40/1.56
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__List__Olist_It__Complex__Ocomplex_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
% 1.40/1.56 set_complex: $tType ).
% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Filter__Ofilter_It__Real__Oreal_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Option__Ooption_It__Num__Onum_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__List__Olist_It__Real__Oreal_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 1.40/1.56 set_real: $tType ).
% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 1.40/1.56 list_nat: $tType ).
% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
% 1.40/1.56 list_int: $tType ).
% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 vEBT_VEBT: $tType ).
% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Code____Numeral__Ointeger,type,
% 1.40/1.56 code_integer: $tType ).
% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Extended____Nat__Oenat,type,
% 1.40/1.56 extended_enat: $tType ).
% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__List__Olist_I_Eo_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Complex__Ocomplex,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Set__Oset_I_Eo_J,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__String__Ochar,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Real__Oreal,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Rat__Orat,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Num__Onum,type,
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% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Nat__Onat,type,
% 1.40/1.56 nat: $tType ).
% 1.40/1.56
% 1.40/1.56 thf(ty_n_t__Int__Oint,type,
% 1.40/1.56 int: $tType ).
% 1.40/1.56
% 1.40/1.56 % Explicit typings (572)
% 1.40/1.56 thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
% 1.40/1.56 archim7802044766580827645g_real: real > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Binomial_Obinomial,type,
% 1.40/1.56 binomial: nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 1.40/1.56 bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Oand__not__num,type,
% 1.40/1.56 bit_and_not_num: num > num > option_num ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Oand__not__num__rel,type,
% 1.40/1.56 bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 1.40/1.56 bit_concat_bit: nat > int > int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
% 1.40/1.56 bit_or_not_num_neg: num > num > num ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Oor__not__num__neg__rel,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
% 1.40/1.56 bit_se727722235901077358nd_nat: nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Int__Oint,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Nat__Onat,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Int__Oint,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
% 1.40/1.56 bit_se1412395901928357646or_nat: nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Int__Oint,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Nat__Onat,type,
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% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Int__Oint,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Nat__Onat,type,
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% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Int__Oint,type,
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% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Nat__Onat,type,
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% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Int__Oint,type,
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% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Nat__Onat,type,
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% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Int__Oint,type,
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% 1.40/1.56 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Nat__Onat,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Otake__bit__num,type,
% 1.40/1.56 bit_take_bit_num: nat > num > option_num ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations_Oand__num,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations_Oand__num__rel,type,
% 1.40/1.56 bit_un5425074673868309765um_rel: product_prod_num_num > product_prod_num_num > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations_Oxor__num,type,
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% 1.40/1.56 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations_Oxor__num__rel,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oand__num,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oand__num__rel,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oxor__num,type,
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% 1.40/1.56 thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oxor__num__rel,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Numeral_Obit__cut__integer,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Numeral_Odivmod__abs,type,
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% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Numeral_Odivmod__integer,type,
% 1.40/1.56 code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Numeral_Ointeger_Oint__of__integer,type,
% 1.40/1.56 code_int_of_integer: code_integer > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Numeral_Ointeger_Ointeger__of__int,type,
% 1.40/1.56 code_integer_of_int: int > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Numeral_Ointeger__of__num,type,
% 1.40/1.56 code_integer_of_num: num > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Numeral_Onat__of__integer,type,
% 1.40/1.56 code_nat_of_integer: code_integer > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Numeral_Onegative,type,
% 1.40/1.56 code_negative: num > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Numeral_Onum__of__integer,type,
% 1.40/1.56 code_num_of_integer: code_integer > num ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Numeral_Opositive,type,
% 1.40/1.56 code_positive: num > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Target__Int_Onegative,type,
% 1.40/1.56 code_Target_negative: num > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Code__Target__Int_Opositive,type,
% 1.40/1.56 code_Target_positive: num > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Real__Oreal,type,
% 1.40/1.56 comple4887499456419720421f_real: set_real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Int__Oint,type,
% 1.40/1.56 complete_Sup_Sup_int: set_int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Real__Oreal,type,
% 1.40/1.56 comple1385675409528146559p_real: set_real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complex_OArg,type,
% 1.40/1.56 arg: complex > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complex_Ocis,type,
% 1.40/1.56 cis: real > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complex_Ocnj,type,
% 1.40/1.56 cnj: complex > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complex_Ocomplex_OComplex,type,
% 1.40/1.56 complex2: real > real > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complex_Ocomplex_OIm,type,
% 1.40/1.56 im: complex > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complex_Ocomplex_ORe,type,
% 1.40/1.56 re: complex > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complex_Ocsqrt,type,
% 1.40/1.56 csqrt: complex > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Complex_Oimaginary__unit,type,
% 1.40/1.56 imaginary_unit: complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Deriv_Odifferentiable_001t__Real__Oreal_001t__Real__Oreal,type,
% 1.40/1.56 differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Deriv_Ohas__field__derivative_001t__Real__Oreal,type,
% 1.40/1.56 has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Divides_Oadjust__div,type,
% 1.40/1.56 adjust_div: product_prod_int_int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Divides_Oadjust__mod,type,
% 1.40/1.56 adjust_mod: int > int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Divides_Odivmod__nat,type,
% 1.40/1.56 divmod_nat: nat > nat > product_prod_nat_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Divides_Oeucl__rel__int,type,
% 1.40/1.56 eucl_rel_int: int > int > product_prod_int_int > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
% 1.40/1.56 unique5052692396658037445od_int: num > num > product_prod_int_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
% 1.40/1.56 unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 1.40/1.56 unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 1.40/1.56 unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 1.40/1.56 semiri1408675320244567234ct_nat: nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 1.40/1.56 semiri2265585572941072030t_real: nat > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 1.40/1.56 invers8013647133539491842omplex: complex > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 1.40/1.56 inverse_inverse_rat: rat > rat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 1.40/1.56 inverse_inverse_real: real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 1.40/1.56 at_bot_real: filter_real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 1.40/1.56 at_top_nat: filter_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 1.40/1.56 at_top_real: filter_real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 1.40/1.56 eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 1.40/1.56 eventually_real: ( real > $o ) > filter_real > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.56 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 1.40/1.56 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 1.40/1.56 filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 1.40/1.56 finite_card_o: set_o > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 1.40/1.56 finite_card_complex: set_complex > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 1.40/1.56 finite_card_int: set_int > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
% 1.40/1.56 finite_card_list_nat: set_list_nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 1.40/1.56 finite_card_nat: set_nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 1.40/1.56 finite410649719033368117t_unit: set_Product_unit > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 1.40/1.56 finite_card_char: set_char > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 1.40/1.56 finite3207457112153483333omplex: set_complex > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 1.40/1.56 finite_finite_int: set_int > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 1.40/1.56 finite_finite_nat: set_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 1.40/1.56 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 1.40/1.56 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.56 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 1.40/1.56
% 1.40/1.56 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,
% 1.40/1.56 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 1.40/1.56
% 1.40/1.56 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,
% 1.40/1.56 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 1.40/1.56 comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 1.40/1.56 comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.56 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Real__Oreal_001t__Nat__Onat,type,
% 1.40/1.56 comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Oid_001_Eo,type,
% 1.40/1.56 id_o: $o > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 1.40/1.56 id_nat: nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.56 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
% 1.40/1.56 inj_on_nat_char: ( nat > char ) > set_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 1.40/1.56 inj_on_real_real: ( real > real ) > set_real > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 1.40/1.56 map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.56 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
% 1.40/1.56 the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 1.40/1.56 gcd_Gcd_int: set_int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 1.40/1.56 gcd_Gcd_nat: set_nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_GCD_Obezw,type,
% 1.40/1.56 bezw: nat > nat > product_prod_int_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_GCD_Obezw__rel,type,
% 1.40/1.56 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 1.40/1.56 gcd_gcd_int: int > int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 1.40/1.56 gcd_gcd_nat: nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 abs_abs_Code_integer: code_integer > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 1.40/1.56 abs_abs_int: int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 1.40/1.56 abs_abs_real: real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
% 1.40/1.56 minus_minus_complex: complex > complex > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ominus__class_Ominus_001t__Extended____Nat__Oenat,type,
% 1.40/1.56 minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 1.40/1.56 minus_minus_int: int > int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 1.40/1.56 minus_minus_nat: nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 1.40/1.56 minus_minus_rat: rat > rat > rat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 1.40/1.56 minus_minus_real: real > real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
% 1.40/1.56 minus_minus_set_nat: set_nat > set_nat > set_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 one_one_Code_integer: code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex,type,
% 1.40/1.56 one_one_complex: complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oone__class_Oone_001t__Extended____Nat__Oenat,type,
% 1.40/1.56 one_on7984719198319812577d_enat: extended_enat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 1.40/1.56 one_one_int: int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 1.40/1.56 one_one_nat: nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oone__class_Oone_001t__Rat__Orat,type,
% 1.40/1.56 one_one_rat: rat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 1.40/1.56 one_one_real: real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex,type,
% 1.40/1.56 plus_plus_complex: complex > complex > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oplus__class_Oplus_001t__Extended____Nat__Oenat,type,
% 1.40/1.56 plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 1.40/1.56 plus_plus_int: int > int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 1.40/1.56 plus_plus_nat: nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
% 1.40/1.56 plus_plus_num: num > num > num ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oplus__class_Oplus_001t__Rat__Orat,type,
% 1.40/1.56 plus_plus_rat: rat > rat > rat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 1.40/1.56 plus_plus_real: real > real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Osgn__class_Osgn_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 sgn_sgn_Code_integer: code_integer > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Osgn__class_Osgn_001t__Complex__Ocomplex,type,
% 1.40/1.56 sgn_sgn_complex: complex > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Osgn__class_Osgn_001t__Int__Oint,type,
% 1.40/1.56 sgn_sgn_int: int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Osgn__class_Osgn_001t__Rat__Orat,type,
% 1.40/1.56 sgn_sgn_rat: rat > rat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Osgn__class_Osgn_001t__Real__Oreal,type,
% 1.40/1.56 sgn_sgn_real: real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Otimes__class_Otimes_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 times_3573771949741848930nteger: code_integer > code_integer > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex,type,
% 1.40/1.56 times_times_complex: complex > complex > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Otimes__class_Otimes_001t__Extended____Nat__Oenat,type,
% 1.40/1.56 times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
% 1.40/1.56 times_times_int: int > int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 1.40/1.56 times_times_nat: nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum,type,
% 1.40/1.56 times_times_num: num > num > num ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Otimes__class_Otimes_001t__Rat__Orat,type,
% 1.40/1.56 times_times_rat: rat > rat > rat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
% 1.40/1.56 times_times_real: real > real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 uminus1351360451143612070nteger: code_integer > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex,type,
% 1.40/1.56 uminus1482373934393186551omplex: complex > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
% 1.40/1.56 uminus_uminus_int: int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Rat__Orat,type,
% 1.40/1.56 uminus_uminus_rat: rat > rat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
% 1.40/1.56 uminus_uminus_real: real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 zero_z3403309356797280102nteger: code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex,type,
% 1.40/1.56 zero_zero_complex: complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Extended____Nat__Oenat,type,
% 1.40/1.56 zero_z5237406670263579293d_enat: extended_enat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 1.40/1.56 zero_zero_int: int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 1.40/1.56 zero_zero_nat: nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Rat__Orat,type,
% 1.40/1.56 zero_zero_rat: rat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 1.40/1.56 zero_zero_real: real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 1.40/1.56 groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Int__Oint,type,
% 1.40/1.56 groups4538972089207619220nt_int: ( int > int ) > set_int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.56 groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Real__Oreal,type,
% 1.40/1.56 groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Int__Oint,type,
% 1.40/1.56 groups1705073143266064639nt_int: ( int > int ) > set_int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Int__Oint,type,
% 1.40/1.56 groups705719431365010083at_int: ( nat > int ) > set_nat > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.56 groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups__List_Ocomm__semiring__0__class_Ohorner__sum_001_Eo_001t__Int__Oint,type,
% 1.40/1.56 groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Groups__List_Omonoid__add__class_Osum__list_001t__Nat__Onat,type,
% 1.40/1.56 groups4561878855575611511st_nat: list_nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_HOL_OThe_001t__Int__Oint,type,
% 1.40/1.56 the_int: ( int > $o ) > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_HOL_OThe_001t__Real__Oreal,type,
% 1.40/1.56 the_real: ( real > $o ) > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Code____Numeral__Ointeger,type,
% 1.40/1.56 if_Code_integer: $o > code_integer > code_integer > code_integer ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Int__Oint,type,
% 1.40/1.56 if_int: $o > int > int > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__List__Olist_It__Int__Oint_J,type,
% 1.40/1.56 if_list_int: $o > list_int > list_int > list_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__List__Olist_It__Nat__Onat_J,type,
% 1.40/1.56 if_list_nat: $o > list_nat > list_nat > list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Nat__Onat,type,
% 1.40/1.56 if_nat: $o > nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Num__Onum,type,
% 1.40/1.56 if_num: $o > num > num > num ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Option__Ooption_It__Num__Onum_J,type,
% 1.40/1.56 if_option_num: $o > option_num > option_num > option_num ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 1.40/1.56 if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 1.40/1.56 if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 1.40/1.56 if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.56 if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Rat__Orat,type,
% 1.40/1.56 if_rat: $o > rat > rat > rat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Real__Oreal,type,
% 1.40/1.56 if_real: $o > real > real > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 1.40/1.56 if_set_int: $o > set_int > set_int > set_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Int_OAbs__Integ,type,
% 1.40/1.56 abs_Integ: product_prod_nat_nat > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Int_ORep__Integ,type,
% 1.40/1.56 rep_Integ: int > product_prod_nat_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Int_Oint__ge__less__than,type,
% 1.40/1.56 int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Int_Oint__ge__less__than2,type,
% 1.40/1.56 int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Int_Onat,type,
% 1.40/1.56 nat2: int > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Int_Opower__int_001t__Real__Oreal,type,
% 1.40/1.56 power_int_real: real > int > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 1.40/1.56 ring_1_Ints_real: set_real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 1.40/1.56 ring_1_of_int_rat: int > rat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 1.40/1.56 ring_1_of_int_real: int > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Extended____Nat__Oenat,type,
% 1.40/1.56 inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 1.40/1.56 inf_inf_nat: nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 1.40/1.56 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 1.40/1.56 sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 1.40/1.56 sup_sup_nat: nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 1.40/1.56 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 1.40/1.56 lattic8265883725875713057ax_nat: set_nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 1.40/1.56 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 1.40/1.56 at_infinity_real: filter_real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Oappend_001_Eo,type,
% 1.40/1.56 append_o: list_o > list_o > list_o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 1.40/1.56 append_int: list_int > list_int > list_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 1.40/1.56 append_nat: list_nat > list_nat > list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Oappend_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 append_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 1.40/1.56 distinct_int: list_int > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 1.40/1.56 distinct_nat: list_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Odrop_001_Eo,type,
% 1.40/1.56 drop_o: nat > list_o > list_o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Odrop_001t__Complex__Ocomplex,type,
% 1.40/1.56 drop_complex: nat > list_complex > list_complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Odrop_001t__Int__Oint,type,
% 1.40/1.56 drop_int: nat > list_int > list_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 1.40/1.56 drop_nat: nat > list_nat > list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Odrop_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.56 drop_P8868858903918902087at_nat: nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Odrop_001t__Real__Oreal,type,
% 1.40/1.56 drop_real: nat > list_real > list_real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Odrop_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 drop_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 1.40/1.56 linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.56 linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 1.40/1.56 linord2614967742042102400et_nat: set_nat > list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_OCons_001_Eo,type,
% 1.40/1.56 cons_o: $o > list_o > list_o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_OCons_001t__Complex__Ocomplex,type,
% 1.40/1.56 cons_complex: complex > list_complex > list_complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 1.40/1.56 cons_int: int > list_int > list_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Int__Oint_J,type,
% 1.40/1.56 cons_list_int: list_int > list_list_int > list_list_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Nat__Onat_J,type,
% 1.40/1.56 cons_list_nat: list_nat > list_list_nat > list_list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 1.40/1.56 cons_list_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT > list_list_VEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 1.40/1.56 cons_nat: nat > list_nat > list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.56 cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_OCons_001t__Real__Oreal,type,
% 1.40/1.56 cons_real: real > list_real > list_real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_OCons_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_ONil_001_Eo,type,
% 1.40/1.56 nil_o: list_o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 1.40/1.56 nil_int: list_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Int__Oint_J,type,
% 1.40/1.56 nil_list_int: list_list_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Nat__Onat_J,type,
% 1.40/1.56 nil_list_nat: list_list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 1.40/1.56 nil_list_VEBT_VEBT: list_list_VEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 1.40/1.56 nil_nat: list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_ONil_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 nil_VEBT_VEBT: list_VEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 1.40/1.56 hd_nat: list_nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.56 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 1.40/1.56 set_o2: list_o > set_o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 1.40/1.56 set_complex2: list_complex > set_complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 1.40/1.56 set_int2: list_int > set_int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 1.40/1.56 set_nat2: list_nat > set_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.56 set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 1.40/1.56 set_real2: list_real > set_real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 1.40/1.56 tl_nat: list_nat > list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Onth_001_Eo,type,
% 1.40/1.56 nth_o: list_o > nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 1.40/1.56 nth_complex: list_complex > nat > complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 1.40/1.56 nth_int: list_int > nat > int ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 1.40/1.56 nth_nat: list_nat > nat > nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.56 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 1.40/1.56 nth_real: list_real > nat > real ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 1.40/1.56 remdups_nat: list_nat > list_nat ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.56 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 1.40/1.56 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 1.40/1.56 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Otake_001_Eo,type,
% 1.40/1.56 take_o: nat > list_o > list_o ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Otake_001t__Complex__Ocomplex,type,
% 1.40/1.56 take_complex: nat > list_complex > list_complex ).
% 1.40/1.56
% 1.40/1.56 thf(sy_c_List_Otake_001t__Int__Oint,type,
% 1.40/1.56 take_int: nat > list_int > list_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 1.40/1.57 take_nat: nat > list_nat > list_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_List_Otake_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.57 take_P2173866234530122223at_nat: nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_List_Otake_001t__Real__Oreal,type,
% 1.40/1.57 take_real: nat > list_real > list_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.57 take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_List_Oupt,type,
% 1.40/1.57 upt: nat > nat > list_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_List_Oupto,type,
% 1.40/1.57 upto: int > int > list_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_List_Oupto__aux,type,
% 1.40/1.57 upto_aux: int > int > list_int > list_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_List_Oupto__rel,type,
% 1.40/1.57 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_OSuc,type,
% 1.40/1.57 suc: nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.57 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 1.40/1.57 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 1.40/1.57 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 1.40/1.57 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Onat_Opred,type,
% 1.40/1.57 pred: nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 1.40/1.57 semiri1314217659103216013at_int: nat > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 1.40/1.57 semiri1316708129612266289at_nat: nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 1.40/1.57 semiri681578069525770553at_rat: nat > rat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 1.40/1.57 semiri5074537144036343181t_real: nat > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 1.40/1.57 size_size_list_o: list_o > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 1.40/1.57 size_s3451745648224563538omplex: list_complex > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 1.40/1.57 size_size_list_int: list_int > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 1.40/1.57 size_size_list_nat: list_nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 1.40/1.57 size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 1.40/1.57 size_size_list_real: list_real > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 1.40/1.57 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 1.40/1.57 size_size_num: num > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.57 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 1.40/1.57 nat_list_encode: list_nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 1.40/1.57 nat_list_encode_rel: list_nat > list_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 1.40/1.57 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 1.40/1.57 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 1.40/1.57 nat_prod_encode: product_prod_nat_nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 1.40/1.57 nat_set_decode: nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 1.40/1.57 nat_set_encode: set_nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Nat__Bijection_Otriangle,type,
% 1.40/1.57 nat_triangle: nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_NthRoot_Oroot,type,
% 1.40/1.57 root: nat > real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_NthRoot_Osqrt,type,
% 1.40/1.57 sqrt: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_OBitM,type,
% 1.40/1.57 bitM: num > num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Oinc,type,
% 1.40/1.57 inc: num > num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 1.40/1.57 neg_numeral_sub_int: num > num > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onum_OBit0,type,
% 1.40/1.57 bit0: num > num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onum_OBit1,type,
% 1.40/1.57 bit1: num > num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onum_OOne,type,
% 1.40/1.57 one: num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 1.40/1.57 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onum_Osize__num,type,
% 1.40/1.57 size_num: num > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onum__of__nat,type,
% 1.40/1.57 num_of_nat: nat > num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 1.40/1.57 numera6620942414471956472nteger: num > code_integer ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 1.40/1.57 numera6690914467698888265omplex: num > complex ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 1.40/1.57 numera1916890842035813515d_enat: num > extended_enat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 1.40/1.57 numeral_numeral_int: num > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 1.40/1.57 numeral_numeral_nat: num > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 1.40/1.57 numeral_numeral_rat: num > rat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 1.40/1.57 numeral_numeral_real: num > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Opow,type,
% 1.40/1.57 pow: num > num > num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Opred__numeral,type,
% 1.40/1.57 pred_numeral: num > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Num_Osqr,type,
% 1.40/1.57 sqr: num > num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 1.40/1.57 none_num: option_num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.57 none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 1.40/1.57 some_num: num > option_num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.57 some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.57 case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 1.40/1.57 case_option_int_num: int > ( num > int ) > option_num > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 1.40/1.57 case_option_num_num: num > ( num > num ) > option_num > num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 1.40/1.57 case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
% 1.40/1.57 map_option_num_num: ( num > num ) > option_num > option_num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Obot__class_Obot_001t__Extended____Nat__Oenat,type,
% 1.40/1.57 bot_bo4199563552545308370d_enat: extended_enat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 1.40/1.57 bot_bot_nat: nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
% 1.40/1.57 bot_bot_set_int: set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 1.40/1.57 bot_bot_set_nat: set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 1.40/1.57 bot_bot_set_real: set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Ointeger,type,
% 1.40/1.57 ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless_001t__Extended____Nat__Oenat,type,
% 1.40/1.57 ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 1.40/1.57 ord_less_int: int > int > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 1.40/1.57 ord_less_nat: nat > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
% 1.40/1.57 ord_less_num: num > num > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
% 1.40/1.57 ord_less_rat: rat > rat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 1.40/1.57 ord_less_real: real > real > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Ointeger,type,
% 1.40/1.57 ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Extended____Nat__Oenat,type,
% 1.40/1.57 ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 1.40/1.57 ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Real__Oreal_J,type,
% 1.40/1.57 ord_le4104064031414453916r_real: filter_real > filter_real > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 1.40/1.57 ord_less_eq_int: int > int > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 1.40/1.57 ord_less_eq_nat: nat > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 1.40/1.57 ord_less_eq_num: num > num > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
% 1.40/1.57 ord_less_eq_rat: rat > rat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 1.40/1.57 ord_less_eq_real: real > real > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 1.40/1.57 ord_le211207098394363844omplex: set_complex > set_complex > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
% 1.40/1.57 ord_less_eq_set_int: set_int > set_int > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 1.40/1.57 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 1.40/1.57 ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 1.40/1.57 ord_less_eq_set_real: set_real > set_real > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 1.40/1.57 ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Omax_001t__Extended____Nat__Oenat,type,
% 1.40/1.57 ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
% 1.40/1.57 ord_max_int: int > int > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
% 1.40/1.57 ord_max_nat: nat > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
% 1.40/1.57 ord_max_rat: rat > rat > rat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
% 1.40/1.57 ord_max_real: real > real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Omin_001t__Extended____Nat__Oenat,type,
% 1.40/1.57 ord_mi8085742599997312461d_enat: extended_enat > extended_enat > extended_enat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
% 1.40/1.57 ord_min_nat: nat > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 1.40/1.57 order_Greatest_nat: ( nat > $o ) > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Real__Oreal,type,
% 1.40/1.57 order_9091379641038594480t_real: ( nat > real ) > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.57 order_mono_nat_nat: ( nat > nat ) > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Real__Oreal,type,
% 1.40/1.57 order_mono_nat_real: ( nat > real ) > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.57 order_5726023648592871131at_nat: ( nat > nat ) > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 1.40/1.57 top_top_set_o: set_o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 1.40/1.57 top_top_set_nat: set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 1.40/1.57 top_to1996260823553986621t_unit: set_Product_unit ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 1.40/1.57 top_top_set_real: set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__String__Ochar_J,type,
% 1.40/1.57 top_top_set_char: set_char ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
% 1.40/1.57 power_power_complex: complex > nat > complex ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 1.40/1.57 power_power_int: int > nat > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 1.40/1.57 power_power_nat: nat > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 1.40/1.57 power_power_rat: rat > nat > rat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 1.40/1.57 power_power_real: real > nat > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 1.40/1.57 produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 1.40/1.57 produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 1.40/1.57 product_Pair_int_int: int > int > product_prod_int_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.57 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 1.40/1.57 product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 1.40/1.57 product_Pair_num_num: num > num > product_prod_num_num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 1.40/1.57 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.57 produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 1.40/1.57 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 1.40/1.57 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 1.40/1.57 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 1.40/1.57 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 1.40/1.57
% 1.40/1.57 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,
% 1.40/1.57 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 1.40/1.57
% 1.40/1.57 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,
% 1.40/1.57 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 1.40/1.57 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 1.40/1.57 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 1.40/1.57
% 1.40/1.57 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,
% 1.40/1.57 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 1.40/1.57
% 1.40/1.57 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,
% 1.40/1.57 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 1.40/1.57
% 1.40/1.57 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,
% 1.40/1.57 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 1.40/1.57 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.57 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 1.40/1.57
% 1.40/1.57 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,
% 1.40/1.57 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 1.40/1.57 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 1.40/1.57 product_fst_int_int: product_prod_int_int > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.57 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 1.40/1.57 product_snd_int_int: product_prod_int_int > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.57 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rat_OFract,type,
% 1.40/1.57 fract: int > int > rat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rat_OFrct,type,
% 1.40/1.57 frct: product_prod_int_int > rat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rat_ORep__Rat,type,
% 1.40/1.57 rep_Rat: rat > product_prod_int_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 1.40/1.57 field_5140801741446780682s_real: set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rat_Onormalize,type,
% 1.40/1.57 normalize: product_prod_int_int > product_prod_int_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rat_Oof__int,type,
% 1.40/1.57 of_int: int > rat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rat_Opositive,type,
% 1.40/1.57 positive: rat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rat_Oquotient__of,type,
% 1.40/1.57 quotient_of: rat > product_prod_int_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 1.40/1.57 real_V2521375963428798218omplex: set_complex ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 1.40/1.57 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 1.40/1.57 real_V1022390504157884413omplex: complex > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 1.40/1.57 real_V4546457046886955230omplex: real > complex ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 1.40/1.57 real_V2046097035970521341omplex: real > complex > complex ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 1.40/1.57 real_V1485227260804924795R_real: real > real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 1.40/1.57 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 1.40/1.57 divide1717551699836669952omplex: complex > complex > complex ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 1.40/1.57 divide_divide_int: int > int > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 1.40/1.57 divide_divide_nat: nat > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 1.40/1.57 divide_divide_rat: rat > rat > rat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 1.40/1.57 divide_divide_real: real > real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 1.40/1.57 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 1.40/1.57 dvd_dvd_int: int > int > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 1.40/1.57 dvd_dvd_nat: nat > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 1.40/1.57 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 1.40/1.57 modulo_modulo_int: int > int > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 1.40/1.57 modulo_modulo_nat: nat > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 1.40/1.57 zero_n356916108424825756nteger: $o > code_integer ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 1.40/1.57 zero_n2684676970156552555ol_int: $o > int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 1.40/1.57 zero_n2687167440665602831ol_nat: $o > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 1.40/1.57 suminf_real: ( nat > real ) > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 1.40/1.57 summable_real: ( nat > real ) > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 1.40/1.57 sums_real: ( nat > real ) > real > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 1.40/1.57 collect_complex: ( complex > $o ) > set_complex ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 1.40/1.57 collect_int: ( int > $o ) > set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 1.40/1.57 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
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% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 1.40/1.57 collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.57 collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 1.40/1.57 collect_real: ( real > $o ) > set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 1.40/1.57 image_int_int: ( int > int ) > set_int > set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 1.40/1.57 image_nat_int: ( nat > int ) > set_nat > set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 1.40/1.57 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
% 1.40/1.57 image_nat_real: ( nat > real ) > set_nat > set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 1.40/1.57 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 1.40/1.57 image_real_real: ( real > real ) > set_real > set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 1.40/1.57 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 1.40/1.57 insert_int: int > set_int > set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 1.40/1.57 insert_nat: nat > set_nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 1.40/1.57 insert_real: real > set_real > set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 1.40/1.57 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 1.40/1.57 set_or1266510415728281911st_int: int > int > set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 1.40/1.57 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 1.40/1.57 set_or1222579329274155063t_real: real > real > set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 1.40/1.57 set_or4662586982721622107an_int: int > int > set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 1.40/1.57 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 1.40/1.57 set_ord_atLeast_nat: nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 1.40/1.57 set_ord_atLeast_real: real > set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 1.40/1.57 set_ord_atMost_int: int > set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 1.40/1.57 set_ord_atMost_nat: nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 1.40/1.57 set_or6656581121297822940st_int: int > int > set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 1.40/1.57 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 1.40/1.57 set_or5832277885323065728an_int: int > int > set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 1.40/1.57 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 1.40/1.57 set_or1633881224788618240n_real: real > real > set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 1.40/1.57 set_or1210151606488870762an_nat: nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 1.40/1.57 set_or5849166863359141190n_real: real > set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 1.40/1.57 set_ord_lessThan_int: int > set_int ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 1.40/1.57 set_ord_lessThan_nat: nat > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 1.40/1.57 set_or5984915006950818249n_real: real > set_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_String_Oascii__of,type,
% 1.40/1.57 ascii_of: char > char ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_String_Ochar_OChar,type,
% 1.40/1.57 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 1.40/1.57 comm_s629917340098488124ar_nat: char > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_String_Ointeger__of__char,type,
% 1.40/1.57 integer_of_char: char > code_integer ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 1.40/1.57 unique3096191561947761185of_nat: nat > char ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 1.40/1.57 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 1.40/1.57 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 1.40/1.57 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 1.40/1.57 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 1.40/1.57 topolo2815343760600316023s_real: real > filter_real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 1.40/1.57 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Oarccos,type,
% 1.40/1.57 arccos: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 1.40/1.57 arcosh_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Oarcsin,type,
% 1.40/1.57 arcsin: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Oarctan,type,
% 1.40/1.57 arctan: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 1.40/1.57 arsinh_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 1.40/1.57 artanh_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 1.40/1.57 cos_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Ocos__coeff,type,
% 1.40/1.57 cos_coeff: nat > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 1.40/1.57 cosh_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 1.40/1.57 cot_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 1.40/1.57 exp_complex: complex > complex ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 1.40/1.57 exp_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 1.40/1.57 ln_ln_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Olog,type,
% 1.40/1.57 log: real > real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Opi,type,
% 1.40/1.57 pi: real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 1.40/1.57 powr_real: real > real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 1.40/1.57 sin_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Osin__coeff,type,
% 1.40/1.57 sin_coeff: nat > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 1.40/1.57 sinh_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 1.40/1.57 tan_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 1.40/1.57 tanh_real: real > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 1.40/1.57 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 1.40/1.57 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 1.40/1.57 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 1.40/1.57 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 1.40/1.57 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 1.40/1.57 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 1.40/1.57 vEBT_VEBT_high: nat > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 1.40/1.57 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 1.40/1.57 vEBT_VEBT_low: nat > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 1.40/1.57 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 1.40/1.57 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 1.40/1.57 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 1.40/1.57 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 1.40/1.57 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 1.40/1.57 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 1.40/1.57 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 1.40/1.57 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 1.40/1.57 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 1.40/1.57 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 1.40/1.57 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 1.40/1.57 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 1.40/1.57 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 1.40/1.57 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 1.40/1.57 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 1.40/1.57 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 1.40/1.57 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 1.40/1.57 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 1.40/1.57 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 1.40/1.57 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 1.40/1.57 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.57 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 1.40/1.57 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 1.40/1.57 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.57 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_Wellfounded_Opred__nat,type,
% 1.40/1.57 pred_nat: set_Pr1261947904930325089at_nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 1.40/1.57 fChoice_real: ( real > $o ) > real ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_member_001_Eo,type,
% 1.40/1.57 member_o: $o > set_o > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 1.40/1.57 member_complex: complex > set_complex > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_member_001t__Int__Oint,type,
% 1.40/1.57 member_int: int > set_int > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 1.40/1.57 member_list_nat: list_nat > set_list_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_member_001t__Nat__Onat,type,
% 1.40/1.57 member_nat: nat > set_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 1.40/1.57 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_member_001t__Real__Oreal,type,
% 1.40/1.57 member_real: real > set_real > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 1.40/1.57 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 1.40/1.57
% 1.40/1.57 thf(sy_v_deg____,type,
% 1.40/1.57 deg: nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_v_m____,type,
% 1.40/1.57 m: nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_v_ma____,type,
% 1.40/1.57 ma: nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_v_mi____,type,
% 1.40/1.57 mi: nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_v_na____,type,
% 1.40/1.57 na: nat ).
% 1.40/1.57
% 1.40/1.57 thf(sy_v_summary____,type,
% 1.40/1.57 summary: vEBT_VEBT ).
% 1.40/1.57
% 1.40/1.57 thf(sy_v_treeList____,type,
% 1.40/1.57 treeList: list_VEBT_VEBT ).
% 1.40/1.57
% 1.40/1.57 thf(sy_v_xa____,type,
% 1.40/1.57 xa: nat ).
% 1.40/1.57
% 1.40/1.57 % Relevant facts (3076)
% 1.40/1.57 thf(fact_0_abcdef,axiom,
% 1.40/1.57 ord_less_nat @ mi @ xa ).
% 1.40/1.57
% 1.40/1.57 % abcdef
% 1.40/1.57 thf(fact_1__C4_Ohyps_C_I7_J,axiom,
% 1.40/1.57 ord_less_eq_nat @ mi @ ma ).
% 1.40/1.57
% 1.40/1.57 % "4.hyps"(7)
% 1.40/1.57 thf(fact_2_False,axiom,
% 1.40/1.57 ~ ( ( xa = mi )
% 1.40/1.57 | ( xa = ma ) ) ).
% 1.40/1.57
% 1.40/1.57 % False
% 1.40/1.57 thf(fact_3__092_060open_062mi_A_092_060noteq_062_Amax_Ama_Ax_092_060close_062,axiom,
% 1.40/1.57 ( mi
% 1.40/1.57 != ( ord_max_nat @ ma @ xa ) ) ).
% 1.40/1.57
% 1.40/1.57 % \<open>mi \<noteq> max ma x\<close>
% 1.40/1.57 thf(fact_4__C8_C,axiom,
% 1.40/1.57 na = m ).
% 1.40/1.57
% 1.40/1.57 % "8"
% 1.40/1.57 thf(fact_5_bit__split__inv,axiom,
% 1.40/1.57 ! [X: nat,D: nat] :
% 1.40/1.57 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 1.40/1.57 = X ) ).
% 1.40/1.57
% 1.40/1.57 % bit_split_inv
% 1.40/1.57 thf(fact_6_mimaxrel,axiom,
% 1.40/1.57 ( ( xa != mi )
% 1.40/1.57 & ( xa != ma ) ) ).
% 1.40/1.57
% 1.40/1.57 % mimaxrel
% 1.40/1.57 thf(fact_7_high__bound__aux,axiom,
% 1.40/1.57 ! [Ma: nat,N: nat,M: nat] :
% 1.40/1.57 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 1.40/1.57 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % high_bound_aux
% 1.40/1.57 thf(fact_8__C3_C,axiom,
% 1.40/1.57 ( deg
% 1.40/1.57 = ( plus_plus_nat @ na @ m ) ) ).
% 1.40/1.57
% 1.40/1.57 % "3"
% 1.40/1.57 thf(fact_9__C4_Oprems_C,axiom,
% 1.40/1.57 ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 1.40/1.57
% 1.40/1.57 % "4.prems"
% 1.40/1.57 thf(fact_10__C7_C,axiom,
% 1.40/1.57 ( ( mi != ma )
% 1.40/1.57 => ! [I: nat] :
% 1.40/1.57 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 1.40/1.57 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 1.40/1.57 = I )
% 1.40/1.57 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 1.40/1.57 & ! [Y: nat] :
% 1.40/1.57 ( ( ( ( vEBT_VEBT_high @ Y @ na )
% 1.40/1.57 = I )
% 1.40/1.57 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ Y @ na ) ) )
% 1.40/1.57 => ( ( ord_less_nat @ mi @ Y )
% 1.40/1.57 & ( ord_less_eq_nat @ Y @ ma ) ) ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % "7"
% 1.40/1.57 thf(fact_11__C4_Ohyps_C_I8_J,axiom,
% 1.40/1.57 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 1.40/1.57
% 1.40/1.57 % "4.hyps"(8)
% 1.40/1.57 thf(fact_12_highlowprop,axiom,
% 1.40/1.57 ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 1.40/1.57 & ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % highlowprop
% 1.40/1.57 thf(fact_13__C4_C,axiom,
% 1.40/1.57 ! [I: nat] :
% 1.40/1.57 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 1.40/1.57 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X2 ) )
% 1.40/1.57 = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % "4"
% 1.40/1.57 thf(fact_14__C5_C,axiom,
% 1.40/1.57 ( ( mi = ma )
% 1.40/1.57 => ! [X3: vEBT_VEBT] :
% 1.40/1.57 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 1.40/1.57 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % "5"
% 1.40/1.57 thf(fact_15__C2_C,axiom,
% 1.40/1.57 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 1.40/1.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 1.40/1.57
% 1.40/1.57 % "2"
% 1.40/1.57 thf(fact_16__C15_C,axiom,
% 1.40/1.57 ( ( ord_less_eq_nat @ mi @ ( ord_max_nat @ ma @ xa ) )
% 1.40/1.57 & ( ord_less_nat @ ( ord_max_nat @ ma @ xa ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % "15"
% 1.40/1.57 thf(fact_17_in__children__def,axiom,
% 1.40/1.57 ( vEBT_V5917875025757280293ildren
% 1.40/1.57 = ( ^ [N2: nat,TreeList: list_VEBT_VEBT,X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X4 @ N2 ) ) @ ( vEBT_VEBT_low @ X4 @ N2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % in_children_def
% 1.40/1.57 thf(fact_18__C6_C,axiom,
% 1.40/1.57 ( ( ord_less_eq_nat @ mi @ ma )
% 1.40/1.57 & ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % "6"
% 1.40/1.57 thf(fact_19__C14_C,axiom,
% 1.40/1.57 ( ( mi
% 1.40/1.57 = ( ord_max_nat @ ma @ xa ) )
% 1.40/1.57 => ! [X3: vEBT_VEBT] :
% 1.40/1.57 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( append_VEBT_VEBT @ ( take_VEBT_VEBT @ ( vEBT_VEBT_high @ xa @ na ) @ treeList ) @ ( append_VEBT_VEBT @ ( cons_VEBT_VEBT @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ nil_VEBT_VEBT ) @ ( drop_VEBT_VEBT @ ( plus_plus_nat @ ( vEBT_VEBT_high @ xa @ na ) @ one_one_nat ) @ treeList ) ) ) ) )
% 1.40/1.57 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % "14"
% 1.40/1.57 thf(fact_20_power__increasing__iff,axiom,
% 1.40/1.57 ! [B: real,X: nat,Y2: nat] :
% 1.40/1.57 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.57 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y2 ) )
% 1.40/1.57 = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_increasing_iff
% 1.40/1.57 thf(fact_21_power__increasing__iff,axiom,
% 1.40/1.57 ! [B: rat,X: nat,Y2: nat] :
% 1.40/1.57 ( ( ord_less_rat @ one_one_rat @ B )
% 1.40/1.57 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y2 ) )
% 1.40/1.57 = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_increasing_iff
% 1.40/1.57 thf(fact_22_power__increasing__iff,axiom,
% 1.40/1.57 ! [B: nat,X: nat,Y2: nat] :
% 1.40/1.57 ( ( ord_less_nat @ one_one_nat @ B )
% 1.40/1.57 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y2 ) )
% 1.40/1.57 = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_increasing_iff
% 1.40/1.57 thf(fact_23_power__increasing__iff,axiom,
% 1.40/1.57 ! [B: int,X: nat,Y2: nat] :
% 1.40/1.57 ( ( ord_less_int @ one_one_int @ B )
% 1.40/1.57 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y2 ) )
% 1.40/1.57 = ( ord_less_eq_nat @ X @ Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_increasing_iff
% 1.40/1.57 thf(fact_24_one__add__one,axiom,
% 1.40/1.57 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 1.40/1.57 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_add_one
% 1.40/1.57 thf(fact_25_one__add__one,axiom,
% 1.40/1.57 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 1.40/1.57 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_add_one
% 1.40/1.57 thf(fact_26_one__add__one,axiom,
% 1.40/1.57 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 1.40/1.57 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_add_one
% 1.40/1.57 thf(fact_27_one__add__one,axiom,
% 1.40/1.57 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 1.40/1.57 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_add_one
% 1.40/1.57 thf(fact_28_one__add__one,axiom,
% 1.40/1.57 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 1.40/1.57 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_add_one
% 1.40/1.57 thf(fact_29_power__strict__increasing__iff,axiom,
% 1.40/1.57 ! [B: real,X: nat,Y2: nat] :
% 1.40/1.57 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.57 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y2 ) )
% 1.40/1.57 = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_strict_increasing_iff
% 1.40/1.57 thf(fact_30_power__strict__increasing__iff,axiom,
% 1.40/1.57 ! [B: rat,X: nat,Y2: nat] :
% 1.40/1.57 ( ( ord_less_rat @ one_one_rat @ B )
% 1.40/1.57 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y2 ) )
% 1.40/1.57 = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_strict_increasing_iff
% 1.40/1.57 thf(fact_31_power__strict__increasing__iff,axiom,
% 1.40/1.57 ! [B: nat,X: nat,Y2: nat] :
% 1.40/1.57 ( ( ord_less_nat @ one_one_nat @ B )
% 1.40/1.57 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y2 ) )
% 1.40/1.57 = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_strict_increasing_iff
% 1.40/1.57 thf(fact_32_power__strict__increasing__iff,axiom,
% 1.40/1.57 ! [B: int,X: nat,Y2: nat] :
% 1.40/1.57 ( ( ord_less_int @ one_one_int @ B )
% 1.40/1.57 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y2 ) )
% 1.40/1.57 = ( ord_less_nat @ X @ Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_strict_increasing_iff
% 1.40/1.57 thf(fact_33_numeral__plus__one,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 1.40/1.57 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_plus_one
% 1.40/1.57 thf(fact_34_numeral__plus__one,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 1.40/1.57 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_plus_one
% 1.40/1.57 thf(fact_35_numeral__plus__one,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 1.40/1.57 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_plus_one
% 1.40/1.57 thf(fact_36_numeral__plus__one,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 1.40/1.57 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_plus_one
% 1.40/1.57 thf(fact_37_numeral__plus__one,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 1.40/1.57 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_plus_one
% 1.40/1.57 thf(fact_38_one__plus__numeral,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 1.40/1.57 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_plus_numeral
% 1.40/1.57 thf(fact_39_one__plus__numeral,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 1.40/1.57 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_plus_numeral
% 1.40/1.57 thf(fact_40_one__plus__numeral,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 1.40/1.57 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_plus_numeral
% 1.40/1.57 thf(fact_41_one__plus__numeral,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 1.40/1.57 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_plus_numeral
% 1.40/1.57 thf(fact_42_one__plus__numeral,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 1.40/1.57 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_plus_numeral
% 1.40/1.57 thf(fact_43_one__less__numeral__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 1.40/1.57 = ( ord_less_num @ one @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_less_numeral_iff
% 1.40/1.57 thf(fact_44_one__less__numeral__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 1.40/1.57 = ( ord_less_num @ one @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_less_numeral_iff
% 1.40/1.57 thf(fact_45_one__less__numeral__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 1.40/1.57 = ( ord_less_num @ one @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_less_numeral_iff
% 1.40/1.57 thf(fact_46_one__less__numeral__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 1.40/1.57 = ( ord_less_num @ one @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_less_numeral_iff
% 1.40/1.57 thf(fact_47_numeral__le__one__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 1.40/1.57 = ( ord_less_eq_num @ N @ one ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_le_one_iff
% 1.40/1.57 thf(fact_48_numeral__le__one__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 1.40/1.57 = ( ord_less_eq_num @ N @ one ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_le_one_iff
% 1.40/1.57 thf(fact_49_numeral__le__one__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 1.40/1.57 = ( ord_less_eq_num @ N @ one ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_le_one_iff
% 1.40/1.57 thf(fact_50_numeral__le__one__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 1.40/1.57 = ( ord_less_eq_num @ N @ one ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_le_one_iff
% 1.40/1.57 thf(fact_51__C13_C,axiom,
% 1.40/1.57 ! [I: nat] :
% 1.40/1.57 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 1.40/1.57 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( append_VEBT_VEBT @ ( take_VEBT_VEBT @ ( vEBT_VEBT_high @ xa @ na ) @ treeList ) @ ( append_VEBT_VEBT @ ( cons_VEBT_VEBT @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ nil_VEBT_VEBT ) @ ( drop_VEBT_VEBT @ ( plus_plus_nat @ ( vEBT_VEBT_high @ xa @ na ) @ one_one_nat ) @ treeList ) ) ) @ I ) @ X2 ) )
% 1.40/1.57 = ( vEBT_V8194947554948674370ptions @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ summary ) @ I ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % "13"
% 1.40/1.57 thf(fact_52_not__min__Null__member,axiom,
% 1.40/1.57 ! [T: vEBT_VEBT] :
% 1.40/1.57 ( ~ ( vEBT_VEBT_minNull @ T )
% 1.40/1.57 => ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) ).
% 1.40/1.57
% 1.40/1.57 % not_min_Null_member
% 1.40/1.57 thf(fact_53_inthall,axiom,
% 1.40/1.57 ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N: nat] :
% 1.40/1.57 ( ! [X5: product_prod_nat_nat] :
% 1.40/1.57 ( ( member8440522571783428010at_nat @ X5 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 1.40/1.57 => ( P @ X5 ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs ) )
% 1.40/1.57 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ N ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % inthall
% 1.40/1.57 thf(fact_54_inthall,axiom,
% 1.40/1.57 ! [Xs: list_complex,P: complex > $o,N: nat] :
% 1.40/1.57 ( ! [X5: complex] :
% 1.40/1.57 ( ( member_complex @ X5 @ ( set_complex2 @ Xs ) )
% 1.40/1.57 => ( P @ X5 ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 1.40/1.57 => ( P @ ( nth_complex @ Xs @ N ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % inthall
% 1.40/1.57 thf(fact_55_inthall,axiom,
% 1.40/1.57 ! [Xs: list_real,P: real > $o,N: nat] :
% 1.40/1.57 ( ! [X5: real] :
% 1.40/1.57 ( ( member_real @ X5 @ ( set_real2 @ Xs ) )
% 1.40/1.57 => ( P @ X5 ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 1.40/1.57 => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % inthall
% 1.40/1.57 thf(fact_56_inthall,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 1.40/1.57 ( ! [X5: vEBT_VEBT] :
% 1.40/1.57 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 1.40/1.57 => ( P @ X5 ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 1.40/1.57 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % inthall
% 1.40/1.57 thf(fact_57_inthall,axiom,
% 1.40/1.57 ! [Xs: list_o,P: $o > $o,N: nat] :
% 1.40/1.57 ( ! [X5: $o] :
% 1.40/1.57 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 1.40/1.57 => ( P @ X5 ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 1.40/1.57 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % inthall
% 1.40/1.57 thf(fact_58_inthall,axiom,
% 1.40/1.57 ! [Xs: list_nat,P: nat > $o,N: nat] :
% 1.40/1.57 ( ! [X5: nat] :
% 1.40/1.57 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 1.40/1.57 => ( P @ X5 ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 1.40/1.57 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % inthall
% 1.40/1.57 thf(fact_59_inthall,axiom,
% 1.40/1.57 ! [Xs: list_int,P: int > $o,N: nat] :
% 1.40/1.57 ( ! [X5: int] :
% 1.40/1.57 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 1.40/1.57 => ( P @ X5 ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 1.40/1.57 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % inthall
% 1.40/1.57 thf(fact_60_numeral__eq__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ( numera6690914467698888265omplex @ M )
% 1.40/1.57 = ( numera6690914467698888265omplex @ N ) )
% 1.40/1.57 = ( M = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_eq_iff
% 1.40/1.57 thf(fact_61_numeral__eq__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ( numeral_numeral_real @ M )
% 1.40/1.57 = ( numeral_numeral_real @ N ) )
% 1.40/1.57 = ( M = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_eq_iff
% 1.40/1.57 thf(fact_62_numeral__eq__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ( numeral_numeral_rat @ M )
% 1.40/1.57 = ( numeral_numeral_rat @ N ) )
% 1.40/1.57 = ( M = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_eq_iff
% 1.40/1.57 thf(fact_63_numeral__eq__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ( numeral_numeral_nat @ M )
% 1.40/1.57 = ( numeral_numeral_nat @ N ) )
% 1.40/1.57 = ( M = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_eq_iff
% 1.40/1.57 thf(fact_64_numeral__eq__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ( numeral_numeral_int @ M )
% 1.40/1.57 = ( numeral_numeral_int @ N ) )
% 1.40/1.57 = ( M = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_eq_iff
% 1.40/1.57 thf(fact_65_concat__inth,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.57 ( ( nth_VEBT_VEBT @ ( append_VEBT_VEBT @ Xs @ ( append_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ nil_VEBT_VEBT ) @ Ys ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 1.40/1.57 = X ) ).
% 1.40/1.57
% 1.40/1.57 % concat_inth
% 1.40/1.57 thf(fact_66_concat__inth,axiom,
% 1.40/1.57 ! [Xs: list_o,X: $o,Ys: list_o] :
% 1.40/1.57 ( ( nth_o @ ( append_o @ Xs @ ( append_o @ ( cons_o @ X @ nil_o ) @ Ys ) ) @ ( size_size_list_o @ Xs ) )
% 1.40/1.57 = X ) ).
% 1.40/1.57
% 1.40/1.57 % concat_inth
% 1.40/1.57 thf(fact_67_concat__inth,axiom,
% 1.40/1.57 ! [Xs: list_nat,X: nat,Ys: list_nat] :
% 1.40/1.57 ( ( nth_nat @ ( append_nat @ Xs @ ( append_nat @ ( cons_nat @ X @ nil_nat ) @ Ys ) ) @ ( size_size_list_nat @ Xs ) )
% 1.40/1.57 = X ) ).
% 1.40/1.57
% 1.40/1.57 % concat_inth
% 1.40/1.57 thf(fact_68_concat__inth,axiom,
% 1.40/1.57 ! [Xs: list_int,X: int,Ys: list_int] :
% 1.40/1.57 ( ( nth_int @ ( append_int @ Xs @ ( append_int @ ( cons_int @ X @ nil_int ) @ Ys ) ) @ ( size_size_list_int @ Xs ) )
% 1.40/1.57 = X ) ).
% 1.40/1.57
% 1.40/1.57 % concat_inth
% 1.40/1.57 thf(fact_69_power__one,axiom,
% 1.40/1.57 ! [N: nat] :
% 1.40/1.57 ( ( power_power_rat @ one_one_rat @ N )
% 1.40/1.57 = one_one_rat ) ).
% 1.40/1.57
% 1.40/1.57 % power_one
% 1.40/1.57 thf(fact_70_power__one,axiom,
% 1.40/1.57 ! [N: nat] :
% 1.40/1.57 ( ( power_power_nat @ one_one_nat @ N )
% 1.40/1.57 = one_one_nat ) ).
% 1.40/1.57
% 1.40/1.57 % power_one
% 1.40/1.57 thf(fact_71_power__one,axiom,
% 1.40/1.57 ! [N: nat] :
% 1.40/1.57 ( ( power_power_real @ one_one_real @ N )
% 1.40/1.57 = one_one_real ) ).
% 1.40/1.57
% 1.40/1.57 % power_one
% 1.40/1.57 thf(fact_72_power__one,axiom,
% 1.40/1.57 ! [N: nat] :
% 1.40/1.57 ( ( power_power_int @ one_one_int @ N )
% 1.40/1.57 = one_one_int ) ).
% 1.40/1.57
% 1.40/1.57 % power_one
% 1.40/1.57 thf(fact_73_power__one,axiom,
% 1.40/1.57 ! [N: nat] :
% 1.40/1.57 ( ( power_power_complex @ one_one_complex @ N )
% 1.40/1.57 = one_one_complex ) ).
% 1.40/1.57
% 1.40/1.57 % power_one
% 1.40/1.57 thf(fact_74_power__one__right,axiom,
% 1.40/1.57 ! [A: nat] :
% 1.40/1.57 ( ( power_power_nat @ A @ one_one_nat )
% 1.40/1.57 = A ) ).
% 1.40/1.57
% 1.40/1.57 % power_one_right
% 1.40/1.57 thf(fact_75_power__one__right,axiom,
% 1.40/1.57 ! [A: real] :
% 1.40/1.57 ( ( power_power_real @ A @ one_one_nat )
% 1.40/1.57 = A ) ).
% 1.40/1.57
% 1.40/1.57 % power_one_right
% 1.40/1.57 thf(fact_76_power__one__right,axiom,
% 1.40/1.57 ! [A: int] :
% 1.40/1.57 ( ( power_power_int @ A @ one_one_nat )
% 1.40/1.57 = A ) ).
% 1.40/1.57
% 1.40/1.57 % power_one_right
% 1.40/1.57 thf(fact_77_power__one__right,axiom,
% 1.40/1.57 ! [A: complex] :
% 1.40/1.57 ( ( power_power_complex @ A @ one_one_nat )
% 1.40/1.57 = A ) ).
% 1.40/1.57
% 1.40/1.57 % power_one_right
% 1.40/1.57 thf(fact_78_nth__repl,axiom,
% 1.40/1.57 ! [M: nat,Xs: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 1.40/1.57 ( ( ord_less_nat @ M @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 1.40/1.57 => ( ( M != N )
% 1.40/1.57 => ( ( nth_VEBT_VEBT @ ( append_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ Xs ) @ ( append_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ nil_VEBT_VEBT ) @ ( drop_VEBT_VEBT @ ( plus_plus_nat @ N @ one_one_nat ) @ Xs ) ) ) @ M )
% 1.40/1.57 = ( nth_VEBT_VEBT @ Xs @ M ) ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_repl
% 1.40/1.57 thf(fact_79_nth__repl,axiom,
% 1.40/1.57 ! [M: nat,Xs: list_o,N: nat,X: $o] :
% 1.40/1.57 ( ( ord_less_nat @ M @ ( size_size_list_o @ Xs ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 1.40/1.57 => ( ( M != N )
% 1.40/1.57 => ( ( nth_o @ ( append_o @ ( take_o @ N @ Xs ) @ ( append_o @ ( cons_o @ X @ nil_o ) @ ( drop_o @ ( plus_plus_nat @ N @ one_one_nat ) @ Xs ) ) ) @ M )
% 1.40/1.57 = ( nth_o @ Xs @ M ) ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_repl
% 1.40/1.57 thf(fact_80_nth__repl,axiom,
% 1.40/1.57 ! [M: nat,Xs: list_nat,N: nat,X: nat] :
% 1.40/1.57 ( ( ord_less_nat @ M @ ( size_size_list_nat @ Xs ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 1.40/1.57 => ( ( M != N )
% 1.40/1.57 => ( ( nth_nat @ ( append_nat @ ( take_nat @ N @ Xs ) @ ( append_nat @ ( cons_nat @ X @ nil_nat ) @ ( drop_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ Xs ) ) ) @ M )
% 1.40/1.57 = ( nth_nat @ Xs @ M ) ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_repl
% 1.40/1.57 thf(fact_81_nth__repl,axiom,
% 1.40/1.57 ! [M: nat,Xs: list_int,N: nat,X: int] :
% 1.40/1.57 ( ( ord_less_nat @ M @ ( size_size_list_int @ Xs ) )
% 1.40/1.57 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 1.40/1.57 => ( ( M != N )
% 1.40/1.57 => ( ( nth_int @ ( append_int @ ( take_int @ N @ Xs ) @ ( append_int @ ( cons_int @ X @ nil_int ) @ ( drop_int @ ( plus_plus_nat @ N @ one_one_nat ) @ Xs ) ) ) @ M )
% 1.40/1.57 = ( nth_int @ Xs @ M ) ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_repl
% 1.40/1.57 thf(fact_82_one__eq__numeral__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( one_one_complex
% 1.40/1.57 = ( numera6690914467698888265omplex @ N ) )
% 1.40/1.57 = ( one = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_eq_numeral_iff
% 1.40/1.57 thf(fact_83_one__eq__numeral__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( one_one_real
% 1.40/1.57 = ( numeral_numeral_real @ N ) )
% 1.40/1.57 = ( one = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_eq_numeral_iff
% 1.40/1.57 thf(fact_84_one__eq__numeral__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( one_one_rat
% 1.40/1.57 = ( numeral_numeral_rat @ N ) )
% 1.40/1.57 = ( one = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_eq_numeral_iff
% 1.40/1.57 thf(fact_85_one__eq__numeral__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( one_one_nat
% 1.40/1.57 = ( numeral_numeral_nat @ N ) )
% 1.40/1.57 = ( one = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_eq_numeral_iff
% 1.40/1.57 thf(fact_86_one__eq__numeral__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( one_one_int
% 1.40/1.57 = ( numeral_numeral_int @ N ) )
% 1.40/1.57 = ( one = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_eq_numeral_iff
% 1.40/1.57 thf(fact_87_numeral__eq__one__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ( numera6690914467698888265omplex @ N )
% 1.40/1.57 = one_one_complex )
% 1.40/1.57 = ( N = one ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_eq_one_iff
% 1.40/1.57 thf(fact_88_numeral__eq__one__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ( numeral_numeral_real @ N )
% 1.40/1.57 = one_one_real )
% 1.40/1.57 = ( N = one ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_eq_one_iff
% 1.40/1.57 thf(fact_89_numeral__eq__one__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ( numeral_numeral_rat @ N )
% 1.40/1.57 = one_one_rat )
% 1.40/1.57 = ( N = one ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_eq_one_iff
% 1.40/1.57 thf(fact_90_numeral__eq__one__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ( numeral_numeral_nat @ N )
% 1.40/1.57 = one_one_nat )
% 1.40/1.57 = ( N = one ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_eq_one_iff
% 1.40/1.57 thf(fact_91_numeral__eq__one__iff,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( ( numeral_numeral_int @ N )
% 1.40/1.57 = one_one_int )
% 1.40/1.57 = ( N = one ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_eq_one_iff
% 1.40/1.57 thf(fact_92_power__inject__exp,axiom,
% 1.40/1.57 ! [A: real,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.57 => ( ( ( power_power_real @ A @ M )
% 1.40/1.57 = ( power_power_real @ A @ N ) )
% 1.40/1.57 = ( M = N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_inject_exp
% 1.40/1.57 thf(fact_93_power__inject__exp,axiom,
% 1.40/1.57 ! [A: rat,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_rat @ one_one_rat @ A )
% 1.40/1.57 => ( ( ( power_power_rat @ A @ M )
% 1.40/1.57 = ( power_power_rat @ A @ N ) )
% 1.40/1.57 = ( M = N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_inject_exp
% 1.40/1.57 thf(fact_94_power__inject__exp,axiom,
% 1.40/1.57 ! [A: nat,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_nat @ one_one_nat @ A )
% 1.40/1.57 => ( ( ( power_power_nat @ A @ M )
% 1.40/1.57 = ( power_power_nat @ A @ N ) )
% 1.40/1.57 = ( M = N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_inject_exp
% 1.40/1.57 thf(fact_95_power__inject__exp,axiom,
% 1.40/1.57 ! [A: int,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_int @ one_one_int @ A )
% 1.40/1.57 => ( ( ( power_power_int @ A @ M )
% 1.40/1.57 = ( power_power_int @ A @ N ) )
% 1.40/1.57 = ( M = N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_inject_exp
% 1.40/1.57 thf(fact_96_max__number__of_I1_J,axiom,
% 1.40/1.57 ! [U: num,V: num] :
% 1.40/1.57 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 1.40/1.57 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 1.40/1.57 = ( numera1916890842035813515d_enat @ V ) ) )
% 1.40/1.57 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 1.40/1.57 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 1.40/1.57 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_number_of(1)
% 1.40/1.57 thf(fact_97_max__number__of_I1_J,axiom,
% 1.40/1.57 ! [U: num,V: num] :
% 1.40/1.57 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 1.40/1.57 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 1.40/1.57 = ( numeral_numeral_real @ V ) ) )
% 1.40/1.57 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 1.40/1.57 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 1.40/1.57 = ( numeral_numeral_real @ U ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_number_of(1)
% 1.40/1.57 thf(fact_98_max__number__of_I1_J,axiom,
% 1.40/1.57 ! [U: num,V: num] :
% 1.40/1.57 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 1.40/1.57 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 1.40/1.57 = ( numeral_numeral_rat @ V ) ) )
% 1.40/1.57 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 1.40/1.57 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 1.40/1.57 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_number_of(1)
% 1.40/1.57 thf(fact_99_max__number__of_I1_J,axiom,
% 1.40/1.57 ! [U: num,V: num] :
% 1.40/1.57 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 1.40/1.57 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 1.40/1.57 = ( numeral_numeral_nat @ V ) ) )
% 1.40/1.57 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 1.40/1.57 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 1.40/1.57 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_number_of(1)
% 1.40/1.57 thf(fact_100_max__number__of_I1_J,axiom,
% 1.40/1.57 ! [U: num,V: num] :
% 1.40/1.57 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 1.40/1.57 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 1.40/1.57 = ( numeral_numeral_int @ V ) ) )
% 1.40/1.57 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 1.40/1.57 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 1.40/1.57 = ( numeral_numeral_int @ U ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_number_of(1)
% 1.40/1.57 thf(fact_101_max__0__1_I5_J,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 1.40/1.57 = ( numera1916890842035813515d_enat @ X ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_0_1(5)
% 1.40/1.57 thf(fact_102_max__0__1_I5_J,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 1.40/1.57 = ( numeral_numeral_real @ X ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_0_1(5)
% 1.40/1.57 thf(fact_103_max__0__1_I5_J,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 1.40/1.57 = ( numeral_numeral_rat @ X ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_0_1(5)
% 1.40/1.57 thf(fact_104_max__0__1_I5_J,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 1.40/1.57 = ( numeral_numeral_nat @ X ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_0_1(5)
% 1.40/1.57 thf(fact_105_max__0__1_I5_J,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 1.40/1.57 = ( numeral_numeral_int @ X ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_0_1(5)
% 1.40/1.57 thf(fact_106_max__0__1_I6_J,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 1.40/1.57 = ( numera1916890842035813515d_enat @ X ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_0_1(6)
% 1.40/1.57 thf(fact_107_max__0__1_I6_J,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 1.40/1.57 = ( numeral_numeral_real @ X ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_0_1(6)
% 1.40/1.57 thf(fact_108_max__0__1_I6_J,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 1.40/1.57 = ( numeral_numeral_rat @ X ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_0_1(6)
% 1.40/1.57 thf(fact_109_max__0__1_I6_J,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 1.40/1.57 = ( numeral_numeral_nat @ X ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_0_1(6)
% 1.40/1.57 thf(fact_110_max__0__1_I6_J,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 1.40/1.57 = ( numeral_numeral_int @ X ) ) ).
% 1.40/1.57
% 1.40/1.57 % max_0_1(6)
% 1.40/1.57 thf(fact_111_add__numeral__left,axiom,
% 1.40/1.57 ! [V: num,W: num,Z: complex] :
% 1.40/1.57 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 1.40/1.57 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 1.40/1.57
% 1.40/1.57 % add_numeral_left
% 1.40/1.57 thf(fact_112_add__numeral__left,axiom,
% 1.40/1.57 ! [V: num,W: num,Z: real] :
% 1.40/1.57 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 1.40/1.57 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 1.40/1.57
% 1.40/1.57 % add_numeral_left
% 1.40/1.57 thf(fact_113_add__numeral__left,axiom,
% 1.40/1.57 ! [V: num,W: num,Z: rat] :
% 1.40/1.57 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 1.40/1.57 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 1.40/1.57
% 1.40/1.57 % add_numeral_left
% 1.40/1.57 thf(fact_114_add__numeral__left,axiom,
% 1.40/1.57 ! [V: num,W: num,Z: nat] :
% 1.40/1.57 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 1.40/1.57 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 1.40/1.57
% 1.40/1.57 % add_numeral_left
% 1.40/1.57 thf(fact_115_add__numeral__left,axiom,
% 1.40/1.57 ! [V: num,W: num,Z: int] :
% 1.40/1.57 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 1.40/1.57 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 1.40/1.57
% 1.40/1.57 % add_numeral_left
% 1.40/1.57 thf(fact_116_numeral__plus__numeral,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 1.40/1.57 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_plus_numeral
% 1.40/1.57 thf(fact_117_numeral__plus__numeral,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 1.40/1.57 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_plus_numeral
% 1.40/1.57 thf(fact_118_numeral__plus__numeral,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 1.40/1.57 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_plus_numeral
% 1.40/1.57 thf(fact_119_numeral__plus__numeral,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 1.40/1.57 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_plus_numeral
% 1.40/1.57 thf(fact_120_numeral__plus__numeral,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.57 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_plus_numeral
% 1.40/1.57 thf(fact_121_numeral__le__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 1.40/1.57 = ( ord_less_eq_num @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_le_iff
% 1.40/1.57 thf(fact_122_numeral__le__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 1.40/1.57 = ( ord_less_eq_num @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_le_iff
% 1.40/1.57 thf(fact_123_numeral__le__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 1.40/1.57 = ( ord_less_eq_num @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_le_iff
% 1.40/1.57 thf(fact_124_numeral__le__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.57 = ( ord_less_eq_num @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_le_iff
% 1.40/1.57 thf(fact_125_mem__Collect__eq,axiom,
% 1.40/1.57 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 1.40/1.57 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 1.40/1.57 = ( P @ A ) ) ).
% 1.40/1.57
% 1.40/1.57 % mem_Collect_eq
% 1.40/1.57 thf(fact_126_mem__Collect__eq,axiom,
% 1.40/1.57 ! [A: complex,P: complex > $o] :
% 1.40/1.57 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 1.40/1.57 = ( P @ A ) ) ).
% 1.40/1.57
% 1.40/1.57 % mem_Collect_eq
% 1.40/1.57 thf(fact_127_mem__Collect__eq,axiom,
% 1.40/1.57 ! [A: real,P: real > $o] :
% 1.40/1.57 ( ( member_real @ A @ ( collect_real @ P ) )
% 1.40/1.57 = ( P @ A ) ) ).
% 1.40/1.57
% 1.40/1.57 % mem_Collect_eq
% 1.40/1.57 thf(fact_128_mem__Collect__eq,axiom,
% 1.40/1.57 ! [A: list_nat,P: list_nat > $o] :
% 1.40/1.57 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 1.40/1.57 = ( P @ A ) ) ).
% 1.40/1.57
% 1.40/1.57 % mem_Collect_eq
% 1.40/1.57 thf(fact_129_mem__Collect__eq,axiom,
% 1.40/1.57 ! [A: nat,P: nat > $o] :
% 1.40/1.57 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 1.40/1.57 = ( P @ A ) ) ).
% 1.40/1.57
% 1.40/1.57 % mem_Collect_eq
% 1.40/1.57 thf(fact_130_mem__Collect__eq,axiom,
% 1.40/1.57 ! [A: int,P: int > $o] :
% 1.40/1.57 ( ( member_int @ A @ ( collect_int @ P ) )
% 1.40/1.57 = ( P @ A ) ) ).
% 1.40/1.57
% 1.40/1.57 % mem_Collect_eq
% 1.40/1.57 thf(fact_131_Collect__mem__eq,axiom,
% 1.40/1.57 ! [A2: set_Pr1261947904930325089at_nat] :
% 1.40/1.57 ( ( collec3392354462482085612at_nat
% 1.40/1.57 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A2 ) )
% 1.40/1.57 = A2 ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_mem_eq
% 1.40/1.57 thf(fact_132_Collect__mem__eq,axiom,
% 1.40/1.57 ! [A2: set_complex] :
% 1.40/1.57 ( ( collect_complex
% 1.40/1.57 @ ^ [X4: complex] : ( member_complex @ X4 @ A2 ) )
% 1.40/1.57 = A2 ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_mem_eq
% 1.40/1.57 thf(fact_133_Collect__mem__eq,axiom,
% 1.40/1.57 ! [A2: set_real] :
% 1.40/1.57 ( ( collect_real
% 1.40/1.57 @ ^ [X4: real] : ( member_real @ X4 @ A2 ) )
% 1.40/1.57 = A2 ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_mem_eq
% 1.40/1.57 thf(fact_134_Collect__mem__eq,axiom,
% 1.40/1.57 ! [A2: set_list_nat] :
% 1.40/1.57 ( ( collect_list_nat
% 1.40/1.57 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A2 ) )
% 1.40/1.57 = A2 ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_mem_eq
% 1.40/1.57 thf(fact_135_Collect__mem__eq,axiom,
% 1.40/1.57 ! [A2: set_nat] :
% 1.40/1.57 ( ( collect_nat
% 1.40/1.57 @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 1.40/1.57 = A2 ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_mem_eq
% 1.40/1.57 thf(fact_136_Collect__mem__eq,axiom,
% 1.40/1.57 ! [A2: set_int] :
% 1.40/1.57 ( ( collect_int
% 1.40/1.57 @ ^ [X4: int] : ( member_int @ X4 @ A2 ) )
% 1.40/1.57 = A2 ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_mem_eq
% 1.40/1.57 thf(fact_137_Collect__cong,axiom,
% 1.40/1.57 ! [P: complex > $o,Q: complex > $o] :
% 1.40/1.57 ( ! [X5: complex] :
% 1.40/1.57 ( ( P @ X5 )
% 1.40/1.57 = ( Q @ X5 ) )
% 1.40/1.57 => ( ( collect_complex @ P )
% 1.40/1.57 = ( collect_complex @ Q ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_cong
% 1.40/1.57 thf(fact_138_Collect__cong,axiom,
% 1.40/1.57 ! [P: real > $o,Q: real > $o] :
% 1.40/1.57 ( ! [X5: real] :
% 1.40/1.57 ( ( P @ X5 )
% 1.40/1.57 = ( Q @ X5 ) )
% 1.40/1.57 => ( ( collect_real @ P )
% 1.40/1.57 = ( collect_real @ Q ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_cong
% 1.40/1.57 thf(fact_139_Collect__cong,axiom,
% 1.40/1.57 ! [P: list_nat > $o,Q: list_nat > $o] :
% 1.40/1.57 ( ! [X5: list_nat] :
% 1.40/1.57 ( ( P @ X5 )
% 1.40/1.57 = ( Q @ X5 ) )
% 1.40/1.57 => ( ( collect_list_nat @ P )
% 1.40/1.57 = ( collect_list_nat @ Q ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_cong
% 1.40/1.57 thf(fact_140_Collect__cong,axiom,
% 1.40/1.57 ! [P: nat > $o,Q: nat > $o] :
% 1.40/1.57 ( ! [X5: nat] :
% 1.40/1.57 ( ( P @ X5 )
% 1.40/1.57 = ( Q @ X5 ) )
% 1.40/1.57 => ( ( collect_nat @ P )
% 1.40/1.57 = ( collect_nat @ Q ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_cong
% 1.40/1.57 thf(fact_141_Collect__cong,axiom,
% 1.40/1.57 ! [P: int > $o,Q: int > $o] :
% 1.40/1.57 ( ! [X5: int] :
% 1.40/1.57 ( ( P @ X5 )
% 1.40/1.57 = ( Q @ X5 ) )
% 1.40/1.57 => ( ( collect_int @ P )
% 1.40/1.57 = ( collect_int @ Q ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % Collect_cong
% 1.40/1.57 thf(fact_142_numeral__less__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 1.40/1.57 = ( ord_less_num @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_less_iff
% 1.40/1.57 thf(fact_143_numeral__less__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 1.40/1.57 = ( ord_less_num @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_less_iff
% 1.40/1.57 thf(fact_144_numeral__less__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 1.40/1.57 = ( ord_less_num @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_less_iff
% 1.40/1.57 thf(fact_145_numeral__less__iff,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.57 = ( ord_less_num @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_less_iff
% 1.40/1.57 thf(fact_146__C1_C,axiom,
% 1.40/1.57 vEBT_invar_vebt @ summary @ m ).
% 1.40/1.57
% 1.40/1.57 % "1"
% 1.40/1.57 thf(fact_147__C4_OIH_C_I1_J,axiom,
% 1.40/1.57 ! [X3: vEBT_VEBT] :
% 1.40/1.57 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 1.40/1.57 => ( ( vEBT_invar_vebt @ X3 @ na )
% 1.40/1.57 & ! [Xa: nat] :
% 1.40/1.57 ( ( ord_less_nat @ Xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 1.40/1.57 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ X3 @ Xa ) @ na ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % "4.IH"(1)
% 1.40/1.57 thf(fact_148_add__One__commute,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( plus_plus_num @ one @ N )
% 1.40/1.57 = ( plus_plus_num @ N @ one ) ) ).
% 1.40/1.57
% 1.40/1.57 % add_One_commute
% 1.40/1.57 thf(fact_149_le__num__One__iff,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( ord_less_eq_num @ X @ one )
% 1.40/1.57 = ( X = one ) ) ).
% 1.40/1.57
% 1.40/1.57 % le_num_One_iff
% 1.40/1.57 thf(fact_150_is__num__normalize_I1_J,axiom,
% 1.40/1.57 ! [A: real,B: real,C: real] :
% 1.40/1.57 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 1.40/1.57 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % is_num_normalize(1)
% 1.40/1.57 thf(fact_151_is__num__normalize_I1_J,axiom,
% 1.40/1.57 ! [A: rat,B: rat,C: rat] :
% 1.40/1.57 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 1.40/1.57 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % is_num_normalize(1)
% 1.40/1.57 thf(fact_152_is__num__normalize_I1_J,axiom,
% 1.40/1.57 ! [A: int,B: int,C: int] :
% 1.40/1.57 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 1.40/1.57 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % is_num_normalize(1)
% 1.40/1.57 thf(fact_153_le__numeral__extra_I4_J,axiom,
% 1.40/1.57 ord_less_eq_real @ one_one_real @ one_one_real ).
% 1.40/1.57
% 1.40/1.57 % le_numeral_extra(4)
% 1.40/1.57 thf(fact_154_le__numeral__extra_I4_J,axiom,
% 1.40/1.57 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 1.40/1.57
% 1.40/1.57 % le_numeral_extra(4)
% 1.40/1.57 thf(fact_155_le__numeral__extra_I4_J,axiom,
% 1.40/1.57 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 1.40/1.57
% 1.40/1.57 % le_numeral_extra(4)
% 1.40/1.57 thf(fact_156_le__numeral__extra_I4_J,axiom,
% 1.40/1.57 ord_less_eq_int @ one_one_int @ one_one_int ).
% 1.40/1.57
% 1.40/1.57 % le_numeral_extra(4)
% 1.40/1.57 thf(fact_157_less__numeral__extra_I4_J,axiom,
% 1.40/1.57 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 1.40/1.57
% 1.40/1.57 % less_numeral_extra(4)
% 1.40/1.57 thf(fact_158_less__numeral__extra_I4_J,axiom,
% 1.40/1.57 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 1.40/1.57
% 1.40/1.57 % less_numeral_extra(4)
% 1.40/1.57 thf(fact_159_less__numeral__extra_I4_J,axiom,
% 1.40/1.57 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 1.40/1.57
% 1.40/1.57 % less_numeral_extra(4)
% 1.40/1.57 thf(fact_160_less__numeral__extra_I4_J,axiom,
% 1.40/1.57 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 1.40/1.57
% 1.40/1.57 % less_numeral_extra(4)
% 1.40/1.57 thf(fact_161_one__le__numeral,axiom,
% 1.40/1.57 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_le_numeral
% 1.40/1.57 thf(fact_162_one__le__numeral,axiom,
% 1.40/1.57 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_le_numeral
% 1.40/1.57 thf(fact_163_one__le__numeral,axiom,
% 1.40/1.57 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_le_numeral
% 1.40/1.57 thf(fact_164_one__le__numeral,axiom,
% 1.40/1.57 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_le_numeral
% 1.40/1.57 thf(fact_165_not__numeral__less__one,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 1.40/1.57
% 1.40/1.57 % not_numeral_less_one
% 1.40/1.57 thf(fact_166_not__numeral__less__one,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 1.40/1.57
% 1.40/1.57 % not_numeral_less_one
% 1.40/1.57 thf(fact_167_not__numeral__less__one,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 1.40/1.57
% 1.40/1.57 % not_numeral_less_one
% 1.40/1.57 thf(fact_168_not__numeral__less__one,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 1.40/1.57
% 1.40/1.57 % not_numeral_less_one
% 1.40/1.57 thf(fact_169_numeral__Bit0,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 1.40/1.57 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_Bit0
% 1.40/1.57 thf(fact_170_numeral__Bit0,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 1.40/1.57 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_Bit0
% 1.40/1.57 thf(fact_171_numeral__Bit0,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 1.40/1.57 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_Bit0
% 1.40/1.57 thf(fact_172_numeral__Bit0,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 1.40/1.57 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_Bit0
% 1.40/1.57 thf(fact_173_numeral__Bit0,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 1.40/1.57 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_Bit0
% 1.40/1.57 thf(fact_174_one__plus__numeral__commute,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 1.40/1.57 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_plus_numeral_commute
% 1.40/1.57 thf(fact_175_one__plus__numeral__commute,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 1.40/1.57 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_plus_numeral_commute
% 1.40/1.57 thf(fact_176_one__plus__numeral__commute,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 1.40/1.57 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_plus_numeral_commute
% 1.40/1.57 thf(fact_177_one__plus__numeral__commute,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 1.40/1.57 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_plus_numeral_commute
% 1.40/1.57 thf(fact_178_one__plus__numeral__commute,axiom,
% 1.40/1.57 ! [X: num] :
% 1.40/1.57 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 1.40/1.57 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_plus_numeral_commute
% 1.40/1.57 thf(fact_179_numeral__One,axiom,
% 1.40/1.57 ( ( numera6690914467698888265omplex @ one )
% 1.40/1.57 = one_one_complex ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_One
% 1.40/1.57 thf(fact_180_numeral__One,axiom,
% 1.40/1.57 ( ( numeral_numeral_real @ one )
% 1.40/1.57 = one_one_real ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_One
% 1.40/1.57 thf(fact_181_numeral__One,axiom,
% 1.40/1.57 ( ( numeral_numeral_rat @ one )
% 1.40/1.57 = one_one_rat ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_One
% 1.40/1.57 thf(fact_182_numeral__One,axiom,
% 1.40/1.57 ( ( numeral_numeral_nat @ one )
% 1.40/1.57 = one_one_nat ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_One
% 1.40/1.57 thf(fact_183_numeral__One,axiom,
% 1.40/1.57 ( ( numeral_numeral_int @ one )
% 1.40/1.57 = one_one_int ) ).
% 1.40/1.57
% 1.40/1.57 % numeral_One
% 1.40/1.57 thf(fact_184_one__le__power,axiom,
% 1.40/1.57 ! [A: real,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_real @ one_one_real @ A )
% 1.40/1.57 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_le_power
% 1.40/1.57 thf(fact_185_one__le__power,axiom,
% 1.40/1.57 ! [A: rat,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 1.40/1.57 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_le_power
% 1.40/1.57 thf(fact_186_one__le__power,axiom,
% 1.40/1.57 ! [A: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 1.40/1.57 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_le_power
% 1.40/1.57 thf(fact_187_one__le__power,axiom,
% 1.40/1.57 ! [A: int,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_int @ one_one_int @ A )
% 1.40/1.57 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % one_le_power
% 1.40/1.57 thf(fact_188_numerals_I1_J,axiom,
% 1.40/1.57 ( ( numeral_numeral_nat @ one )
% 1.40/1.57 = one_one_nat ) ).
% 1.40/1.57
% 1.40/1.57 % numerals(1)
% 1.40/1.57 thf(fact_189_power__strict__increasing,axiom,
% 1.40/1.57 ! [N: nat,N3: nat,A: real] :
% 1.40/1.57 ( ( ord_less_nat @ N @ N3 )
% 1.40/1.57 => ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.57 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N3 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_strict_increasing
% 1.40/1.57 thf(fact_190_power__strict__increasing,axiom,
% 1.40/1.57 ! [N: nat,N3: nat,A: rat] :
% 1.40/1.57 ( ( ord_less_nat @ N @ N3 )
% 1.40/1.57 => ( ( ord_less_rat @ one_one_rat @ A )
% 1.40/1.57 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N3 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_strict_increasing
% 1.40/1.57 thf(fact_191_power__strict__increasing,axiom,
% 1.40/1.57 ! [N: nat,N3: nat,A: nat] :
% 1.40/1.57 ( ( ord_less_nat @ N @ N3 )
% 1.40/1.57 => ( ( ord_less_nat @ one_one_nat @ A )
% 1.40/1.57 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N3 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_strict_increasing
% 1.40/1.57 thf(fact_192_power__strict__increasing,axiom,
% 1.40/1.57 ! [N: nat,N3: nat,A: int] :
% 1.40/1.57 ( ( ord_less_nat @ N @ N3 )
% 1.40/1.57 => ( ( ord_less_int @ one_one_int @ A )
% 1.40/1.57 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N3 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_strict_increasing
% 1.40/1.57 thf(fact_193_power__less__imp__less__exp,axiom,
% 1.40/1.57 ! [A: real,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.57 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 1.40/1.57 => ( ord_less_nat @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_less_imp_less_exp
% 1.40/1.57 thf(fact_194_power__less__imp__less__exp,axiom,
% 1.40/1.57 ! [A: rat,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_rat @ one_one_rat @ A )
% 1.40/1.57 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 1.40/1.57 => ( ord_less_nat @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_less_imp_less_exp
% 1.40/1.57 thf(fact_195_power__less__imp__less__exp,axiom,
% 1.40/1.57 ! [A: nat,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_nat @ one_one_nat @ A )
% 1.40/1.57 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 1.40/1.57 => ( ord_less_nat @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_less_imp_less_exp
% 1.40/1.57 thf(fact_196_power__less__imp__less__exp,axiom,
% 1.40/1.57 ! [A: int,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_int @ one_one_int @ A )
% 1.40/1.57 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 1.40/1.57 => ( ord_less_nat @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_less_imp_less_exp
% 1.40/1.57 thf(fact_197_power__increasing,axiom,
% 1.40/1.57 ! [N: nat,N3: nat,A: real] :
% 1.40/1.57 ( ( ord_less_eq_nat @ N @ N3 )
% 1.40/1.57 => ( ( ord_less_eq_real @ one_one_real @ A )
% 1.40/1.57 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N3 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_increasing
% 1.40/1.57 thf(fact_198_power__increasing,axiom,
% 1.40/1.57 ! [N: nat,N3: nat,A: rat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ N @ N3 )
% 1.40/1.57 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 1.40/1.57 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N3 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_increasing
% 1.40/1.57 thf(fact_199_power__increasing,axiom,
% 1.40/1.57 ! [N: nat,N3: nat,A: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ N @ N3 )
% 1.40/1.57 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 1.40/1.57 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N3 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_increasing
% 1.40/1.57 thf(fact_200_power__increasing,axiom,
% 1.40/1.57 ! [N: nat,N3: nat,A: int] :
% 1.40/1.57 ( ( ord_less_eq_nat @ N @ N3 )
% 1.40/1.57 => ( ( ord_less_eq_int @ one_one_int @ A )
% 1.40/1.57 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N3 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_increasing
% 1.40/1.57 thf(fact_201_power__le__imp__le__exp,axiom,
% 1.40/1.57 ! [A: real,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.57 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 1.40/1.57 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_le_imp_le_exp
% 1.40/1.57 thf(fact_202_power__le__imp__le__exp,axiom,
% 1.40/1.57 ! [A: rat,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_rat @ one_one_rat @ A )
% 1.40/1.57 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 1.40/1.57 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_le_imp_le_exp
% 1.40/1.57 thf(fact_203_power__le__imp__le__exp,axiom,
% 1.40/1.57 ! [A: nat,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_nat @ one_one_nat @ A )
% 1.40/1.57 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 1.40/1.57 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_le_imp_le_exp
% 1.40/1.57 thf(fact_204_power__le__imp__le__exp,axiom,
% 1.40/1.57 ! [A: int,M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_int @ one_one_int @ A )
% 1.40/1.57 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 1.40/1.57 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % power_le_imp_le_exp
% 1.40/1.57 thf(fact_205_one__power2,axiom,
% 1.40/1.57 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.57 = one_one_rat ) ).
% 1.40/1.57
% 1.40/1.57 % one_power2
% 1.40/1.57 thf(fact_206_one__power2,axiom,
% 1.40/1.57 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.57 = one_one_nat ) ).
% 1.40/1.57
% 1.40/1.57 % one_power2
% 1.40/1.57 thf(fact_207_one__power2,axiom,
% 1.40/1.57 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.57 = one_one_real ) ).
% 1.40/1.57
% 1.40/1.57 % one_power2
% 1.40/1.57 thf(fact_208_one__power2,axiom,
% 1.40/1.57 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.57 = one_one_int ) ).
% 1.40/1.57
% 1.40/1.57 % one_power2
% 1.40/1.57 thf(fact_209_one__power2,axiom,
% 1.40/1.57 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.57 = one_one_complex ) ).
% 1.40/1.57
% 1.40/1.57 % one_power2
% 1.40/1.57 thf(fact_210_less__exp,axiom,
% 1.40/1.57 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % less_exp
% 1.40/1.57 thf(fact_211_nat__1__add__1,axiom,
% 1.40/1.57 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 1.40/1.57 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nat_1_add_1
% 1.40/1.57 thf(fact_212_power2__nat__le__imp__le,axiom,
% 1.40/1.57 ! [M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 1.40/1.57 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % power2_nat_le_imp_le
% 1.40/1.57 thf(fact_213_power2__nat__le__eq__le,axiom,
% 1.40/1.57 ! [M: nat,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.57 = ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % power2_nat_le_eq_le
% 1.40/1.57 thf(fact_214_self__le__ge2__pow,axiom,
% 1.40/1.57 ! [K: nat,M: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 1.40/1.57 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % self_le_ge2_pow
% 1.40/1.57 thf(fact_215_ex__power__ivl2,axiom,
% 1.40/1.57 ! [B: nat,K: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 1.40/1.57 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 1.40/1.57 => ? [N4: nat] :
% 1.40/1.57 ( ( ord_less_nat @ ( power_power_nat @ B @ N4 ) @ K )
% 1.40/1.57 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % ex_power_ivl2
% 1.40/1.57 thf(fact_216_ex__power__ivl1,axiom,
% 1.40/1.57 ! [B: nat,K: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 1.40/1.57 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 1.40/1.57 => ? [N4: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N4 ) @ K )
% 1.40/1.57 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % ex_power_ivl1
% 1.40/1.57 thf(fact_217__C11_C,axiom,
% 1.40/1.57 ! [X3: vEBT_VEBT] :
% 1.40/1.57 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( append_VEBT_VEBT @ ( take_VEBT_VEBT @ ( vEBT_VEBT_high @ xa @ na ) @ treeList ) @ ( append_VEBT_VEBT @ ( cons_VEBT_VEBT @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ nil_VEBT_VEBT ) @ ( drop_VEBT_VEBT @ ( plus_plus_nat @ ( vEBT_VEBT_high @ xa @ na ) @ one_one_nat ) @ treeList ) ) ) ) )
% 1.40/1.57 => ( vEBT_invar_vebt @ X3 @ na ) ) ).
% 1.40/1.57
% 1.40/1.57 % "11"
% 1.40/1.57 thf(fact_218_nth__drop,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_VEBT_VEBT,I2: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 1.40/1.57 => ( ( nth_VEBT_VEBT @ ( drop_VEBT_VEBT @ N @ Xs ) @ I2 )
% 1.40/1.57 = ( nth_VEBT_VEBT @ Xs @ ( plus_plus_nat @ N @ I2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_drop
% 1.40/1.57 thf(fact_219_nth__drop,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_o,I2: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ Xs ) )
% 1.40/1.57 => ( ( nth_o @ ( drop_o @ N @ Xs ) @ I2 )
% 1.40/1.57 = ( nth_o @ Xs @ ( plus_plus_nat @ N @ I2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_drop
% 1.40/1.57 thf(fact_220_nth__drop,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_nat,I2: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs ) )
% 1.40/1.57 => ( ( nth_nat @ ( drop_nat @ N @ Xs ) @ I2 )
% 1.40/1.57 = ( nth_nat @ Xs @ ( plus_plus_nat @ N @ I2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_drop
% 1.40/1.57 thf(fact_221_nth__drop,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_int,I2: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Xs ) )
% 1.40/1.57 => ( ( nth_int @ ( drop_int @ N @ Xs ) @ I2 )
% 1.40/1.57 = ( nth_int @ Xs @ ( plus_plus_nat @ N @ I2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_drop
% 1.40/1.57 thf(fact_222_drop__eq__Nil2,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( nil_VEBT_VEBT
% 1.40/1.57 = ( drop_VEBT_VEBT @ N @ Xs ) )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_eq_Nil2
% 1.40/1.57 thf(fact_223_drop__eq__Nil2,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_o] :
% 1.40/1.57 ( ( nil_o
% 1.40/1.57 = ( drop_o @ N @ Xs ) )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_eq_Nil2
% 1.40/1.57 thf(fact_224_drop__eq__Nil2,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_nat] :
% 1.40/1.57 ( ( nil_nat
% 1.40/1.57 = ( drop_nat @ N @ Xs ) )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_eq_Nil2
% 1.40/1.57 thf(fact_225_drop__eq__Nil2,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_int] :
% 1.40/1.57 ( ( nil_int
% 1.40/1.57 = ( drop_int @ N @ Xs ) )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_eq_Nil2
% 1.40/1.57 thf(fact_226_drop__eq__Nil,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( drop_VEBT_VEBT @ N @ Xs )
% 1.40/1.57 = nil_VEBT_VEBT )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_eq_Nil
% 1.40/1.57 thf(fact_227_drop__eq__Nil,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_o] :
% 1.40/1.57 ( ( ( drop_o @ N @ Xs )
% 1.40/1.57 = nil_o )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_eq_Nil
% 1.40/1.57 thf(fact_228_drop__eq__Nil,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_nat] :
% 1.40/1.57 ( ( ( drop_nat @ N @ Xs )
% 1.40/1.57 = nil_nat )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_eq_Nil
% 1.40/1.57 thf(fact_229_drop__eq__Nil,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_int] :
% 1.40/1.57 ( ( ( drop_int @ N @ Xs )
% 1.40/1.57 = nil_int )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_eq_Nil
% 1.40/1.57 thf(fact_230_drop__all,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N )
% 1.40/1.57 => ( ( drop_VEBT_VEBT @ N @ Xs )
% 1.40/1.57 = nil_VEBT_VEBT ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_all
% 1.40/1.57 thf(fact_231_drop__all,axiom,
% 1.40/1.57 ! [Xs: list_o,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N )
% 1.40/1.57 => ( ( drop_o @ N @ Xs )
% 1.40/1.57 = nil_o ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_all
% 1.40/1.57 thf(fact_232_drop__all,axiom,
% 1.40/1.57 ! [Xs: list_nat,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N )
% 1.40/1.57 => ( ( drop_nat @ N @ Xs )
% 1.40/1.57 = nil_nat ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_all
% 1.40/1.57 thf(fact_233_drop__all,axiom,
% 1.40/1.57 ! [Xs: list_int,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N )
% 1.40/1.57 => ( ( drop_int @ N @ Xs )
% 1.40/1.57 = nil_int ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_all
% 1.40/1.57 thf(fact_234_nth__append__length__plus,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,N: nat] :
% 1.40/1.57 ( ( nth_VEBT_VEBT @ ( append_VEBT_VEBT @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) )
% 1.40/1.57 = ( nth_VEBT_VEBT @ Ys @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_append_length_plus
% 1.40/1.57 thf(fact_235_nth__append__length__plus,axiom,
% 1.40/1.57 ! [Xs: list_o,Ys: list_o,N: nat] :
% 1.40/1.57 ( ( nth_o @ ( append_o @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_size_list_o @ Xs ) @ N ) )
% 1.40/1.57 = ( nth_o @ Ys @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_append_length_plus
% 1.40/1.57 thf(fact_236_nth__append__length__plus,axiom,
% 1.40/1.57 ! [Xs: list_nat,Ys: list_nat,N: nat] :
% 1.40/1.57 ( ( nth_nat @ ( append_nat @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_size_list_nat @ Xs ) @ N ) )
% 1.40/1.57 = ( nth_nat @ Ys @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_append_length_plus
% 1.40/1.57 thf(fact_237_nth__append__length__plus,axiom,
% 1.40/1.57 ! [Xs: list_int,Ys: list_int,N: nat] :
% 1.40/1.57 ( ( nth_int @ ( append_int @ Xs @ Ys ) @ ( plus_plus_nat @ ( size_size_list_int @ Xs ) @ N ) )
% 1.40/1.57 = ( nth_int @ Ys @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_append_length_plus
% 1.40/1.57 thf(fact_238_nth__append__length,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.57 ( ( nth_VEBT_VEBT @ ( append_VEBT_VEBT @ Xs @ ( cons_VEBT_VEBT @ X @ Ys ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 1.40/1.57 = X ) ).
% 1.40/1.57
% 1.40/1.57 % nth_append_length
% 1.40/1.57 thf(fact_239_nth__append__length,axiom,
% 1.40/1.57 ! [Xs: list_o,X: $o,Ys: list_o] :
% 1.40/1.57 ( ( nth_o @ ( append_o @ Xs @ ( cons_o @ X @ Ys ) ) @ ( size_size_list_o @ Xs ) )
% 1.40/1.57 = X ) ).
% 1.40/1.57
% 1.40/1.57 % nth_append_length
% 1.40/1.57 thf(fact_240_nth__append__length,axiom,
% 1.40/1.57 ! [Xs: list_nat,X: nat,Ys: list_nat] :
% 1.40/1.57 ( ( nth_nat @ ( append_nat @ Xs @ ( cons_nat @ X @ Ys ) ) @ ( size_size_list_nat @ Xs ) )
% 1.40/1.57 = X ) ).
% 1.40/1.57
% 1.40/1.57 % nth_append_length
% 1.40/1.57 thf(fact_241_nth__append__length,axiom,
% 1.40/1.57 ! [Xs: list_int,X: int,Ys: list_int] :
% 1.40/1.57 ( ( nth_int @ ( append_int @ Xs @ ( cons_int @ X @ Ys ) ) @ ( size_size_list_int @ Xs ) )
% 1.40/1.57 = X ) ).
% 1.40/1.57
% 1.40/1.57 % nth_append_length
% 1.40/1.57 thf(fact_242_append__take__drop__id,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( append_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ Xs ) @ ( drop_VEBT_VEBT @ N @ Xs ) )
% 1.40/1.57 = Xs ) ).
% 1.40/1.57
% 1.40/1.57 % append_take_drop_id
% 1.40/1.57 thf(fact_243_append__take__drop__id,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_int] :
% 1.40/1.57 ( ( append_int @ ( take_int @ N @ Xs ) @ ( drop_int @ N @ Xs ) )
% 1.40/1.57 = Xs ) ).
% 1.40/1.57
% 1.40/1.57 % append_take_drop_id
% 1.40/1.57 thf(fact_244_append__take__drop__id,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_nat] :
% 1.40/1.57 ( ( append_nat @ ( take_nat @ N @ Xs ) @ ( drop_nat @ N @ Xs ) )
% 1.40/1.57 = Xs ) ).
% 1.40/1.57
% 1.40/1.57 % append_take_drop_id
% 1.40/1.57 thf(fact_245_semiring__norm_I76_J,axiom,
% 1.40/1.57 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(76)
% 1.40/1.57 thf(fact_246_semiring__norm_I69_J,axiom,
% 1.40/1.57 ! [M: num] :
% 1.40/1.57 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(69)
% 1.40/1.57 thf(fact_247__C12_C,axiom,
% 1.40/1.57 vEBT_invar_vebt @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ summary ) @ na ).
% 1.40/1.57
% 1.40/1.57 % "12"
% 1.40/1.57 thf(fact_248_nth__take,axiom,
% 1.40/1.57 ! [I2: nat,N: nat,Xs: list_int] :
% 1.40/1.57 ( ( ord_less_nat @ I2 @ N )
% 1.40/1.57 => ( ( nth_int @ ( take_int @ N @ Xs ) @ I2 )
% 1.40/1.57 = ( nth_int @ Xs @ I2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_take
% 1.40/1.57 thf(fact_249_nth__take,axiom,
% 1.40/1.57 ! [I2: nat,N: nat,Xs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ord_less_nat @ I2 @ N )
% 1.40/1.57 => ( ( nth_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ Xs ) @ I2 )
% 1.40/1.57 = ( nth_VEBT_VEBT @ Xs @ I2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_take
% 1.40/1.57 thf(fact_250_nth__take,axiom,
% 1.40/1.57 ! [I2: nat,N: nat,Xs: list_nat] :
% 1.40/1.57 ( ( ord_less_nat @ I2 @ N )
% 1.40/1.57 => ( ( nth_nat @ ( take_nat @ N @ Xs ) @ I2 )
% 1.40/1.57 = ( nth_nat @ Xs @ I2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % nth_take
% 1.40/1.57 thf(fact_251_semiring__norm_I87_J,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ( bit0 @ M )
% 1.40/1.57 = ( bit0 @ N ) )
% 1.40/1.57 = ( M = N ) ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(87)
% 1.40/1.57 thf(fact_252_list_Oinject,axiom,
% 1.40/1.57 ! [X21: vEBT_VEBT,X22: list_VEBT_VEBT,Y21: vEBT_VEBT,Y22: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( cons_VEBT_VEBT @ X21 @ X22 )
% 1.40/1.57 = ( cons_VEBT_VEBT @ Y21 @ Y22 ) )
% 1.40/1.57 = ( ( X21 = Y21 )
% 1.40/1.57 & ( X22 = Y22 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % list.inject
% 1.40/1.57 thf(fact_253_list_Oinject,axiom,
% 1.40/1.57 ! [X21: int,X22: list_int,Y21: int,Y22: list_int] :
% 1.40/1.57 ( ( ( cons_int @ X21 @ X22 )
% 1.40/1.57 = ( cons_int @ Y21 @ Y22 ) )
% 1.40/1.57 = ( ( X21 = Y21 )
% 1.40/1.57 & ( X22 = Y22 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % list.inject
% 1.40/1.57 thf(fact_254_list_Oinject,axiom,
% 1.40/1.57 ! [X21: nat,X22: list_nat,Y21: nat,Y22: list_nat] :
% 1.40/1.57 ( ( ( cons_nat @ X21 @ X22 )
% 1.40/1.57 = ( cons_nat @ Y21 @ Y22 ) )
% 1.40/1.57 = ( ( X21 = Y21 )
% 1.40/1.57 & ( X22 = Y22 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % list.inject
% 1.40/1.57 thf(fact_255_append_Oassoc,axiom,
% 1.40/1.57 ! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,C: list_VEBT_VEBT] :
% 1.40/1.57 ( ( append_VEBT_VEBT @ ( append_VEBT_VEBT @ A @ B ) @ C )
% 1.40/1.57 = ( append_VEBT_VEBT @ A @ ( append_VEBT_VEBT @ B @ C ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append.assoc
% 1.40/1.57 thf(fact_256_append_Oassoc,axiom,
% 1.40/1.57 ! [A: list_int,B: list_int,C: list_int] :
% 1.40/1.57 ( ( append_int @ ( append_int @ A @ B ) @ C )
% 1.40/1.57 = ( append_int @ A @ ( append_int @ B @ C ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append.assoc
% 1.40/1.57 thf(fact_257_append_Oassoc,axiom,
% 1.40/1.57 ! [A: list_nat,B: list_nat,C: list_nat] :
% 1.40/1.57 ( ( append_nat @ ( append_nat @ A @ B ) @ C )
% 1.40/1.57 = ( append_nat @ A @ ( append_nat @ B @ C ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append.assoc
% 1.40/1.57 thf(fact_258_append__assoc,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Zs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( append_VEBT_VEBT @ ( append_VEBT_VEBT @ Xs @ Ys ) @ Zs )
% 1.40/1.57 = ( append_VEBT_VEBT @ Xs @ ( append_VEBT_VEBT @ Ys @ Zs ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_assoc
% 1.40/1.57 thf(fact_259_append__assoc,axiom,
% 1.40/1.57 ! [Xs: list_int,Ys: list_int,Zs: list_int] :
% 1.40/1.57 ( ( append_int @ ( append_int @ Xs @ Ys ) @ Zs )
% 1.40/1.57 = ( append_int @ Xs @ ( append_int @ Ys @ Zs ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_assoc
% 1.40/1.57 thf(fact_260_append__assoc,axiom,
% 1.40/1.57 ! [Xs: list_nat,Ys: list_nat,Zs: list_nat] :
% 1.40/1.57 ( ( append_nat @ ( append_nat @ Xs @ Ys ) @ Zs )
% 1.40/1.57 = ( append_nat @ Xs @ ( append_nat @ Ys @ Zs ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_assoc
% 1.40/1.57 thf(fact_261_append__same__eq,axiom,
% 1.40/1.57 ! [Ys: list_VEBT_VEBT,Xs: list_VEBT_VEBT,Zs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( append_VEBT_VEBT @ Ys @ Xs )
% 1.40/1.57 = ( append_VEBT_VEBT @ Zs @ Xs ) )
% 1.40/1.57 = ( Ys = Zs ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_same_eq
% 1.40/1.57 thf(fact_262_append__same__eq,axiom,
% 1.40/1.57 ! [Ys: list_int,Xs: list_int,Zs: list_int] :
% 1.40/1.57 ( ( ( append_int @ Ys @ Xs )
% 1.40/1.57 = ( append_int @ Zs @ Xs ) )
% 1.40/1.57 = ( Ys = Zs ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_same_eq
% 1.40/1.57 thf(fact_263_append__same__eq,axiom,
% 1.40/1.57 ! [Ys: list_nat,Xs: list_nat,Zs: list_nat] :
% 1.40/1.57 ( ( ( append_nat @ Ys @ Xs )
% 1.40/1.57 = ( append_nat @ Zs @ Xs ) )
% 1.40/1.57 = ( Ys = Zs ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_same_eq
% 1.40/1.57 thf(fact_264_same__append__eq,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Zs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( append_VEBT_VEBT @ Xs @ Ys )
% 1.40/1.57 = ( append_VEBT_VEBT @ Xs @ Zs ) )
% 1.40/1.57 = ( Ys = Zs ) ) ).
% 1.40/1.57
% 1.40/1.57 % same_append_eq
% 1.40/1.57 thf(fact_265_same__append__eq,axiom,
% 1.40/1.57 ! [Xs: list_int,Ys: list_int,Zs: list_int] :
% 1.40/1.57 ( ( ( append_int @ Xs @ Ys )
% 1.40/1.57 = ( append_int @ Xs @ Zs ) )
% 1.40/1.57 = ( Ys = Zs ) ) ).
% 1.40/1.57
% 1.40/1.57 % same_append_eq
% 1.40/1.57 thf(fact_266_same__append__eq,axiom,
% 1.40/1.57 ! [Xs: list_nat,Ys: list_nat,Zs: list_nat] :
% 1.40/1.57 ( ( ( append_nat @ Xs @ Ys )
% 1.40/1.57 = ( append_nat @ Xs @ Zs ) )
% 1.40/1.57 = ( Ys = Zs ) ) ).
% 1.40/1.57
% 1.40/1.57 % same_append_eq
% 1.40/1.57 thf(fact_267__C0_C,axiom,
% 1.40/1.57 ! [X3: vEBT_VEBT] :
% 1.40/1.57 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 1.40/1.57 => ( vEBT_invar_vebt @ X3 @ na ) ) ).
% 1.40/1.57
% 1.40/1.57 % "0"
% 1.40/1.57 thf(fact_268_semiring__norm_I85_J,axiom,
% 1.40/1.57 ! [M: num] :
% 1.40/1.57 ( ( bit0 @ M )
% 1.40/1.57 != one ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(85)
% 1.40/1.57 thf(fact_269_semiring__norm_I83_J,axiom,
% 1.40/1.57 ! [N: num] :
% 1.40/1.57 ( one
% 1.40/1.57 != ( bit0 @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(83)
% 1.40/1.57 thf(fact_270_valid__insert__both__member__options__add,axiom,
% 1.40/1.57 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 1.40/1.57 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.57 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.57 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % valid_insert_both_member_options_add
% 1.40/1.57 thf(fact_271_valid__insert__both__member__options__pres,axiom,
% 1.40/1.57 ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 1.40/1.57 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.57 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.57 => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.57 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 1.40/1.57 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y2 ) @ X ) ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % valid_insert_both_member_options_pres
% 1.40/1.57 thf(fact_272_append_Oright__neutral,axiom,
% 1.40/1.57 ! [A: list_VEBT_VEBT] :
% 1.40/1.57 ( ( append_VEBT_VEBT @ A @ nil_VEBT_VEBT )
% 1.40/1.57 = A ) ).
% 1.40/1.57
% 1.40/1.57 % append.right_neutral
% 1.40/1.57 thf(fact_273_append_Oright__neutral,axiom,
% 1.40/1.57 ! [A: list_int] :
% 1.40/1.57 ( ( append_int @ A @ nil_int )
% 1.40/1.57 = A ) ).
% 1.40/1.57
% 1.40/1.57 % append.right_neutral
% 1.40/1.57 thf(fact_274_append_Oright__neutral,axiom,
% 1.40/1.57 ! [A: list_nat] :
% 1.40/1.57 ( ( append_nat @ A @ nil_nat )
% 1.40/1.57 = A ) ).
% 1.40/1.57
% 1.40/1.57 % append.right_neutral
% 1.40/1.57 thf(fact_275_append__Nil2,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( append_VEBT_VEBT @ Xs @ nil_VEBT_VEBT )
% 1.40/1.57 = Xs ) ).
% 1.40/1.57
% 1.40/1.57 % append_Nil2
% 1.40/1.57 thf(fact_276_append__Nil2,axiom,
% 1.40/1.57 ! [Xs: list_int] :
% 1.40/1.57 ( ( append_int @ Xs @ nil_int )
% 1.40/1.57 = Xs ) ).
% 1.40/1.57
% 1.40/1.57 % append_Nil2
% 1.40/1.57 thf(fact_277_append__Nil2,axiom,
% 1.40/1.57 ! [Xs: list_nat] :
% 1.40/1.57 ( ( append_nat @ Xs @ nil_nat )
% 1.40/1.57 = Xs ) ).
% 1.40/1.57
% 1.40/1.57 % append_Nil2
% 1.40/1.57 thf(fact_278_append__self__conv,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( append_VEBT_VEBT @ Xs @ Ys )
% 1.40/1.57 = Xs )
% 1.40/1.57 = ( Ys = nil_VEBT_VEBT ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_self_conv
% 1.40/1.57 thf(fact_279_append__self__conv,axiom,
% 1.40/1.57 ! [Xs: list_int,Ys: list_int] :
% 1.40/1.57 ( ( ( append_int @ Xs @ Ys )
% 1.40/1.57 = Xs )
% 1.40/1.57 = ( Ys = nil_int ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_self_conv
% 1.40/1.57 thf(fact_280_append__self__conv,axiom,
% 1.40/1.57 ! [Xs: list_nat,Ys: list_nat] :
% 1.40/1.57 ( ( ( append_nat @ Xs @ Ys )
% 1.40/1.57 = Xs )
% 1.40/1.57 = ( Ys = nil_nat ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_self_conv
% 1.40/1.57 thf(fact_281_self__append__conv,axiom,
% 1.40/1.57 ! [Y2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.57 ( ( Y2
% 1.40/1.57 = ( append_VEBT_VEBT @ Y2 @ Ys ) )
% 1.40/1.57 = ( Ys = nil_VEBT_VEBT ) ) ).
% 1.40/1.57
% 1.40/1.57 % self_append_conv
% 1.40/1.57 thf(fact_282_self__append__conv,axiom,
% 1.40/1.57 ! [Y2: list_int,Ys: list_int] :
% 1.40/1.57 ( ( Y2
% 1.40/1.57 = ( append_int @ Y2 @ Ys ) )
% 1.40/1.57 = ( Ys = nil_int ) ) ).
% 1.40/1.57
% 1.40/1.57 % self_append_conv
% 1.40/1.57 thf(fact_283_self__append__conv,axiom,
% 1.40/1.57 ! [Y2: list_nat,Ys: list_nat] :
% 1.40/1.57 ( ( Y2
% 1.40/1.57 = ( append_nat @ Y2 @ Ys ) )
% 1.40/1.57 = ( Ys = nil_nat ) ) ).
% 1.40/1.57
% 1.40/1.57 % self_append_conv
% 1.40/1.57 thf(fact_284_append__self__conv2,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( append_VEBT_VEBT @ Xs @ Ys )
% 1.40/1.57 = Ys )
% 1.40/1.57 = ( Xs = nil_VEBT_VEBT ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_self_conv2
% 1.40/1.57 thf(fact_285_append__self__conv2,axiom,
% 1.40/1.57 ! [Xs: list_int,Ys: list_int] :
% 1.40/1.57 ( ( ( append_int @ Xs @ Ys )
% 1.40/1.57 = Ys )
% 1.40/1.57 = ( Xs = nil_int ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_self_conv2
% 1.40/1.57 thf(fact_286_append__self__conv2,axiom,
% 1.40/1.57 ! [Xs: list_nat,Ys: list_nat] :
% 1.40/1.57 ( ( ( append_nat @ Xs @ Ys )
% 1.40/1.57 = Ys )
% 1.40/1.57 = ( Xs = nil_nat ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_self_conv2
% 1.40/1.57 thf(fact_287_self__append__conv2,axiom,
% 1.40/1.57 ! [Y2: list_VEBT_VEBT,Xs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( Y2
% 1.40/1.57 = ( append_VEBT_VEBT @ Xs @ Y2 ) )
% 1.40/1.57 = ( Xs = nil_VEBT_VEBT ) ) ).
% 1.40/1.57
% 1.40/1.57 % self_append_conv2
% 1.40/1.57 thf(fact_288_self__append__conv2,axiom,
% 1.40/1.57 ! [Y2: list_int,Xs: list_int] :
% 1.40/1.57 ( ( Y2
% 1.40/1.57 = ( append_int @ Xs @ Y2 ) )
% 1.40/1.57 = ( Xs = nil_int ) ) ).
% 1.40/1.57
% 1.40/1.57 % self_append_conv2
% 1.40/1.57 thf(fact_289_self__append__conv2,axiom,
% 1.40/1.57 ! [Y2: list_nat,Xs: list_nat] :
% 1.40/1.57 ( ( Y2
% 1.40/1.57 = ( append_nat @ Xs @ Y2 ) )
% 1.40/1.57 = ( Xs = nil_nat ) ) ).
% 1.40/1.57
% 1.40/1.57 % self_append_conv2
% 1.40/1.57 thf(fact_290_Nil__is__append__conv,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.57 ( ( nil_VEBT_VEBT
% 1.40/1.57 = ( append_VEBT_VEBT @ Xs @ Ys ) )
% 1.40/1.57 = ( ( Xs = nil_VEBT_VEBT )
% 1.40/1.57 & ( Ys = nil_VEBT_VEBT ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % Nil_is_append_conv
% 1.40/1.57 thf(fact_291_Nil__is__append__conv,axiom,
% 1.40/1.57 ! [Xs: list_int,Ys: list_int] :
% 1.40/1.57 ( ( nil_int
% 1.40/1.57 = ( append_int @ Xs @ Ys ) )
% 1.40/1.57 = ( ( Xs = nil_int )
% 1.40/1.57 & ( Ys = nil_int ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % Nil_is_append_conv
% 1.40/1.57 thf(fact_292_Nil__is__append__conv,axiom,
% 1.40/1.57 ! [Xs: list_nat,Ys: list_nat] :
% 1.40/1.57 ( ( nil_nat
% 1.40/1.57 = ( append_nat @ Xs @ Ys ) )
% 1.40/1.57 = ( ( Xs = nil_nat )
% 1.40/1.57 & ( Ys = nil_nat ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % Nil_is_append_conv
% 1.40/1.57 thf(fact_293_append__is__Nil__conv,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( append_VEBT_VEBT @ Xs @ Ys )
% 1.40/1.57 = nil_VEBT_VEBT )
% 1.40/1.57 = ( ( Xs = nil_VEBT_VEBT )
% 1.40/1.57 & ( Ys = nil_VEBT_VEBT ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_is_Nil_conv
% 1.40/1.57 thf(fact_294_append__is__Nil__conv,axiom,
% 1.40/1.57 ! [Xs: list_int,Ys: list_int] :
% 1.40/1.57 ( ( ( append_int @ Xs @ Ys )
% 1.40/1.57 = nil_int )
% 1.40/1.57 = ( ( Xs = nil_int )
% 1.40/1.57 & ( Ys = nil_int ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_is_Nil_conv
% 1.40/1.57 thf(fact_295_append__is__Nil__conv,axiom,
% 1.40/1.57 ! [Xs: list_nat,Ys: list_nat] :
% 1.40/1.57 ( ( ( append_nat @ Xs @ Ys )
% 1.40/1.57 = nil_nat )
% 1.40/1.57 = ( ( Xs = nil_nat )
% 1.40/1.57 & ( Ys = nil_nat ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_is_Nil_conv
% 1.40/1.57 thf(fact_296_append__eq__append__conv,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Us: list_VEBT_VEBT,Vs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.57 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 1.40/1.57 | ( ( size_s6755466524823107622T_VEBT @ Us )
% 1.40/1.57 = ( size_s6755466524823107622T_VEBT @ Vs ) ) )
% 1.40/1.57 => ( ( ( append_VEBT_VEBT @ Xs @ Us )
% 1.40/1.57 = ( append_VEBT_VEBT @ Ys @ Vs ) )
% 1.40/1.57 = ( ( Xs = Ys )
% 1.40/1.57 & ( Us = Vs ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_eq_append_conv
% 1.40/1.57 thf(fact_297_append__eq__append__conv,axiom,
% 1.40/1.57 ! [Xs: list_o,Ys: list_o,Us: list_o,Vs: list_o] :
% 1.40/1.57 ( ( ( ( size_size_list_o @ Xs )
% 1.40/1.57 = ( size_size_list_o @ Ys ) )
% 1.40/1.57 | ( ( size_size_list_o @ Us )
% 1.40/1.57 = ( size_size_list_o @ Vs ) ) )
% 1.40/1.57 => ( ( ( append_o @ Xs @ Us )
% 1.40/1.57 = ( append_o @ Ys @ Vs ) )
% 1.40/1.57 = ( ( Xs = Ys )
% 1.40/1.57 & ( Us = Vs ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_eq_append_conv
% 1.40/1.57 thf(fact_298_append__eq__append__conv,axiom,
% 1.40/1.57 ! [Xs: list_nat,Ys: list_nat,Us: list_nat,Vs: list_nat] :
% 1.40/1.57 ( ( ( ( size_size_list_nat @ Xs )
% 1.40/1.57 = ( size_size_list_nat @ Ys ) )
% 1.40/1.57 | ( ( size_size_list_nat @ Us )
% 1.40/1.57 = ( size_size_list_nat @ Vs ) ) )
% 1.40/1.57 => ( ( ( append_nat @ Xs @ Us )
% 1.40/1.57 = ( append_nat @ Ys @ Vs ) )
% 1.40/1.57 = ( ( Xs = Ys )
% 1.40/1.57 & ( Us = Vs ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_eq_append_conv
% 1.40/1.57 thf(fact_299_append__eq__append__conv,axiom,
% 1.40/1.57 ! [Xs: list_int,Ys: list_int,Us: list_int,Vs: list_int] :
% 1.40/1.57 ( ( ( ( size_size_list_int @ Xs )
% 1.40/1.57 = ( size_size_list_int @ Ys ) )
% 1.40/1.57 | ( ( size_size_list_int @ Us )
% 1.40/1.57 = ( size_size_list_int @ Vs ) ) )
% 1.40/1.57 => ( ( ( append_int @ Xs @ Us )
% 1.40/1.57 = ( append_int @ Ys @ Vs ) )
% 1.40/1.57 = ( ( Xs = Ys )
% 1.40/1.57 & ( Us = Vs ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_eq_append_conv
% 1.40/1.57 thf(fact_300_semiring__norm_I6_J,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 1.40/1.57 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(6)
% 1.40/1.57 thf(fact_301_drop__drop,axiom,
% 1.40/1.57 ! [N: nat,M: nat,Xs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( drop_VEBT_VEBT @ N @ ( drop_VEBT_VEBT @ M @ Xs ) )
% 1.40/1.57 = ( drop_VEBT_VEBT @ ( plus_plus_nat @ N @ M ) @ Xs ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_drop
% 1.40/1.57 thf(fact_302_drop__drop,axiom,
% 1.40/1.57 ! [N: nat,M: nat,Xs: list_nat] :
% 1.40/1.57 ( ( drop_nat @ N @ ( drop_nat @ M @ Xs ) )
% 1.40/1.57 = ( drop_nat @ ( plus_plus_nat @ N @ M ) @ Xs ) ) ).
% 1.40/1.57
% 1.40/1.57 % drop_drop
% 1.40/1.57 thf(fact_303_semiring__norm_I71_J,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 1.40/1.57 = ( ord_less_eq_num @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(71)
% 1.40/1.57 thf(fact_304_semiring__norm_I78_J,axiom,
% 1.40/1.57 ! [M: num,N: num] :
% 1.40/1.57 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 1.40/1.57 = ( ord_less_num @ M @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(78)
% 1.40/1.57 thf(fact_305_semiring__norm_I68_J,axiom,
% 1.40/1.57 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(68)
% 1.40/1.57 thf(fact_306_semiring__norm_I75_J,axiom,
% 1.40/1.57 ! [M: num] :
% 1.40/1.57 ~ ( ord_less_num @ M @ one ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(75)
% 1.40/1.57 thf(fact_307_set__n__deg__not__0,axiom,
% 1.40/1.57 ! [TreeList2: list_VEBT_VEBT,N: nat,M: nat] :
% 1.40/1.57 ( ! [X5: vEBT_VEBT] :
% 1.40/1.57 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.57 => ( vEBT_invar_vebt @ X5 @ N ) )
% 1.40/1.57 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 1.40/1.57 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 1.40/1.57 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % set_n_deg_not_0
% 1.40/1.57 thf(fact_308__C4_OIH_C_I2_J,axiom,
% 1.40/1.57 ! [X: nat] :
% 1.40/1.57 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 1.40/1.57 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ summary @ X ) @ m ) ) ).
% 1.40/1.57
% 1.40/1.57 % "4.IH"(2)
% 1.40/1.57 thf(fact_309_myIHs,axiom,
% 1.40/1.57 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.57 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 1.40/1.57 => ( ( vEBT_invar_vebt @ X @ na )
% 1.40/1.57 => ( ( ord_less_nat @ Xa2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 1.40/1.57 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ X @ Xa2 ) @ na ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % myIHs
% 1.40/1.57 thf(fact_310_append1__eq__conv,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT,Ys: list_VEBT_VEBT,Y2: vEBT_VEBT] :
% 1.40/1.57 ( ( ( append_VEBT_VEBT @ Xs @ ( cons_VEBT_VEBT @ X @ nil_VEBT_VEBT ) )
% 1.40/1.57 = ( append_VEBT_VEBT @ Ys @ ( cons_VEBT_VEBT @ Y2 @ nil_VEBT_VEBT ) ) )
% 1.40/1.57 = ( ( Xs = Ys )
% 1.40/1.57 & ( X = Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append1_eq_conv
% 1.40/1.57 thf(fact_311_append1__eq__conv,axiom,
% 1.40/1.57 ! [Xs: list_int,X: int,Ys: list_int,Y2: int] :
% 1.40/1.57 ( ( ( append_int @ Xs @ ( cons_int @ X @ nil_int ) )
% 1.40/1.57 = ( append_int @ Ys @ ( cons_int @ Y2 @ nil_int ) ) )
% 1.40/1.57 = ( ( Xs = Ys )
% 1.40/1.57 & ( X = Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append1_eq_conv
% 1.40/1.57 thf(fact_312_append1__eq__conv,axiom,
% 1.40/1.57 ! [Xs: list_nat,X: nat,Ys: list_nat,Y2: nat] :
% 1.40/1.57 ( ( ( append_nat @ Xs @ ( cons_nat @ X @ nil_nat ) )
% 1.40/1.57 = ( append_nat @ Ys @ ( cons_nat @ Y2 @ nil_nat ) ) )
% 1.40/1.57 = ( ( Xs = Ys )
% 1.40/1.57 & ( X = Y2 ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append1_eq_conv
% 1.40/1.57 thf(fact_313_length__append,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.57 ( ( size_s6755466524823107622T_VEBT @ ( append_VEBT_VEBT @ Xs @ Ys ) )
% 1.40/1.57 = ( plus_plus_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % length_append
% 1.40/1.57 thf(fact_314_length__append,axiom,
% 1.40/1.57 ! [Xs: list_o,Ys: list_o] :
% 1.40/1.57 ( ( size_size_list_o @ ( append_o @ Xs @ Ys ) )
% 1.40/1.57 = ( plus_plus_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % length_append
% 1.40/1.57 thf(fact_315_length__append,axiom,
% 1.40/1.57 ! [Xs: list_nat,Ys: list_nat] :
% 1.40/1.57 ( ( size_size_list_nat @ ( append_nat @ Xs @ Ys ) )
% 1.40/1.57 = ( plus_plus_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % length_append
% 1.40/1.57 thf(fact_316_length__append,axiom,
% 1.40/1.57 ! [Xs: list_int,Ys: list_int] :
% 1.40/1.57 ( ( size_size_list_int @ ( append_int @ Xs @ Ys ) )
% 1.40/1.57 = ( plus_plus_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % length_append
% 1.40/1.57 thf(fact_317_semiring__norm_I2_J,axiom,
% 1.40/1.57 ( ( plus_plus_num @ one @ one )
% 1.40/1.57 = ( bit0 @ one ) ) ).
% 1.40/1.57
% 1.40/1.57 % semiring_norm(2)
% 1.40/1.57 thf(fact_318_take__all,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N )
% 1.40/1.57 => ( ( take_VEBT_VEBT @ N @ Xs )
% 1.40/1.57 = Xs ) ) ).
% 1.40/1.57
% 1.40/1.57 % take_all
% 1.40/1.57 thf(fact_319_take__all,axiom,
% 1.40/1.57 ! [Xs: list_o,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N )
% 1.40/1.57 => ( ( take_o @ N @ Xs )
% 1.40/1.57 = Xs ) ) ).
% 1.40/1.57
% 1.40/1.57 % take_all
% 1.40/1.57 thf(fact_320_take__all,axiom,
% 1.40/1.57 ! [Xs: list_nat,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N )
% 1.40/1.57 => ( ( take_nat @ N @ Xs )
% 1.40/1.57 = Xs ) ) ).
% 1.40/1.57
% 1.40/1.57 % take_all
% 1.40/1.57 thf(fact_321_take__all,axiom,
% 1.40/1.57 ! [Xs: list_int,N: nat] :
% 1.40/1.57 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N )
% 1.40/1.57 => ( ( take_int @ N @ Xs )
% 1.40/1.57 = Xs ) ) ).
% 1.40/1.57
% 1.40/1.57 % take_all
% 1.40/1.57 thf(fact_322_take__all__iff,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( take_VEBT_VEBT @ N @ Xs )
% 1.40/1.57 = Xs )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % take_all_iff
% 1.40/1.57 thf(fact_323_take__all__iff,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_o] :
% 1.40/1.57 ( ( ( take_o @ N @ Xs )
% 1.40/1.57 = Xs )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % take_all_iff
% 1.40/1.57 thf(fact_324_take__all__iff,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_nat] :
% 1.40/1.57 ( ( ( take_nat @ N @ Xs )
% 1.40/1.57 = Xs )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % take_all_iff
% 1.40/1.57 thf(fact_325_take__all__iff,axiom,
% 1.40/1.57 ! [N: nat,Xs: list_int] :
% 1.40/1.57 ( ( ( take_int @ N @ Xs )
% 1.40/1.57 = Xs )
% 1.40/1.57 = ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ).
% 1.40/1.57
% 1.40/1.57 % take_all_iff
% 1.40/1.57 thf(fact_326_not__Cons__self2,axiom,
% 1.40/1.57 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 1.40/1.57 ( ( cons_VEBT_VEBT @ X @ Xs )
% 1.40/1.57 != Xs ) ).
% 1.40/1.57
% 1.40/1.57 % not_Cons_self2
% 1.40/1.57 thf(fact_327_not__Cons__self2,axiom,
% 1.40/1.57 ! [X: int,Xs: list_int] :
% 1.40/1.57 ( ( cons_int @ X @ Xs )
% 1.40/1.57 != Xs ) ).
% 1.40/1.57
% 1.40/1.57 % not_Cons_self2
% 1.40/1.57 thf(fact_328_not__Cons__self2,axiom,
% 1.40/1.57 ! [X: nat,Xs: list_nat] :
% 1.40/1.57 ( ( cons_nat @ X @ Xs )
% 1.40/1.57 != Xs ) ).
% 1.40/1.57
% 1.40/1.57 % not_Cons_self2
% 1.40/1.57 thf(fact_329_subset__code_I1_J,axiom,
% 1.40/1.57 ! [Xs: list_P6011104703257516679at_nat,B2: set_Pr1261947904930325089at_nat] :
% 1.40/1.57 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ B2 )
% 1.40/1.57 = ( ! [X4: product_prod_nat_nat] :
% 1.40/1.57 ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 1.40/1.57 => ( member8440522571783428010at_nat @ X4 @ B2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % subset_code(1)
% 1.40/1.57 thf(fact_330_subset__code_I1_J,axiom,
% 1.40/1.57 ! [Xs: list_complex,B2: set_complex] :
% 1.40/1.57 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B2 )
% 1.40/1.57 = ( ! [X4: complex] :
% 1.40/1.57 ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 1.40/1.57 => ( member_complex @ X4 @ B2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % subset_code(1)
% 1.40/1.57 thf(fact_331_subset__code_I1_J,axiom,
% 1.40/1.57 ! [Xs: list_real,B2: set_real] :
% 1.40/1.57 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B2 )
% 1.40/1.57 = ( ! [X4: real] :
% 1.40/1.57 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 1.40/1.57 => ( member_real @ X4 @ B2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % subset_code(1)
% 1.40/1.57 thf(fact_332_subset__code_I1_J,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,B2: set_VEBT_VEBT] :
% 1.40/1.57 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B2 )
% 1.40/1.57 = ( ! [X4: vEBT_VEBT] :
% 1.40/1.57 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 1.40/1.57 => ( member_VEBT_VEBT @ X4 @ B2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % subset_code(1)
% 1.40/1.57 thf(fact_333_subset__code_I1_J,axiom,
% 1.40/1.57 ! [Xs: list_nat,B2: set_nat] :
% 1.40/1.57 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B2 )
% 1.40/1.57 = ( ! [X4: nat] :
% 1.40/1.57 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 1.40/1.57 => ( member_nat @ X4 @ B2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % subset_code(1)
% 1.40/1.57 thf(fact_334_subset__code_I1_J,axiom,
% 1.40/1.57 ! [Xs: list_int,B2: set_int] :
% 1.40/1.57 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B2 )
% 1.40/1.57 = ( ! [X4: int] :
% 1.40/1.57 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 1.40/1.57 => ( member_int @ X4 @ B2 ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % subset_code(1)
% 1.40/1.57 thf(fact_335_neq__if__length__neq,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.57 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 1.40/1.57 => ( Xs != Ys ) ) ).
% 1.40/1.57
% 1.40/1.57 % neq_if_length_neq
% 1.40/1.57 thf(fact_336_neq__if__length__neq,axiom,
% 1.40/1.57 ! [Xs: list_o,Ys: list_o] :
% 1.40/1.57 ( ( ( size_size_list_o @ Xs )
% 1.40/1.57 != ( size_size_list_o @ Ys ) )
% 1.40/1.57 => ( Xs != Ys ) ) ).
% 1.40/1.57
% 1.40/1.57 % neq_if_length_neq
% 1.40/1.57 thf(fact_337_neq__if__length__neq,axiom,
% 1.40/1.57 ! [Xs: list_nat,Ys: list_nat] :
% 1.40/1.57 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.57 != ( size_size_list_nat @ Ys ) )
% 1.40/1.57 => ( Xs != Ys ) ) ).
% 1.40/1.57
% 1.40/1.57 % neq_if_length_neq
% 1.40/1.57 thf(fact_338_neq__if__length__neq,axiom,
% 1.40/1.57 ! [Xs: list_int,Ys: list_int] :
% 1.40/1.57 ( ( ( size_size_list_int @ Xs )
% 1.40/1.57 != ( size_size_list_int @ Ys ) )
% 1.40/1.57 => ( Xs != Ys ) ) ).
% 1.40/1.57
% 1.40/1.57 % neq_if_length_neq
% 1.40/1.57 thf(fact_339_Ex__list__of__length,axiom,
% 1.40/1.57 ! [N: nat] :
% 1.40/1.57 ? [Xs2: list_VEBT_VEBT] :
% 1.40/1.57 ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.57 = N ) ).
% 1.40/1.57
% 1.40/1.57 % Ex_list_of_length
% 1.40/1.57 thf(fact_340_Ex__list__of__length,axiom,
% 1.40/1.57 ! [N: nat] :
% 1.40/1.57 ? [Xs2: list_o] :
% 1.40/1.57 ( ( size_size_list_o @ Xs2 )
% 1.40/1.57 = N ) ).
% 1.40/1.57
% 1.40/1.57 % Ex_list_of_length
% 1.40/1.57 thf(fact_341_Ex__list__of__length,axiom,
% 1.40/1.57 ! [N: nat] :
% 1.40/1.57 ? [Xs2: list_nat] :
% 1.40/1.57 ( ( size_size_list_nat @ Xs2 )
% 1.40/1.57 = N ) ).
% 1.40/1.57
% 1.40/1.57 % Ex_list_of_length
% 1.40/1.57 thf(fact_342_Ex__list__of__length,axiom,
% 1.40/1.57 ! [N: nat] :
% 1.40/1.57 ? [Xs2: list_int] :
% 1.40/1.57 ( ( size_size_list_int @ Xs2 )
% 1.40/1.57 = N ) ).
% 1.40/1.57
% 1.40/1.57 % Ex_list_of_length
% 1.40/1.57 thf(fact_343_append__eq__appendI,axiom,
% 1.40/1.57 ! [Xs: list_VEBT_VEBT,Xs1: list_VEBT_VEBT,Zs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Us: list_VEBT_VEBT] :
% 1.40/1.57 ( ( ( append_VEBT_VEBT @ Xs @ Xs1 )
% 1.40/1.57 = Zs )
% 1.40/1.57 => ( ( Ys
% 1.40/1.57 = ( append_VEBT_VEBT @ Xs1 @ Us ) )
% 1.40/1.57 => ( ( append_VEBT_VEBT @ Xs @ Ys )
% 1.40/1.57 = ( append_VEBT_VEBT @ Zs @ Us ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_eq_appendI
% 1.40/1.57 thf(fact_344_append__eq__appendI,axiom,
% 1.40/1.57 ! [Xs: list_int,Xs1: list_int,Zs: list_int,Ys: list_int,Us: list_int] :
% 1.40/1.57 ( ( ( append_int @ Xs @ Xs1 )
% 1.40/1.57 = Zs )
% 1.40/1.57 => ( ( Ys
% 1.40/1.57 = ( append_int @ Xs1 @ Us ) )
% 1.40/1.57 => ( ( append_int @ Xs @ Ys )
% 1.40/1.57 = ( append_int @ Zs @ Us ) ) ) ) ).
% 1.40/1.57
% 1.40/1.57 % append_eq_appendI
% 1.40/1.57 thf(fact_345_append__eq__appendI,axiom,
% 1.40/1.57 ! [Xs: list_nat,Xs1: list_nat,Zs: list_nat,Ys: list_nat,Us: list_nat] :
% 1.40/1.57 ( ( ( append_nat @ Xs @ Xs1 )
% 1.40/1.57 = Zs )
% 1.40/1.57 => ( ( Ys
% 1.40/1.57 = ( append_nat @ Xs1 @ Us ) )
% 1.40/1.57 => ( ( append_nat @ Xs @ Ys )
% 1.40/1.57 = ( append_nat @ Zs @ Us ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % append_eq_appendI
% 1.40/1.58 thf(fact_346_append__eq__append__conv2,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Zs: list_VEBT_VEBT,Ts: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( append_VEBT_VEBT @ Xs @ Ys )
% 1.40/1.58 = ( append_VEBT_VEBT @ Zs @ Ts ) )
% 1.40/1.58 = ( ? [Us2: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( Xs
% 1.40/1.58 = ( append_VEBT_VEBT @ Zs @ Us2 ) )
% 1.40/1.58 & ( ( append_VEBT_VEBT @ Us2 @ Ys )
% 1.40/1.58 = Ts ) )
% 1.40/1.58 | ( ( ( append_VEBT_VEBT @ Xs @ Us2 )
% 1.40/1.58 = Zs )
% 1.40/1.58 & ( Ys
% 1.40/1.58 = ( append_VEBT_VEBT @ Us2 @ Ts ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % append_eq_append_conv2
% 1.40/1.58 thf(fact_347_append__eq__append__conv2,axiom,
% 1.40/1.58 ! [Xs: list_int,Ys: list_int,Zs: list_int,Ts: list_int] :
% 1.40/1.58 ( ( ( append_int @ Xs @ Ys )
% 1.40/1.58 = ( append_int @ Zs @ Ts ) )
% 1.40/1.58 = ( ? [Us2: list_int] :
% 1.40/1.58 ( ( ( Xs
% 1.40/1.58 = ( append_int @ Zs @ Us2 ) )
% 1.40/1.58 & ( ( append_int @ Us2 @ Ys )
% 1.40/1.58 = Ts ) )
% 1.40/1.58 | ( ( ( append_int @ Xs @ Us2 )
% 1.40/1.58 = Zs )
% 1.40/1.58 & ( Ys
% 1.40/1.58 = ( append_int @ Us2 @ Ts ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % append_eq_append_conv2
% 1.40/1.58 thf(fact_348_append__eq__append__conv2,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_nat,Zs: list_nat,Ts: list_nat] :
% 1.40/1.58 ( ( ( append_nat @ Xs @ Ys )
% 1.40/1.58 = ( append_nat @ Zs @ Ts ) )
% 1.40/1.58 = ( ? [Us2: list_nat] :
% 1.40/1.58 ( ( ( Xs
% 1.40/1.58 = ( append_nat @ Zs @ Us2 ) )
% 1.40/1.58 & ( ( append_nat @ Us2 @ Ys )
% 1.40/1.58 = Ts ) )
% 1.40/1.58 | ( ( ( append_nat @ Xs @ Us2 )
% 1.40/1.58 = Zs )
% 1.40/1.58 & ( Ys
% 1.40/1.58 = ( append_nat @ Us2 @ Ts ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % append_eq_append_conv2
% 1.40/1.58 thf(fact_349_take__equalityI,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.58 ( ! [I3: nat] :
% 1.40/1.58 ( ( take_VEBT_VEBT @ I3 @ Xs )
% 1.40/1.58 = ( take_VEBT_VEBT @ I3 @ Ys ) )
% 1.40/1.58 => ( Xs = Ys ) ) ).
% 1.40/1.58
% 1.40/1.58 % take_equalityI
% 1.40/1.58 thf(fact_350_take__equalityI,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_nat] :
% 1.40/1.58 ( ! [I3: nat] :
% 1.40/1.58 ( ( take_nat @ I3 @ Xs )
% 1.40/1.58 = ( take_nat @ I3 @ Ys ) )
% 1.40/1.58 => ( Xs = Ys ) ) ).
% 1.40/1.58
% 1.40/1.58 % take_equalityI
% 1.40/1.58 thf(fact_351_list_Odistinct_I1_J,axiom,
% 1.40/1.58 ! [X21: vEBT_VEBT,X22: list_VEBT_VEBT] :
% 1.40/1.58 ( nil_VEBT_VEBT
% 1.40/1.58 != ( cons_VEBT_VEBT @ X21 @ X22 ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.distinct(1)
% 1.40/1.58 thf(fact_352_list_Odistinct_I1_J,axiom,
% 1.40/1.58 ! [X21: int,X22: list_int] :
% 1.40/1.58 ( nil_int
% 1.40/1.58 != ( cons_int @ X21 @ X22 ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.distinct(1)
% 1.40/1.58 thf(fact_353_list_Odistinct_I1_J,axiom,
% 1.40/1.58 ! [X21: nat,X22: list_nat] :
% 1.40/1.58 ( nil_nat
% 1.40/1.58 != ( cons_nat @ X21 @ X22 ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.distinct(1)
% 1.40/1.58 thf(fact_354_list_OdiscI,axiom,
% 1.40/1.58 ! [List: list_VEBT_VEBT,X21: vEBT_VEBT,X22: list_VEBT_VEBT] :
% 1.40/1.58 ( ( List
% 1.40/1.58 = ( cons_VEBT_VEBT @ X21 @ X22 ) )
% 1.40/1.58 => ( List != nil_VEBT_VEBT ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.discI
% 1.40/1.58 thf(fact_355_list_OdiscI,axiom,
% 1.40/1.58 ! [List: list_int,X21: int,X22: list_int] :
% 1.40/1.58 ( ( List
% 1.40/1.58 = ( cons_int @ X21 @ X22 ) )
% 1.40/1.58 => ( List != nil_int ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.discI
% 1.40/1.58 thf(fact_356_list_OdiscI,axiom,
% 1.40/1.58 ! [List: list_nat,X21: nat,X22: list_nat] :
% 1.40/1.58 ( ( List
% 1.40/1.58 = ( cons_nat @ X21 @ X22 ) )
% 1.40/1.58 => ( List != nil_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.discI
% 1.40/1.58 thf(fact_357_list_Oexhaust,axiom,
% 1.40/1.58 ! [Y2: list_VEBT_VEBT] :
% 1.40/1.58 ( ( Y2 != nil_VEBT_VEBT )
% 1.40/1.58 => ~ ! [X212: vEBT_VEBT,X222: list_VEBT_VEBT] :
% 1.40/1.58 ( Y2
% 1.40/1.58 != ( cons_VEBT_VEBT @ X212 @ X222 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.exhaust
% 1.40/1.58 thf(fact_358_list_Oexhaust,axiom,
% 1.40/1.58 ! [Y2: list_int] :
% 1.40/1.58 ( ( Y2 != nil_int )
% 1.40/1.58 => ~ ! [X212: int,X222: list_int] :
% 1.40/1.58 ( Y2
% 1.40/1.58 != ( cons_int @ X212 @ X222 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.exhaust
% 1.40/1.58 thf(fact_359_list_Oexhaust,axiom,
% 1.40/1.58 ! [Y2: list_nat] :
% 1.40/1.58 ( ( Y2 != nil_nat )
% 1.40/1.58 => ~ ! [X212: nat,X222: list_nat] :
% 1.40/1.58 ( Y2
% 1.40/1.58 != ( cons_nat @ X212 @ X222 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.exhaust
% 1.40/1.58 thf(fact_360_min__list_Ocases,axiom,
% 1.40/1.58 ! [X: list_int] :
% 1.40/1.58 ( ! [X5: int,Xs2: list_int] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_int @ X5 @ Xs2 ) )
% 1.40/1.58 => ( X = nil_int ) ) ).
% 1.40/1.58
% 1.40/1.58 % min_list.cases
% 1.40/1.58 thf(fact_361_min__list_Ocases,axiom,
% 1.40/1.58 ! [X: list_nat] :
% 1.40/1.58 ( ! [X5: nat,Xs2: list_nat] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_nat @ X5 @ Xs2 ) )
% 1.40/1.58 => ( X = nil_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % min_list.cases
% 1.40/1.58 thf(fact_362_transpose_Ocases,axiom,
% 1.40/1.58 ! [X: list_list_VEBT_VEBT] :
% 1.40/1.58 ( ( X != nil_list_VEBT_VEBT )
% 1.40/1.58 => ( ! [Xss: list_list_VEBT_VEBT] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_list_VEBT_VEBT @ nil_VEBT_VEBT @ Xss ) )
% 1.40/1.58 => ~ ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Xss: list_list_VEBT_VEBT] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_list_VEBT_VEBT @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ Xss ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % transpose.cases
% 1.40/1.58 thf(fact_363_transpose_Ocases,axiom,
% 1.40/1.58 ! [X: list_list_int] :
% 1.40/1.58 ( ( X != nil_list_int )
% 1.40/1.58 => ( ! [Xss: list_list_int] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_list_int @ nil_int @ Xss ) )
% 1.40/1.58 => ~ ! [X5: int,Xs2: list_int,Xss: list_list_int] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_list_int @ ( cons_int @ X5 @ Xs2 ) @ Xss ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % transpose.cases
% 1.40/1.58 thf(fact_364_transpose_Ocases,axiom,
% 1.40/1.58 ! [X: list_list_nat] :
% 1.40/1.58 ( ( X != nil_list_nat )
% 1.40/1.58 => ( ! [Xss: list_list_nat] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_list_nat @ nil_nat @ Xss ) )
% 1.40/1.58 => ~ ! [X5: nat,Xs2: list_nat,Xss: list_list_nat] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_list_nat @ ( cons_nat @ X5 @ Xs2 ) @ Xss ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % transpose.cases
% 1.40/1.58 thf(fact_365_remdups__adj_Ocases,axiom,
% 1.40/1.58 ! [X: list_VEBT_VEBT] :
% 1.40/1.58 ( ( X != nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_VEBT_VEBT @ X5 @ nil_VEBT_VEBT ) )
% 1.40/1.58 => ~ ! [X5: vEBT_VEBT,Y3: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_VEBT_VEBT @ X5 @ ( cons_VEBT_VEBT @ Y3 @ Xs2 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % remdups_adj.cases
% 1.40/1.58 thf(fact_366_remdups__adj_Ocases,axiom,
% 1.40/1.58 ! [X: list_int] :
% 1.40/1.58 ( ( X != nil_int )
% 1.40/1.58 => ( ! [X5: int] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_int @ X5 @ nil_int ) )
% 1.40/1.58 => ~ ! [X5: int,Y3: int,Xs2: list_int] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_int @ X5 @ ( cons_int @ Y3 @ Xs2 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % remdups_adj.cases
% 1.40/1.58 thf(fact_367_remdups__adj_Ocases,axiom,
% 1.40/1.58 ! [X: list_nat] :
% 1.40/1.58 ( ( X != nil_nat )
% 1.40/1.58 => ( ! [X5: nat] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_nat @ X5 @ nil_nat ) )
% 1.40/1.58 => ~ ! [X5: nat,Y3: nat,Xs2: list_nat] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( cons_nat @ X5 @ ( cons_nat @ Y3 @ Xs2 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % remdups_adj.cases
% 1.40/1.58 thf(fact_368_neq__Nil__conv,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT] :
% 1.40/1.58 ( ( Xs != nil_VEBT_VEBT )
% 1.40/1.58 = ( ? [Y4: vEBT_VEBT,Ys2: list_VEBT_VEBT] :
% 1.40/1.58 ( Xs
% 1.40/1.58 = ( cons_VEBT_VEBT @ Y4 @ Ys2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % neq_Nil_conv
% 1.40/1.58 thf(fact_369_neq__Nil__conv,axiom,
% 1.40/1.58 ! [Xs: list_int] :
% 1.40/1.58 ( ( Xs != nil_int )
% 1.40/1.58 = ( ? [Y4: int,Ys2: list_int] :
% 1.40/1.58 ( Xs
% 1.40/1.58 = ( cons_int @ Y4 @ Ys2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % neq_Nil_conv
% 1.40/1.58 thf(fact_370_neq__Nil__conv,axiom,
% 1.40/1.58 ! [Xs: list_nat] :
% 1.40/1.58 ( ( Xs != nil_nat )
% 1.40/1.58 = ( ? [Y4: nat,Ys2: list_nat] :
% 1.40/1.58 ( Xs
% 1.40/1.58 = ( cons_nat @ Y4 @ Ys2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % neq_Nil_conv
% 1.40/1.58 thf(fact_371_list__induct2_H,axiom,
% 1.40/1.58 ! [P: list_VEBT_VEBT > list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.58 ( ( P @ nil_VEBT_VEBT @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT] : ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT] : ( P @ nil_VEBT_VEBT @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 1.40/1.58 ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2'
% 1.40/1.58 thf(fact_372_list__induct2_H,axiom,
% 1.40/1.58 ! [P: list_VEBT_VEBT > list_int > $o,Xs: list_VEBT_VEBT,Ys: list_int] :
% 1.40/1.58 ( ( P @ nil_VEBT_VEBT @ nil_int )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT] : ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ nil_int )
% 1.40/1.58 => ( ! [Y3: int,Ys3: list_int] : ( P @ nil_VEBT_VEBT @ ( cons_int @ Y3 @ Ys3 ) )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: int,Ys3: list_int] :
% 1.40/1.58 ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2'
% 1.40/1.58 thf(fact_373_list__induct2_H,axiom,
% 1.40/1.58 ! [P: list_VEBT_VEBT > list_nat > $o,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 1.40/1.58 ( ( P @ nil_VEBT_VEBT @ nil_nat )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT] : ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ nil_nat )
% 1.40/1.58 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_VEBT_VEBT @ ( cons_nat @ Y3 @ Ys3 ) )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: nat,Ys3: list_nat] :
% 1.40/1.58 ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2'
% 1.40/1.58 thf(fact_374_list__induct2_H,axiom,
% 1.40/1.58 ! [P: list_int > list_VEBT_VEBT > $o,Xs: list_int,Ys: list_VEBT_VEBT] :
% 1.40/1.58 ( ( P @ nil_int @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: int,Xs2: list_int] : ( P @ ( cons_int @ X5 @ Xs2 ) @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT] : ( P @ nil_int @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) )
% 1.40/1.58 => ( ! [X5: int,Xs2: list_int,Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 1.40/1.58 ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_int @ X5 @ Xs2 ) @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2'
% 1.40/1.58 thf(fact_375_list__induct2_H,axiom,
% 1.40/1.58 ! [P: list_int > list_int > $o,Xs: list_int,Ys: list_int] :
% 1.40/1.58 ( ( P @ nil_int @ nil_int )
% 1.40/1.58 => ( ! [X5: int,Xs2: list_int] : ( P @ ( cons_int @ X5 @ Xs2 ) @ nil_int )
% 1.40/1.58 => ( ! [Y3: int,Ys3: list_int] : ( P @ nil_int @ ( cons_int @ Y3 @ Ys3 ) )
% 1.40/1.58 => ( ! [X5: int,Xs2: list_int,Y3: int,Ys3: list_int] :
% 1.40/1.58 ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_int @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2'
% 1.40/1.58 thf(fact_376_list__induct2_H,axiom,
% 1.40/1.58 ! [P: list_int > list_nat > $o,Xs: list_int,Ys: list_nat] :
% 1.40/1.58 ( ( P @ nil_int @ nil_nat )
% 1.40/1.58 => ( ! [X5: int,Xs2: list_int] : ( P @ ( cons_int @ X5 @ Xs2 ) @ nil_nat )
% 1.40/1.58 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_int @ ( cons_nat @ Y3 @ Ys3 ) )
% 1.40/1.58 => ( ! [X5: int,Xs2: list_int,Y3: nat,Ys3: list_nat] :
% 1.40/1.58 ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_int @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2'
% 1.40/1.58 thf(fact_377_list__induct2_H,axiom,
% 1.40/1.58 ! [P: list_nat > list_VEBT_VEBT > $o,Xs: list_nat,Ys: list_VEBT_VEBT] :
% 1.40/1.58 ( ( P @ nil_nat @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X5 @ Xs2 ) @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT] : ( P @ nil_nat @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 1.40/1.58 ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2'
% 1.40/1.58 thf(fact_378_list__induct2_H,axiom,
% 1.40/1.58 ! [P: list_nat > list_int > $o,Xs: list_nat,Ys: list_int] :
% 1.40/1.58 ( ( P @ nil_nat @ nil_int )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X5 @ Xs2 ) @ nil_int )
% 1.40/1.58 => ( ! [Y3: int,Ys3: list_int] : ( P @ nil_nat @ ( cons_int @ Y3 @ Ys3 ) )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: int,Ys3: list_int] :
% 1.40/1.58 ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2'
% 1.40/1.58 thf(fact_379_list__induct2_H,axiom,
% 1.40/1.58 ! [P: list_nat > list_nat > $o,Xs: list_nat,Ys: list_nat] :
% 1.40/1.58 ( ( P @ nil_nat @ nil_nat )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X5 @ Xs2 ) @ nil_nat )
% 1.40/1.58 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y3 @ Ys3 ) )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 1.40/1.58 ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2'
% 1.40/1.58 thf(fact_380_list__nonempty__induct,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,P: list_VEBT_VEBT > $o] :
% 1.40/1.58 ( ( Xs != nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT] : ( P @ ( cons_VEBT_VEBT @ X5 @ nil_VEBT_VEBT ) )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 1.40/1.58 ( ( Xs2 != nil_VEBT_VEBT )
% 1.40/1.58 => ( ( P @ Xs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) ) ) )
% 1.40/1.58 => ( P @ Xs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_nonempty_induct
% 1.40/1.58 thf(fact_381_list__nonempty__induct,axiom,
% 1.40/1.58 ! [Xs: list_int,P: list_int > $o] :
% 1.40/1.58 ( ( Xs != nil_int )
% 1.40/1.58 => ( ! [X5: int] : ( P @ ( cons_int @ X5 @ nil_int ) )
% 1.40/1.58 => ( ! [X5: int,Xs2: list_int] :
% 1.40/1.58 ( ( Xs2 != nil_int )
% 1.40/1.58 => ( ( P @ Xs2 )
% 1.40/1.58 => ( P @ ( cons_int @ X5 @ Xs2 ) ) ) )
% 1.40/1.58 => ( P @ Xs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_nonempty_induct
% 1.40/1.58 thf(fact_382_list__nonempty__induct,axiom,
% 1.40/1.58 ! [Xs: list_nat,P: list_nat > $o] :
% 1.40/1.58 ( ( Xs != nil_nat )
% 1.40/1.58 => ( ! [X5: nat] : ( P @ ( cons_nat @ X5 @ nil_nat ) )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat] :
% 1.40/1.58 ( ( Xs2 != nil_nat )
% 1.40/1.58 => ( ( P @ Xs2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) ) ) )
% 1.40/1.58 => ( P @ Xs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_nonempty_induct
% 1.40/1.58 thf(fact_383_list_Oset__intros_I2_J,axiom,
% 1.40/1.58 ! [Y2: product_prod_nat_nat,X22: list_P6011104703257516679at_nat,X21: product_prod_nat_nat] :
% 1.40/1.58 ( ( member8440522571783428010at_nat @ Y2 @ ( set_Pr5648618587558075414at_nat @ X22 ) )
% 1.40/1.58 => ( member8440522571783428010at_nat @ Y2 @ ( set_Pr5648618587558075414at_nat @ ( cons_P6512896166579812791at_nat @ X21 @ X22 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(2)
% 1.40/1.58 thf(fact_384_list_Oset__intros_I2_J,axiom,
% 1.40/1.58 ! [Y2: complex,X22: list_complex,X21: complex] :
% 1.40/1.58 ( ( member_complex @ Y2 @ ( set_complex2 @ X22 ) )
% 1.40/1.58 => ( member_complex @ Y2 @ ( set_complex2 @ ( cons_complex @ X21 @ X22 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(2)
% 1.40/1.58 thf(fact_385_list_Oset__intros_I2_J,axiom,
% 1.40/1.58 ! [Y2: real,X22: list_real,X21: real] :
% 1.40/1.58 ( ( member_real @ Y2 @ ( set_real2 @ X22 ) )
% 1.40/1.58 => ( member_real @ Y2 @ ( set_real2 @ ( cons_real @ X21 @ X22 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(2)
% 1.40/1.58 thf(fact_386_list_Oset__intros_I2_J,axiom,
% 1.40/1.58 ! [Y2: vEBT_VEBT,X22: list_VEBT_VEBT,X21: vEBT_VEBT] :
% 1.40/1.58 ( ( member_VEBT_VEBT @ Y2 @ ( set_VEBT_VEBT2 @ X22 ) )
% 1.40/1.58 => ( member_VEBT_VEBT @ Y2 @ ( set_VEBT_VEBT2 @ ( cons_VEBT_VEBT @ X21 @ X22 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(2)
% 1.40/1.58 thf(fact_387_list_Oset__intros_I2_J,axiom,
% 1.40/1.58 ! [Y2: int,X22: list_int,X21: int] :
% 1.40/1.58 ( ( member_int @ Y2 @ ( set_int2 @ X22 ) )
% 1.40/1.58 => ( member_int @ Y2 @ ( set_int2 @ ( cons_int @ X21 @ X22 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(2)
% 1.40/1.58 thf(fact_388_list_Oset__intros_I2_J,axiom,
% 1.40/1.58 ! [Y2: nat,X22: list_nat,X21: nat] :
% 1.40/1.58 ( ( member_nat @ Y2 @ ( set_nat2 @ X22 ) )
% 1.40/1.58 => ( member_nat @ Y2 @ ( set_nat2 @ ( cons_nat @ X21 @ X22 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(2)
% 1.40/1.58 thf(fact_389_list_Oset__intros_I1_J,axiom,
% 1.40/1.58 ! [X21: product_prod_nat_nat,X22: list_P6011104703257516679at_nat] : ( member8440522571783428010at_nat @ X21 @ ( set_Pr5648618587558075414at_nat @ ( cons_P6512896166579812791at_nat @ X21 @ X22 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(1)
% 1.40/1.58 thf(fact_390_list_Oset__intros_I1_J,axiom,
% 1.40/1.58 ! [X21: complex,X22: list_complex] : ( member_complex @ X21 @ ( set_complex2 @ ( cons_complex @ X21 @ X22 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(1)
% 1.40/1.58 thf(fact_391_list_Oset__intros_I1_J,axiom,
% 1.40/1.58 ! [X21: real,X22: list_real] : ( member_real @ X21 @ ( set_real2 @ ( cons_real @ X21 @ X22 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(1)
% 1.40/1.58 thf(fact_392_list_Oset__intros_I1_J,axiom,
% 1.40/1.58 ! [X21: vEBT_VEBT,X22: list_VEBT_VEBT] : ( member_VEBT_VEBT @ X21 @ ( set_VEBT_VEBT2 @ ( cons_VEBT_VEBT @ X21 @ X22 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(1)
% 1.40/1.58 thf(fact_393_list_Oset__intros_I1_J,axiom,
% 1.40/1.58 ! [X21: int,X22: list_int] : ( member_int @ X21 @ ( set_int2 @ ( cons_int @ X21 @ X22 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(1)
% 1.40/1.58 thf(fact_394_list_Oset__intros_I1_J,axiom,
% 1.40/1.58 ! [X21: nat,X22: list_nat] : ( member_nat @ X21 @ ( set_nat2 @ ( cons_nat @ X21 @ X22 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_intros(1)
% 1.40/1.58 thf(fact_395_list_Oset__cases,axiom,
% 1.40/1.58 ! [E: product_prod_nat_nat,A: list_P6011104703257516679at_nat] :
% 1.40/1.58 ( ( member8440522571783428010at_nat @ E @ ( set_Pr5648618587558075414at_nat @ A ) )
% 1.40/1.58 => ( ! [Z2: list_P6011104703257516679at_nat] :
% 1.40/1.58 ( A
% 1.40/1.58 != ( cons_P6512896166579812791at_nat @ E @ Z2 ) )
% 1.40/1.58 => ~ ! [Z1: product_prod_nat_nat,Z2: list_P6011104703257516679at_nat] :
% 1.40/1.58 ( ( A
% 1.40/1.58 = ( cons_P6512896166579812791at_nat @ Z1 @ Z2 ) )
% 1.40/1.58 => ~ ( member8440522571783428010at_nat @ E @ ( set_Pr5648618587558075414at_nat @ Z2 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_cases
% 1.40/1.58 thf(fact_396_list_Oset__cases,axiom,
% 1.40/1.58 ! [E: complex,A: list_complex] :
% 1.40/1.58 ( ( member_complex @ E @ ( set_complex2 @ A ) )
% 1.40/1.58 => ( ! [Z2: list_complex] :
% 1.40/1.58 ( A
% 1.40/1.58 != ( cons_complex @ E @ Z2 ) )
% 1.40/1.58 => ~ ! [Z1: complex,Z2: list_complex] :
% 1.40/1.58 ( ( A
% 1.40/1.58 = ( cons_complex @ Z1 @ Z2 ) )
% 1.40/1.58 => ~ ( member_complex @ E @ ( set_complex2 @ Z2 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_cases
% 1.40/1.58 thf(fact_397_list_Oset__cases,axiom,
% 1.40/1.58 ! [E: real,A: list_real] :
% 1.40/1.58 ( ( member_real @ E @ ( set_real2 @ A ) )
% 1.40/1.58 => ( ! [Z2: list_real] :
% 1.40/1.58 ( A
% 1.40/1.58 != ( cons_real @ E @ Z2 ) )
% 1.40/1.58 => ~ ! [Z1: real,Z2: list_real] :
% 1.40/1.58 ( ( A
% 1.40/1.58 = ( cons_real @ Z1 @ Z2 ) )
% 1.40/1.58 => ~ ( member_real @ E @ ( set_real2 @ Z2 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_cases
% 1.40/1.58 thf(fact_398_list_Oset__cases,axiom,
% 1.40/1.58 ! [E: vEBT_VEBT,A: list_VEBT_VEBT] :
% 1.40/1.58 ( ( member_VEBT_VEBT @ E @ ( set_VEBT_VEBT2 @ A ) )
% 1.40/1.58 => ( ! [Z2: list_VEBT_VEBT] :
% 1.40/1.58 ( A
% 1.40/1.58 != ( cons_VEBT_VEBT @ E @ Z2 ) )
% 1.40/1.58 => ~ ! [Z1: vEBT_VEBT,Z2: list_VEBT_VEBT] :
% 1.40/1.58 ( ( A
% 1.40/1.58 = ( cons_VEBT_VEBT @ Z1 @ Z2 ) )
% 1.40/1.58 => ~ ( member_VEBT_VEBT @ E @ ( set_VEBT_VEBT2 @ Z2 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_cases
% 1.40/1.58 thf(fact_399_list_Oset__cases,axiom,
% 1.40/1.58 ! [E: int,A: list_int] :
% 1.40/1.58 ( ( member_int @ E @ ( set_int2 @ A ) )
% 1.40/1.58 => ( ! [Z2: list_int] :
% 1.40/1.58 ( A
% 1.40/1.58 != ( cons_int @ E @ Z2 ) )
% 1.40/1.58 => ~ ! [Z1: int,Z2: list_int] :
% 1.40/1.58 ( ( A
% 1.40/1.58 = ( cons_int @ Z1 @ Z2 ) )
% 1.40/1.58 => ~ ( member_int @ E @ ( set_int2 @ Z2 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_cases
% 1.40/1.58 thf(fact_400_list_Oset__cases,axiom,
% 1.40/1.58 ! [E: nat,A: list_nat] :
% 1.40/1.58 ( ( member_nat @ E @ ( set_nat2 @ A ) )
% 1.40/1.58 => ( ! [Z2: list_nat] :
% 1.40/1.58 ( A
% 1.40/1.58 != ( cons_nat @ E @ Z2 ) )
% 1.40/1.58 => ~ ! [Z1: nat,Z2: list_nat] :
% 1.40/1.58 ( ( A
% 1.40/1.58 = ( cons_nat @ Z1 @ Z2 ) )
% 1.40/1.58 => ~ ( member_nat @ E @ ( set_nat2 @ Z2 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list.set_cases
% 1.40/1.58 thf(fact_401_set__ConsD,axiom,
% 1.40/1.58 ! [Y2: product_prod_nat_nat,X: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 1.40/1.58 ( ( member8440522571783428010at_nat @ Y2 @ ( set_Pr5648618587558075414at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs ) ) )
% 1.40/1.58 => ( ( Y2 = X )
% 1.40/1.58 | ( member8440522571783428010at_nat @ Y2 @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_ConsD
% 1.40/1.58 thf(fact_402_set__ConsD,axiom,
% 1.40/1.58 ! [Y2: complex,X: complex,Xs: list_complex] :
% 1.40/1.58 ( ( member_complex @ Y2 @ ( set_complex2 @ ( cons_complex @ X @ Xs ) ) )
% 1.40/1.58 => ( ( Y2 = X )
% 1.40/1.58 | ( member_complex @ Y2 @ ( set_complex2 @ Xs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_ConsD
% 1.40/1.58 thf(fact_403_set__ConsD,axiom,
% 1.40/1.58 ! [Y2: real,X: real,Xs: list_real] :
% 1.40/1.58 ( ( member_real @ Y2 @ ( set_real2 @ ( cons_real @ X @ Xs ) ) )
% 1.40/1.58 => ( ( Y2 = X )
% 1.40/1.58 | ( member_real @ Y2 @ ( set_real2 @ Xs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_ConsD
% 1.40/1.58 thf(fact_404_set__ConsD,axiom,
% 1.40/1.58 ! [Y2: vEBT_VEBT,X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 1.40/1.58 ( ( member_VEBT_VEBT @ Y2 @ ( set_VEBT_VEBT2 @ ( cons_VEBT_VEBT @ X @ Xs ) ) )
% 1.40/1.58 => ( ( Y2 = X )
% 1.40/1.58 | ( member_VEBT_VEBT @ Y2 @ ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_ConsD
% 1.40/1.58 thf(fact_405_set__ConsD,axiom,
% 1.40/1.58 ! [Y2: int,X: int,Xs: list_int] :
% 1.40/1.58 ( ( member_int @ Y2 @ ( set_int2 @ ( cons_int @ X @ Xs ) ) )
% 1.40/1.58 => ( ( Y2 = X )
% 1.40/1.58 | ( member_int @ Y2 @ ( set_int2 @ Xs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_ConsD
% 1.40/1.58 thf(fact_406_set__ConsD,axiom,
% 1.40/1.58 ! [Y2: nat,X: nat,Xs: list_nat] :
% 1.40/1.58 ( ( member_nat @ Y2 @ ( set_nat2 @ ( cons_nat @ X @ Xs ) ) )
% 1.40/1.58 => ( ( Y2 = X )
% 1.40/1.58 | ( member_nat @ Y2 @ ( set_nat2 @ Xs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_ConsD
% 1.40/1.58 thf(fact_407_set__subset__Cons,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( set_VEBT_VEBT2 @ ( cons_VEBT_VEBT @ X @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_subset_Cons
% 1.40/1.58 thf(fact_408_set__subset__Cons,axiom,
% 1.40/1.58 ! [Xs: list_nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ ( set_nat2 @ ( cons_nat @ X @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_subset_Cons
% 1.40/1.58 thf(fact_409_set__subset__Cons,axiom,
% 1.40/1.58 ! [Xs: list_int,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ ( set_int2 @ ( cons_int @ X @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_subset_Cons
% 1.40/1.58 thf(fact_410_length__induct,axiom,
% 1.40/1.58 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 1.40/1.58 ( ! [Xs2: list_VEBT_VEBT] :
% 1.40/1.58 ( ! [Ys4: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys4 ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 1.40/1.58 => ( P @ Ys4 ) )
% 1.40/1.58 => ( P @ Xs2 ) )
% 1.40/1.58 => ( P @ Xs ) ) ).
% 1.40/1.58
% 1.40/1.58 % length_induct
% 1.40/1.58 thf(fact_411_length__induct,axiom,
% 1.40/1.58 ! [P: list_o > $o,Xs: list_o] :
% 1.40/1.58 ( ! [Xs2: list_o] :
% 1.40/1.58 ( ! [Ys4: list_o] :
% 1.40/1.58 ( ( ord_less_nat @ ( size_size_list_o @ Ys4 ) @ ( size_size_list_o @ Xs2 ) )
% 1.40/1.58 => ( P @ Ys4 ) )
% 1.40/1.58 => ( P @ Xs2 ) )
% 1.40/1.58 => ( P @ Xs ) ) ).
% 1.40/1.58
% 1.40/1.58 % length_induct
% 1.40/1.58 thf(fact_412_length__induct,axiom,
% 1.40/1.58 ! [P: list_nat > $o,Xs: list_nat] :
% 1.40/1.58 ( ! [Xs2: list_nat] :
% 1.40/1.58 ( ! [Ys4: list_nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( size_size_list_nat @ Ys4 ) @ ( size_size_list_nat @ Xs2 ) )
% 1.40/1.58 => ( P @ Ys4 ) )
% 1.40/1.58 => ( P @ Xs2 ) )
% 1.40/1.58 => ( P @ Xs ) ) ).
% 1.40/1.58
% 1.40/1.58 % length_induct
% 1.40/1.58 thf(fact_413_length__induct,axiom,
% 1.40/1.58 ! [P: list_int > $o,Xs: list_int] :
% 1.40/1.58 ( ! [Xs2: list_int] :
% 1.40/1.58 ( ! [Ys4: list_int] :
% 1.40/1.58 ( ( ord_less_nat @ ( size_size_list_int @ Ys4 ) @ ( size_size_list_int @ Xs2 ) )
% 1.40/1.58 => ( P @ Ys4 ) )
% 1.40/1.58 => ( P @ Xs2 ) )
% 1.40/1.58 => ( P @ Xs ) ) ).
% 1.40/1.58
% 1.40/1.58 % length_induct
% 1.40/1.58 thf(fact_414_append__Cons,axiom,
% 1.40/1.58 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.58 ( ( append_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ Ys )
% 1.40/1.58 = ( cons_VEBT_VEBT @ X @ ( append_VEBT_VEBT @ Xs @ Ys ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % append_Cons
% 1.40/1.58 thf(fact_415_append__Cons,axiom,
% 1.40/1.58 ! [X: int,Xs: list_int,Ys: list_int] :
% 1.40/1.58 ( ( append_int @ ( cons_int @ X @ Xs ) @ Ys )
% 1.40/1.58 = ( cons_int @ X @ ( append_int @ Xs @ Ys ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % append_Cons
% 1.40/1.58 thf(fact_416_append__Cons,axiom,
% 1.40/1.58 ! [X: nat,Xs: list_nat,Ys: list_nat] :
% 1.40/1.58 ( ( append_nat @ ( cons_nat @ X @ Xs ) @ Ys )
% 1.40/1.58 = ( cons_nat @ X @ ( append_nat @ Xs @ Ys ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % append_Cons
% 1.40/1.58 thf(fact_417_Cons__eq__appendI,axiom,
% 1.40/1.58 ! [X: vEBT_VEBT,Xs1: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Xs: list_VEBT_VEBT,Zs: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( cons_VEBT_VEBT @ X @ Xs1 )
% 1.40/1.58 = Ys )
% 1.40/1.58 => ( ( Xs
% 1.40/1.58 = ( append_VEBT_VEBT @ Xs1 @ Zs ) )
% 1.40/1.58 => ( ( cons_VEBT_VEBT @ X @ Xs )
% 1.40/1.58 = ( append_VEBT_VEBT @ Ys @ Zs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Cons_eq_appendI
% 1.40/1.58 thf(fact_418_Cons__eq__appendI,axiom,
% 1.40/1.58 ! [X: int,Xs1: list_int,Ys: list_int,Xs: list_int,Zs: list_int] :
% 1.40/1.58 ( ( ( cons_int @ X @ Xs1 )
% 1.40/1.58 = Ys )
% 1.40/1.58 => ( ( Xs
% 1.40/1.58 = ( append_int @ Xs1 @ Zs ) )
% 1.40/1.58 => ( ( cons_int @ X @ Xs )
% 1.40/1.58 = ( append_int @ Ys @ Zs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Cons_eq_appendI
% 1.40/1.58 thf(fact_419_Cons__eq__appendI,axiom,
% 1.40/1.58 ! [X: nat,Xs1: list_nat,Ys: list_nat,Xs: list_nat,Zs: list_nat] :
% 1.40/1.58 ( ( ( cons_nat @ X @ Xs1 )
% 1.40/1.58 = Ys )
% 1.40/1.58 => ( ( Xs
% 1.40/1.58 = ( append_nat @ Xs1 @ Zs ) )
% 1.40/1.58 => ( ( cons_nat @ X @ Xs )
% 1.40/1.58 = ( append_nat @ Ys @ Zs ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Cons_eq_appendI
% 1.40/1.58 thf(fact_420_append__Nil,axiom,
% 1.40/1.58 ! [Ys: list_VEBT_VEBT] :
% 1.40/1.58 ( ( append_VEBT_VEBT @ nil_VEBT_VEBT @ Ys )
% 1.40/1.58 = Ys ) ).
% 1.40/1.58
% 1.40/1.58 % append_Nil
% 1.40/1.58 thf(fact_421_append__Nil,axiom,
% 1.40/1.58 ! [Ys: list_int] :
% 1.40/1.58 ( ( append_int @ nil_int @ Ys )
% 1.40/1.58 = Ys ) ).
% 1.40/1.58
% 1.40/1.58 % append_Nil
% 1.40/1.58 thf(fact_422_append__Nil,axiom,
% 1.40/1.58 ! [Ys: list_nat] :
% 1.40/1.58 ( ( append_nat @ nil_nat @ Ys )
% 1.40/1.58 = Ys ) ).
% 1.40/1.58
% 1.40/1.58 % append_Nil
% 1.40/1.58 thf(fact_423_append_Oleft__neutral,axiom,
% 1.40/1.58 ! [A: list_VEBT_VEBT] :
% 1.40/1.58 ( ( append_VEBT_VEBT @ nil_VEBT_VEBT @ A )
% 1.40/1.58 = A ) ).
% 1.40/1.58
% 1.40/1.58 % append.left_neutral
% 1.40/1.58 thf(fact_424_append_Oleft__neutral,axiom,
% 1.40/1.58 ! [A: list_int] :
% 1.40/1.58 ( ( append_int @ nil_int @ A )
% 1.40/1.58 = A ) ).
% 1.40/1.58
% 1.40/1.58 % append.left_neutral
% 1.40/1.58 thf(fact_425_append_Oleft__neutral,axiom,
% 1.40/1.58 ! [A: list_nat] :
% 1.40/1.58 ( ( append_nat @ nil_nat @ A )
% 1.40/1.58 = A ) ).
% 1.40/1.58
% 1.40/1.58 % append.left_neutral
% 1.40/1.58 thf(fact_426_eq__Nil__appendI,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 1.40/1.58 ( ( Xs = Ys )
% 1.40/1.58 => ( Xs
% 1.40/1.58 = ( append_VEBT_VEBT @ nil_VEBT_VEBT @ Ys ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % eq_Nil_appendI
% 1.40/1.58 thf(fact_427_eq__Nil__appendI,axiom,
% 1.40/1.58 ! [Xs: list_int,Ys: list_int] :
% 1.40/1.58 ( ( Xs = Ys )
% 1.40/1.58 => ( Xs
% 1.40/1.58 = ( append_int @ nil_int @ Ys ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % eq_Nil_appendI
% 1.40/1.58 thf(fact_428_eq__Nil__appendI,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_nat] :
% 1.40/1.58 ( ( Xs = Ys )
% 1.40/1.58 => ( Xs
% 1.40/1.58 = ( append_nat @ nil_nat @ Ys ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % eq_Nil_appendI
% 1.40/1.58 thf(fact_429_take__Nil,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( take_VEBT_VEBT @ N @ nil_VEBT_VEBT )
% 1.40/1.58 = nil_VEBT_VEBT ) ).
% 1.40/1.58
% 1.40/1.58 % take_Nil
% 1.40/1.58 thf(fact_430_take__Nil,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( take_int @ N @ nil_int )
% 1.40/1.58 = nil_int ) ).
% 1.40/1.58
% 1.40/1.58 % take_Nil
% 1.40/1.58 thf(fact_431_take__Nil,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( take_nat @ N @ nil_nat )
% 1.40/1.58 = nil_nat ) ).
% 1.40/1.58
% 1.40/1.58 % take_Nil
% 1.40/1.58 thf(fact_432_in__set__takeD,axiom,
% 1.40/1.58 ! [X: product_prod_nat_nat,N: nat,Xs: list_P6011104703257516679at_nat] :
% 1.40/1.58 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( take_P2173866234530122223at_nat @ N @ Xs ) ) )
% 1.40/1.58 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_takeD
% 1.40/1.58 thf(fact_433_in__set__takeD,axiom,
% 1.40/1.58 ! [X: complex,N: nat,Xs: list_complex] :
% 1.40/1.58 ( ( member_complex @ X @ ( set_complex2 @ ( take_complex @ N @ Xs ) ) )
% 1.40/1.58 => ( member_complex @ X @ ( set_complex2 @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_takeD
% 1.40/1.58 thf(fact_434_in__set__takeD,axiom,
% 1.40/1.58 ! [X: real,N: nat,Xs: list_real] :
% 1.40/1.58 ( ( member_real @ X @ ( set_real2 @ ( take_real @ N @ Xs ) ) )
% 1.40/1.58 => ( member_real @ X @ ( set_real2 @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_takeD
% 1.40/1.58 thf(fact_435_in__set__takeD,axiom,
% 1.40/1.58 ! [X: vEBT_VEBT,N: nat,Xs: list_VEBT_VEBT] :
% 1.40/1.58 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( take_VEBT_VEBT @ N @ Xs ) ) )
% 1.40/1.58 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_takeD
% 1.40/1.58 thf(fact_436_in__set__takeD,axiom,
% 1.40/1.58 ! [X: int,N: nat,Xs: list_int] :
% 1.40/1.58 ( ( member_int @ X @ ( set_int2 @ ( take_int @ N @ Xs ) ) )
% 1.40/1.58 => ( member_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_takeD
% 1.40/1.58 thf(fact_437_in__set__takeD,axiom,
% 1.40/1.58 ! [X: nat,N: nat,Xs: list_nat] :
% 1.40/1.58 ( ( member_nat @ X @ ( set_nat2 @ ( take_nat @ N @ Xs ) ) )
% 1.40/1.58 => ( member_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_takeD
% 1.40/1.58 thf(fact_438_set__take__subset,axiom,
% 1.40/1.58 ! [N: nat,Xs: list_VEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( take_VEBT_VEBT @ N @ Xs ) ) @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_take_subset
% 1.40/1.58 thf(fact_439_set__take__subset,axiom,
% 1.40/1.58 ! [N: nat,Xs: list_nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( take_nat @ N @ Xs ) ) @ ( set_nat2 @ Xs ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_take_subset
% 1.40/1.58 thf(fact_440_set__take__subset,axiom,
% 1.40/1.58 ! [N: nat,Xs: list_int] : ( ord_less_eq_set_int @ ( set_int2 @ ( take_int @ N @ Xs ) ) @ ( set_int2 @ Xs ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_take_subset
% 1.40/1.58 thf(fact_441_drop__Nil,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( drop_VEBT_VEBT @ N @ nil_VEBT_VEBT )
% 1.40/1.58 = nil_VEBT_VEBT ) ).
% 1.40/1.58
% 1.40/1.58 % drop_Nil
% 1.40/1.58 thf(fact_442_drop__Nil,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( drop_int @ N @ nil_int )
% 1.40/1.58 = nil_int ) ).
% 1.40/1.58
% 1.40/1.58 % drop_Nil
% 1.40/1.58 thf(fact_443_drop__Nil,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( drop_nat @ N @ nil_nat )
% 1.40/1.58 = nil_nat ) ).
% 1.40/1.58
% 1.40/1.58 % drop_Nil
% 1.40/1.58 thf(fact_444_in__set__dropD,axiom,
% 1.40/1.58 ! [X: product_prod_nat_nat,N: nat,Xs: list_P6011104703257516679at_nat] :
% 1.40/1.58 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ ( drop_P8868858903918902087at_nat @ N @ Xs ) ) )
% 1.40/1.58 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_dropD
% 1.40/1.58 thf(fact_445_in__set__dropD,axiom,
% 1.40/1.58 ! [X: complex,N: nat,Xs: list_complex] :
% 1.40/1.58 ( ( member_complex @ X @ ( set_complex2 @ ( drop_complex @ N @ Xs ) ) )
% 1.40/1.58 => ( member_complex @ X @ ( set_complex2 @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_dropD
% 1.40/1.58 thf(fact_446_in__set__dropD,axiom,
% 1.40/1.58 ! [X: real,N: nat,Xs: list_real] :
% 1.40/1.58 ( ( member_real @ X @ ( set_real2 @ ( drop_real @ N @ Xs ) ) )
% 1.40/1.58 => ( member_real @ X @ ( set_real2 @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_dropD
% 1.40/1.58 thf(fact_447_in__set__dropD,axiom,
% 1.40/1.58 ! [X: vEBT_VEBT,N: nat,Xs: list_VEBT_VEBT] :
% 1.40/1.58 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( drop_VEBT_VEBT @ N @ Xs ) ) )
% 1.40/1.58 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_dropD
% 1.40/1.58 thf(fact_448_in__set__dropD,axiom,
% 1.40/1.58 ! [X: int,N: nat,Xs: list_int] :
% 1.40/1.58 ( ( member_int @ X @ ( set_int2 @ ( drop_int @ N @ Xs ) ) )
% 1.40/1.58 => ( member_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_dropD
% 1.40/1.58 thf(fact_449_in__set__dropD,axiom,
% 1.40/1.58 ! [X: nat,N: nat,Xs: list_nat] :
% 1.40/1.58 ( ( member_nat @ X @ ( set_nat2 @ ( drop_nat @ N @ Xs ) ) )
% 1.40/1.58 => ( member_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % in_set_dropD
% 1.40/1.58 thf(fact_450_set__drop__subset,axiom,
% 1.40/1.58 ! [N: nat,Xs: list_VEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( drop_VEBT_VEBT @ N @ Xs ) ) @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_drop_subset
% 1.40/1.58 thf(fact_451_set__drop__subset,axiom,
% 1.40/1.58 ! [N: nat,Xs: list_nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( drop_nat @ N @ Xs ) ) @ ( set_nat2 @ Xs ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_drop_subset
% 1.40/1.58 thf(fact_452_set__drop__subset,axiom,
% 1.40/1.58 ! [N: nat,Xs: list_int] : ( ord_less_eq_set_int @ ( set_int2 @ ( drop_int @ N @ Xs ) ) @ ( set_int2 @ Xs ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_drop_subset
% 1.40/1.58 thf(fact_453_list__induct2,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,P: list_VEBT_VEBT > list_VEBT_VEBT > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2
% 1.40/1.58 thf(fact_454_list__induct2,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_o,P: list_VEBT_VEBT > list_o > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_size_list_o @ Ys ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_o )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: $o,Ys3: list_o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_size_list_o @ Ys3 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_o @ Y3 @ Ys3 ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2
% 1.40/1.58 thf(fact_455_list__induct2,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_nat,P: list_VEBT_VEBT > list_nat > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_size_list_nat @ Ys ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_nat )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: nat,Ys3: list_nat] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_size_list_nat @ Ys3 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2
% 1.40/1.58 thf(fact_456_list__induct2,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_int,P: list_VEBT_VEBT > list_int > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_size_list_int @ Ys ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_int )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: int,Ys3: list_int] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_size_list_int @ Ys3 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2
% 1.40/1.58 thf(fact_457_list__induct2,axiom,
% 1.40/1.58 ! [Xs: list_o,Ys: list_VEBT_VEBT,P: list_o > list_VEBT_VEBT > $o] :
% 1.40/1.58 ( ( ( size_size_list_o @ Xs )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 1.40/1.58 => ( ( P @ nil_o @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: $o,Xs2: list_o,Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( size_size_list_o @ Xs2 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_o @ X5 @ Xs2 ) @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2
% 1.40/1.58 thf(fact_458_list__induct2,axiom,
% 1.40/1.58 ! [Xs: list_o,Ys: list_o,P: list_o > list_o > $o] :
% 1.40/1.58 ( ( ( size_size_list_o @ Xs )
% 1.40/1.58 = ( size_size_list_o @ Ys ) )
% 1.40/1.58 => ( ( P @ nil_o @ nil_o )
% 1.40/1.58 => ( ! [X5: $o,Xs2: list_o,Y3: $o,Ys3: list_o] :
% 1.40/1.58 ( ( ( size_size_list_o @ Xs2 )
% 1.40/1.58 = ( size_size_list_o @ Ys3 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_o @ X5 @ Xs2 ) @ ( cons_o @ Y3 @ Ys3 ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2
% 1.40/1.58 thf(fact_459_list__induct2,axiom,
% 1.40/1.58 ! [Xs: list_o,Ys: list_nat,P: list_o > list_nat > $o] :
% 1.40/1.58 ( ( ( size_size_list_o @ Xs )
% 1.40/1.58 = ( size_size_list_nat @ Ys ) )
% 1.40/1.58 => ( ( P @ nil_o @ nil_nat )
% 1.40/1.58 => ( ! [X5: $o,Xs2: list_o,Y3: nat,Ys3: list_nat] :
% 1.40/1.58 ( ( ( size_size_list_o @ Xs2 )
% 1.40/1.58 = ( size_size_list_nat @ Ys3 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_o @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2
% 1.40/1.58 thf(fact_460_list__induct2,axiom,
% 1.40/1.58 ! [Xs: list_o,Ys: list_int,P: list_o > list_int > $o] :
% 1.40/1.58 ( ( ( size_size_list_o @ Xs )
% 1.40/1.58 = ( size_size_list_int @ Ys ) )
% 1.40/1.58 => ( ( P @ nil_o @ nil_int )
% 1.40/1.58 => ( ! [X5: $o,Xs2: list_o,Y3: int,Ys3: list_int] :
% 1.40/1.58 ( ( ( size_size_list_o @ Xs2 )
% 1.40/1.58 = ( size_size_list_int @ Ys3 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_o @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2
% 1.40/1.58 thf(fact_461_list__induct2,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_VEBT_VEBT,P: list_nat > list_VEBT_VEBT > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2
% 1.40/1.58 thf(fact_462_list__induct2,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_o,P: list_nat > list_o > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_o @ Ys ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_o )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: $o,Ys3: list_o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_o @ Ys3 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_o @ Y3 @ Ys3 ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct2
% 1.40/1.58 thf(fact_463_list__induct3,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Zs: list_VEBT_VEBT,P: list_VEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Ys )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_VEBT_VEBT @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT,Z3: vEBT_VEBT,Zs2: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) @ ( cons_VEBT_VEBT @ Z3 @ Zs2 ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct3
% 1.40/1.58 thf(fact_464_list__induct3,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Zs: list_o,P: list_VEBT_VEBT > list_VEBT_VEBT > list_o > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Ys )
% 1.40/1.58 = ( size_size_list_o @ Zs ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_VEBT_VEBT @ nil_o )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT,Z3: $o,Zs2: list_o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 1.40/1.58 = ( size_size_list_o @ Zs2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) @ ( cons_o @ Z3 @ Zs2 ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct3
% 1.40/1.58 thf(fact_465_list__induct3,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Zs: list_nat,P: list_VEBT_VEBT > list_VEBT_VEBT > list_nat > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Ys )
% 1.40/1.58 = ( size_size_list_nat @ Zs ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_VEBT_VEBT @ nil_nat )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT,Z3: nat,Zs2: list_nat] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 1.40/1.58 = ( size_size_list_nat @ Zs2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) @ ( cons_nat @ Z3 @ Zs2 ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct3
% 1.40/1.58 thf(fact_466_list__induct3,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Zs: list_int,P: list_VEBT_VEBT > list_VEBT_VEBT > list_int > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Ys )
% 1.40/1.58 = ( size_size_list_int @ Zs ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_VEBT_VEBT @ nil_int )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: vEBT_VEBT,Ys3: list_VEBT_VEBT,Z3: int,Zs2: list_int] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 1.40/1.58 = ( size_size_list_int @ Zs2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_VEBT_VEBT @ Y3 @ Ys3 ) @ ( cons_int @ Z3 @ Zs2 ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct3
% 1.40/1.58 thf(fact_467_list__induct3,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_o,Zs: list_VEBT_VEBT,P: list_VEBT_VEBT > list_o > list_VEBT_VEBT > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_size_list_o @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Ys )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_o @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: $o,Ys3: list_o,Z3: vEBT_VEBT,Zs2: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_size_list_o @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Ys3 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_o @ Y3 @ Ys3 ) @ ( cons_VEBT_VEBT @ Z3 @ Zs2 ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct3
% 1.40/1.58 thf(fact_468_list__induct3,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_o,Zs: list_o,P: list_VEBT_VEBT > list_o > list_o > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_size_list_o @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Ys )
% 1.40/1.58 = ( size_size_list_o @ Zs ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_o @ nil_o )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: $o,Ys3: list_o,Z3: $o,Zs2: list_o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_size_list_o @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Ys3 )
% 1.40/1.58 = ( size_size_list_o @ Zs2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_o @ Y3 @ Ys3 ) @ ( cons_o @ Z3 @ Zs2 ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct3
% 1.40/1.58 thf(fact_469_list__induct3,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_o,Zs: list_nat,P: list_VEBT_VEBT > list_o > list_nat > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_size_list_o @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Ys )
% 1.40/1.58 = ( size_size_list_nat @ Zs ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_o @ nil_nat )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: $o,Ys3: list_o,Z3: nat,Zs2: list_nat] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_size_list_o @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Ys3 )
% 1.40/1.58 = ( size_size_list_nat @ Zs2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_o @ Y3 @ Ys3 ) @ ( cons_nat @ Z3 @ Zs2 ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct3
% 1.40/1.58 thf(fact_470_list__induct3,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_o,Zs: list_int,P: list_VEBT_VEBT > list_o > list_int > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_size_list_o @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Ys )
% 1.40/1.58 = ( size_size_list_int @ Zs ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_o @ nil_int )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: $o,Ys3: list_o,Z3: int,Zs2: list_int] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_size_list_o @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Ys3 )
% 1.40/1.58 = ( size_size_list_int @ Zs2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_o @ Y3 @ Ys3 ) @ ( cons_int @ Z3 @ Zs2 ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct3
% 1.40/1.58 thf(fact_471_list__induct3,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_nat,Zs: list_VEBT_VEBT,P: list_VEBT_VEBT > list_nat > list_VEBT_VEBT > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_size_list_nat @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_nat @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: nat,Ys3: list_nat,Z3: vEBT_VEBT,Zs2: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_size_list_nat @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys3 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) @ ( cons_VEBT_VEBT @ Z3 @ Zs2 ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct3
% 1.40/1.58 thf(fact_472_list__induct3,axiom,
% 1.40/1.58 ! [Xs: list_VEBT_VEBT,Ys: list_nat,Zs: list_o,P: list_VEBT_VEBT > list_nat > list_o > $o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 1.40/1.58 = ( size_size_list_nat @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys )
% 1.40/1.58 = ( size_size_list_o @ Zs ) )
% 1.40/1.58 => ( ( P @ nil_VEBT_VEBT @ nil_nat @ nil_o )
% 1.40/1.58 => ( ! [X5: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y3: nat,Ys3: list_nat,Z3: $o,Zs2: list_o] :
% 1.40/1.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 1.40/1.58 = ( size_size_list_nat @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys3 )
% 1.40/1.58 = ( size_size_list_o @ Zs2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 )
% 1.40/1.58 => ( P @ ( cons_VEBT_VEBT @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) @ ( cons_o @ Z3 @ Zs2 ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct3
% 1.40/1.58 thf(fact_473_list__induct4,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_nat,Zs: list_int,Ws: list_VEBT_VEBT,P: list_nat > list_nat > list_int > list_VEBT_VEBT > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_nat @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys )
% 1.40/1.58 = ( size_size_list_int @ Zs ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Zs )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ws ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_nat @ nil_int @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat,Z3: int,Zs2: list_int,W2: vEBT_VEBT,Ws2: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_nat @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys3 )
% 1.40/1.58 = ( size_size_list_int @ Zs2 ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Zs2 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ws2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 @ Ws2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) @ ( cons_int @ Z3 @ Zs2 ) @ ( cons_VEBT_VEBT @ W2 @ Ws2 ) ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct4
% 1.40/1.58 thf(fact_474_list__induct4,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_nat,Zs: list_int,Ws: list_o,P: list_nat > list_nat > list_int > list_o > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_nat @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys )
% 1.40/1.58 = ( size_size_list_int @ Zs ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Zs )
% 1.40/1.58 = ( size_size_list_o @ Ws ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_nat @ nil_int @ nil_o )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat,Z3: int,Zs2: list_int,W2: $o,Ws2: list_o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_nat @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys3 )
% 1.40/1.58 = ( size_size_list_int @ Zs2 ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Zs2 )
% 1.40/1.58 = ( size_size_list_o @ Ws2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 @ Ws2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) @ ( cons_int @ Z3 @ Zs2 ) @ ( cons_o @ W2 @ Ws2 ) ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct4
% 1.40/1.58 thf(fact_475_list__induct4,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_nat,Zs: list_int,Ws: list_nat,P: list_nat > list_nat > list_int > list_nat > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_nat @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys )
% 1.40/1.58 = ( size_size_list_int @ Zs ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Zs )
% 1.40/1.58 = ( size_size_list_nat @ Ws ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_nat @ nil_int @ nil_nat )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat,Z3: int,Zs2: list_int,W2: nat,Ws2: list_nat] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_nat @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys3 )
% 1.40/1.58 = ( size_size_list_int @ Zs2 ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Zs2 )
% 1.40/1.58 = ( size_size_list_nat @ Ws2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 @ Ws2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) @ ( cons_int @ Z3 @ Zs2 ) @ ( cons_nat @ W2 @ Ws2 ) ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct4
% 1.40/1.58 thf(fact_476_list__induct4,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_nat,Zs: list_int,Ws: list_int,P: list_nat > list_nat > list_int > list_int > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_nat @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys )
% 1.40/1.58 = ( size_size_list_int @ Zs ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Zs )
% 1.40/1.58 = ( size_size_list_int @ Ws ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_nat @ nil_int @ nil_int )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat,Z3: int,Zs2: list_int,W2: int,Ws2: list_int] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_nat @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_nat @ Ys3 )
% 1.40/1.58 = ( size_size_list_int @ Zs2 ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Zs2 )
% 1.40/1.58 = ( size_size_list_int @ Ws2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 @ Ws2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) @ ( cons_int @ Z3 @ Zs2 ) @ ( cons_int @ W2 @ Ws2 ) ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct4
% 1.40/1.58 thf(fact_477_list__induct4,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_int,Zs: list_VEBT_VEBT,Ws: list_VEBT_VEBT,P: list_nat > list_int > list_VEBT_VEBT > list_VEBT_VEBT > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_int @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Zs )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ws ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_int @ nil_VEBT_VEBT @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: int,Ys3: list_int,Z3: vEBT_VEBT,Zs2: list_VEBT_VEBT,W2: vEBT_VEBT,Ws2: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_int @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys3 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs2 ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Zs2 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ws2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 @ Ws2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_VEBT_VEBT @ Z3 @ Zs2 ) @ ( cons_VEBT_VEBT @ W2 @ Ws2 ) ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct4
% 1.40/1.58 thf(fact_478_list__induct4,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_int,Zs: list_VEBT_VEBT,Ws: list_o,P: list_nat > list_int > list_VEBT_VEBT > list_o > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_int @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Zs )
% 1.40/1.58 = ( size_size_list_o @ Ws ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_int @ nil_VEBT_VEBT @ nil_o )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: int,Ys3: list_int,Z3: vEBT_VEBT,Zs2: list_VEBT_VEBT,W2: $o,Ws2: list_o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_int @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys3 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs2 ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Zs2 )
% 1.40/1.58 = ( size_size_list_o @ Ws2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 @ Ws2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_VEBT_VEBT @ Z3 @ Zs2 ) @ ( cons_o @ W2 @ Ws2 ) ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct4
% 1.40/1.58 thf(fact_479_list__induct4,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_int,Zs: list_VEBT_VEBT,Ws: list_nat,P: list_nat > list_int > list_VEBT_VEBT > list_nat > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_int @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Zs )
% 1.40/1.58 = ( size_size_list_nat @ Ws ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_int @ nil_VEBT_VEBT @ nil_nat )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: int,Ys3: list_int,Z3: vEBT_VEBT,Zs2: list_VEBT_VEBT,W2: nat,Ws2: list_nat] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_int @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys3 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs2 ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Zs2 )
% 1.40/1.58 = ( size_size_list_nat @ Ws2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 @ Ws2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_VEBT_VEBT @ Z3 @ Zs2 ) @ ( cons_nat @ W2 @ Ws2 ) ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct4
% 1.40/1.58 thf(fact_480_list__induct4,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_int,Zs: list_VEBT_VEBT,Ws: list_int,P: list_nat > list_int > list_VEBT_VEBT > list_int > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_int @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Zs )
% 1.40/1.58 = ( size_size_list_int @ Ws ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_int @ nil_VEBT_VEBT @ nil_int )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: int,Ys3: list_int,Z3: vEBT_VEBT,Zs2: list_VEBT_VEBT,W2: int,Ws2: list_int] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_int @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys3 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Zs2 ) )
% 1.40/1.58 => ( ( ( size_s6755466524823107622T_VEBT @ Zs2 )
% 1.40/1.58 = ( size_size_list_int @ Ws2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 @ Ws2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_VEBT_VEBT @ Z3 @ Zs2 ) @ ( cons_int @ W2 @ Ws2 ) ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct4
% 1.40/1.58 thf(fact_481_list__induct4,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_int,Zs: list_o,Ws: list_VEBT_VEBT,P: list_nat > list_int > list_o > list_VEBT_VEBT > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_int @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys )
% 1.40/1.58 = ( size_size_list_o @ Zs ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Zs )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ws ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_int @ nil_o @ nil_VEBT_VEBT )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: int,Ys3: list_int,Z3: $o,Zs2: list_o,W2: vEBT_VEBT,Ws2: list_VEBT_VEBT] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_int @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys3 )
% 1.40/1.58 = ( size_size_list_o @ Zs2 ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Zs2 )
% 1.40/1.58 = ( size_s6755466524823107622T_VEBT @ Ws2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 @ Ws2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_o @ Z3 @ Zs2 ) @ ( cons_VEBT_VEBT @ W2 @ Ws2 ) ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct4
% 1.40/1.58 thf(fact_482_list__induct4,axiom,
% 1.40/1.58 ! [Xs: list_nat,Ys: list_int,Zs: list_o,Ws: list_o,P: list_nat > list_int > list_o > list_o > $o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs )
% 1.40/1.58 = ( size_size_list_int @ Ys ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys )
% 1.40/1.58 = ( size_size_list_o @ Zs ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Zs )
% 1.40/1.58 = ( size_size_list_o @ Ws ) )
% 1.40/1.58 => ( ( P @ nil_nat @ nil_int @ nil_o @ nil_o )
% 1.40/1.58 => ( ! [X5: nat,Xs2: list_nat,Y3: int,Ys3: list_int,Z3: $o,Zs2: list_o,W2: $o,Ws2: list_o] :
% 1.40/1.58 ( ( ( size_size_list_nat @ Xs2 )
% 1.40/1.58 = ( size_size_list_int @ Ys3 ) )
% 1.40/1.58 => ( ( ( size_size_list_int @ Ys3 )
% 1.40/1.58 = ( size_size_list_o @ Zs2 ) )
% 1.40/1.58 => ( ( ( size_size_list_o @ Zs2 )
% 1.40/1.58 = ( size_size_list_o @ Ws2 ) )
% 1.40/1.58 => ( ( P @ Xs2 @ Ys3 @ Zs2 @ Ws2 )
% 1.40/1.58 => ( P @ ( cons_nat @ X5 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_o @ Z3 @ Zs2 ) @ ( cons_o @ W2 @ Ws2 ) ) ) ) ) )
% 1.40/1.58 => ( P @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % list_induct4
% 1.40/1.58 thf(fact_483_post__member__pre__member,axiom,
% 1.40/1.58 ! [T: vEBT_VEBT,N: nat,X: nat,Y2: nat] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.58 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.58 => ( ( ord_less_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.58 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y2 )
% 1.40/1.58 => ( ( vEBT_vebt_member @ T @ Y2 )
% 1.40/1.58 | ( X = Y2 ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % post_member_pre_member
% 1.40/1.58 thf(fact_484_member__bound,axiom,
% 1.40/1.58 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 1.40/1.58 ( ( vEBT_vebt_member @ Tree @ X )
% 1.40/1.58 => ( ( vEBT_invar_vebt @ Tree @ N )
% 1.40/1.58 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % member_bound
% 1.40/1.58 thf(fact_485_bit__concat__def,axiom,
% 1.40/1.58 ( vEBT_VEBT_bit_concat
% 1.40/1.58 = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % bit_concat_def
% 1.40/1.58 thf(fact_486_low__inv,axiom,
% 1.40/1.58 ! [X: nat,N: nat,Y2: nat] :
% 1.40/1.58 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.58 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 1.40/1.58 = X ) ) ).
% 1.40/1.58
% 1.40/1.58 % low_inv
% 1.40/1.58 thf(fact_487_high__inv,axiom,
% 1.40/1.58 ! [X: nat,N: nat,Y2: nat] :
% 1.40/1.58 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.58 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 1.40/1.58 = Y2 ) ) ).
% 1.40/1.58
% 1.40/1.58 % high_inv
% 1.40/1.58 thf(fact_488__C9_C,axiom,
% 1.40/1.58 ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.58 = na ) ).
% 1.40/1.58
% 1.40/1.58 % "9"
% 1.40/1.58 thf(fact_489_nat__add__left__cancel__le,axiom,
% 1.40/1.58 ! [K: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 1.40/1.58 = ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_add_left_cancel_le
% 1.40/1.58 thf(fact_490_even__odd__cases,axiom,
% 1.40/1.58 ! [X: nat] :
% 1.40/1.58 ( ! [N4: nat] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( plus_plus_nat @ N4 @ N4 ) )
% 1.40/1.58 => ~ ! [N4: nat] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % even_odd_cases
% 1.40/1.58 thf(fact_491_min__Null__member,axiom,
% 1.40/1.58 ! [T: vEBT_VEBT,X: nat] :
% 1.40/1.58 ( ( vEBT_VEBT_minNull @ T )
% 1.40/1.58 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 1.40/1.58
% 1.40/1.58 % min_Null_member
% 1.40/1.58 thf(fact_492_valid__member__both__member__options,axiom,
% 1.40/1.58 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.58 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 1.40/1.58 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % valid_member_both_member_options
% 1.40/1.58 thf(fact_493_both__member__options__equiv__member,axiom,
% 1.40/1.58 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.58 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 1.40/1.58 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % both_member_options_equiv_member
% 1.40/1.58 thf(fact_494_nat_Oinject,axiom,
% 1.40/1.58 ! [X23: nat,Y23: nat] :
% 1.40/1.58 ( ( ( suc @ X23 )
% 1.40/1.58 = ( suc @ Y23 ) )
% 1.40/1.58 = ( X23 = Y23 ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat.inject
% 1.40/1.58 thf(fact_495_old_Onat_Oinject,axiom,
% 1.40/1.58 ! [Nat: nat,Nat2: nat] :
% 1.40/1.58 ( ( ( suc @ Nat )
% 1.40/1.58 = ( suc @ Nat2 ) )
% 1.40/1.58 = ( Nat = Nat2 ) ) ).
% 1.40/1.58
% 1.40/1.58 % old.nat.inject
% 1.40/1.58 thf(fact_496_member__correct,axiom,
% 1.40/1.58 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.58 => ( ( vEBT_vebt_member @ T @ X )
% 1.40/1.58 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % member_correct
% 1.40/1.58 thf(fact_497_pow__sum,axiom,
% 1.40/1.58 ! [A: nat,B: nat] :
% 1.40/1.58 ( ( 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 ) )
% 1.40/1.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 1.40/1.58
% 1.40/1.58 % pow_sum
% 1.40/1.58 thf(fact_498_high__def,axiom,
% 1.40/1.58 ( vEBT_VEBT_high
% 1.40/1.58 = ( ^ [X4: nat,N2: nat] : ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % high_def
% 1.40/1.58 thf(fact_499_Suc__less__eq,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 1.40/1.58 = ( ord_less_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_less_eq
% 1.40/1.58 thf(fact_500_Suc__mono,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ N )
% 1.40/1.58 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_mono
% 1.40/1.58 thf(fact_501_lessI,axiom,
% 1.40/1.58 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % lessI
% 1.40/1.58 thf(fact_502_Suc__le__mono,axiom,
% 1.40/1.58 ! [N: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 1.40/1.58 = ( ord_less_eq_nat @ N @ M ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_le_mono
% 1.40/1.58 thf(fact_503_add__Suc__right,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 1.40/1.58 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_Suc_right
% 1.40/1.58 thf(fact_504_nat__add__left__cancel__less,axiom,
% 1.40/1.58 ! [K: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 1.40/1.58 = ( ord_less_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_add_left_cancel_less
% 1.40/1.58 thf(fact_505_nat__mult__eq__1__iff,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ( times_times_nat @ M @ N )
% 1.40/1.58 = one_one_nat )
% 1.40/1.58 = ( ( M = one_one_nat )
% 1.40/1.58 & ( N = one_one_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_mult_eq_1_iff
% 1.40/1.58 thf(fact_506_nat__1__eq__mult__iff,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( one_one_nat
% 1.40/1.58 = ( times_times_nat @ M @ N ) )
% 1.40/1.58 = ( ( M = one_one_nat )
% 1.40/1.58 & ( N = one_one_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_1_eq_mult_iff
% 1.40/1.58 thf(fact_507_max__Suc__Suc,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 1.40/1.58 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % max_Suc_Suc
% 1.40/1.58 thf(fact_508_mult__Suc__right,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( times_times_nat @ M @ ( suc @ N ) )
% 1.40/1.58 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_Suc_right
% 1.40/1.58 thf(fact_509_Suc__numeral,axiom,
% 1.40/1.58 ! [N: num] :
% 1.40/1.58 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 1.40/1.58 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_numeral
% 1.40/1.58 thf(fact_510_add__2__eq__Suc_H,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.58 = ( suc @ ( suc @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_2_eq_Suc'
% 1.40/1.58 thf(fact_511_add__2__eq__Suc,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.58 = ( suc @ ( suc @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_2_eq_Suc
% 1.40/1.58 thf(fact_512_Suc__1,axiom,
% 1.40/1.58 ( ( suc @ one_one_nat )
% 1.40/1.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_1
% 1.40/1.58 thf(fact_513_Suc__inject,axiom,
% 1.40/1.58 ! [X: nat,Y2: nat] :
% 1.40/1.58 ( ( ( suc @ X )
% 1.40/1.58 = ( suc @ Y2 ) )
% 1.40/1.58 => ( X = Y2 ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_inject
% 1.40/1.58 thf(fact_514_n__not__Suc__n,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( N
% 1.40/1.58 != ( suc @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % n_not_Suc_n
% 1.40/1.58 thf(fact_515_Suc__mult__cancel1,axiom,
% 1.40/1.58 ! [K: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 1.40/1.58 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 1.40/1.58 = ( M = N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_mult_cancel1
% 1.40/1.58 thf(fact_516_Suc__mult__less__cancel1,axiom,
% 1.40/1.58 ! [K: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 1.40/1.58 = ( ord_less_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_mult_less_cancel1
% 1.40/1.58 thf(fact_517_Suc__mult__le__cancel1,axiom,
% 1.40/1.58 ! [K: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 1.40/1.58 = ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_mult_le_cancel1
% 1.40/1.58 thf(fact_518_mult__Suc,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( times_times_nat @ ( suc @ M ) @ N )
% 1.40/1.58 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_Suc
% 1.40/1.58 thf(fact_519_not__less__less__Suc__eq,axiom,
% 1.40/1.58 ! [N: nat,M: nat] :
% 1.40/1.58 ( ~ ( ord_less_nat @ N @ M )
% 1.40/1.58 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 1.40/1.58 = ( N = M ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % not_less_less_Suc_eq
% 1.40/1.58 thf(fact_520_strict__inc__induct,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,P: nat > $o] :
% 1.40/1.58 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.58 => ( ! [I3: nat] :
% 1.40/1.58 ( ( J
% 1.40/1.58 = ( suc @ I3 ) )
% 1.40/1.58 => ( P @ I3 ) )
% 1.40/1.58 => ( ! [I3: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I3 @ J )
% 1.40/1.58 => ( ( P @ ( suc @ I3 ) )
% 1.40/1.58 => ( P @ I3 ) ) )
% 1.40/1.58 => ( P @ I2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % strict_inc_induct
% 1.40/1.58 thf(fact_521_less__Suc__induct,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,P: nat > nat > $o] :
% 1.40/1.58 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.58 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 1.40/1.58 => ( ! [I3: nat,J2: nat,K2: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I3 @ J2 )
% 1.40/1.58 => ( ( ord_less_nat @ J2 @ K2 )
% 1.40/1.58 => ( ( P @ I3 @ J2 )
% 1.40/1.58 => ( ( P @ J2 @ K2 )
% 1.40/1.58 => ( P @ I3 @ K2 ) ) ) ) )
% 1.40/1.58 => ( P @ I2 @ J ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_Suc_induct
% 1.40/1.58 thf(fact_522_less__trans__Suc,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.58 => ( ( ord_less_nat @ J @ K )
% 1.40/1.58 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_trans_Suc
% 1.40/1.58 thf(fact_523_Suc__less__SucD,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 1.40/1.58 => ( ord_less_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_less_SucD
% 1.40/1.58 thf(fact_524_less__antisym,axiom,
% 1.40/1.58 ! [N: nat,M: nat] :
% 1.40/1.58 ( ~ ( ord_less_nat @ N @ M )
% 1.40/1.58 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 1.40/1.58 => ( M = N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_antisym
% 1.40/1.58 thf(fact_525_Suc__less__eq2,axiom,
% 1.40/1.58 ! [N: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 1.40/1.58 = ( ? [M2: nat] :
% 1.40/1.58 ( ( M
% 1.40/1.58 = ( suc @ M2 ) )
% 1.40/1.58 & ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_less_eq2
% 1.40/1.58 thf(fact_526_All__less__Suc,axiom,
% 1.40/1.58 ! [N: nat,P: nat > $o] :
% 1.40/1.58 ( ( ! [I4: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 1.40/1.58 => ( P @ I4 ) ) )
% 1.40/1.58 = ( ( P @ N )
% 1.40/1.58 & ! [I4: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I4 @ N )
% 1.40/1.58 => ( P @ I4 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % All_less_Suc
% 1.40/1.58 thf(fact_527_not__less__eq,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ~ ( ord_less_nat @ M @ N ) )
% 1.40/1.58 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % not_less_eq
% 1.40/1.58 thf(fact_528_less__Suc__eq,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 1.40/1.58 = ( ( ord_less_nat @ M @ N )
% 1.40/1.58 | ( M = N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_Suc_eq
% 1.40/1.58 thf(fact_529_Ex__less__Suc,axiom,
% 1.40/1.58 ! [N: nat,P: nat > $o] :
% 1.40/1.58 ( ( ? [I4: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 1.40/1.58 & ( P @ I4 ) ) )
% 1.40/1.58 = ( ( P @ N )
% 1.40/1.58 | ? [I4: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I4 @ N )
% 1.40/1.58 & ( P @ I4 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Ex_less_Suc
% 1.40/1.58 thf(fact_530_less__SucI,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ N )
% 1.40/1.58 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_SucI
% 1.40/1.58 thf(fact_531_less__SucE,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 1.40/1.58 => ( ~ ( ord_less_nat @ M @ N )
% 1.40/1.58 => ( M = N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_SucE
% 1.40/1.58 thf(fact_532_Suc__lessI,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ N )
% 1.40/1.58 => ( ( ( suc @ M )
% 1.40/1.58 != N )
% 1.40/1.58 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_lessI
% 1.40/1.58 thf(fact_533_Suc__lessE,axiom,
% 1.40/1.58 ! [I2: nat,K: nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 1.40/1.58 => ~ ! [J2: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I2 @ J2 )
% 1.40/1.58 => ( K
% 1.40/1.58 != ( suc @ J2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_lessE
% 1.40/1.58 thf(fact_534_Suc__lessD,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 1.40/1.58 => ( ord_less_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_lessD
% 1.40/1.58 thf(fact_535_Nat_OlessE,axiom,
% 1.40/1.58 ! [I2: nat,K: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I2 @ K )
% 1.40/1.58 => ( ( K
% 1.40/1.58 != ( suc @ I2 ) )
% 1.40/1.58 => ~ ! [J2: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I2 @ J2 )
% 1.40/1.58 => ( K
% 1.40/1.58 != ( suc @ J2 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Nat.lessE
% 1.40/1.58 thf(fact_536_transitive__stepwise__le,axiom,
% 1.40/1.58 ! [M: nat,N: nat,R: nat > nat > $o] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 => ( ! [X5: nat] : ( R @ X5 @ X5 )
% 1.40/1.58 => ( ! [X5: nat,Y3: nat,Z3: nat] :
% 1.40/1.58 ( ( R @ X5 @ Y3 )
% 1.40/1.58 => ( ( R @ Y3 @ Z3 )
% 1.40/1.58 => ( R @ X5 @ Z3 ) ) )
% 1.40/1.58 => ( ! [N4: nat] : ( R @ N4 @ ( suc @ N4 ) )
% 1.40/1.58 => ( R @ M @ N ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % transitive_stepwise_le
% 1.40/1.58 thf(fact_537_nat__induct__at__least,axiom,
% 1.40/1.58 ! [M: nat,N: nat,P: nat > $o] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 => ( ( P @ M )
% 1.40/1.58 => ( ! [N4: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ N4 )
% 1.40/1.58 => ( ( P @ N4 )
% 1.40/1.58 => ( P @ ( suc @ N4 ) ) ) )
% 1.40/1.58 => ( P @ N ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_induct_at_least
% 1.40/1.58 thf(fact_538_full__nat__induct,axiom,
% 1.40/1.58 ! [P: nat > $o,N: nat] :
% 1.40/1.58 ( ! [N4: nat] :
% 1.40/1.58 ( ! [M3: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N4 )
% 1.40/1.58 => ( P @ M3 ) )
% 1.40/1.58 => ( P @ N4 ) )
% 1.40/1.58 => ( P @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % full_nat_induct
% 1.40/1.58 thf(fact_539_not__less__eq__eq,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 1.40/1.58 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 1.40/1.58
% 1.40/1.58 % not_less_eq_eq
% 1.40/1.58 thf(fact_540_Suc__n__not__le__n,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_n_not_le_n
% 1.40/1.58 thf(fact_541_le__Suc__eq,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 1.40/1.58 = ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 | ( M
% 1.40/1.58 = ( suc @ N ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_Suc_eq
% 1.40/1.58 thf(fact_542_Suc__le__D,axiom,
% 1.40/1.58 ! [N: nat,M4: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
% 1.40/1.58 => ? [M5: nat] :
% 1.40/1.58 ( M4
% 1.40/1.58 = ( suc @ M5 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_le_D
% 1.40/1.58 thf(fact_543_le__SucI,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_SucI
% 1.40/1.58 thf(fact_544_le__SucE,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 1.40/1.58 => ( ~ ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 => ( M
% 1.40/1.58 = ( suc @ N ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_SucE
% 1.40/1.58 thf(fact_545_Suc__leD,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 1.40/1.58 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_leD
% 1.40/1.58 thf(fact_546_mult__le__mono2,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_le_mono2
% 1.40/1.58 thf(fact_547_mult__le__mono1,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_le_mono1
% 1.40/1.58 thf(fact_548_mult__le__mono,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ( ord_less_eq_nat @ K @ L2 )
% 1.40/1.58 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_le_mono
% 1.40/1.58 thf(fact_549_le__square,axiom,
% 1.40/1.58 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_square
% 1.40/1.58 thf(fact_550_le__cube,axiom,
% 1.40/1.58 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_cube
% 1.40/1.58 thf(fact_551_add__Suc__shift,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 1.40/1.58 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_Suc_shift
% 1.40/1.58 thf(fact_552_add__Suc,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 1.40/1.58 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_Suc
% 1.40/1.58 thf(fact_553_nat__arith_Osuc1,axiom,
% 1.40/1.58 ! [A2: nat,K: nat,A: nat] :
% 1.40/1.58 ( ( A2
% 1.40/1.58 = ( plus_plus_nat @ K @ A ) )
% 1.40/1.58 => ( ( suc @ A2 )
% 1.40/1.58 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_arith.suc1
% 1.40/1.58 thf(fact_554_add__mult__distrib2,axiom,
% 1.40/1.58 ! [K: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 1.40/1.58 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_mult_distrib2
% 1.40/1.58 thf(fact_555_add__mult__distrib,axiom,
% 1.40/1.58 ! [M: nat,N: nat,K: nat] :
% 1.40/1.58 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 1.40/1.58 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_mult_distrib
% 1.40/1.58 thf(fact_556_nat__mult__1__right,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( times_times_nat @ N @ one_one_nat )
% 1.40/1.58 = N ) ).
% 1.40/1.58
% 1.40/1.58 % nat_mult_1_right
% 1.40/1.58 thf(fact_557_nat__mult__1,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( times_times_nat @ one_one_nat @ N )
% 1.40/1.58 = N ) ).
% 1.40/1.58
% 1.40/1.58 % nat_mult_1
% 1.40/1.58 thf(fact_558_nat__mult__max__right,axiom,
% 1.40/1.58 ! [M: nat,N: nat,Q2: nat] :
% 1.40/1.58 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 1.40/1.58 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_mult_max_right
% 1.40/1.58 thf(fact_559_nat__mult__max__left,axiom,
% 1.40/1.58 ! [M: nat,N: nat,Q2: nat] :
% 1.40/1.58 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 1.40/1.58 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_mult_max_left
% 1.40/1.58 thf(fact_560_left__add__mult__distrib,axiom,
% 1.40/1.58 ! [I2: nat,U: nat,J: nat,K: nat] :
% 1.40/1.58 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 1.40/1.58 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) ).
% 1.40/1.58
% 1.40/1.58 % left_add_mult_distrib
% 1.40/1.58 thf(fact_561_le__imp__less__Suc,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_imp_less_Suc
% 1.40/1.58 thf(fact_562_less__eq__Suc__le,axiom,
% 1.40/1.58 ( ord_less_nat
% 1.40/1.58 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_eq_Suc_le
% 1.40/1.58 thf(fact_563_less__Suc__eq__le,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 1.40/1.58 = ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_Suc_eq_le
% 1.40/1.58 thf(fact_564_le__less__Suc__eq,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 1.40/1.58 = ( N = M ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_less_Suc_eq
% 1.40/1.58 thf(fact_565_Suc__le__lessD,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 1.40/1.58 => ( ord_less_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_le_lessD
% 1.40/1.58 thf(fact_566_inc__induct,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,P: nat > $o] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ( P @ J )
% 1.40/1.58 => ( ! [N4: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ N4 )
% 1.40/1.58 => ( ( ord_less_nat @ N4 @ J )
% 1.40/1.58 => ( ( P @ ( suc @ N4 ) )
% 1.40/1.58 => ( P @ N4 ) ) ) )
% 1.40/1.58 => ( P @ I2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % inc_induct
% 1.40/1.58 thf(fact_567_dec__induct,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,P: nat > $o] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ( P @ I2 )
% 1.40/1.58 => ( ! [N4: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ N4 )
% 1.40/1.58 => ( ( ord_less_nat @ N4 @ J )
% 1.40/1.58 => ( ( P @ N4 )
% 1.40/1.58 => ( P @ ( suc @ N4 ) ) ) ) )
% 1.40/1.58 => ( P @ J ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % dec_induct
% 1.40/1.58 thf(fact_568_Suc__le__eq,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 1.40/1.58 = ( ord_less_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_le_eq
% 1.40/1.58 thf(fact_569_Suc__leI,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ N )
% 1.40/1.58 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_leI
% 1.40/1.58 thf(fact_570_less__imp__Suc__add,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ N )
% 1.40/1.58 => ? [K2: nat] :
% 1.40/1.58 ( N
% 1.40/1.58 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_imp_Suc_add
% 1.40/1.58 thf(fact_571_less__iff__Suc__add,axiom,
% 1.40/1.58 ( ord_less_nat
% 1.40/1.58 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.58 ? [K3: nat] :
% 1.40/1.58 ( N2
% 1.40/1.58 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_iff_Suc_add
% 1.40/1.58 thf(fact_572_less__add__Suc2,axiom,
% 1.40/1.58 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_add_Suc2
% 1.40/1.58 thf(fact_573_less__add__Suc1,axiom,
% 1.40/1.58 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_add_Suc1
% 1.40/1.58 thf(fact_574_less__natE,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ N )
% 1.40/1.58 => ~ ! [Q3: nat] :
% 1.40/1.58 ( N
% 1.40/1.58 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_natE
% 1.40/1.58 thf(fact_575_Suc__eq__plus1__left,axiom,
% 1.40/1.58 ( suc
% 1.40/1.58 = ( plus_plus_nat @ one_one_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_eq_plus1_left
% 1.40/1.58 thf(fact_576_plus__1__eq__Suc,axiom,
% 1.40/1.58 ( ( plus_plus_nat @ one_one_nat )
% 1.40/1.58 = suc ) ).
% 1.40/1.58
% 1.40/1.58 % plus_1_eq_Suc
% 1.40/1.58 thf(fact_577_Suc__eq__plus1,axiom,
% 1.40/1.58 ( suc
% 1.40/1.58 = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_eq_plus1
% 1.40/1.58 thf(fact_578_linorder__neqE__nat,axiom,
% 1.40/1.58 ! [X: nat,Y2: nat] :
% 1.40/1.58 ( ( X != Y2 )
% 1.40/1.58 => ( ~ ( ord_less_nat @ X @ Y2 )
% 1.40/1.58 => ( ord_less_nat @ Y2 @ X ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % linorder_neqE_nat
% 1.40/1.58 thf(fact_579_infinite__descent,axiom,
% 1.40/1.58 ! [P: nat > $o,N: nat] :
% 1.40/1.58 ( ! [N4: nat] :
% 1.40/1.58 ( ~ ( P @ N4 )
% 1.40/1.58 => ? [M3: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M3 @ N4 )
% 1.40/1.58 & ~ ( P @ M3 ) ) )
% 1.40/1.58 => ( P @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % infinite_descent
% 1.40/1.58 thf(fact_580_nat__less__induct,axiom,
% 1.40/1.58 ! [P: nat > $o,N: nat] :
% 1.40/1.58 ( ! [N4: nat] :
% 1.40/1.58 ( ! [M3: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M3 @ N4 )
% 1.40/1.58 => ( P @ M3 ) )
% 1.40/1.58 => ( P @ N4 ) )
% 1.40/1.58 => ( P @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_less_induct
% 1.40/1.58 thf(fact_581_less__irrefl__nat,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ~ ( ord_less_nat @ N @ N ) ).
% 1.40/1.58
% 1.40/1.58 % less_irrefl_nat
% 1.40/1.58 thf(fact_582_less__not__refl3,axiom,
% 1.40/1.58 ! [S: nat,T: nat] :
% 1.40/1.58 ( ( ord_less_nat @ S @ T )
% 1.40/1.58 => ( S != T ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_not_refl3
% 1.40/1.58 thf(fact_583_less__not__refl2,axiom,
% 1.40/1.58 ! [N: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_nat @ N @ M )
% 1.40/1.58 => ( M != N ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_not_refl2
% 1.40/1.58 thf(fact_584_less__not__refl,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ~ ( ord_less_nat @ N @ N ) ).
% 1.40/1.58
% 1.40/1.58 % less_not_refl
% 1.40/1.58 thf(fact_585_nat__neq__iff,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( M != N )
% 1.40/1.58 = ( ( ord_less_nat @ M @ N )
% 1.40/1.58 | ( ord_less_nat @ N @ M ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_neq_iff
% 1.40/1.58 thf(fact_586_Nat_Oex__has__greatest__nat,axiom,
% 1.40/1.58 ! [P: nat > $o,K: nat,B: nat] :
% 1.40/1.58 ( ( P @ K )
% 1.40/1.58 => ( ! [Y3: nat] :
% 1.40/1.58 ( ( P @ Y3 )
% 1.40/1.58 => ( ord_less_eq_nat @ Y3 @ B ) )
% 1.40/1.58 => ? [X5: nat] :
% 1.40/1.58 ( ( P @ X5 )
% 1.40/1.58 & ! [Y: nat] :
% 1.40/1.58 ( ( P @ Y )
% 1.40/1.58 => ( ord_less_eq_nat @ Y @ X5 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % Nat.ex_has_greatest_nat
% 1.40/1.58 thf(fact_587_nat__le__linear,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 | ( ord_less_eq_nat @ N @ M ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_le_linear
% 1.40/1.58 thf(fact_588_le__antisym,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 => ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.58 => ( M = N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_antisym
% 1.40/1.58 thf(fact_589_eq__imp__le,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( M = N )
% 1.40/1.58 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % eq_imp_le
% 1.40/1.58 thf(fact_590_le__trans,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ( ord_less_eq_nat @ J @ K )
% 1.40/1.58 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_trans
% 1.40/1.58 thf(fact_591_le__refl,axiom,
% 1.40/1.58 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 1.40/1.58
% 1.40/1.58 % le_refl
% 1.40/1.58 thf(fact_592_Suc__nat__number__of__add,axiom,
% 1.40/1.58 ! [V: num,N: nat] :
% 1.40/1.58 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 1.40/1.58 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_nat_number_of_add
% 1.40/1.58 thf(fact_593_less__mono__imp__le__mono,axiom,
% 1.40/1.58 ! [F: nat > nat,I2: nat,J: nat] :
% 1.40/1.58 ( ! [I3: nat,J2: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I3 @ J2 )
% 1.40/1.58 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 1.40/1.58 => ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_mono_imp_le_mono
% 1.40/1.58 thf(fact_594_le__neq__implies__less,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 => ( ( M != N )
% 1.40/1.58 => ( ord_less_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_neq_implies_less
% 1.40/1.58 thf(fact_595_less__or__eq__imp__le,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ( ord_less_nat @ M @ N )
% 1.40/1.58 | ( M = N ) )
% 1.40/1.58 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_or_eq_imp_le
% 1.40/1.58 thf(fact_596_le__eq__less__or__eq,axiom,
% 1.40/1.58 ( ord_less_eq_nat
% 1.40/1.58 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M6 @ N2 )
% 1.40/1.58 | ( M6 = N2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_eq_less_or_eq
% 1.40/1.58 thf(fact_597_less__imp__le__nat,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ N )
% 1.40/1.58 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_imp_le_nat
% 1.40/1.58 thf(fact_598_nat__less__le,axiom,
% 1.40/1.58 ( ord_less_nat
% 1.40/1.58 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M6 @ N2 )
% 1.40/1.58 & ( M6 != N2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_less_le
% 1.40/1.58 thf(fact_599_less__add__eq__less,axiom,
% 1.40/1.58 ! [K: nat,L2: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ K @ L2 )
% 1.40/1.58 => ( ( ( plus_plus_nat @ M @ L2 )
% 1.40/1.58 = ( plus_plus_nat @ K @ N ) )
% 1.40/1.58 => ( ord_less_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_add_eq_less
% 1.40/1.58 thf(fact_600_trans__less__add2,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.58 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % trans_less_add2
% 1.40/1.58 thf(fact_601_trans__less__add1,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.58 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % trans_less_add1
% 1.40/1.58 thf(fact_602_add__less__mono1,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.58 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_less_mono1
% 1.40/1.58 thf(fact_603_not__add__less2,axiom,
% 1.40/1.58 ! [J: nat,I2: nat] :
% 1.40/1.58 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 1.40/1.58
% 1.40/1.58 % not_add_less2
% 1.40/1.58 thf(fact_604_not__add__less1,axiom,
% 1.40/1.58 ! [I2: nat,J: nat] :
% 1.40/1.58 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 1.40/1.58
% 1.40/1.58 % not_add_less1
% 1.40/1.58 thf(fact_605_add__less__mono,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 1.40/1.58 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.58 => ( ( ord_less_nat @ K @ L2 )
% 1.40/1.58 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_less_mono
% 1.40/1.58 thf(fact_606_add__lessD1,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 1.40/1.58 => ( ord_less_nat @ I2 @ K ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_lessD1
% 1.40/1.58 thf(fact_607_nat__le__iff__add,axiom,
% 1.40/1.58 ( ord_less_eq_nat
% 1.40/1.58 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.58 ? [K3: nat] :
% 1.40/1.58 ( N2
% 1.40/1.58 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_le_iff_add
% 1.40/1.58 thf(fact_608_trans__le__add2,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % trans_le_add2
% 1.40/1.58 thf(fact_609_trans__le__add1,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % trans_le_add1
% 1.40/1.58 thf(fact_610_add__le__mono1,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_le_mono1
% 1.40/1.58 thf(fact_611_add__le__mono,axiom,
% 1.40/1.58 ! [I2: nat,J: nat,K: nat,L2: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.58 => ( ( ord_less_eq_nat @ K @ L2 )
% 1.40/1.58 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_le_mono
% 1.40/1.58 thf(fact_612_le__Suc__ex,axiom,
% 1.40/1.58 ! [K: nat,L2: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ K @ L2 )
% 1.40/1.58 => ? [N4: nat] :
% 1.40/1.58 ( L2
% 1.40/1.58 = ( plus_plus_nat @ K @ N4 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_Suc_ex
% 1.40/1.58 thf(fact_613_add__leD2,axiom,
% 1.40/1.58 ! [M: nat,K: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 1.40/1.58 => ( ord_less_eq_nat @ K @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_leD2
% 1.40/1.58 thf(fact_614_add__leD1,axiom,
% 1.40/1.58 ! [M: nat,K: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 1.40/1.58 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_leD1
% 1.40/1.58 thf(fact_615_le__add2,axiom,
% 1.40/1.58 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_add2
% 1.40/1.58 thf(fact_616_le__add1,axiom,
% 1.40/1.58 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 1.40/1.58
% 1.40/1.58 % le_add1
% 1.40/1.58 thf(fact_617_add__leE,axiom,
% 1.40/1.58 ! [M: nat,K: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 1.40/1.58 => ~ ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_leE
% 1.40/1.58 thf(fact_618_nat__add__max__right,axiom,
% 1.40/1.58 ! [M: nat,N: nat,Q2: nat] :
% 1.40/1.58 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 1.40/1.58 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_add_max_right
% 1.40/1.58 thf(fact_619_nat__add__max__left,axiom,
% 1.40/1.58 ! [M: nat,N: nat,Q2: nat] :
% 1.40/1.58 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 1.40/1.58 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_add_max_left
% 1.40/1.58 thf(fact_620_mono__nat__linear__lb,axiom,
% 1.40/1.58 ! [F: nat > nat,M: nat,K: nat] :
% 1.40/1.58 ( ! [M5: nat,N4: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M5 @ N4 )
% 1.40/1.58 => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N4 ) ) )
% 1.40/1.58 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mono_nat_linear_lb
% 1.40/1.58 thf(fact_621_add__self__div__2,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.58 = M ) ).
% 1.40/1.58
% 1.40/1.58 % add_self_div_2
% 1.40/1.58 thf(fact_622_div2__Suc__Suc,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.58 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % div2_Suc_Suc
% 1.40/1.58 thf(fact_623_both__member__options__ding,axiom,
% 1.40/1.58 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 1.40/1.58 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 1.40/1.58 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.58 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % both_member_options_ding
% 1.40/1.58 thf(fact_624_div__nat__eqI,axiom,
% 1.40/1.58 ! [N: nat,Q2: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 1.40/1.58 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 1.40/1.58 => ( ( divide_divide_nat @ M @ N )
% 1.40/1.58 = Q2 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % div_nat_eqI
% 1.40/1.58 thf(fact_625_enat__ord__number_I1_J,axiom,
% 1.40/1.58 ! [M: num,N: num] :
% 1.40/1.58 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 1.40/1.58 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % enat_ord_number(1)
% 1.40/1.58 thf(fact_626_enat__ord__number_I2_J,axiom,
% 1.40/1.58 ! [M: num,N: num] :
% 1.40/1.58 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 1.40/1.58 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % enat_ord_number(2)
% 1.40/1.58 thf(fact_627_double__not__eq__Suc__double,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 1.40/1.58 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % double_not_eq_Suc_double
% 1.40/1.58 thf(fact_628_deg__deg__n,axiom,
% 1.40/1.58 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 1.40/1.58 => ( Deg = N ) ) ).
% 1.40/1.58
% 1.40/1.58 % deg_deg_n
% 1.40/1.58 thf(fact_629_deg__SUcn__Node,axiom,
% 1.40/1.58 ! [Tree: vEBT_VEBT,N: nat] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 1.40/1.58 => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 1.40/1.58 ( Tree
% 1.40/1.58 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList3 @ S2 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % deg_SUcn_Node
% 1.40/1.58 thf(fact_630_semiring__norm_I13_J,axiom,
% 1.40/1.58 ! [M: num,N: num] :
% 1.40/1.58 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 1.40/1.58 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % semiring_norm(13)
% 1.40/1.58 thf(fact_631_semiring__norm_I12_J,axiom,
% 1.40/1.58 ! [N: num] :
% 1.40/1.58 ( ( times_times_num @ one @ N )
% 1.40/1.58 = N ) ).
% 1.40/1.58
% 1.40/1.58 % semiring_norm(12)
% 1.40/1.58 thf(fact_632_semiring__norm_I11_J,axiom,
% 1.40/1.58 ! [M: num] :
% 1.40/1.58 ( ( times_times_num @ M @ one )
% 1.40/1.58 = M ) ).
% 1.40/1.58
% 1.40/1.58 % semiring_norm(11)
% 1.40/1.58 thf(fact_633_set__vebt__set__vebt_H__valid,axiom,
% 1.40/1.58 ! [T: vEBT_VEBT,N: nat] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.58 => ( ( vEBT_set_vebt @ T )
% 1.40/1.58 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % set_vebt_set_vebt'_valid
% 1.40/1.58 thf(fact_634_num__double,axiom,
% 1.40/1.58 ! [N: num] :
% 1.40/1.58 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 1.40/1.58 = ( bit0 @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % num_double
% 1.40/1.58 thf(fact_635_enat__less__induct,axiom,
% 1.40/1.58 ! [P: extended_enat > $o,N: extended_enat] :
% 1.40/1.58 ( ! [N4: extended_enat] :
% 1.40/1.58 ( ! [M3: extended_enat] :
% 1.40/1.58 ( ( ord_le72135733267957522d_enat @ M3 @ N4 )
% 1.40/1.58 => ( P @ M3 ) )
% 1.40/1.58 => ( P @ N4 ) )
% 1.40/1.58 => ( P @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % enat_less_induct
% 1.40/1.58 thf(fact_636_four__x__squared,axiom,
% 1.40/1.58 ! [X: real] :
% 1.40/1.58 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.58 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % four_x_squared
% 1.40/1.58 thf(fact_637_L2__set__mult__ineq__lemma,axiom,
% 1.40/1.58 ! [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 ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % L2_set_mult_ineq_lemma
% 1.40/1.58 thf(fact_638_two__realpow__ge__one,axiom,
% 1.40/1.58 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % two_realpow_ge_one
% 1.40/1.58 thf(fact_639_div__le__mono,axiom,
% 1.40/1.58 ! [M: nat,N: nat,K: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.58 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % div_le_mono
% 1.40/1.58 thf(fact_640_div__le__dividend,axiom,
% 1.40/1.58 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 1.40/1.58
% 1.40/1.58 % div_le_dividend
% 1.40/1.58 thf(fact_641_div__mult2__eq,axiom,
% 1.40/1.58 ! [M: nat,N: nat,Q2: nat] :
% 1.40/1.58 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 1.40/1.58 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 1.40/1.58
% 1.40/1.58 % div_mult2_eq
% 1.40/1.58 thf(fact_642_Suc__div__le__mono,axiom,
% 1.40/1.58 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_div_le_mono
% 1.40/1.58 thf(fact_643_less__mult__imp__div__less,axiom,
% 1.40/1.58 ! [M: nat,I2: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N ) )
% 1.40/1.58 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I2 ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_mult_imp_div_less
% 1.40/1.58 thf(fact_644_div__times__less__eq__dividend,axiom,
% 1.40/1.58 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 1.40/1.58
% 1.40/1.58 % div_times_less_eq_dividend
% 1.40/1.58 thf(fact_645_times__div__less__eq__dividend,axiom,
% 1.40/1.58 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 1.40/1.58
% 1.40/1.58 % times_div_less_eq_dividend
% 1.40/1.58 thf(fact_646_Suc__double__not__eq__double,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 1.40/1.58 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_double_not_eq_double
% 1.40/1.58 thf(fact_647_real__divide__square__eq,axiom,
% 1.40/1.58 ! [R2: real,A: real] :
% 1.40/1.58 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 1.40/1.58 = ( divide_divide_real @ A @ R2 ) ) ).
% 1.40/1.58
% 1.40/1.58 % real_divide_square_eq
% 1.40/1.58 thf(fact_648_less__eq__real__def,axiom,
% 1.40/1.58 ( ord_less_eq_real
% 1.40/1.58 = ( ^ [X4: real,Y4: real] :
% 1.40/1.58 ( ( ord_less_real @ X4 @ Y4 )
% 1.40/1.58 | ( X4 = Y4 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_eq_real_def
% 1.40/1.58 thf(fact_649_complete__real,axiom,
% 1.40/1.58 ! [S3: set_real] :
% 1.40/1.58 ( ? [X3: real] : ( member_real @ X3 @ S3 )
% 1.40/1.58 => ( ? [Z4: real] :
% 1.40/1.58 ! [X5: real] :
% 1.40/1.58 ( ( member_real @ X5 @ S3 )
% 1.40/1.58 => ( ord_less_eq_real @ X5 @ Z4 ) )
% 1.40/1.58 => ? [Y3: real] :
% 1.40/1.58 ( ! [X3: real] :
% 1.40/1.58 ( ( member_real @ X3 @ S3 )
% 1.40/1.58 => ( ord_less_eq_real @ X3 @ Y3 ) )
% 1.40/1.58 & ! [Z4: real] :
% 1.40/1.58 ( ! [X5: real] :
% 1.40/1.58 ( ( member_real @ X5 @ S3 )
% 1.40/1.58 => ( ord_less_eq_real @ X5 @ Z4 ) )
% 1.40/1.58 => ( ord_less_eq_real @ Y3 @ Z4 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % complete_real
% 1.40/1.58 thf(fact_650_real__arch__pow,axiom,
% 1.40/1.58 ! [X: real,Y2: real] :
% 1.40/1.58 ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.58 => ? [N4: nat] : ( ord_less_real @ Y2 @ ( power_power_real @ X @ N4 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % real_arch_pow
% 1.40/1.58 thf(fact_651_low__def,axiom,
% 1.40/1.58 ( vEBT_VEBT_low
% 1.40/1.58 = ( ^ [X4: nat,N2: nat] : ( modulo_modulo_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % low_def
% 1.40/1.58 thf(fact_652_both__member__options__from__chilf__to__complete__tree,axiom,
% 1.40/1.58 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 1.40/1.58 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 1.40/1.58 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 1.40/1.58 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.58 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % both_member_options_from_chilf_to_complete_tree
% 1.40/1.58 thf(fact_653_VEBT_Oinject_I1_J,axiom,
% 1.40/1.58 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 1.40/1.58 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 1.40/1.58 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 1.40/1.58 = ( ( X11 = Y11 )
% 1.40/1.58 & ( X12 = Y12 )
% 1.40/1.58 & ( X13 = Y13 )
% 1.40/1.58 & ( X14 = Y14 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % VEBT.inject(1)
% 1.40/1.58 thf(fact_654_member__inv,axiom,
% 1.40/1.58 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 1.40/1.58 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 1.40/1.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 1.40/1.58 & ( ( X = Mi )
% 1.40/1.58 | ( X = Ma )
% 1.40/1.58 | ( ( ord_less_nat @ X @ Ma )
% 1.40/1.58 & ( ord_less_nat @ Mi @ X )
% 1.40/1.58 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 1.40/1.58 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % member_inv
% 1.40/1.58 thf(fact_655__C10_C,axiom,
% 1.40/1.58 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 1.40/1.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ( ord_max_nat @ xa @ ma ) ) ) @ deg @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ summary ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % "10"
% 1.40/1.58 thf(fact_656_valid__tree__deg__neq__0,axiom,
% 1.40/1.58 ! [T: vEBT_VEBT] :
% 1.40/1.58 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 1.40/1.58
% 1.40/1.58 % valid_tree_deg_neq_0
% 1.40/1.58 thf(fact_657_valid__0__not,axiom,
% 1.40/1.58 ! [T: vEBT_VEBT] :
% 1.40/1.58 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 1.40/1.58
% 1.40/1.58 % valid_0_not
% 1.40/1.58 thf(fact_658_deg__not__0,axiom,
% 1.40/1.58 ! [T: vEBT_VEBT,N: nat] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.58 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % deg_not_0
% 1.40/1.58 thf(fact_659_zdiv__numeral__Bit0,axiom,
% 1.40/1.58 ! [V: num,W: num] :
% 1.40/1.58 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 1.40/1.58 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % zdiv_numeral_Bit0
% 1.40/1.58 thf(fact_660_bot__nat__0_Onot__eq__extremum,axiom,
% 1.40/1.58 ! [A: nat] :
% 1.40/1.58 ( ( A != zero_zero_nat )
% 1.40/1.58 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 1.40/1.58
% 1.40/1.58 % bot_nat_0.not_eq_extremum
% 1.40/1.58 thf(fact_661_neq0__conv,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( N != zero_zero_nat )
% 1.40/1.58 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % neq0_conv
% 1.40/1.58 thf(fact_662_less__nat__zero__code,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 1.40/1.58
% 1.40/1.58 % less_nat_zero_code
% 1.40/1.58 thf(fact_663_bot__nat__0_Oextremum,axiom,
% 1.40/1.58 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 1.40/1.58
% 1.40/1.58 % bot_nat_0.extremum
% 1.40/1.58 thf(fact_664_le0,axiom,
% 1.40/1.58 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 1.40/1.58
% 1.40/1.58 % le0
% 1.40/1.58 thf(fact_665_add__is__0,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ( plus_plus_nat @ M @ N )
% 1.40/1.58 = zero_zero_nat )
% 1.40/1.58 = ( ( M = zero_zero_nat )
% 1.40/1.58 & ( N = zero_zero_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_is_0
% 1.40/1.58 thf(fact_666_Nat_Oadd__0__right,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 1.40/1.58 = M ) ).
% 1.40/1.58
% 1.40/1.58 % Nat.add_0_right
% 1.40/1.58 thf(fact_667_mult__cancel2,axiom,
% 1.40/1.58 ! [M: nat,K: nat,N: nat] :
% 1.40/1.58 ( ( ( times_times_nat @ M @ K )
% 1.40/1.58 = ( times_times_nat @ N @ K ) )
% 1.40/1.58 = ( ( M = N )
% 1.40/1.58 | ( K = zero_zero_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_cancel2
% 1.40/1.58 thf(fact_668_mult__cancel1,axiom,
% 1.40/1.58 ! [K: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( ( times_times_nat @ K @ M )
% 1.40/1.58 = ( times_times_nat @ K @ N ) )
% 1.40/1.58 = ( ( M = N )
% 1.40/1.58 | ( K = zero_zero_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_cancel1
% 1.40/1.58 thf(fact_669_mult__0__right,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( ( times_times_nat @ M @ zero_zero_nat )
% 1.40/1.58 = zero_zero_nat ) ).
% 1.40/1.58
% 1.40/1.58 % mult_0_right
% 1.40/1.58 thf(fact_670_mult__is__0,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ( times_times_nat @ M @ N )
% 1.40/1.58 = zero_zero_nat )
% 1.40/1.58 = ( ( M = zero_zero_nat )
% 1.40/1.58 | ( N = zero_zero_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_is_0
% 1.40/1.58 thf(fact_671_max__nat_Oeq__neutr__iff,axiom,
% 1.40/1.58 ! [A: nat,B: nat] :
% 1.40/1.58 ( ( ( ord_max_nat @ A @ B )
% 1.40/1.58 = zero_zero_nat )
% 1.40/1.58 = ( ( A = zero_zero_nat )
% 1.40/1.58 & ( B = zero_zero_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % max_nat.eq_neutr_iff
% 1.40/1.58 thf(fact_672_max__nat_Oleft__neutral,axiom,
% 1.40/1.58 ! [A: nat] :
% 1.40/1.58 ( ( ord_max_nat @ zero_zero_nat @ A )
% 1.40/1.58 = A ) ).
% 1.40/1.58
% 1.40/1.58 % max_nat.left_neutral
% 1.40/1.58 thf(fact_673_max__nat_Oneutr__eq__iff,axiom,
% 1.40/1.58 ! [A: nat,B: nat] :
% 1.40/1.58 ( ( zero_zero_nat
% 1.40/1.58 = ( ord_max_nat @ A @ B ) )
% 1.40/1.58 = ( ( A = zero_zero_nat )
% 1.40/1.58 & ( B = zero_zero_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % max_nat.neutr_eq_iff
% 1.40/1.58 thf(fact_674_max__nat_Oright__neutral,axiom,
% 1.40/1.58 ! [A: nat] :
% 1.40/1.58 ( ( ord_max_nat @ A @ zero_zero_nat )
% 1.40/1.58 = A ) ).
% 1.40/1.58
% 1.40/1.58 % max_nat.right_neutral
% 1.40/1.58 thf(fact_675_max__0L,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( ord_max_nat @ zero_zero_nat @ N )
% 1.40/1.58 = N ) ).
% 1.40/1.58
% 1.40/1.58 % max_0L
% 1.40/1.58 thf(fact_676_max__0R,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( ord_max_nat @ N @ zero_zero_nat )
% 1.40/1.58 = N ) ).
% 1.40/1.58
% 1.40/1.58 % max_0R
% 1.40/1.58 thf(fact_677_i0__less,axiom,
% 1.40/1.58 ! [N: extended_enat] :
% 1.40/1.58 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 1.40/1.58 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 1.40/1.58
% 1.40/1.58 % i0_less
% 1.40/1.58 thf(fact_678_mi__eq__ma__no__ch,axiom,
% 1.40/1.58 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 1.40/1.58 => ( ( Mi = Ma )
% 1.40/1.58 => ( ! [X3: vEBT_VEBT] :
% 1.40/1.58 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.58 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 1.40/1.58 & ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mi_eq_ma_no_ch
% 1.40/1.58 thf(fact_679_half__nonnegative__int__iff,axiom,
% 1.40/1.58 ! [K: int] :
% 1.40/1.58 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 1.40/1.58 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 1.40/1.58
% 1.40/1.58 % half_nonnegative_int_iff
% 1.40/1.58 thf(fact_680_half__negative__int__iff,axiom,
% 1.40/1.58 ! [K: int] :
% 1.40/1.58 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 1.40/1.58 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 1.40/1.58
% 1.40/1.58 % half_negative_int_iff
% 1.40/1.58 thf(fact_681_less__Suc0,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 1.40/1.58 = ( N = zero_zero_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_Suc0
% 1.40/1.58 thf(fact_682_zero__less__Suc,axiom,
% 1.40/1.58 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % zero_less_Suc
% 1.40/1.58 thf(fact_683_insert__simp__mima,axiom,
% 1.40/1.58 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 1.40/1.58 ( ( ( X = Mi )
% 1.40/1.58 | ( X = Ma ) )
% 1.40/1.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 1.40/1.58 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 1.40/1.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % insert_simp_mima
% 1.40/1.58 thf(fact_684_add__gr__0,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 1.40/1.58 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.58 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % add_gr_0
% 1.40/1.58 thf(fact_685_one__eq__mult__iff,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ( suc @ zero_zero_nat )
% 1.40/1.58 = ( times_times_nat @ M @ N ) )
% 1.40/1.58 = ( ( M
% 1.40/1.58 = ( suc @ zero_zero_nat ) )
% 1.40/1.58 & ( N
% 1.40/1.58 = ( suc @ zero_zero_nat ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % one_eq_mult_iff
% 1.40/1.58 thf(fact_686_mult__eq__1__iff,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ( times_times_nat @ M @ N )
% 1.40/1.58 = ( suc @ zero_zero_nat ) )
% 1.40/1.58 = ( ( M
% 1.40/1.58 = ( suc @ zero_zero_nat ) )
% 1.40/1.58 & ( N
% 1.40/1.58 = ( suc @ zero_zero_nat ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_eq_1_iff
% 1.40/1.58 thf(fact_687_nat__mult__less__cancel__disj,axiom,
% 1.40/1.58 ! [K: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 1.40/1.58 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.58 & ( ord_less_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_mult_less_cancel_disj
% 1.40/1.58 thf(fact_688_mult__less__cancel2,axiom,
% 1.40/1.58 ! [M: nat,K: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 1.40/1.58 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.58 & ( ord_less_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_less_cancel2
% 1.40/1.58 thf(fact_689_nat__0__less__mult__iff,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 1.40/1.58 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.58 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_0_less_mult_iff
% 1.40/1.58 thf(fact_690_not__real__square__gt__zero,axiom,
% 1.40/1.58 ! [X: real] :
% 1.40/1.58 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 1.40/1.58 = ( X = zero_zero_real ) ) ).
% 1.40/1.58
% 1.40/1.58 % not_real_square_gt_zero
% 1.40/1.58 thf(fact_691_div__by__Suc__0,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 1.40/1.58 = M ) ).
% 1.40/1.58
% 1.40/1.58 % div_by_Suc_0
% 1.40/1.58 thf(fact_692_less__one,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ N @ one_one_nat )
% 1.40/1.58 = ( N = zero_zero_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % less_one
% 1.40/1.58 thf(fact_693_div__less,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ N )
% 1.40/1.58 => ( ( divide_divide_nat @ M @ N )
% 1.40/1.58 = zero_zero_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % div_less
% 1.40/1.58 thf(fact_694_nat__power__eq__Suc__0__iff,axiom,
% 1.40/1.58 ! [X: nat,M: nat] :
% 1.40/1.58 ( ( ( power_power_nat @ X @ M )
% 1.40/1.58 = ( suc @ zero_zero_nat ) )
% 1.40/1.58 = ( ( M = zero_zero_nat )
% 1.40/1.58 | ( X
% 1.40/1.58 = ( suc @ zero_zero_nat ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_power_eq_Suc_0_iff
% 1.40/1.58 thf(fact_695_power__Suc__0,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.58 = ( suc @ zero_zero_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % power_Suc_0
% 1.40/1.58 thf(fact_696_nat__zero__less__power__iff,axiom,
% 1.40/1.58 ! [X: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 1.40/1.58 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 1.40/1.58 | ( N = zero_zero_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_zero_less_power_iff
% 1.40/1.58 thf(fact_697_mod__by__Suc__0,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 1.40/1.58 = zero_zero_nat ) ).
% 1.40/1.58
% 1.40/1.58 % mod_by_Suc_0
% 1.40/1.58 thf(fact_698_nat__mult__div__cancel__disj,axiom,
% 1.40/1.58 ! [K: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( ( K = zero_zero_nat )
% 1.40/1.58 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 1.40/1.58 = zero_zero_nat ) )
% 1.40/1.58 & ( ( K != zero_zero_nat )
% 1.40/1.58 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 1.40/1.58 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_mult_div_cancel_disj
% 1.40/1.58 thf(fact_699_mod__less,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_nat @ M @ N )
% 1.40/1.58 => ( ( modulo_modulo_nat @ M @ N )
% 1.40/1.58 = M ) ) ).
% 1.40/1.58
% 1.40/1.58 % mod_less
% 1.40/1.58 thf(fact_700_mi__ma__2__deg,axiom,
% 1.40/1.58 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 1.40/1.58 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 1.40/1.58 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 1.40/1.58 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mi_ma_2_deg
% 1.40/1.58 thf(fact_701_one__le__mult__iff,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 1.40/1.58 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 1.40/1.58 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % one_le_mult_iff
% 1.40/1.58 thf(fact_702_nat__mult__le__cancel__disj,axiom,
% 1.40/1.58 ! [K: nat,M: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 1.40/1.58 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.58 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_mult_le_cancel_disj
% 1.40/1.58 thf(fact_703_mult__le__cancel2,axiom,
% 1.40/1.58 ! [M: nat,K: nat,N: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 1.40/1.58 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.58 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mult_le_cancel2
% 1.40/1.58 thf(fact_704_div__mult__self__is__m,axiom,
% 1.40/1.58 ! [N: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.58 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 1.40/1.58 = M ) ) ).
% 1.40/1.58
% 1.40/1.58 % div_mult_self_is_m
% 1.40/1.58 thf(fact_705_div__mult__self1__is__m,axiom,
% 1.40/1.58 ! [N: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.58 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 1.40/1.58 = M ) ) ).
% 1.40/1.58
% 1.40/1.58 % div_mult_self1_is_m
% 1.40/1.58 thf(fact_706_both__member__options__from__complete__tree__to__child,axiom,
% 1.40/1.58 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 1.40/1.58 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 1.40/1.58 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 1.40/1.58 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.58 | ( X = Mi )
% 1.40/1.58 | ( X = Ma ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % both_member_options_from_complete_tree_to_child
% 1.40/1.58 thf(fact_707_Suc__mod__mult__self1,axiom,
% 1.40/1.58 ! [M: nat,K: nat,N: nat] :
% 1.40/1.58 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 1.40/1.58 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_mod_mult_self1
% 1.40/1.58 thf(fact_708_Suc__mod__mult__self2,axiom,
% 1.40/1.58 ! [M: nat,N: nat,K: nat] :
% 1.40/1.58 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 1.40/1.58 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_mod_mult_self2
% 1.40/1.58 thf(fact_709_Suc__mod__mult__self3,axiom,
% 1.40/1.58 ! [K: nat,N: nat,M: nat] :
% 1.40/1.58 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 1.40/1.58 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_mod_mult_self3
% 1.40/1.58 thf(fact_710_Suc__mod__mult__self4,axiom,
% 1.40/1.58 ! [N: nat,K: nat,M: nat] :
% 1.40/1.58 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 1.40/1.58 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_mod_mult_self4
% 1.40/1.58 thf(fact_711_insert__simp__excp,axiom,
% 1.40/1.58 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 1.40/1.58 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 1.40/1.58 => ( ( ord_less_nat @ X @ Mi )
% 1.40/1.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 1.40/1.58 => ( ( X != Ma )
% 1.40/1.58 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 1.40/1.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % insert_simp_excp
% 1.40/1.58 thf(fact_712_insert__simp__norm,axiom,
% 1.40/1.58 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 1.40/1.58 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 1.40/1.58 => ( ( ord_less_nat @ Mi @ X )
% 1.40/1.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 1.40/1.58 => ( ( X != Ma )
% 1.40/1.58 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 1.40/1.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % insert_simp_norm
% 1.40/1.58 thf(fact_713_not__mod2__eq__Suc__0__eq__0,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.58 != ( suc @ zero_zero_nat ) )
% 1.40/1.58 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.58 = zero_zero_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % not_mod2_eq_Suc_0_eq_0
% 1.40/1.58 thf(fact_714_mod2__Suc__Suc,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.58 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mod2_Suc_Suc
% 1.40/1.58 thf(fact_715_add__self__mod__2,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.58 = zero_zero_nat ) ).
% 1.40/1.58
% 1.40/1.58 % add_self_mod_2
% 1.40/1.58 thf(fact_716_Suc__times__numeral__mod__eq,axiom,
% 1.40/1.58 ! [K: num,N: nat] :
% 1.40/1.58 ( ( ( numeral_numeral_nat @ K )
% 1.40/1.58 != one_one_nat )
% 1.40/1.58 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 1.40/1.58 = one_one_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_times_numeral_mod_eq
% 1.40/1.58 thf(fact_717_mod2__gr__0,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.58 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.58 = one_one_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % mod2_gr_0
% 1.40/1.58 thf(fact_718_mod__eq__0D,axiom,
% 1.40/1.58 ! [M: nat,D: nat] :
% 1.40/1.58 ( ( ( modulo_modulo_nat @ M @ D )
% 1.40/1.58 = zero_zero_nat )
% 1.40/1.58 => ? [Q3: nat] :
% 1.40/1.58 ( M
% 1.40/1.58 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mod_eq_0D
% 1.40/1.58 thf(fact_719_mod__Suc,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 1.40/1.58 = N )
% 1.40/1.58 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 1.40/1.58 = zero_zero_nat ) )
% 1.40/1.58 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 1.40/1.58 != N )
% 1.40/1.58 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 1.40/1.58 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % mod_Suc
% 1.40/1.58 thf(fact_720_mod__less__divisor,axiom,
% 1.40/1.58 ! [N: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.58 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % mod_less_divisor
% 1.40/1.58 thf(fact_721_vebt__buildup_Ocases,axiom,
% 1.40/1.58 ! [X: nat] :
% 1.40/1.58 ( ( X != zero_zero_nat )
% 1.40/1.58 => ( ( X
% 1.40/1.58 != ( suc @ zero_zero_nat ) )
% 1.40/1.58 => ~ ! [Va: nat] :
% 1.40/1.58 ( X
% 1.40/1.58 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % vebt_buildup.cases
% 1.40/1.58 thf(fact_722_mod__le__divisor,axiom,
% 1.40/1.58 ! [N: nat,M: nat] :
% 1.40/1.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.58 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % mod_le_divisor
% 1.40/1.58 thf(fact_723_realpow__pos__nth,axiom,
% 1.40/1.58 ! [N: nat,A: real] :
% 1.40/1.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.58 => ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.58 => ? [R3: real] :
% 1.40/1.58 ( ( ord_less_real @ zero_zero_real @ R3 )
% 1.40/1.58 & ( ( power_power_real @ R3 @ N )
% 1.40/1.58 = A ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % realpow_pos_nth
% 1.40/1.58 thf(fact_724_realpow__pos__nth__unique,axiom,
% 1.40/1.58 ! [N: nat,A: real] :
% 1.40/1.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.58 => ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.58 => ? [X5: real] :
% 1.40/1.58 ( ( ord_less_real @ zero_zero_real @ X5 )
% 1.40/1.58 & ( ( power_power_real @ X5 @ N )
% 1.40/1.58 = A )
% 1.40/1.58 & ! [Y: real] :
% 1.40/1.58 ( ( ( ord_less_real @ zero_zero_real @ Y )
% 1.40/1.58 & ( ( power_power_real @ Y @ N )
% 1.40/1.58 = A ) )
% 1.40/1.58 => ( Y = X5 ) ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % realpow_pos_nth_unique
% 1.40/1.58 thf(fact_725_mod__Suc__Suc__eq,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 1.40/1.58 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % mod_Suc_Suc_eq
% 1.40/1.58 thf(fact_726_mod__Suc__eq,axiom,
% 1.40/1.58 ! [M: nat,N: nat] :
% 1.40/1.58 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 1.40/1.58 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 1.40/1.58
% 1.40/1.58 % mod_Suc_eq
% 1.40/1.58 thf(fact_727_mod__less__eq__dividend,axiom,
% 1.40/1.58 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 1.40/1.58
% 1.40/1.58 % mod_less_eq_dividend
% 1.40/1.58 thf(fact_728_num_Osize_I4_J,axiom,
% 1.40/1.58 ( ( size_size_num @ one )
% 1.40/1.58 = zero_zero_nat ) ).
% 1.40/1.58
% 1.40/1.58 % num.size(4)
% 1.40/1.58 thf(fact_729_not0__implies__Suc,axiom,
% 1.40/1.58 ! [N: nat] :
% 1.40/1.58 ( ( N != zero_zero_nat )
% 1.40/1.58 => ? [M5: nat] :
% 1.40/1.58 ( N
% 1.40/1.58 = ( suc @ M5 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % not0_implies_Suc
% 1.40/1.58 thf(fact_730_Zero__not__Suc,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( zero_zero_nat
% 1.40/1.58 != ( suc @ M ) ) ).
% 1.40/1.58
% 1.40/1.58 % Zero_not_Suc
% 1.40/1.58 thf(fact_731_Zero__neq__Suc,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( zero_zero_nat
% 1.40/1.58 != ( suc @ M ) ) ).
% 1.40/1.58
% 1.40/1.58 % Zero_neq_Suc
% 1.40/1.58 thf(fact_732_Suc__neq__Zero,axiom,
% 1.40/1.58 ! [M: nat] :
% 1.40/1.58 ( ( suc @ M )
% 1.40/1.58 != zero_zero_nat ) ).
% 1.40/1.58
% 1.40/1.58 % Suc_neq_Zero
% 1.40/1.58 thf(fact_733_zero__induct,axiom,
% 1.40/1.58 ! [P: nat > $o,K: nat] :
% 1.40/1.58 ( ( P @ K )
% 1.40/1.58 => ( ! [N4: nat] :
% 1.40/1.58 ( ( P @ ( suc @ N4 ) )
% 1.40/1.58 => ( P @ N4 ) )
% 1.40/1.58 => ( P @ zero_zero_nat ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % zero_induct
% 1.40/1.58 thf(fact_734_diff__induct,axiom,
% 1.40/1.58 ! [P: nat > nat > $o,M: nat,N: nat] :
% 1.40/1.58 ( ! [X5: nat] : ( P @ X5 @ zero_zero_nat )
% 1.40/1.58 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 1.40/1.58 => ( ! [X5: nat,Y3: nat] :
% 1.40/1.58 ( ( P @ X5 @ Y3 )
% 1.40/1.58 => ( P @ ( suc @ X5 ) @ ( suc @ Y3 ) ) )
% 1.40/1.58 => ( P @ M @ N ) ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % diff_induct
% 1.40/1.58 thf(fact_735_nat__induct,axiom,
% 1.40/1.58 ! [P: nat > $o,N: nat] :
% 1.40/1.58 ( ( P @ zero_zero_nat )
% 1.40/1.58 => ( ! [N4: nat] :
% 1.40/1.58 ( ( P @ N4 )
% 1.40/1.58 => ( P @ ( suc @ N4 ) ) )
% 1.40/1.58 => ( P @ N ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat_induct
% 1.40/1.58 thf(fact_736_old_Onat_Oexhaust,axiom,
% 1.40/1.58 ! [Y2: nat] :
% 1.40/1.58 ( ( Y2 != zero_zero_nat )
% 1.40/1.58 => ~ ! [Nat3: nat] :
% 1.40/1.58 ( Y2
% 1.40/1.58 != ( suc @ Nat3 ) ) ) ).
% 1.40/1.58
% 1.40/1.58 % old.nat.exhaust
% 1.40/1.58 thf(fact_737_nat_OdiscI,axiom,
% 1.40/1.58 ! [Nat: nat,X23: nat] :
% 1.40/1.58 ( ( Nat
% 1.40/1.58 = ( suc @ X23 ) )
% 1.40/1.58 => ( Nat != zero_zero_nat ) ) ).
% 1.40/1.58
% 1.40/1.58 % nat.discI
% 1.40/1.58 thf(fact_738_old_Onat_Odistinct_I1_J,axiom,
% 1.40/1.58 ! [Nat2: nat] :
% 1.40/1.58 ( zero_zero_nat
% 1.40/1.58 != ( suc @ Nat2 ) ) ).
% 1.40/1.58
% 1.40/1.58 % old.nat.distinct(1)
% 1.40/1.58 thf(fact_739_old_Onat_Odistinct_I2_J,axiom,
% 1.40/1.58 ! [Nat2: nat] :
% 1.40/1.58 ( ( suc @ Nat2 )
% 1.40/1.58 != zero_zero_nat ) ).
% 1.40/1.58
% 1.40/1.58 % old.nat.distinct(2)
% 1.40/1.58 thf(fact_740_nat_Odistinct_I1_J,axiom,
% 1.40/1.58 ! [X23: nat] :
% 1.40/1.58 ( zero_zero_nat
% 1.40/1.59 != ( suc @ X23 ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat.distinct(1)
% 1.40/1.59 thf(fact_741_bot__nat__0_Oextremum__strict,axiom,
% 1.40/1.59 ! [A: nat] :
% 1.40/1.59 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 1.40/1.59
% 1.40/1.59 % bot_nat_0.extremum_strict
% 1.40/1.59 thf(fact_742_gr0I,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( N != zero_zero_nat )
% 1.40/1.59 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 1.40/1.59
% 1.40/1.59 % gr0I
% 1.40/1.59 thf(fact_743_not__gr0,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 1.40/1.59 = ( N = zero_zero_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % not_gr0
% 1.40/1.59 thf(fact_744_not__less0,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 1.40/1.59
% 1.40/1.59 % not_less0
% 1.40/1.59 thf(fact_745_less__zeroE,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 1.40/1.59
% 1.40/1.59 % less_zeroE
% 1.40/1.59 thf(fact_746_gr__implies__not0,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ M @ N )
% 1.40/1.59 => ( N != zero_zero_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % gr_implies_not0
% 1.40/1.59 thf(fact_747_infinite__descent0,axiom,
% 1.40/1.59 ! [P: nat > $o,N: nat] :
% 1.40/1.59 ( ( P @ zero_zero_nat )
% 1.40/1.59 => ( ! [N4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 1.40/1.59 => ( ~ ( P @ N4 )
% 1.40/1.59 => ? [M3: nat] :
% 1.40/1.59 ( ( ord_less_nat @ M3 @ N4 )
% 1.40/1.59 & ~ ( P @ M3 ) ) ) )
% 1.40/1.59 => ( P @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % infinite_descent0
% 1.40/1.59 thf(fact_748_less__eq__nat_Osimps_I1_J,axiom,
% 1.40/1.59 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 1.40/1.59
% 1.40/1.59 % less_eq_nat.simps(1)
% 1.40/1.59 thf(fact_749_bot__nat__0_Oextremum__unique,axiom,
% 1.40/1.59 ! [A: nat] :
% 1.40/1.59 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 1.40/1.59 = ( A = zero_zero_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % bot_nat_0.extremum_unique
% 1.40/1.59 thf(fact_750_bot__nat__0_Oextremum__uniqueI,axiom,
% 1.40/1.59 ! [A: nat] :
% 1.40/1.59 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 1.40/1.59 => ( A = zero_zero_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % bot_nat_0.extremum_uniqueI
% 1.40/1.59 thf(fact_751_le__0__eq,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 1.40/1.59 = ( N = zero_zero_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % le_0_eq
% 1.40/1.59 thf(fact_752_plus__nat_Oadd__0,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 1.40/1.59 = N ) ).
% 1.40/1.59
% 1.40/1.59 % plus_nat.add_0
% 1.40/1.59 thf(fact_753_add__eq__self__zero,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ( plus_plus_nat @ M @ N )
% 1.40/1.59 = M )
% 1.40/1.59 => ( N = zero_zero_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % add_eq_self_zero
% 1.40/1.59 thf(fact_754_mult__0,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( times_times_nat @ zero_zero_nat @ N )
% 1.40/1.59 = zero_zero_nat ) ).
% 1.40/1.59
% 1.40/1.59 % mult_0
% 1.40/1.59 thf(fact_755_nat__mult__eq__cancel__disj,axiom,
% 1.40/1.59 ! [K: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( ( times_times_nat @ K @ M )
% 1.40/1.59 = ( times_times_nat @ K @ N ) )
% 1.40/1.59 = ( ( K = zero_zero_nat )
% 1.40/1.59 | ( M = N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_mult_eq_cancel_disj
% 1.40/1.59 thf(fact_756_nat__mod__eq__iff,axiom,
% 1.40/1.59 ! [X: nat,N: nat,Y2: nat] :
% 1.40/1.59 ( ( ( modulo_modulo_nat @ X @ N )
% 1.40/1.59 = ( modulo_modulo_nat @ Y2 @ N ) )
% 1.40/1.59 = ( ? [Q1: nat,Q22: nat] :
% 1.40/1.59 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 1.40/1.59 = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_mod_eq_iff
% 1.40/1.59 thf(fact_757_neg__zdiv__mult__2,axiom,
% 1.40/1.59 ! [A: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 1.40/1.59 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 1.40/1.59 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % neg_zdiv_mult_2
% 1.40/1.59 thf(fact_758_pos__zdiv__mult__2,axiom,
% 1.40/1.59 ! [A: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 1.40/1.59 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 1.40/1.59 = ( divide_divide_int @ B @ A ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % pos_zdiv_mult_2
% 1.40/1.59 thf(fact_759_enat__0__less__mult__iff,axiom,
% 1.40/1.59 ! [M: extended_enat,N: extended_enat] :
% 1.40/1.59 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 1.40/1.59 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 1.40/1.59 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % enat_0_less_mult_iff
% 1.40/1.59 thf(fact_760_not__iless0,axiom,
% 1.40/1.59 ! [N: extended_enat] :
% 1.40/1.59 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 1.40/1.59
% 1.40/1.59 % not_iless0
% 1.40/1.59 thf(fact_761_split__mod,axiom,
% 1.40/1.59 ! [P: nat > $o,M: nat,N: nat] :
% 1.40/1.59 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 1.40/1.59 = ( ( ( N = zero_zero_nat )
% 1.40/1.59 => ( P @ M ) )
% 1.40/1.59 & ( ( N != zero_zero_nat )
% 1.40/1.59 => ! [I4: nat,J3: nat] :
% 1.40/1.59 ( ( ord_less_nat @ J3 @ N )
% 1.40/1.59 => ( ( M
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 1.40/1.59 => ( P @ J3 ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % split_mod
% 1.40/1.59 thf(fact_762_ile0__eq,axiom,
% 1.40/1.59 ! [N: extended_enat] :
% 1.40/1.59 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 1.40/1.59 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 1.40/1.59
% 1.40/1.59 % ile0_eq
% 1.40/1.59 thf(fact_763_i0__lb,axiom,
% 1.40/1.59 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 1.40/1.59
% 1.40/1.59 % i0_lb
% 1.40/1.59 thf(fact_764_Suc__times__mod__eq,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 1.40/1.59 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 1.40/1.59 = one_one_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % Suc_times_mod_eq
% 1.40/1.59 thf(fact_765_mod__induct,axiom,
% 1.40/1.59 ! [P: nat > $o,N: nat,P2: nat,M: nat] :
% 1.40/1.59 ( ( P @ N )
% 1.40/1.59 => ( ( ord_less_nat @ N @ P2 )
% 1.40/1.59 => ( ( ord_less_nat @ M @ P2 )
% 1.40/1.59 => ( ! [N4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ N4 @ P2 )
% 1.40/1.59 => ( ( P @ N4 )
% 1.40/1.59 => ( P @ ( modulo_modulo_nat @ ( suc @ N4 ) @ P2 ) ) ) )
% 1.40/1.59 => ( P @ M ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mod_induct
% 1.40/1.59 thf(fact_766_mod__Suc__le__divisor,axiom,
% 1.40/1.59 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 1.40/1.59
% 1.40/1.59 % mod_Suc_le_divisor
% 1.40/1.59 thf(fact_767_mod__eq__nat1E,axiom,
% 1.40/1.59 ! [M: nat,Q2: nat,N: nat] :
% 1.40/1.59 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 1.40/1.59 = ( modulo_modulo_nat @ N @ Q2 ) )
% 1.40/1.59 => ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.59 => ~ ! [S2: nat] :
% 1.40/1.59 ( M
% 1.40/1.59 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mod_eq_nat1E
% 1.40/1.59 thf(fact_768_mod__eq__nat2E,axiom,
% 1.40/1.59 ! [M: nat,Q2: nat,N: nat] :
% 1.40/1.59 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 1.40/1.59 = ( modulo_modulo_nat @ N @ Q2 ) )
% 1.40/1.59 => ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.59 => ~ ! [S2: nat] :
% 1.40/1.59 ( N
% 1.40/1.59 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S2 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mod_eq_nat2E
% 1.40/1.59 thf(fact_769_nat__mod__eq__lemma,axiom,
% 1.40/1.59 ! [X: nat,N: nat,Y2: nat] :
% 1.40/1.59 ( ( ( modulo_modulo_nat @ X @ N )
% 1.40/1.59 = ( modulo_modulo_nat @ Y2 @ N ) )
% 1.40/1.59 => ( ( ord_less_eq_nat @ Y2 @ X )
% 1.40/1.59 => ? [Q3: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( plus_plus_nat @ Y2 @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_mod_eq_lemma
% 1.40/1.59 thf(fact_770_not__exp__less__eq__0__int,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 1.40/1.59
% 1.40/1.59 % not_exp_less_eq_0_int
% 1.40/1.59 thf(fact_771_Ex__less__Suc2,axiom,
% 1.40/1.59 ! [N: nat,P: nat > $o] :
% 1.40/1.59 ( ( ? [I4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 1.40/1.59 & ( P @ I4 ) ) )
% 1.40/1.59 = ( ( P @ zero_zero_nat )
% 1.40/1.59 | ? [I4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I4 @ N )
% 1.40/1.59 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % Ex_less_Suc2
% 1.40/1.59 thf(fact_772_gr0__conv__Suc,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 = ( ? [M6: nat] :
% 1.40/1.59 ( N
% 1.40/1.59 = ( suc @ M6 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % gr0_conv_Suc
% 1.40/1.59 thf(fact_773_All__less__Suc2,axiom,
% 1.40/1.59 ! [N: nat,P: nat > $o] :
% 1.40/1.59 ( ( ! [I4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 1.40/1.59 => ( P @ I4 ) ) )
% 1.40/1.59 = ( ( P @ zero_zero_nat )
% 1.40/1.59 & ! [I4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I4 @ N )
% 1.40/1.59 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % All_less_Suc2
% 1.40/1.59 thf(fact_774_gr0__implies__Suc,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ? [M5: nat] :
% 1.40/1.59 ( N
% 1.40/1.59 = ( suc @ M5 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % gr0_implies_Suc
% 1.40/1.59 thf(fact_775_less__Suc__eq__0__disj,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 1.40/1.59 = ( ( M = zero_zero_nat )
% 1.40/1.59 | ? [J3: nat] :
% 1.40/1.59 ( ( M
% 1.40/1.59 = ( suc @ J3 ) )
% 1.40/1.59 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % less_Suc_eq_0_disj
% 1.40/1.59 thf(fact_776_add__is__1,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ( plus_plus_nat @ M @ N )
% 1.40/1.59 = ( suc @ zero_zero_nat ) )
% 1.40/1.59 = ( ( ( M
% 1.40/1.59 = ( suc @ zero_zero_nat ) )
% 1.40/1.59 & ( N = zero_zero_nat ) )
% 1.40/1.59 | ( ( M = zero_zero_nat )
% 1.40/1.59 & ( N
% 1.40/1.59 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % add_is_1
% 1.40/1.59 thf(fact_777_one__is__add,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ( suc @ zero_zero_nat )
% 1.40/1.59 = ( plus_plus_nat @ M @ N ) )
% 1.40/1.59 = ( ( ( M
% 1.40/1.59 = ( suc @ zero_zero_nat ) )
% 1.40/1.59 & ( N = zero_zero_nat ) )
% 1.40/1.59 | ( ( M = zero_zero_nat )
% 1.40/1.59 & ( N
% 1.40/1.59 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % one_is_add
% 1.40/1.59 thf(fact_778_ex__least__nat__le,axiom,
% 1.40/1.59 ! [P: nat > $o,N: nat] :
% 1.40/1.59 ( ( P @ N )
% 1.40/1.59 => ( ~ ( P @ zero_zero_nat )
% 1.40/1.59 => ? [K2: nat] :
% 1.40/1.59 ( ( ord_less_eq_nat @ K2 @ N )
% 1.40/1.59 & ! [I: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I @ K2 )
% 1.40/1.59 => ~ ( P @ I ) )
% 1.40/1.59 & ( P @ K2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % ex_least_nat_le
% 1.40/1.59 thf(fact_779_less__imp__add__positive,axiom,
% 1.40/1.59 ! [I2: nat,J: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.59 => ? [K2: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 1.40/1.59 & ( ( plus_plus_nat @ I2 @ K2 )
% 1.40/1.59 = J ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % less_imp_add_positive
% 1.40/1.59 thf(fact_780_realpow__pos__nth2,axiom,
% 1.40/1.59 ! [A: real,N: nat] :
% 1.40/1.59 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.59 => ? [R3: real] :
% 1.40/1.59 ( ( ord_less_real @ zero_zero_real @ R3 )
% 1.40/1.59 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 1.40/1.59 = A ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % realpow_pos_nth2
% 1.40/1.59 thf(fact_781_nat__mult__eq__cancel1,axiom,
% 1.40/1.59 ! [K: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.59 => ( ( ( times_times_nat @ K @ M )
% 1.40/1.59 = ( times_times_nat @ K @ N ) )
% 1.40/1.59 = ( M = N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_mult_eq_cancel1
% 1.40/1.59 thf(fact_782_nat__mult__less__cancel1,axiom,
% 1.40/1.59 ! [K: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.59 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 1.40/1.59 = ( ord_less_nat @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_mult_less_cancel1
% 1.40/1.59 thf(fact_783_mult__less__mono1,axiom,
% 1.40/1.59 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.59 => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mult_less_mono1
% 1.40/1.59 thf(fact_784_mult__less__mono2,axiom,
% 1.40/1.59 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.59 => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mult_less_mono2
% 1.40/1.59 thf(fact_785_One__nat__def,axiom,
% 1.40/1.59 ( one_one_nat
% 1.40/1.59 = ( suc @ zero_zero_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % One_nat_def
% 1.40/1.59 thf(fact_786_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ( divide_divide_nat @ M @ N )
% 1.40/1.59 = zero_zero_nat )
% 1.40/1.59 = ( ( ord_less_nat @ M @ N )
% 1.40/1.59 | ( N = zero_zero_nat ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % Euclidean_Division.div_eq_0_iff
% 1.40/1.59 thf(fact_787_nat__power__less__imp__less,axiom,
% 1.40/1.59 ! [I2: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 1.40/1.59 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 1.40/1.59 => ( ord_less_nat @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_power_less_imp_less
% 1.40/1.59 thf(fact_788_real__arch__pow__inv,axiom,
% 1.40/1.59 ! [Y2: real,X: real] :
% 1.40/1.59 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 1.40/1.59 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.59 => ? [N4: nat] : ( ord_less_real @ ( power_power_real @ X @ N4 ) @ Y2 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % real_arch_pow_inv
% 1.40/1.59 thf(fact_789_mult__eq__self__implies__10,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( M
% 1.40/1.59 = ( times_times_nat @ M @ N ) )
% 1.40/1.59 => ( ( N = one_one_nat )
% 1.40/1.59 | ( M = zero_zero_nat ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mult_eq_self_implies_10
% 1.40/1.59 thf(fact_790_pow_Osimps_I1_J,axiom,
% 1.40/1.59 ! [X: num] :
% 1.40/1.59 ( ( pow @ X @ one )
% 1.40/1.59 = X ) ).
% 1.40/1.59
% 1.40/1.59 % pow.simps(1)
% 1.40/1.59 thf(fact_791_mod__mult2__eq,axiom,
% 1.40/1.59 ! [M: nat,N: nat,Q2: nat] :
% 1.40/1.59 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mod_mult2_eq
% 1.40/1.59 thf(fact_792_bounded__Max__nat,axiom,
% 1.40/1.59 ! [P: nat > $o,X: nat,M7: nat] :
% 1.40/1.59 ( ( P @ X )
% 1.40/1.59 => ( ! [X5: nat] :
% 1.40/1.59 ( ( P @ X5 )
% 1.40/1.59 => ( ord_less_eq_nat @ X5 @ M7 ) )
% 1.40/1.59 => ~ ! [M5: nat] :
% 1.40/1.59 ( ( P @ M5 )
% 1.40/1.59 => ~ ! [X3: nat] :
% 1.40/1.59 ( ( P @ X3 )
% 1.40/1.59 => ( ord_less_eq_nat @ X3 @ M5 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % bounded_Max_nat
% 1.40/1.59 thf(fact_793_numeral__1__eq__Suc__0,axiom,
% 1.40/1.59 ( ( numeral_numeral_nat @ one )
% 1.40/1.59 = ( suc @ zero_zero_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % numeral_1_eq_Suc_0
% 1.40/1.59 thf(fact_794_num_Osize_I5_J,axiom,
% 1.40/1.59 ! [X23: num] :
% 1.40/1.59 ( ( size_size_num @ ( bit0 @ X23 ) )
% 1.40/1.59 = ( plus_plus_nat @ ( size_size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % num.size(5)
% 1.40/1.59 thf(fact_795_ex__least__nat__less,axiom,
% 1.40/1.59 ! [P: nat > $o,N: nat] :
% 1.40/1.59 ( ( P @ N )
% 1.40/1.59 => ( ~ ( P @ zero_zero_nat )
% 1.40/1.59 => ? [K2: nat] :
% 1.40/1.59 ( ( ord_less_nat @ K2 @ N )
% 1.40/1.59 & ! [I: nat] :
% 1.40/1.59 ( ( ord_less_eq_nat @ I @ K2 )
% 1.40/1.59 => ~ ( P @ I ) )
% 1.40/1.59 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % ex_least_nat_less
% 1.40/1.59 thf(fact_796_one__less__mult,axiom,
% 1.40/1.59 ! [N: nat,M: nat] :
% 1.40/1.59 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.59 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 1.40/1.59 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % one_less_mult
% 1.40/1.59 thf(fact_797_n__less__m__mult__n,axiom,
% 1.40/1.59 ! [N: nat,M: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 1.40/1.59 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % n_less_m_mult_n
% 1.40/1.59 thf(fact_798_n__less__n__mult__m,axiom,
% 1.40/1.59 ! [N: nat,M: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 1.40/1.59 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % n_less_n_mult_m
% 1.40/1.59 thf(fact_799_nat__induct__non__zero,axiom,
% 1.40/1.59 ! [N: nat,P: nat > $o] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ( P @ one_one_nat )
% 1.40/1.59 => ( ! [N4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 1.40/1.59 => ( ( P @ N4 )
% 1.40/1.59 => ( P @ ( suc @ N4 ) ) ) )
% 1.40/1.59 => ( P @ N ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_induct_non_zero
% 1.40/1.59 thf(fact_800_nat__mult__le__cancel1,axiom,
% 1.40/1.59 ! [K: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.59 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 1.40/1.59 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_mult_le_cancel1
% 1.40/1.59 thf(fact_801_power__gt__expt,axiom,
% 1.40/1.59 ! [N: nat,K: nat] :
% 1.40/1.59 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.59 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % power_gt_expt
% 1.40/1.59 thf(fact_802_div__le__mono2,axiom,
% 1.40/1.59 ! [M: nat,N: nat,K: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.59 => ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.59 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_le_mono2
% 1.40/1.59 thf(fact_803_div__greater__zero__iff,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 1.40/1.59 = ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.59 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_greater_zero_iff
% 1.40/1.59 thf(fact_804_nat__one__le__power,axiom,
% 1.40/1.59 ! [I2: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 1.40/1.59 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_one_le_power
% 1.40/1.59 thf(fact_805_div__less__iff__less__mult,axiom,
% 1.40/1.59 ! [Q2: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 1.40/1.59 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 1.40/1.59 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_less_iff_less_mult
% 1.40/1.59 thf(fact_806_nat__mult__div__cancel1,axiom,
% 1.40/1.59 ! [K: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.59 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 1.40/1.59 = ( divide_divide_nat @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_mult_div_cancel1
% 1.40/1.59 thf(fact_807_div__less__dividend,axiom,
% 1.40/1.59 ! [N: nat,M: nat] :
% 1.40/1.59 ( ( ord_less_nat @ one_one_nat @ N )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.59 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_less_dividend
% 1.40/1.59 thf(fact_808_div__eq__dividend__iff,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.59 => ( ( ( divide_divide_nat @ M @ N )
% 1.40/1.59 = M )
% 1.40/1.59 = ( N = one_one_nat ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_eq_dividend_iff
% 1.40/1.59 thf(fact_809_numeral__2__eq__2,axiom,
% 1.40/1.59 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 1.40/1.59 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % numeral_2_eq_2
% 1.40/1.59 thf(fact_810_pos2,axiom,
% 1.40/1.59 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 1.40/1.59
% 1.40/1.59 % pos2
% 1.40/1.59 thf(fact_811_less__eq__div__iff__mult__less__eq,axiom,
% 1.40/1.59 ! [Q2: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 1.40/1.59 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 1.40/1.59 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % less_eq_div_iff_mult_less_eq
% 1.40/1.59 thf(fact_812_split__div,axiom,
% 1.40/1.59 ! [P: nat > $o,M: nat,N: nat] :
% 1.40/1.59 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 1.40/1.59 = ( ( ( N = zero_zero_nat )
% 1.40/1.59 => ( P @ zero_zero_nat ) )
% 1.40/1.59 & ( ( N != zero_zero_nat )
% 1.40/1.59 => ! [I4: nat,J3: nat] :
% 1.40/1.59 ( ( ord_less_nat @ J3 @ N )
% 1.40/1.59 => ( ( M
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 1.40/1.59 => ( P @ I4 ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % split_div
% 1.40/1.59 thf(fact_813_dividend__less__div__times,axiom,
% 1.40/1.59 ! [N: nat,M: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % dividend_less_div_times
% 1.40/1.59 thf(fact_814_dividend__less__times__div,axiom,
% 1.40/1.59 ! [N: nat,M: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % dividend_less_times_div
% 1.40/1.59 thf(fact_815_less__2__cases,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.59 => ( ( N = zero_zero_nat )
% 1.40/1.59 | ( N
% 1.40/1.59 = ( suc @ zero_zero_nat ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % less_2_cases
% 1.40/1.59 thf(fact_816_less__2__cases__iff,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.59 = ( ( N = zero_zero_nat )
% 1.40/1.59 | ( N
% 1.40/1.59 = ( suc @ zero_zero_nat ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % less_2_cases_iff
% 1.40/1.59 thf(fact_817_nat__induct2,axiom,
% 1.40/1.59 ! [P: nat > $o,N: nat] :
% 1.40/1.59 ( ( P @ zero_zero_nat )
% 1.40/1.59 => ( ( P @ one_one_nat )
% 1.40/1.59 => ( ! [N4: nat] :
% 1.40/1.59 ( ( P @ N4 )
% 1.40/1.59 => ( P @ ( plus_plus_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.59 => ( P @ N ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_induct2
% 1.40/1.59 thf(fact_818_split__div_H,axiom,
% 1.40/1.59 ! [P: nat > $o,M: nat,N: nat] :
% 1.40/1.59 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 1.40/1.59 = ( ( ( N = zero_zero_nat )
% 1.40/1.59 & ( P @ zero_zero_nat ) )
% 1.40/1.59 | ? [Q4: nat] :
% 1.40/1.59 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 1.40/1.59 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 1.40/1.59 & ( P @ Q4 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % split_div'
% 1.40/1.59 thf(fact_819_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 1.40/1.59 ! [X: nat,N: nat,M: nat] :
% 1.40/1.59 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.59 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.exp_split_high_low(1)
% 1.40/1.59 thf(fact_820_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 1.40/1.59 ! [X: nat,N: nat,M: nat] :
% 1.40/1.59 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.59 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.exp_split_high_low(2)
% 1.40/1.59 thf(fact_821_invar__vebt_Ointros_I4_J,axiom,
% 1.40/1.59 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 1.40/1.59 ( ! [X5: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X5 @ N ) )
% 1.40/1.59 => ( ( vEBT_invar_vebt @ Summary @ M )
% 1.40/1.59 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 1.40/1.59 => ( ( M = N )
% 1.40/1.59 => ( ( Deg
% 1.40/1.59 = ( plus_plus_nat @ N @ M ) )
% 1.40/1.59 => ( ! [I3: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 1.40/1.59 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X2 ) )
% 1.40/1.59 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 1.40/1.59 => ( ( ( Mi = Ma )
% 1.40/1.59 => ! [X5: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.59 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 1.40/1.59 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 1.40/1.59 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 1.40/1.59 => ( ( ( Mi != Ma )
% 1.40/1.59 => ! [I3: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 1.40/1.59 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 1.40/1.59 = I3 )
% 1.40/1.59 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 1.40/1.59 & ! [X5: nat] :
% 1.40/1.59 ( ( ( ( vEBT_VEBT_high @ X5 @ N )
% 1.40/1.59 = I3 )
% 1.40/1.59 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X5 @ N ) ) )
% 1.40/1.59 => ( ( ord_less_nat @ Mi @ X5 )
% 1.40/1.59 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % invar_vebt.intros(4)
% 1.40/1.59 thf(fact_822_nat__bit__induct,axiom,
% 1.40/1.59 ! [P: nat > $o,N: nat] :
% 1.40/1.59 ( ( P @ zero_zero_nat )
% 1.40/1.59 => ( ! [N4: nat] :
% 1.40/1.59 ( ( P @ N4 )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 1.40/1.59 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 1.40/1.59 => ( ! [N4: nat] :
% 1.40/1.59 ( ( P @ N4 )
% 1.40/1.59 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 1.40/1.59 => ( P @ N ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_bit_induct
% 1.40/1.59 thf(fact_823_div__2__gt__zero,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.59 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_2_gt_zero
% 1.40/1.59 thf(fact_824_Suc__n__div__2__gt__zero,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % Suc_n_div_2_gt_zero
% 1.40/1.59 thf(fact_825_invar__vebt_Ointros_I5_J,axiom,
% 1.40/1.59 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 1.40/1.59 ( ! [X5: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X5 @ N ) )
% 1.40/1.59 => ( ( vEBT_invar_vebt @ Summary @ M )
% 1.40/1.59 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 1.40/1.59 => ( ( M
% 1.40/1.59 = ( suc @ N ) )
% 1.40/1.59 => ( ( Deg
% 1.40/1.59 = ( plus_plus_nat @ N @ M ) )
% 1.40/1.59 => ( ! [I3: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 1.40/1.59 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X2 ) )
% 1.40/1.59 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 1.40/1.59 => ( ( ( Mi = Ma )
% 1.40/1.59 => ! [X5: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.59 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 1.40/1.59 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 1.40/1.59 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 1.40/1.59 => ( ( ( Mi != Ma )
% 1.40/1.59 => ! [I3: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 1.40/1.59 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 1.40/1.59 = I3 )
% 1.40/1.59 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 1.40/1.59 & ! [X5: nat] :
% 1.40/1.59 ( ( ( ( vEBT_VEBT_high @ X5 @ N )
% 1.40/1.59 = I3 )
% 1.40/1.59 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X5 @ N ) ) )
% 1.40/1.59 => ( ( ord_less_nat @ Mi @ X5 )
% 1.40/1.59 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % invar_vebt.intros(5)
% 1.40/1.59 thf(fact_826_verit__le__mono__div,axiom,
% 1.40/1.59 ! [A2: nat,B2: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ A2 @ B2 )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ord_less_eq_nat
% 1.40/1.59 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 1.40/1.59 @ ( if_nat
% 1.40/1.59 @ ( ( modulo_modulo_nat @ B2 @ N )
% 1.40/1.59 = zero_zero_nat )
% 1.40/1.59 @ one_one_nat
% 1.40/1.59 @ zero_zero_nat ) )
% 1.40/1.59 @ ( divide_divide_nat @ B2 @ N ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % verit_le_mono_div
% 1.40/1.59 thf(fact_827_buildup__gives__valid,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 1.40/1.59
% 1.40/1.59 % buildup_gives_valid
% 1.40/1.59 thf(fact_828_vebt__member_Osimps_I4_J,axiom,
% 1.40/1.59 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 1.40/1.59 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_member.simps(4)
% 1.40/1.59 thf(fact_829_div__mod__decomp,axiom,
% 1.40/1.59 ! [A2: nat,N: nat] :
% 1.40/1.59 ( A2
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_mod_decomp
% 1.40/1.59 thf(fact_830_verit__eq__simplify_I8_J,axiom,
% 1.40/1.59 ! [X23: num,Y23: num] :
% 1.40/1.59 ( ( ( bit0 @ X23 )
% 1.40/1.59 = ( bit0 @ Y23 ) )
% 1.40/1.59 = ( X23 = Y23 ) ) ).
% 1.40/1.59
% 1.40/1.59 % verit_eq_simplify(8)
% 1.40/1.59 thf(fact_831_max__enat__simps_I2_J,axiom,
% 1.40/1.59 ! [Q2: extended_enat] :
% 1.40/1.59 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 1.40/1.59 = Q2 ) ).
% 1.40/1.59
% 1.40/1.59 % max_enat_simps(2)
% 1.40/1.59 thf(fact_832_max__enat__simps_I3_J,axiom,
% 1.40/1.59 ! [Q2: extended_enat] :
% 1.40/1.59 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 1.40/1.59 = Q2 ) ).
% 1.40/1.59
% 1.40/1.59 % max_enat_simps(3)
% 1.40/1.59 thf(fact_833_unset__bit__nonnegative__int__iff,axiom,
% 1.40/1.59 ! [N: nat,K: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 1.40/1.59 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 1.40/1.59
% 1.40/1.59 % unset_bit_nonnegative_int_iff
% 1.40/1.59 thf(fact_834_set__bit__nonnegative__int__iff,axiom,
% 1.40/1.59 ! [N: nat,K: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 1.40/1.59 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 1.40/1.59
% 1.40/1.59 % set_bit_nonnegative_int_iff
% 1.40/1.59 thf(fact_835_flip__bit__nonnegative__int__iff,axiom,
% 1.40/1.59 ! [N: nat,K: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 1.40/1.59 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 1.40/1.59
% 1.40/1.59 % flip_bit_nonnegative_int_iff
% 1.40/1.59 thf(fact_836_unset__bit__negative__int__iff,axiom,
% 1.40/1.59 ! [N: nat,K: int] :
% 1.40/1.59 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 1.40/1.59 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 1.40/1.59
% 1.40/1.59 % unset_bit_negative_int_iff
% 1.40/1.59 thf(fact_837_set__bit__negative__int__iff,axiom,
% 1.40/1.59 ! [N: nat,K: int] :
% 1.40/1.59 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 1.40/1.59 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 1.40/1.59
% 1.40/1.59 % set_bit_negative_int_iff
% 1.40/1.59 thf(fact_838_flip__bit__negative__int__iff,axiom,
% 1.40/1.59 ! [N: nat,K: int] :
% 1.40/1.59 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 1.40/1.59 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 1.40/1.59
% 1.40/1.59 % flip_bit_negative_int_iff
% 1.40/1.59 thf(fact_839_mod__pos__pos__trivial,axiom,
% 1.40/1.59 ! [K: int,L2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.59 => ( ( ord_less_int @ K @ L2 )
% 1.40/1.59 => ( ( modulo_modulo_int @ K @ L2 )
% 1.40/1.59 = K ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mod_pos_pos_trivial
% 1.40/1.59 thf(fact_840_mod__neg__neg__trivial,axiom,
% 1.40/1.59 ! [K: int,L2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_int @ L2 @ K )
% 1.40/1.59 => ( ( modulo_modulo_int @ K @ L2 )
% 1.40/1.59 = K ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mod_neg_neg_trivial
% 1.40/1.59 thf(fact_841_zmod__numeral__Bit0,axiom,
% 1.40/1.59 ! [V: num,W: num] :
% 1.40/1.59 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 1.40/1.59 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zmod_numeral_Bit0
% 1.40/1.59 thf(fact_842_zle__add1__eq__le,axiom,
% 1.40/1.59 ! [W: int,Z: int] :
% 1.40/1.59 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 1.40/1.59 = ( ord_less_eq_int @ W @ Z ) ) ).
% 1.40/1.59
% 1.40/1.59 % zle_add1_eq_le
% 1.40/1.59 thf(fact_843_div__pos__pos__trivial,axiom,
% 1.40/1.59 ! [K: int,L2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.59 => ( ( ord_less_int @ K @ L2 )
% 1.40/1.59 => ( ( divide_divide_int @ K @ L2 )
% 1.40/1.59 = zero_zero_int ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_pos_pos_trivial
% 1.40/1.59 thf(fact_844_div__neg__neg__trivial,axiom,
% 1.40/1.59 ! [K: int,L2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_int @ L2 @ K )
% 1.40/1.59 => ( ( divide_divide_int @ K @ L2 )
% 1.40/1.59 = zero_zero_int ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_neg_neg_trivial
% 1.40/1.59 thf(fact_845_times__int__code_I2_J,axiom,
% 1.40/1.59 ! [L2: int] :
% 1.40/1.59 ( ( times_times_int @ zero_zero_int @ L2 )
% 1.40/1.59 = zero_zero_int ) ).
% 1.40/1.59
% 1.40/1.59 % times_int_code(2)
% 1.40/1.59 thf(fact_846_times__int__code_I1_J,axiom,
% 1.40/1.59 ! [K: int] :
% 1.40/1.59 ( ( times_times_int @ K @ zero_zero_int )
% 1.40/1.59 = zero_zero_int ) ).
% 1.40/1.59
% 1.40/1.59 % times_int_code(1)
% 1.40/1.59 thf(fact_847_zmod__eq__0D,axiom,
% 1.40/1.59 ! [M: int,D: int] :
% 1.40/1.59 ( ( ( modulo_modulo_int @ M @ D )
% 1.40/1.59 = zero_zero_int )
% 1.40/1.59 => ? [Q3: int] :
% 1.40/1.59 ( M
% 1.40/1.59 = ( times_times_int @ D @ Q3 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zmod_eq_0D
% 1.40/1.59 thf(fact_848_zmod__eq__0__iff,axiom,
% 1.40/1.59 ! [M: int,D: int] :
% 1.40/1.59 ( ( ( modulo_modulo_int @ M @ D )
% 1.40/1.59 = zero_zero_int )
% 1.40/1.59 = ( ? [Q4: int] :
% 1.40/1.59 ( M
% 1.40/1.59 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zmod_eq_0_iff
% 1.40/1.59 thf(fact_849_imult__is__0,axiom,
% 1.40/1.59 ! [M: extended_enat,N: extended_enat] :
% 1.40/1.59 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 1.40/1.59 = zero_z5237406670263579293d_enat )
% 1.40/1.59 = ( ( M = zero_z5237406670263579293d_enat )
% 1.40/1.59 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % imult_is_0
% 1.40/1.59 thf(fact_850_mod__pos__neg__trivial,axiom,
% 1.40/1.59 ! [K: int,L2: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.59 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 1.40/1.59 => ( ( modulo_modulo_int @ K @ L2 )
% 1.40/1.59 = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mod_pos_neg_trivial
% 1.40/1.59 thf(fact_851_zmod__zmult2__eq,axiom,
% 1.40/1.59 ! [C: int,A: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 1.40/1.59 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zmod_zmult2_eq
% 1.40/1.59 thf(fact_852_zdiv__zmult2__eq,axiom,
% 1.40/1.59 ! [C: int,A: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 1.40/1.59 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 1.40/1.59 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdiv_zmult2_eq
% 1.40/1.59 thf(fact_853_unique__quotient__lemma__neg,axiom,
% 1.40/1.59 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 1.40/1.59 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_int @ B @ R2 )
% 1.40/1.59 => ( ( ord_less_int @ B @ R4 )
% 1.40/1.59 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % unique_quotient_lemma_neg
% 1.40/1.59 thf(fact_854_nonneg1__imp__zdiv__pos__iff,axiom,
% 1.40/1.59 ! [A: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 1.40/1.59 = ( ( ord_less_eq_int @ B @ A )
% 1.40/1.59 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nonneg1_imp_zdiv_pos_iff
% 1.40/1.59 thf(fact_855_Euclidean__Division_Opos__mod__sign,axiom,
% 1.40/1.59 ! [L2: int,K: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ L2 )
% 1.40/1.59 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % Euclidean_Division.pos_mod_sign
% 1.40/1.59 thf(fact_856_neg__mod__sign,axiom,
% 1.40/1.59 ! [L2: int,K: int] :
% 1.40/1.59 ( ( ord_less_int @ L2 @ zero_zero_int )
% 1.40/1.59 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 1.40/1.59
% 1.40/1.59 % neg_mod_sign
% 1.40/1.59 thf(fact_857_zmod__le__nonneg__dividend,axiom,
% 1.40/1.59 ! [M: int,K: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 1.40/1.59 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 1.40/1.59
% 1.40/1.59 % zmod_le_nonneg_dividend
% 1.40/1.59 thf(fact_858_pos__imp__zdiv__nonneg__iff,axiom,
% 1.40/1.59 ! [B: int,A: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 1.40/1.59 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % pos_imp_zdiv_nonneg_iff
% 1.40/1.59 thf(fact_859_neg__imp__zdiv__nonneg__iff,axiom,
% 1.40/1.59 ! [B: int,A: int] :
% 1.40/1.59 ( ( ord_less_int @ B @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 1.40/1.59 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % neg_imp_zdiv_nonneg_iff
% 1.40/1.59 thf(fact_860_unique__quotient__lemma,axiom,
% 1.40/1.59 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 1.40/1.59 => ( ( ord_less_int @ R4 @ B )
% 1.40/1.59 => ( ( ord_less_int @ R2 @ B )
% 1.40/1.59 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % unique_quotient_lemma
% 1.40/1.59 thf(fact_861_int__one__le__iff__zero__less,axiom,
% 1.40/1.59 ! [Z: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ one_one_int @ Z )
% 1.40/1.59 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_one_le_iff_zero_less
% 1.40/1.59 thf(fact_862_zdiv__mono2__neg__lemma,axiom,
% 1.40/1.59 ! [B: int,Q2: int,R2: int,B3: int,Q5: int,R4: int] :
% 1.40/1.59 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R4 ) )
% 1.40/1.59 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R4 ) @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_int @ R2 @ B )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 1.40/1.59 => ( ( ord_less_eq_int @ B3 @ B )
% 1.40/1.59 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdiv_mono2_neg_lemma
% 1.40/1.59 thf(fact_863_pos__imp__zdiv__pos__iff,axiom,
% 1.40/1.59 ! [K: int,I2: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 1.40/1.59 = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % pos_imp_zdiv_pos_iff
% 1.40/1.59 thf(fact_864_div__nonpos__pos__le0,axiom,
% 1.40/1.59 ! [A: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.59 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_nonpos_pos_le0
% 1.40/1.59 thf(fact_865_div__nonneg__neg__le0,axiom,
% 1.40/1.59 ! [A: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 1.40/1.59 => ( ( ord_less_int @ B @ zero_zero_int )
% 1.40/1.59 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_nonneg_neg_le0
% 1.40/1.59 thf(fact_866_verit__le__mono__div__int,axiom,
% 1.40/1.59 ! [A2: int,B2: int,N: int] :
% 1.40/1.59 ( ( ord_less_int @ A2 @ B2 )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ N )
% 1.40/1.59 => ( ord_less_eq_int
% 1.40/1.59 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 1.40/1.59 @ ( if_int
% 1.40/1.59 @ ( ( modulo_modulo_int @ B2 @ N )
% 1.40/1.59 = zero_zero_int )
% 1.40/1.59 @ one_one_int
% 1.40/1.59 @ zero_zero_int ) )
% 1.40/1.59 @ ( divide_divide_int @ B2 @ N ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % verit_le_mono_div_int
% 1.40/1.59 thf(fact_867_int__div__less__self,axiom,
% 1.40/1.59 ! [X: int,K: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ X )
% 1.40/1.59 => ( ( ord_less_int @ one_one_int @ K )
% 1.40/1.59 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_div_less_self
% 1.40/1.59 thf(fact_868_zmod__trivial__iff,axiom,
% 1.40/1.59 ! [I2: int,K: int] :
% 1.40/1.59 ( ( ( modulo_modulo_int @ I2 @ K )
% 1.40/1.59 = I2 )
% 1.40/1.59 = ( ( K = zero_zero_int )
% 1.40/1.59 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 1.40/1.59 & ( ord_less_int @ I2 @ K ) )
% 1.40/1.59 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 1.40/1.59 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zmod_trivial_iff
% 1.40/1.59 thf(fact_869_zdiv__mono2__lemma,axiom,
% 1.40/1.59 ! [B: int,Q2: int,R2: int,B3: int,Q5: int,R4: int] :
% 1.40/1.59 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R4 ) )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R4 ) )
% 1.40/1.59 => ( ( ord_less_int @ R4 @ B3 )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 1.40/1.59 => ( ( ord_less_eq_int @ B3 @ B )
% 1.40/1.59 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdiv_mono2_lemma
% 1.40/1.59 thf(fact_870_div__positive__int,axiom,
% 1.40/1.59 ! [L2: int,K: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ L2 @ K )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ L2 )
% 1.40/1.59 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_positive_int
% 1.40/1.59 thf(fact_871_split__pos__lemma,axiom,
% 1.40/1.59 ! [K: int,P: int > int > $o,N: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.59 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 1.40/1.59 = ( ! [I4: int,J3: int] :
% 1.40/1.59 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 1.40/1.59 & ( ord_less_int @ J3 @ K )
% 1.40/1.59 & ( N
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 1.40/1.59 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % split_pos_lemma
% 1.40/1.59 thf(fact_872_split__neg__lemma,axiom,
% 1.40/1.59 ! [K: int,P: int > int > $o,N: int] :
% 1.40/1.59 ( ( ord_less_int @ K @ zero_zero_int )
% 1.40/1.59 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 1.40/1.59 = ( ! [I4: int,J3: int] :
% 1.40/1.59 ( ( ( ord_less_int @ K @ J3 )
% 1.40/1.59 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 1.40/1.59 & ( N
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 1.40/1.59 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % split_neg_lemma
% 1.40/1.59 thf(fact_873_div__int__pos__iff,axiom,
% 1.40/1.59 ! [K: int,L2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 1.40/1.59 = ( ( K = zero_zero_int )
% 1.40/1.59 | ( L2 = zero_zero_int )
% 1.40/1.59 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.59 & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 1.40/1.59 | ( ( ord_less_int @ K @ zero_zero_int )
% 1.40/1.59 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_int_pos_iff
% 1.40/1.59 thf(fact_874_div__mod__decomp__int,axiom,
% 1.40/1.59 ! [A2: int,N: int] :
% 1.40/1.59 ( A2
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_mod_decomp_int
% 1.40/1.59 thf(fact_875_zless__imp__add1__zle,axiom,
% 1.40/1.59 ! [W: int,Z: int] :
% 1.40/1.59 ( ( ord_less_int @ W @ Z )
% 1.40/1.59 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 1.40/1.59
% 1.40/1.59 % zless_imp_add1_zle
% 1.40/1.59 thf(fact_876_pos__zmult__eq__1__iff,axiom,
% 1.40/1.59 ! [M: int,N: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ M )
% 1.40/1.59 => ( ( ( times_times_int @ M @ N )
% 1.40/1.59 = one_one_int )
% 1.40/1.59 = ( ( M = one_one_int )
% 1.40/1.59 & ( N = one_one_int ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % pos_zmult_eq_1_iff
% 1.40/1.59 thf(fact_877_zdiv__mono2__neg,axiom,
% 1.40/1.59 ! [A: int,B3: int,B: int] :
% 1.40/1.59 ( ( ord_less_int @ A @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 1.40/1.59 => ( ( ord_less_eq_int @ B3 @ B )
% 1.40/1.59 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B3 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdiv_mono2_neg
% 1.40/1.59 thf(fact_878_zdiv__mono1__neg,axiom,
% 1.40/1.59 ! [A: int,A3: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ A @ A3 )
% 1.40/1.59 => ( ( ord_less_int @ B @ zero_zero_int )
% 1.40/1.59 => ( ord_less_eq_int @ ( divide_divide_int @ A3 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdiv_mono1_neg
% 1.40/1.59 thf(fact_879_int__mod__pos__eq,axiom,
% 1.40/1.59 ! [A: int,B: int,Q2: int,R2: int] :
% 1.40/1.59 ( ( A
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 1.40/1.59 => ( ( ord_less_int @ R2 @ B )
% 1.40/1.59 => ( ( modulo_modulo_int @ A @ B )
% 1.40/1.59 = R2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_mod_pos_eq
% 1.40/1.59 thf(fact_880_int__mod__neg__eq,axiom,
% 1.40/1.59 ! [A: int,B: int,Q2: int,R2: int] :
% 1.40/1.59 ( ( A
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 1.40/1.59 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_int @ B @ R2 )
% 1.40/1.59 => ( ( modulo_modulo_int @ A @ B )
% 1.40/1.59 = R2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_mod_neg_eq
% 1.40/1.59 thf(fact_881_int__div__pos__eq,axiom,
% 1.40/1.59 ! [A: int,B: int,Q2: int,R2: int] :
% 1.40/1.59 ( ( A
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 1.40/1.59 => ( ( ord_less_int @ R2 @ B )
% 1.40/1.59 => ( ( divide_divide_int @ A @ B )
% 1.40/1.59 = Q2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_div_pos_eq
% 1.40/1.59 thf(fact_882_int__div__neg__eq,axiom,
% 1.40/1.59 ! [A: int,B: int,Q2: int,R2: int] :
% 1.40/1.59 ( ( A
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 1.40/1.59 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_int @ B @ R2 )
% 1.40/1.59 => ( ( divide_divide_int @ A @ B )
% 1.40/1.59 = Q2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_div_neg_eq
% 1.40/1.59 thf(fact_883_zmult__zless__mono2,axiom,
% 1.40/1.59 ! [I2: int,J: int,K: int] :
% 1.40/1.59 ( ( ord_less_int @ I2 @ J )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.59 => ( ord_less_int @ ( times_times_int @ K @ I2 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zmult_zless_mono2
% 1.40/1.59 thf(fact_884_zdiv__eq__0__iff,axiom,
% 1.40/1.59 ! [I2: int,K: int] :
% 1.40/1.59 ( ( ( divide_divide_int @ I2 @ K )
% 1.40/1.59 = zero_zero_int )
% 1.40/1.59 = ( ( K = zero_zero_int )
% 1.40/1.59 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 1.40/1.59 & ( ord_less_int @ I2 @ K ) )
% 1.40/1.59 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 1.40/1.59 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdiv_eq_0_iff
% 1.40/1.59 thf(fact_885_pos__mod__conj,axiom,
% 1.40/1.59 ! [B: int,A: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 1.40/1.59 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % pos_mod_conj
% 1.40/1.59 thf(fact_886_neg__mod__conj,axiom,
% 1.40/1.59 ! [B: int,A: int] :
% 1.40/1.59 ( ( ord_less_int @ B @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 1.40/1.59 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % neg_mod_conj
% 1.40/1.59 thf(fact_887_q__pos__lemma,axiom,
% 1.40/1.59 ! [B3: int,Q5: int,R4: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R4 ) )
% 1.40/1.59 => ( ( ord_less_int @ R4 @ B3 )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 1.40/1.59 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % q_pos_lemma
% 1.40/1.59 thf(fact_888_zdiv__mono2,axiom,
% 1.40/1.59 ! [A: int,B3: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 1.40/1.59 => ( ( ord_less_eq_int @ B3 @ B )
% 1.40/1.59 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B3 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdiv_mono2
% 1.40/1.59 thf(fact_889_zdiv__mono1,axiom,
% 1.40/1.59 ! [A: int,A3: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ A @ A3 )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.59 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A3 @ B ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdiv_mono1
% 1.40/1.59 thf(fact_890_split__zmod,axiom,
% 1.40/1.59 ! [P: int > $o,N: int,K: int] :
% 1.40/1.59 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 1.40/1.59 = ( ( ( K = zero_zero_int )
% 1.40/1.59 => ( P @ N ) )
% 1.40/1.59 & ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.59 => ! [I4: int,J3: int] :
% 1.40/1.59 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 1.40/1.59 & ( ord_less_int @ J3 @ K )
% 1.40/1.59 & ( N
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 1.40/1.59 => ( P @ J3 ) ) )
% 1.40/1.59 & ( ( ord_less_int @ K @ zero_zero_int )
% 1.40/1.59 => ! [I4: int,J3: int] :
% 1.40/1.59 ( ( ( ord_less_int @ K @ J3 )
% 1.40/1.59 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 1.40/1.59 & ( N
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 1.40/1.59 => ( P @ J3 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % split_zmod
% 1.40/1.59 thf(fact_891_split__zdiv,axiom,
% 1.40/1.59 ! [P: int > $o,N: int,K: int] :
% 1.40/1.59 ( ( P @ ( divide_divide_int @ N @ K ) )
% 1.40/1.59 = ( ( ( K = zero_zero_int )
% 1.40/1.59 => ( P @ zero_zero_int ) )
% 1.40/1.59 & ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.59 => ! [I4: int,J3: int] :
% 1.40/1.59 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 1.40/1.59 & ( ord_less_int @ J3 @ K )
% 1.40/1.59 & ( N
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 1.40/1.59 => ( P @ I4 ) ) )
% 1.40/1.59 & ( ( ord_less_int @ K @ zero_zero_int )
% 1.40/1.59 => ! [I4: int,J3: int] :
% 1.40/1.59 ( ( ( ord_less_int @ K @ J3 )
% 1.40/1.59 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 1.40/1.59 & ( N
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 1.40/1.59 => ( P @ I4 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % split_zdiv
% 1.40/1.59 thf(fact_892_le__imp__0__less,axiom,
% 1.40/1.59 ! [Z: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.59 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % le_imp_0_less
% 1.40/1.59 thf(fact_893_add1__zle__eq,axiom,
% 1.40/1.59 ! [W: int,Z: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 1.40/1.59 = ( ord_less_int @ W @ Z ) ) ).
% 1.40/1.59
% 1.40/1.59 % add1_zle_eq
% 1.40/1.59 thf(fact_894_less__eq__int__code_I1_J,axiom,
% 1.40/1.59 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 1.40/1.59
% 1.40/1.59 % less_eq_int_code(1)
% 1.40/1.59 thf(fact_895_zero__one__enat__neq_I1_J,axiom,
% 1.40/1.59 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 1.40/1.59
% 1.40/1.59 % zero_one_enat_neq(1)
% 1.40/1.59 thf(fact_896_int__gr__induct,axiom,
% 1.40/1.59 ! [K: int,I2: int,P: int > $o] :
% 1.40/1.59 ( ( ord_less_int @ K @ I2 )
% 1.40/1.59 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 1.40/1.59 => ( ! [I3: int] :
% 1.40/1.59 ( ( ord_less_int @ K @ I3 )
% 1.40/1.59 => ( ( P @ I3 )
% 1.40/1.59 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 1.40/1.59 => ( P @ I2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_gr_induct
% 1.40/1.59 thf(fact_897_zless__add1__eq,axiom,
% 1.40/1.59 ! [W: int,Z: int] :
% 1.40/1.59 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 1.40/1.59 = ( ( ord_less_int @ W @ Z )
% 1.40/1.59 | ( W = Z ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zless_add1_eq
% 1.40/1.59 thf(fact_898_odd__less__0__iff,axiom,
% 1.40/1.59 ! [Z: int] :
% 1.40/1.59 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 1.40/1.59 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 1.40/1.59
% 1.40/1.59 % odd_less_0_iff
% 1.40/1.59 thf(fact_899_iadd__is__0,axiom,
% 1.40/1.59 ! [M: extended_enat,N: extended_enat] :
% 1.40/1.59 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 1.40/1.59 = zero_z5237406670263579293d_enat )
% 1.40/1.59 = ( ( M = zero_z5237406670263579293d_enat )
% 1.40/1.59 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % iadd_is_0
% 1.40/1.59 thf(fact_900_odd__nonzero,axiom,
% 1.40/1.59 ! [Z: int] :
% 1.40/1.59 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 1.40/1.59 != zero_zero_int ) ).
% 1.40/1.59
% 1.40/1.59 % odd_nonzero
% 1.40/1.59 thf(fact_901_plus__int__code_I1_J,axiom,
% 1.40/1.59 ! [K: int] :
% 1.40/1.59 ( ( plus_plus_int @ K @ zero_zero_int )
% 1.40/1.59 = K ) ).
% 1.40/1.59
% 1.40/1.59 % plus_int_code(1)
% 1.40/1.59 thf(fact_902_plus__int__code_I2_J,axiom,
% 1.40/1.59 ! [L2: int] :
% 1.40/1.59 ( ( plus_plus_int @ zero_zero_int @ L2 )
% 1.40/1.59 = L2 ) ).
% 1.40/1.59
% 1.40/1.59 % plus_int_code(2)
% 1.40/1.59 thf(fact_903_Euclidean__Division_Opos__mod__bound,axiom,
% 1.40/1.59 ! [L2: int,K: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ L2 )
% 1.40/1.59 => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 1.40/1.59
% 1.40/1.59 % Euclidean_Division.pos_mod_bound
% 1.40/1.59 thf(fact_904_neg__mod__bound,axiom,
% 1.40/1.59 ! [L2: int,K: int] :
% 1.40/1.59 ( ( ord_less_int @ L2 @ zero_zero_int )
% 1.40/1.59 => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % neg_mod_bound
% 1.40/1.59 thf(fact_905_int__distrib_I2_J,axiom,
% 1.40/1.59 ! [W: int,Z12: int,Z22: int] :
% 1.40/1.59 ( ( times_times_int @ W @ ( plus_plus_int @ Z12 @ Z22 ) )
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ W @ Z12 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_distrib(2)
% 1.40/1.59 thf(fact_906_int__distrib_I1_J,axiom,
% 1.40/1.59 ! [Z12: int,Z22: int,W: int] :
% 1.40/1.59 ( ( times_times_int @ ( plus_plus_int @ Z12 @ Z22 ) @ W )
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ Z12 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_distrib(1)
% 1.40/1.59 thf(fact_907_int__ge__induct,axiom,
% 1.40/1.59 ! [K: int,I2: int,P: int > $o] :
% 1.40/1.59 ( ( ord_less_eq_int @ K @ I2 )
% 1.40/1.59 => ( ( P @ K )
% 1.40/1.59 => ( ! [I3: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ K @ I3 )
% 1.40/1.59 => ( ( P @ I3 )
% 1.40/1.59 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 1.40/1.59 => ( P @ I2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_ge_induct
% 1.40/1.59 thf(fact_908_verit__la__generic,axiom,
% 1.40/1.59 ! [A: int,X: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ A @ X )
% 1.40/1.59 | ( A = X )
% 1.40/1.59 | ( ord_less_eq_int @ X @ A ) ) ).
% 1.40/1.59
% 1.40/1.59 % verit_la_generic
% 1.40/1.59 thf(fact_909_unset__bit__less__eq,axiom,
% 1.40/1.59 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 1.40/1.59
% 1.40/1.59 % unset_bit_less_eq
% 1.40/1.59 thf(fact_910_set__bit__greater__eq,axiom,
% 1.40/1.59 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 1.40/1.59
% 1.40/1.59 % set_bit_greater_eq
% 1.40/1.59 thf(fact_911_pos__zmod__mult__2,axiom,
% 1.40/1.59 ! [A: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 1.40/1.59 => ( ( 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 ) )
% 1.40/1.59 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % pos_zmod_mult_2
% 1.40/1.59 thf(fact_912_verit__eq__simplify_I10_J,axiom,
% 1.40/1.59 ! [X23: num] :
% 1.40/1.59 ( one
% 1.40/1.59 != ( bit0 @ X23 ) ) ).
% 1.40/1.59
% 1.40/1.59 % verit_eq_simplify(10)
% 1.40/1.59 thf(fact_913_div__less__mono,axiom,
% 1.40/1.59 ! [A2: nat,B2: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ A2 @ B2 )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 1.40/1.59 = zero_zero_nat )
% 1.40/1.59 => ( ( ( modulo_modulo_nat @ B2 @ N )
% 1.40/1.59 = zero_zero_nat )
% 1.40/1.59 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B2 @ N ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_less_mono
% 1.40/1.59 thf(fact_914_vebt__member_Osimps_I3_J,axiom,
% 1.40/1.59 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 1.40/1.59 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_member.simps(3)
% 1.40/1.59 thf(fact_915_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 1.40/1.59 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 1.40/1.59 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.minNull.simps(5)
% 1.40/1.59 thf(fact_916_incr__mult__lemma,axiom,
% 1.40/1.59 ! [D: int,P: int > $o,K: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ D )
% 1.40/1.59 => ( ! [X5: int] :
% 1.40/1.59 ( ( P @ X5 )
% 1.40/1.59 => ( P @ ( plus_plus_int @ X5 @ D ) ) )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.59 => ! [X3: int] :
% 1.40/1.59 ( ( P @ X3 )
% 1.40/1.59 => ( P @ ( plus_plus_int @ X3 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % incr_mult_lemma
% 1.40/1.59 thf(fact_917_vebt__insert_Osimps_I3_J,axiom,
% 1.40/1.59 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 1.40/1.59 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 1.40/1.59 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_insert.simps(3)
% 1.40/1.59 thf(fact_918_buildup__nothing__in__leaf,axiom,
% 1.40/1.59 ! [N: nat,X: nat] :
% 1.40/1.59 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 1.40/1.59
% 1.40/1.59 % buildup_nothing_in_leaf
% 1.40/1.59 thf(fact_919_invar__vebt_Ointros_I3_J,axiom,
% 1.40/1.59 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 1.40/1.59 ( ! [X5: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X5 @ N ) )
% 1.40/1.59 => ( ( vEBT_invar_vebt @ Summary @ M )
% 1.40/1.59 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 1.40/1.59 => ( ( M
% 1.40/1.59 = ( suc @ N ) )
% 1.40/1.59 => ( ( Deg
% 1.40/1.59 = ( plus_plus_nat @ N @ M ) )
% 1.40/1.59 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 1.40/1.59 => ( ! [X5: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.59 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % invar_vebt.intros(3)
% 1.40/1.59 thf(fact_920_vebt__insert_Osimps_I2_J,axiom,
% 1.40/1.59 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 1.40/1.59 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 1.40/1.59 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_insert.simps(2)
% 1.40/1.59 thf(fact_921_Leaf__0__not,axiom,
% 1.40/1.59 ! [A: $o,B: $o] :
% 1.40/1.59 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 1.40/1.59
% 1.40/1.59 % Leaf_0_not
% 1.40/1.59 thf(fact_922_deg1Leaf,axiom,
% 1.40/1.59 ! [T: vEBT_VEBT] :
% 1.40/1.59 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 1.40/1.59 = ( ? [A4: $o,B4: $o] :
% 1.40/1.59 ( T
% 1.40/1.59 = ( vEBT_Leaf @ A4 @ B4 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % deg1Leaf
% 1.40/1.59 thf(fact_923_deg__1__Leaf,axiom,
% 1.40/1.59 ! [T: vEBT_VEBT] :
% 1.40/1.59 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 1.40/1.59 => ? [A5: $o,B5: $o] :
% 1.40/1.59 ( T
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % deg_1_Leaf
% 1.40/1.59 thf(fact_924_deg__1__Leafy,axiom,
% 1.40/1.59 ! [T: vEBT_VEBT,N: nat] :
% 1.40/1.59 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.59 => ( ( N = one_one_nat )
% 1.40/1.59 => ? [A5: $o,B5: $o] :
% 1.40/1.59 ( T
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % deg_1_Leafy
% 1.40/1.59 thf(fact_925_VEBT__internal_Ovalid_H_Ocases,axiom,
% 1.40/1.59 ! [X: produc9072475918466114483BT_nat] :
% 1.40/1.59 ( ! [Uu: $o,Uv: $o,D3: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ D3 ) )
% 1.40/1.59 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Deg3 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.valid'.cases
% 1.40/1.59 thf(fact_926_VEBT__internal_OminNull_Ocases,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 != ( vEBT_Leaf @ $false @ $false ) )
% 1.40/1.59 => ( ! [Uv: $o] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Leaf @ $true @ Uv ) )
% 1.40/1.59 => ( ! [Uu: $o] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Leaf @ Uu @ $true ) )
% 1.40/1.59 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) )
% 1.40/1.59 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.minNull.cases
% 1.40/1.59 thf(fact_927_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT] :
% 1.40/1.59 ( ( vEBT_VEBT_minNull @ X )
% 1.40/1.59 => ( ( X
% 1.40/1.59 != ( vEBT_Leaf @ $false @ $false ) )
% 1.40/1.59 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.minNull.elims(2)
% 1.40/1.59 thf(fact_928_VEBT_Oexhaust,axiom,
% 1.40/1.59 ! [Y2: vEBT_VEBT] :
% 1.40/1.59 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 1.40/1.59 ( Y2
% 1.40/1.59 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 1.40/1.59 => ~ ! [X212: $o,X222: $o] :
% 1.40/1.59 ( Y2
% 1.40/1.59 != ( vEBT_Leaf @ X212 @ X222 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT.exhaust
% 1.40/1.59 thf(fact_929_VEBT_Odistinct_I1_J,axiom,
% 1.40/1.59 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X22: $o] :
% 1.40/1.59 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 1.40/1.59 != ( vEBT_Leaf @ X21 @ X22 ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT.distinct(1)
% 1.40/1.59 thf(fact_930_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 1.40/1.59 ! [A: $o,B: $o,X: nat] :
% 1.40/1.59 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 1.40/1.59 = ( ( ( X = zero_zero_nat )
% 1.40/1.59 => A )
% 1.40/1.59 & ( ( X != zero_zero_nat )
% 1.40/1.59 => ( ( ( X = one_one_nat )
% 1.40/1.59 => B )
% 1.40/1.59 & ( X = one_one_nat ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.naive_member.simps(1)
% 1.40/1.59 thf(fact_931_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 1.40/1.59 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.minNull.simps(1)
% 1.40/1.59 thf(fact_932_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 1.40/1.59 ! [Uv2: $o] :
% 1.40/1.59 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv2 ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.minNull.simps(2)
% 1.40/1.59 thf(fact_933_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 1.40/1.59 ! [Uu2: $o] :
% 1.40/1.59 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu2 @ $true ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.minNull.simps(3)
% 1.40/1.59 thf(fact_934_vebt__insert_Ocases,axiom,
% 1.40/1.59 ! [X: produc9072475918466114483BT_nat] :
% 1.40/1.59 ( ! [A5: $o,B5: $o,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X5 ) )
% 1.40/1.59 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ X5 ) )
% 1.40/1.59 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X5 ) )
% 1.40/1.59 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X5 ) )
% 1.40/1.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_insert.cases
% 1.40/1.59 thf(fact_935_VEBT__internal_Onaive__member_Ocases,axiom,
% 1.40/1.59 ! [X: produc9072475918466114483BT_nat] :
% 1.40/1.59 ( ! [A5: $o,B5: $o,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X5 ) )
% 1.40/1.59 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) )
% 1.40/1.59 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ X5 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.naive_member.cases
% 1.40/1.59 thf(fact_936_VEBT__internal_Omembermima_Ocases,axiom,
% 1.40/1.59 ! [X: produc9072475918466114483BT_nat] :
% 1.40/1.59 ( ! [Uu: $o,Uv: $o,Uw: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) )
% 1.40/1.59 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) @ Uz2 ) )
% 1.40/1.59 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X5 ) )
% 1.40/1.59 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X5 ) )
% 1.40/1.59 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ X5 ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.membermima.cases
% 1.40/1.59 thf(fact_937_vebt__member_Ocases,axiom,
% 1.40/1.59 ! [X: produc9072475918466114483BT_nat] :
% 1.40/1.59 ( ! [A5: $o,B5: $o,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X5 ) )
% 1.40/1.59 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X5 ) )
% 1.40/1.59 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X5 ) )
% 1.40/1.59 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X5 ) )
% 1.40/1.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_member.cases
% 1.40/1.59 thf(fact_938_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Y2: $o] :
% 1.40/1.59 ( ( ( vEBT_VEBT_minNull @ X )
% 1.40/1.59 = Y2 )
% 1.40/1.59 => ( ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ $false @ $false ) )
% 1.40/1.59 => ~ Y2 )
% 1.40/1.59 => ( ( ? [Uv: $o] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Leaf @ $true @ Uv ) )
% 1.40/1.59 => Y2 )
% 1.40/1.59 => ( ( ? [Uu: $o] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Leaf @ Uu @ $true ) )
% 1.40/1.59 => Y2 )
% 1.40/1.59 => ( ( ? [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) )
% 1.40/1.59 => ~ Y2 )
% 1.40/1.59 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 1.40/1.59 => Y2 ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.minNull.elims(1)
% 1.40/1.59 thf(fact_939_vebt__insert_Osimps_I1_J,axiom,
% 1.40/1.59 ! [X: nat,A: $o,B: $o] :
% 1.40/1.59 ( ( ( X = zero_zero_nat )
% 1.40/1.59 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 1.40/1.59 = ( vEBT_Leaf @ $true @ B ) ) )
% 1.40/1.59 & ( ( X != zero_zero_nat )
% 1.40/1.59 => ( ( ( X = one_one_nat )
% 1.40/1.59 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 1.40/1.59 = ( vEBT_Leaf @ A @ $true ) ) )
% 1.40/1.59 & ( ( X != one_one_nat )
% 1.40/1.59 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 1.40/1.59 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_insert.simps(1)
% 1.40/1.59 thf(fact_940_vebt__member_Osimps_I2_J,axiom,
% 1.40/1.59 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X: nat] :
% 1.40/1.59 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_member.simps(2)
% 1.40/1.59 thf(fact_941_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 1.40/1.59 ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.minNull.simps(4)
% 1.40/1.59 thf(fact_942_invar__vebt_Ointros_I1_J,axiom,
% 1.40/1.59 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % invar_vebt.intros(1)
% 1.40/1.59 thf(fact_943_vebt__buildup_Osimps_I2_J,axiom,
% 1.40/1.59 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 1.40/1.59 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_buildup.simps(2)
% 1.40/1.59 thf(fact_944_vebt__member_Osimps_I1_J,axiom,
% 1.40/1.59 ! [A: $o,B: $o,X: nat] :
% 1.40/1.59 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 1.40/1.59 = ( ( ( X = zero_zero_nat )
% 1.40/1.59 => A )
% 1.40/1.59 & ( ( X != zero_zero_nat )
% 1.40/1.59 => ( ( ( X = one_one_nat )
% 1.40/1.59 => B )
% 1.40/1.59 & ( X = one_one_nat ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_member.simps(1)
% 1.40/1.59 thf(fact_945_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 1.40/1.59 ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 1.40/1.59 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.naive_member.simps(2)
% 1.40/1.59 thf(fact_946_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT] :
% 1.40/1.59 ( ~ ( vEBT_VEBT_minNull @ X )
% 1.40/1.59 => ( ! [Uv: $o] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Leaf @ $true @ Uv ) )
% 1.40/1.59 => ( ! [Uu: $o] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Leaf @ Uu @ $true ) )
% 1.40/1.59 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.minNull.elims(3)
% 1.40/1.59 thf(fact_947_vebt__insert_Osimps_I4_J,axiom,
% 1.40/1.59 ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 1.40/1.59 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X )
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_insert.simps(4)
% 1.40/1.59 thf(fact_948_imp__le__cong,axiom,
% 1.40/1.59 ! [X: int,X6: int,P: $o,P3: $o] :
% 1.40/1.59 ( ( X = X6 )
% 1.40/1.59 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 1.40/1.59 => ( P = P3 ) )
% 1.40/1.59 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.59 => P )
% 1.40/1.59 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 1.40/1.59 => P3 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % imp_le_cong
% 1.40/1.59 thf(fact_949_conj__le__cong,axiom,
% 1.40/1.59 ! [X: int,X6: int,P: $o,P3: $o] :
% 1.40/1.59 ( ( X = X6 )
% 1.40/1.59 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 1.40/1.59 => ( P = P3 ) )
% 1.40/1.59 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.59 & P )
% 1.40/1.59 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 1.40/1.59 & P3 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % conj_le_cong
% 1.40/1.59 thf(fact_950_invar__vebt_Ocases,axiom,
% 1.40/1.59 ! [A1: vEBT_VEBT,A22: nat] :
% 1.40/1.59 ( ( vEBT_invar_vebt @ A1 @ A22 )
% 1.40/1.59 => ( ( ? [A5: $o,B5: $o] :
% 1.40/1.59 ( A1
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ( A22
% 1.40/1.59 != ( suc @ zero_zero_nat ) ) )
% 1.40/1.59 => ( ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat] :
% 1.40/1.59 ( ( A1
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( ( A22 = Deg2 )
% 1.40/1.59 => ( ! [X3: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 1.40/1.59 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 1.40/1.59 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 1.40/1.59 => ( ( M5 = N4 )
% 1.40/1.59 => ( ( Deg2
% 1.40/1.59 = ( plus_plus_nat @ N4 @ M5 ) )
% 1.40/1.59 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 1.40/1.59 => ~ ! [X3: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.59 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) ) ) ) ) ) ) ) )
% 1.40/1.59 => ( ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat] :
% 1.40/1.59 ( ( A1
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( ( A22 = Deg2 )
% 1.40/1.59 => ( ! [X3: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 1.40/1.59 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 1.40/1.59 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 1.40/1.59 => ( ( M5
% 1.40/1.59 = ( suc @ N4 ) )
% 1.40/1.59 => ( ( Deg2
% 1.40/1.59 = ( plus_plus_nat @ N4 @ M5 ) )
% 1.40/1.59 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 1.40/1.59 => ~ ! [X3: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.59 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) ) ) ) ) ) ) ) )
% 1.40/1.59 => ( ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 1.40/1.59 ( ( A1
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( ( A22 = Deg2 )
% 1.40/1.59 => ( ! [X3: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 1.40/1.59 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 1.40/1.59 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 1.40/1.59 => ( ( M5 = N4 )
% 1.40/1.59 => ( ( Deg2
% 1.40/1.59 = ( plus_plus_nat @ N4 @ M5 ) )
% 1.40/1.59 => ( ! [I: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 1.40/1.59 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X2 ) )
% 1.40/1.59 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 1.40/1.59 => ( ( ( Mi2 = Ma2 )
% 1.40/1.59 => ! [X3: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.59 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 1.40/1.59 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 1.40/1.59 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.59 => ~ ( ( Mi2 != Ma2 )
% 1.40/1.59 => ! [I: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 1.40/1.59 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N4 )
% 1.40/1.59 = I )
% 1.40/1.59 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N4 ) ) )
% 1.40/1.59 & ! [X3: nat] :
% 1.40/1.59 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 1.40/1.59 = I )
% 1.40/1.59 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 1.40/1.59 => ( ( ord_less_nat @ Mi2 @ X3 )
% 1.40/1.59 & ( ord_less_eq_nat @ X3 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 1.40/1.59 => ~ ! [TreeList3: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,M5: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 1.40/1.59 ( ( A1
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( ( A22 = Deg2 )
% 1.40/1.59 => ( ! [X3: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 1.40/1.59 => ( ( vEBT_invar_vebt @ Summary2 @ M5 )
% 1.40/1.59 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 1.40/1.59 => ( ( M5
% 1.40/1.59 = ( suc @ N4 ) )
% 1.40/1.59 => ( ( Deg2
% 1.40/1.59 = ( plus_plus_nat @ N4 @ M5 ) )
% 1.40/1.59 => ( ! [I: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 1.40/1.59 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X2 ) )
% 1.40/1.59 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 1.40/1.59 => ( ( ( Mi2 = Ma2 )
% 1.40/1.59 => ! [X3: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.59 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 1.40/1.59 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 1.40/1.59 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.59 => ~ ( ( Mi2 != Ma2 )
% 1.40/1.59 => ! [I: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 1.40/1.59 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N4 )
% 1.40/1.59 = I )
% 1.40/1.59 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N4 ) ) )
% 1.40/1.59 & ! [X3: nat] :
% 1.40/1.59 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 1.40/1.59 = I )
% 1.40/1.59 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 1.40/1.59 => ( ( ord_less_nat @ Mi2 @ X3 )
% 1.40/1.59 & ( ord_less_eq_nat @ X3 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % invar_vebt.cases
% 1.40/1.59 thf(fact_951_invar__vebt_Osimps,axiom,
% 1.40/1.59 ( vEBT_invar_vebt
% 1.40/1.59 = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 1.40/1.59 ( ( ? [A4: $o,B4: $o] :
% 1.40/1.59 ( A12
% 1.40/1.59 = ( vEBT_Leaf @ A4 @ B4 ) )
% 1.40/1.59 & ( A23
% 1.40/1.59 = ( suc @ zero_zero_nat ) ) )
% 1.40/1.59 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 1.40/1.59 ( ( A12
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 1.40/1.59 & ! [X4: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 1.40/1.59 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 1.40/1.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 1.40/1.59 & ( A23
% 1.40/1.59 = ( plus_plus_nat @ N2 @ N2 ) )
% 1.40/1.59 & ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X2 )
% 1.40/1.59 & ! [X4: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 1.40/1.59 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.59 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 1.40/1.59 ( ( A12
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList @ Summary3 ) )
% 1.40/1.59 & ! [X4: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 1.40/1.59 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 1.40/1.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 1.40/1.59 & ( A23
% 1.40/1.59 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 1.40/1.59 & ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X2 )
% 1.40/1.59 & ! [X4: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 1.40/1.59 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.59 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 1.40/1.59 ( ( A12
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 1.40/1.59 & ! [X4: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 1.40/1.59 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 1.40/1.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 1.40/1.59 & ( A23
% 1.40/1.59 = ( plus_plus_nat @ N2 @ N2 ) )
% 1.40/1.59 & ! [I4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 1.40/1.59 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X2 ) )
% 1.40/1.59 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 1.40/1.59 & ( ( Mi3 = Ma3 )
% 1.40/1.59 => ! [X4: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 1.40/1.59 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.59 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 1.40/1.59 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 1.40/1.59 & ( ( Mi3 != Ma3 )
% 1.40/1.59 => ! [I4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 1.40/1.59 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 1.40/1.59 = I4 )
% 1.40/1.59 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 1.40/1.59 & ! [X4: nat] :
% 1.40/1.59 ( ( ( ( vEBT_VEBT_high @ X4 @ N2 )
% 1.40/1.59 = I4 )
% 1.40/1.59 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X4 @ N2 ) ) )
% 1.40/1.59 => ( ( ord_less_nat @ Mi3 @ X4 )
% 1.40/1.59 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) )
% 1.40/1.59 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 1.40/1.59 ( ( A12
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList @ Summary3 ) )
% 1.40/1.59 & ! [X4: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X4 @ N2 ) )
% 1.40/1.59 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 1.40/1.59 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 1.40/1.59 & ( A23
% 1.40/1.59 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 1.40/1.59 & ! [I4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 1.40/1.59 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X2 ) )
% 1.40/1.59 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 1.40/1.59 & ( ( Mi3 = Ma3 )
% 1.40/1.59 => ! [X4: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 1.40/1.59 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.59 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 1.40/1.59 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 1.40/1.59 & ( ( Mi3 != Ma3 )
% 1.40/1.59 => ! [I4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 1.40/1.59 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 1.40/1.59 = I4 )
% 1.40/1.59 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 1.40/1.59 & ! [X4: nat] :
% 1.40/1.59 ( ( ( ( vEBT_VEBT_high @ X4 @ N2 )
% 1.40/1.59 = I4 )
% 1.40/1.59 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X4 @ N2 ) ) )
% 1.40/1.59 => ( ( ord_less_nat @ Mi3 @ X4 )
% 1.40/1.59 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % invar_vebt.simps
% 1.40/1.59 thf(fact_952_invar__vebt_Ointros_I2_J,axiom,
% 1.40/1.59 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 1.40/1.59 ( ! [X5: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ X5 @ N ) )
% 1.40/1.59 => ( ( vEBT_invar_vebt @ Summary @ M )
% 1.40/1.59 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 1.40/1.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 1.40/1.59 => ( ( M = N )
% 1.40/1.59 => ( ( Deg
% 1.40/1.59 = ( plus_plus_nat @ N @ M ) )
% 1.40/1.59 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 1.40/1.59 => ( ! [X5: vEBT_VEBT] :
% 1.40/1.59 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.59 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 1.40/1.59 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % invar_vebt.intros(2)
% 1.40/1.59 thf(fact_953_member__valid__both__member__options,axiom,
% 1.40/1.59 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 1.40/1.59 ( ( vEBT_invar_vebt @ Tree @ N )
% 1.40/1.59 => ( ( vEBT_vebt_member @ Tree @ X )
% 1.40/1.59 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 1.40/1.59 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % member_valid_both_member_options
% 1.40/1.59 thf(fact_954_both__member__options__def,axiom,
% 1.40/1.59 ( vEBT_V8194947554948674370ptions
% 1.40/1.59 = ( ^ [T2: vEBT_VEBT,X4: nat] :
% 1.40/1.59 ( ( vEBT_V5719532721284313246member @ T2 @ X4 )
% 1.40/1.59 | ( vEBT_VEBT_membermima @ T2 @ X4 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % both_member_options_def
% 1.40/1.59 thf(fact_955_pos__eucl__rel__int__mult__2,axiom,
% 1.40/1.59 ! [B: int,A: int,Q2: int,R2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 1.40/1.59 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % pos_eucl_rel_int_mult_2
% 1.40/1.59 thf(fact_956_gcd__nat__induct,axiom,
% 1.40/1.59 ! [P: nat > nat > $o,M: nat,N: nat] :
% 1.40/1.59 ( ! [M5: nat] : ( P @ M5 @ zero_zero_nat )
% 1.40/1.59 => ( ! [M5: nat,N4: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 1.40/1.59 => ( ( P @ N4 @ ( modulo_modulo_nat @ M5 @ N4 ) )
% 1.40/1.59 => ( P @ M5 @ N4 ) ) )
% 1.40/1.59 => ( P @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % gcd_nat_induct
% 1.40/1.59 thf(fact_957_concat__bit__Suc,axiom,
% 1.40/1.59 ! [N: nat,K: int,L2: int] :
% 1.40/1.59 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 1.40/1.59 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % concat_bit_Suc
% 1.40/1.59 thf(fact_958_buildup__nothing__in__min__max,axiom,
% 1.40/1.59 ! [N: nat,X: nat] :
% 1.40/1.59 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 1.40/1.59
% 1.40/1.59 % buildup_nothing_in_min_max
% 1.40/1.59 thf(fact_959_concat__bit__0,axiom,
% 1.40/1.59 ! [K: int,L2: int] :
% 1.40/1.59 ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 1.40/1.59 = L2 ) ).
% 1.40/1.59
% 1.40/1.59 % concat_bit_0
% 1.40/1.59 thf(fact_960_concat__bit__nonnegative__iff,axiom,
% 1.40/1.59 ! [N: nat,K: int,L2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L2 ) )
% 1.40/1.59 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 1.40/1.59
% 1.40/1.59 % concat_bit_nonnegative_iff
% 1.40/1.59 thf(fact_961_concat__bit__negative__iff,axiom,
% 1.40/1.59 ! [N: nat,K: int,L2: int] :
% 1.40/1.59 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L2 ) @ zero_zero_int )
% 1.40/1.59 = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 1.40/1.59
% 1.40/1.59 % concat_bit_negative_iff
% 1.40/1.59 thf(fact_962_concat__bit__assoc,axiom,
% 1.40/1.59 ! [N: nat,K: int,M: nat,L2: int,R2: int] :
% 1.40/1.59 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R2 ) )
% 1.40/1.59 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R2 ) ) ).
% 1.40/1.59
% 1.40/1.59 % concat_bit_assoc
% 1.40/1.59 thf(fact_963_eucl__rel__int__dividesI,axiom,
% 1.40/1.59 ! [L2: int,K: int,Q2: int] :
% 1.40/1.59 ( ( L2 != zero_zero_int )
% 1.40/1.59 => ( ( K
% 1.40/1.59 = ( times_times_int @ Q2 @ L2 ) )
% 1.40/1.59 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % eucl_rel_int_dividesI
% 1.40/1.59 thf(fact_964_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 1.40/1.59 ! [Ux2: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 1.40/1.59 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy ) @ Uz ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.membermima.simps(2)
% 1.40/1.59 thf(fact_965_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 1.40/1.59 ! [Mi: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 1.40/1.59 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X )
% 1.40/1.59 = ( ( X = Mi )
% 1.40/1.59 | ( X = Ma ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.membermima.simps(3)
% 1.40/1.59 thf(fact_966_Euclid__induct,axiom,
% 1.40/1.59 ! [P: nat > nat > $o,A: nat,B: nat] :
% 1.40/1.59 ( ! [A5: nat,B5: nat] :
% 1.40/1.59 ( ( P @ A5 @ B5 )
% 1.40/1.59 = ( P @ B5 @ A5 ) )
% 1.40/1.59 => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 1.40/1.59 => ( ! [A5: nat,B5: nat] :
% 1.40/1.59 ( ( P @ A5 @ B5 )
% 1.40/1.59 => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 1.40/1.59 => ( P @ A @ B ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % Euclid_induct
% 1.40/1.59 thf(fact_967_eucl__rel__int__iff,axiom,
% 1.40/1.59 ! [K: int,L2: int,Q2: int,R2: int] :
% 1.40/1.59 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 1.40/1.59 = ( ( K
% 1.40/1.59 = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R2 ) )
% 1.40/1.59 & ( ( ord_less_int @ zero_zero_int @ L2 )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 1.40/1.59 & ( ord_less_int @ R2 @ L2 ) ) )
% 1.40/1.59 & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 1.40/1.59 => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 1.40/1.59 => ( ( ord_less_int @ L2 @ R2 )
% 1.40/1.59 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 1.40/1.59 & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 1.40/1.59 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % eucl_rel_int_iff
% 1.40/1.59 thf(fact_968_neg__eucl__rel__int__mult__2,axiom,
% 1.40/1.59 ! [B: int,A: int,Q2: int,R2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 1.40/1.59 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % neg_eucl_rel_int_mult_2
% 1.40/1.59 thf(fact_969_vebt__insert_Oelims,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 1.40/1.59 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 1.40/1.59 = Y2 )
% 1.40/1.59 => ( ! [A5: $o,B5: $o] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ~ ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 1.40/1.59 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.59 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 1.40/1.59 & ( ( Xa2 != one_one_nat )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) ) )
% 1.40/1.59 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) ) )
% 1.40/1.59 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) )
% 1.40/1.59 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 1.40/1.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 != ( if_VEBT_VEBT
% 1.40/1.59 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 & ~ ( ( Xa2 = Mi2 )
% 1.40/1.59 | ( Xa2 = Ma2 ) ) )
% 1.40/1.59 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 1.40/1.59 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_insert.elims
% 1.40/1.59 thf(fact_970_set__vebt_H__def,axiom,
% 1.40/1.59 ( vEBT_VEBT_set_vebt
% 1.40/1.59 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % set_vebt'_def
% 1.40/1.59 thf(fact_971_nat__dvd__1__iff__1,axiom,
% 1.40/1.59 ! [M: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 1.40/1.59 = ( M = one_one_nat ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_dvd_1_iff_1
% 1.40/1.59 thf(fact_972_dvd__1__iff__1,axiom,
% 1.40/1.59 ! [M: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 1.40/1.59 = ( M
% 1.40/1.59 = ( suc @ zero_zero_nat ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % dvd_1_iff_1
% 1.40/1.59 thf(fact_973_dvd__1__left,axiom,
% 1.40/1.59 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 1.40/1.59
% 1.40/1.59 % dvd_1_left
% 1.40/1.59 thf(fact_974_nat__mult__dvd__cancel__disj,axiom,
% 1.40/1.59 ! [K: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 1.40/1.59 = ( ( K = zero_zero_nat )
% 1.40/1.59 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_mult_dvd_cancel_disj
% 1.40/1.59 thf(fact_975_even__Suc,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 1.40/1.59 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % even_Suc
% 1.40/1.59 thf(fact_976_even__Suc__Suc__iff,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 1.40/1.59 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.59
% 1.40/1.59 % even_Suc_Suc_iff
% 1.40/1.59 thf(fact_977_zle__diff1__eq,axiom,
% 1.40/1.59 ! [W: int,Z: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 1.40/1.59 = ( ord_less_int @ W @ Z ) ) ).
% 1.40/1.59
% 1.40/1.59 % zle_diff1_eq
% 1.40/1.59 thf(fact_978_odd__Suc__div__two,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.59 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.59 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % odd_Suc_div_two
% 1.40/1.59 thf(fact_979_even__Suc__div__two,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.59 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.59 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % even_Suc_div_two
% 1.40/1.59 thf(fact_980_signed__take__bit__Suc__bit0,axiom,
% 1.40/1.59 ! [N: nat,K: num] :
% 1.40/1.59 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 1.40/1.59 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % signed_take_bit_Suc_bit0
% 1.40/1.59 thf(fact_981_signed__take__bit__diff,axiom,
% 1.40/1.59 ! [N: nat,K: int,L2: int] :
% 1.40/1.59 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 1.40/1.59 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % signed_take_bit_diff
% 1.40/1.59 thf(fact_982_signed__take__bit__mult,axiom,
% 1.40/1.59 ! [N: nat,K: int,L2: int] :
% 1.40/1.59 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 1.40/1.59 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % signed_take_bit_mult
% 1.40/1.59 thf(fact_983_signed__take__bit__add,axiom,
% 1.40/1.59 ! [N: nat,K: int,L2: int] :
% 1.40/1.59 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 1.40/1.59 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % signed_take_bit_add
% 1.40/1.59 thf(fact_984_int__distrib_I4_J,axiom,
% 1.40/1.59 ! [W: int,Z12: int,Z22: int] :
% 1.40/1.59 ( ( times_times_int @ W @ ( minus_minus_int @ Z12 @ Z22 ) )
% 1.40/1.59 = ( minus_minus_int @ ( times_times_int @ W @ Z12 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_distrib(4)
% 1.40/1.59 thf(fact_985_int__distrib_I3_J,axiom,
% 1.40/1.59 ! [Z12: int,Z22: int,W: int] :
% 1.40/1.59 ( ( times_times_int @ ( minus_minus_int @ Z12 @ Z22 ) @ W )
% 1.40/1.59 = ( minus_minus_int @ ( times_times_int @ Z12 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_distrib(3)
% 1.40/1.59 thf(fact_986_set__vebt__def,axiom,
% 1.40/1.59 ( vEBT_set_vebt
% 1.40/1.59 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % set_vebt_def
% 1.40/1.59 thf(fact_987_even__diff__iff,axiom,
% 1.40/1.59 ! [K: int,L2: int] :
% 1.40/1.59 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 1.40/1.59 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % even_diff_iff
% 1.40/1.59 thf(fact_988_nat__dvd__not__less,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.59 => ( ( ord_less_nat @ M @ N )
% 1.40/1.59 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_dvd_not_less
% 1.40/1.59 thf(fact_989_dvd__pos__nat,axiom,
% 1.40/1.59 ! [N: nat,M: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ( dvd_dvd_nat @ M @ N )
% 1.40/1.59 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % dvd_pos_nat
% 1.40/1.59 thf(fact_990_zdvd__antisym__nonneg,axiom,
% 1.40/1.59 ! [M: int,N: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 1.40/1.59 => ( ( dvd_dvd_int @ M @ N )
% 1.40/1.59 => ( ( dvd_dvd_int @ N @ M )
% 1.40/1.59 => ( M = N ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdvd_antisym_nonneg
% 1.40/1.59 thf(fact_991_zdvd__mono,axiom,
% 1.40/1.59 ! [K: int,M: int,T: int] :
% 1.40/1.59 ( ( K != zero_zero_int )
% 1.40/1.59 => ( ( dvd_dvd_int @ M @ T )
% 1.40/1.59 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdvd_mono
% 1.40/1.59 thf(fact_992_zdvd__mult__cancel,axiom,
% 1.40/1.59 ! [K: int,M: int,N: int] :
% 1.40/1.59 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 1.40/1.59 => ( ( K != zero_zero_int )
% 1.40/1.59 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdvd_mult_cancel
% 1.40/1.59 thf(fact_993_bezout__add__nat,axiom,
% 1.40/1.59 ! [A: nat,B: nat] :
% 1.40/1.59 ? [D3: nat,X5: nat,Y3: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ D3 @ A )
% 1.40/1.59 & ( dvd_dvd_nat @ D3 @ B )
% 1.40/1.59 & ( ( ( times_times_nat @ A @ X5 )
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 1.40/1.59 | ( ( times_times_nat @ B @ X5 )
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % bezout_add_nat
% 1.40/1.59 thf(fact_994_bezout__lemma__nat,axiom,
% 1.40/1.59 ! [D: nat,A: nat,B: nat,X: nat,Y2: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ D @ A )
% 1.40/1.59 => ( ( dvd_dvd_nat @ D @ B )
% 1.40/1.59 => ( ( ( ( times_times_nat @ A @ X )
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D ) )
% 1.40/1.59 | ( ( times_times_nat @ B @ X )
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ A @ Y2 ) @ D ) ) )
% 1.40/1.59 => ? [X5: nat,Y3: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ D @ A )
% 1.40/1.59 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 1.40/1.59 & ( ( ( times_times_nat @ A @ X5 )
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 1.40/1.59 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X5 )
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % bezout_lemma_nat
% 1.40/1.59 thf(fact_995_int__le__induct,axiom,
% 1.40/1.59 ! [I2: int,K: int,P: int > $o] :
% 1.40/1.59 ( ( ord_less_eq_int @ I2 @ K )
% 1.40/1.59 => ( ( P @ K )
% 1.40/1.59 => ( ! [I3: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ I3 @ K )
% 1.40/1.59 => ( ( P @ I3 )
% 1.40/1.59 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 1.40/1.59 => ( P @ I2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_le_induct
% 1.40/1.59 thf(fact_996_int__less__induct,axiom,
% 1.40/1.59 ! [I2: int,K: int,P: int > $o] :
% 1.40/1.59 ( ( ord_less_int @ I2 @ K )
% 1.40/1.59 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 1.40/1.59 => ( ! [I3: int] :
% 1.40/1.59 ( ( ord_less_int @ I3 @ K )
% 1.40/1.59 => ( ( P @ I3 )
% 1.40/1.59 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 1.40/1.59 => ( P @ I2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_less_induct
% 1.40/1.59 thf(fact_997_zdvd__reduce,axiom,
% 1.40/1.59 ! [K: int,N: int,M: int] :
% 1.40/1.59 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 1.40/1.59 = ( dvd_dvd_int @ K @ N ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdvd_reduce
% 1.40/1.59 thf(fact_998_zdvd__period,axiom,
% 1.40/1.59 ! [A: int,D: int,X: int,T: int,C: int] :
% 1.40/1.59 ( ( dvd_dvd_int @ A @ D )
% 1.40/1.59 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 1.40/1.59 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdvd_period
% 1.40/1.59 thf(fact_999_signed__take__bit__int__less__eq,axiom,
% 1.40/1.59 ! [N: nat,K: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 1.40/1.59 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % signed_take_bit_int_less_eq
% 1.40/1.59 thf(fact_1000_dvd__imp__le,axiom,
% 1.40/1.59 ! [K: nat,N: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ K @ N )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.59 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % dvd_imp_le
% 1.40/1.59 thf(fact_1001_dvd__mult__cancel,axiom,
% 1.40/1.59 ! [K: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 1.40/1.59 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.59 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % dvd_mult_cancel
% 1.40/1.59 thf(fact_1002_nat__mult__dvd__cancel1,axiom,
% 1.40/1.59 ! [K: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.59 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 1.40/1.59 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % nat_mult_dvd_cancel1
% 1.40/1.59 thf(fact_1003_bezout__add__strong__nat,axiom,
% 1.40/1.59 ! [A: nat,B: nat] :
% 1.40/1.59 ( ( A != zero_zero_nat )
% 1.40/1.59 => ? [D3: nat,X5: nat,Y3: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ D3 @ A )
% 1.40/1.59 & ( dvd_dvd_nat @ D3 @ B )
% 1.40/1.59 & ( ( times_times_nat @ A @ X5 )
% 1.40/1.59 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % bezout_add_strong_nat
% 1.40/1.59 thf(fact_1004_zdvd__imp__le,axiom,
% 1.40/1.59 ! [Z: int,N: int] :
% 1.40/1.59 ( ( dvd_dvd_int @ Z @ N )
% 1.40/1.59 => ( ( ord_less_int @ zero_zero_int @ N )
% 1.40/1.59 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % zdvd_imp_le
% 1.40/1.59 thf(fact_1005_mod__greater__zero__iff__not__dvd,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 1.40/1.59 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mod_greater_zero_iff_not_dvd
% 1.40/1.59 thf(fact_1006_plusinfinity,axiom,
% 1.40/1.59 ! [D: int,P3: int > $o,P: int > $o] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ D )
% 1.40/1.59 => ( ! [X5: int,K2: int] :
% 1.40/1.59 ( ( P3 @ X5 )
% 1.40/1.59 = ( P3 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 1.40/1.59 => ( ? [Z4: int] :
% 1.40/1.59 ! [X5: int] :
% 1.40/1.59 ( ( ord_less_int @ Z4 @ X5 )
% 1.40/1.59 => ( ( P @ X5 )
% 1.40/1.59 = ( P3 @ X5 ) ) )
% 1.40/1.59 => ( ? [X_1: int] : ( P3 @ X_1 )
% 1.40/1.59 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % plusinfinity
% 1.40/1.59 thf(fact_1007_minusinfinity,axiom,
% 1.40/1.59 ! [D: int,P1: int > $o,P: int > $o] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ D )
% 1.40/1.59 => ( ! [X5: int,K2: int] :
% 1.40/1.59 ( ( P1 @ X5 )
% 1.40/1.59 = ( P1 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 1.40/1.59 => ( ? [Z4: int] :
% 1.40/1.59 ! [X5: int] :
% 1.40/1.59 ( ( ord_less_int @ X5 @ Z4 )
% 1.40/1.59 => ( ( P @ X5 )
% 1.40/1.59 = ( P1 @ X5 ) ) )
% 1.40/1.59 => ( ? [X_1: int] : ( P1 @ X_1 )
% 1.40/1.59 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % minusinfinity
% 1.40/1.59 thf(fact_1008_int__induct,axiom,
% 1.40/1.59 ! [P: int > $o,K: int,I2: int] :
% 1.40/1.59 ( ( P @ K )
% 1.40/1.59 => ( ! [I3: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ K @ I3 )
% 1.40/1.59 => ( ( P @ I3 )
% 1.40/1.59 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 1.40/1.59 => ( ! [I3: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ I3 @ K )
% 1.40/1.59 => ( ( P @ I3 )
% 1.40/1.59 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 1.40/1.59 => ( P @ I2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % int_induct
% 1.40/1.59 thf(fact_1009_even__even__mod__4__iff,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.59 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % even_even_mod_4_iff
% 1.40/1.59 thf(fact_1010_dvd__mult__cancel1,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.59 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 1.40/1.59 = ( N = one_one_nat ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % dvd_mult_cancel1
% 1.40/1.59 thf(fact_1011_dvd__mult__cancel2,axiom,
% 1.40/1.59 ! [M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.59 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 1.40/1.59 = ( N = one_one_nat ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % dvd_mult_cancel2
% 1.40/1.59 thf(fact_1012_power__dvd__imp__le,axiom,
% 1.40/1.59 ! [I2: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 1.40/1.59 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 1.40/1.59 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % power_dvd_imp_le
% 1.40/1.59 thf(fact_1013_decr__mult__lemma,axiom,
% 1.40/1.59 ! [D: int,P: int > $o,K: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ D )
% 1.40/1.59 => ( ! [X5: int] :
% 1.40/1.59 ( ( P @ X5 )
% 1.40/1.59 => ( P @ ( minus_minus_int @ X5 @ D ) ) )
% 1.40/1.59 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.59 => ! [X3: int] :
% 1.40/1.59 ( ( P @ X3 )
% 1.40/1.59 => ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % decr_mult_lemma
% 1.40/1.59 thf(fact_1014_mod__int__pos__iff,axiom,
% 1.40/1.59 ! [K: int,L2: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 1.40/1.59 = ( ( dvd_dvd_int @ L2 @ K )
% 1.40/1.59 | ( ( L2 = zero_zero_int )
% 1.40/1.59 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 1.40/1.59 | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mod_int_pos_iff
% 1.40/1.59 thf(fact_1015_mod__pos__geq,axiom,
% 1.40/1.59 ! [L2: int,K: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ L2 )
% 1.40/1.59 => ( ( ord_less_eq_int @ L2 @ K )
% 1.40/1.59 => ( ( modulo_modulo_int @ K @ L2 )
% 1.40/1.59 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % mod_pos_geq
% 1.40/1.59 thf(fact_1016_odd__pos,axiom,
% 1.40/1.59 ! [N: nat] :
% 1.40/1.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.59 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 1.40/1.59
% 1.40/1.59 % odd_pos
% 1.40/1.59 thf(fact_1017_dvd__power__iff__le,axiom,
% 1.40/1.59 ! [K: nat,M: nat,N: nat] :
% 1.40/1.59 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 1.40/1.59 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 1.40/1.59 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % dvd_power_iff_le
% 1.40/1.59 thf(fact_1018_signed__take__bit__int__less__exp,axiom,
% 1.40/1.59 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.59
% 1.40/1.59 % signed_take_bit_int_less_exp
% 1.40/1.59 thf(fact_1019_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 1.40/1.59 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 1.40/1.59 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X )
% 1.40/1.59 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 1.40/1.59 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.naive_member.simps(3)
% 1.40/1.59 thf(fact_1020_signed__take__bit__int__greater__eq__self__iff,axiom,
% 1.40/1.59 ! [K: int,N: nat] :
% 1.40/1.59 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 1.40/1.59 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % signed_take_bit_int_greater_eq_self_iff
% 1.40/1.59 thf(fact_1021_signed__take__bit__int__less__self__iff,axiom,
% 1.40/1.59 ! [N: nat,K: int] :
% 1.40/1.59 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 1.40/1.59 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 1.40/1.59
% 1.40/1.59 % signed_take_bit_int_less_self_iff
% 1.40/1.59 thf(fact_1022_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 1.40/1.59 ! [V: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X: nat] :
% 1.40/1.59 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd2 ) @ X )
% 1.40/1.59 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 1.40/1.59 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.membermima.simps(5)
% 1.40/1.59 thf(fact_1023_div__pos__geq,axiom,
% 1.40/1.59 ! [L2: int,K: int] :
% 1.40/1.59 ( ( ord_less_int @ zero_zero_int @ L2 )
% 1.40/1.59 => ( ( ord_less_eq_int @ L2 @ K )
% 1.40/1.59 => ( ( divide_divide_int @ K @ L2 )
% 1.40/1.59 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div_pos_geq
% 1.40/1.59 thf(fact_1024_vebt__member_Osimps_I5_J,axiom,
% 1.40/1.59 ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 1.40/1.59 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X )
% 1.40/1.59 = ( ( X != Mi )
% 1.40/1.59 => ( ( X != Ma )
% 1.40/1.59 => ( ~ ( ord_less_nat @ X @ Mi )
% 1.40/1.59 & ( ~ ( ord_less_nat @ X @ Mi )
% 1.40/1.59 => ( ~ ( ord_less_nat @ Ma @ X )
% 1.40/1.59 & ( ~ ( ord_less_nat @ Ma @ X )
% 1.40/1.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 1.40/1.59 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_member.simps(5)
% 1.40/1.59 thf(fact_1025_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 1.40/1.59 ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 1.40/1.59 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X )
% 1.40/1.59 = ( ( X = Mi )
% 1.40/1.59 | ( X = Ma )
% 1.40/1.59 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 1.40/1.59 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.membermima.simps(4)
% 1.40/1.59 thf(fact_1026_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.59 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 1.40/1.59 => ( ! [A5: $o,B5: $o] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.59 => A5 )
% 1.40/1.59 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.59 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.59 => B5 )
% 1.40/1.59 & ( Xa2 = one_one_nat ) ) ) ) )
% 1.40/1.59 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 1.40/1.59 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [S2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 1.40/1.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.naive_member.elims(3)
% 1.40/1.59 thf(fact_1027_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.59 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 1.40/1.59 => ( ! [A5: $o,B5: $o] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ~ ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.59 => A5 )
% 1.40/1.59 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.59 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.59 => B5 )
% 1.40/1.59 & ( Xa2 = one_one_nat ) ) ) ) )
% 1.40/1.59 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [S2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 1.40/1.59 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.naive_member.elims(2)
% 1.40/1.59 thf(fact_1028_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 1.40/1.59 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 1.40/1.59 = Y2 )
% 1.40/1.59 => ( ! [A5: $o,B5: $o] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.59 => A5 )
% 1.40/1.59 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.59 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.59 => B5 )
% 1.40/1.59 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 1.40/1.59 => ( ( ? [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 1.40/1.59 => Y2 )
% 1.40/1.59 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [S2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.naive_member.elims(1)
% 1.40/1.59 thf(fact_1029_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.59 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 1.40/1.59 => ( ! [Mi2: nat,Ma2: nat] :
% 1.40/1.59 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 1.40/1.59 => ~ ( ( Xa2 = Mi2 )
% 1.40/1.59 | ( Xa2 = Ma2 ) ) )
% 1.40/1.59 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [Vc2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 1.40/1.59 => ~ ( ( Xa2 = Mi2 )
% 1.40/1.59 | ( Xa2 = Ma2 )
% 1.40/1.59 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 1.40/1.59 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [Vd: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 1.40/1.59 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.membermima.elims(2)
% 1.40/1.59 thf(fact_1030_vebt__member_Oelims_I2_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.59 ( ( vEBT_vebt_member @ X @ Xa2 )
% 1.40/1.59 => ( ! [A5: $o,B5: $o] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ~ ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.59 => A5 )
% 1.40/1.59 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.59 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.59 => B5 )
% 1.40/1.59 & ( Xa2 = one_one_nat ) ) ) ) )
% 1.40/1.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [Summary2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ~ ( ( Xa2 != Mi2 )
% 1.40/1.59 => ( ( Xa2 != Ma2 )
% 1.40/1.59 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.59 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.59 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.59 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_member.elims(2)
% 1.40/1.59 thf(fact_1031_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.59 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 1.40/1.59 => ( ! [Uu: $o,Uv: $o] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Leaf @ Uu @ Uv ) )
% 1.40/1.59 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 1.40/1.59 => ( ! [Mi2: nat,Ma2: nat] :
% 1.40/1.59 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 1.40/1.59 => ( ( Xa2 = Mi2 )
% 1.40/1.59 | ( Xa2 = Ma2 ) ) )
% 1.40/1.59 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [Vc2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 1.40/1.59 => ( ( Xa2 = Mi2 )
% 1.40/1.59 | ( Xa2 = Ma2 )
% 1.40/1.59 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 1.40/1.59 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [Vd: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 1.40/1.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.membermima.elims(3)
% 1.40/1.59 thf(fact_1032_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 1.40/1.59 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 1.40/1.59 = Y2 )
% 1.40/1.59 => ( ( ? [Uu: $o,Uv: $o] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Leaf @ Uu @ Uv ) )
% 1.40/1.59 => Y2 )
% 1.40/1.59 => ( ( ? [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 1.40/1.59 => Y2 )
% 1.40/1.59 => ( ! [Mi2: nat,Ma2: nat] :
% 1.40/1.59 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( ~ ( ( Xa2 = Mi2 )
% 1.40/1.59 | ( Xa2 = Ma2 ) ) ) ) )
% 1.40/1.59 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [Vc2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( ~ ( ( Xa2 = Mi2 )
% 1.40/1.59 | ( Xa2 = Ma2 )
% 1.40/1.59 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 1.40/1.59 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [Vd: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( 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 ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % VEBT_internal.membermima.elims(1)
% 1.40/1.59 thf(fact_1033_vebt__insert_Osimps_I5_J,axiom,
% 1.40/1.59 ! [Mi: nat,Ma: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 1.40/1.59 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) @ X )
% 1.40/1.59 = ( if_VEBT_VEBT
% 1.40/1.59 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 1.40/1.59 & ~ ( ( X = Mi )
% 1.40/1.59 | ( X = Ma ) ) )
% 1.40/1.59 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 1.40/1.59 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_insert.simps(5)
% 1.40/1.59 thf(fact_1034_vebt__member_Oelims_I3_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.59 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 1.40/1.59 => ( ! [A5: $o,B5: $o] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.59 => A5 )
% 1.40/1.59 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.59 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.59 => B5 )
% 1.40/1.59 & ( Xa2 = one_one_nat ) ) ) ) )
% 1.40/1.59 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 1.40/1.59 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 1.40/1.59 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 1.40/1.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [Summary2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( ( Xa2 != Mi2 )
% 1.40/1.59 => ( ( Xa2 != Ma2 )
% 1.40/1.59 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.59 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.59 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.59 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_member.elims(3)
% 1.40/1.59 thf(fact_1035_vebt__member_Oelims_I1_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 1.40/1.59 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 1.40/1.59 = Y2 )
% 1.40/1.59 => ( ! [A5: $o,B5: $o] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.59 => A5 )
% 1.40/1.59 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.59 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.59 => B5 )
% 1.40/1.59 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 1.40/1.59 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 1.40/1.59 => Y2 )
% 1.40/1.59 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 1.40/1.59 => Y2 )
% 1.40/1.59 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 1.40/1.59 => Y2 )
% 1.40/1.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT] :
% 1.40/1.59 ( ? [Summary2: vEBT_VEBT] :
% 1.40/1.59 ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( ~ ( ( Xa2 != Mi2 )
% 1.40/1.59 => ( ( Xa2 != Ma2 )
% 1.40/1.59 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.59 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.59 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.59 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_member.elims(1)
% 1.40/1.59 thf(fact_1036_neg__zmod__mult__2,axiom,
% 1.40/1.59 ! [A: int,B: int] :
% 1.40/1.59 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 1.40/1.59 => ( ( 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 ) )
% 1.40/1.59 = ( 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 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % neg_zmod_mult_2
% 1.40/1.59 thf(fact_1037_vebt__insert_Opelims,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat,Y2: vEBT_VEBT] :
% 1.40/1.59 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 1.40/1.59 = Y2 )
% 1.40/1.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.59 => ( ! [A5: $o,B5: $o] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ( ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 1.40/1.59 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.59 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 1.40/1.59 & ( ( Xa2 != one_one_nat )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) )
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 1.40/1.59 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 1.40/1.59 => ( ( Y2
% 1.40/1.59 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 1.40/1.59 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 1.40/1.59 => ( ( Y2
% 1.40/1.59 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa2 ) ) ) )
% 1.40/1.59 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( ( Y2
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 1.40/1.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( ( Y2
% 1.40/1.59 = ( if_VEBT_VEBT
% 1.40/1.59 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 & ~ ( ( Xa2 = Mi2 )
% 1.40/1.59 | ( Xa2 = Ma2 ) ) )
% 1.40/1.59 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 1.40/1.59 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) ) )
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_insert.pelims
% 1.40/1.59 thf(fact_1038_div2__even__ext__nat,axiom,
% 1.40/1.59 ! [X: nat,Y2: nat] :
% 1.40/1.59 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.59 = ( divide_divide_nat @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.59 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 1.40/1.59 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y2 ) )
% 1.40/1.59 => ( X = Y2 ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % div2_even_ext_nat
% 1.40/1.59 thf(fact_1039_vebt__buildup_Oelims,axiom,
% 1.40/1.59 ! [X: nat,Y2: vEBT_VEBT] :
% 1.40/1.59 ( ( ( vEBT_vebt_buildup @ X )
% 1.40/1.59 = Y2 )
% 1.40/1.59 => ( ( ( X = zero_zero_nat )
% 1.40/1.59 => ( Y2
% 1.40/1.59 != ( vEBT_Leaf @ $false @ $false ) ) )
% 1.40/1.59 => ( ( ( X
% 1.40/1.59 = ( suc @ zero_zero_nat ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 != ( vEBT_Leaf @ $false @ $false ) ) )
% 1.40/1.59 => ~ ! [Va: nat] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( suc @ ( suc @ Va ) ) )
% 1.40/1.59 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( 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 ) ) ) ) ) ) )
% 1.40/1.59 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 1.40/1.59 => ( Y2
% 1.40/1.59 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_buildup.elims
% 1.40/1.59 thf(fact_1040_vebt__member_Opelims_I1_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 1.40/1.59 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 1.40/1.59 = Y2 )
% 1.40/1.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.59 => ( ! [A5: $o,B5: $o] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ( ( Y2
% 1.40/1.59 = ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.59 => A5 )
% 1.40/1.59 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.59 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.59 => B5 )
% 1.40/1.59 & ( Xa2 = one_one_nat ) ) ) ) )
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 1.40/1.59 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 1.40/1.59 => ( ~ Y2
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 1.40/1.59 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 1.40/1.59 => ( ~ Y2
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 1.40/1.59 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 1.40/1.59 => ( ~ Y2
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 1.40/1.59 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.59 => ( ( Y2
% 1.40/1.59 = ( ( Xa2 != Mi2 )
% 1.40/1.59 => ( ( Xa2 != Ma2 )
% 1.40/1.59 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.59 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.59 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.59 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.59 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.59 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.59
% 1.40/1.59 % vebt_member.pelims(1)
% 1.40/1.59 thf(fact_1041_vebt__member_Opelims_I3_J,axiom,
% 1.40/1.59 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.59 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 1.40/1.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.59 => ( ! [A5: $o,B5: $o] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.59 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 1.40/1.59 => ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.59 => A5 )
% 1.40/1.59 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.59 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.59 => B5 )
% 1.40/1.59 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 1.40/1.59 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) )
% 1.40/1.59 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 1.40/1.59 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.59 ( ( X
% 1.40/1.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 1.40/1.59 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 1.40/1.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 1.40/1.60 => ( ( Xa2 != Mi2 )
% 1.40/1.60 => ( ( Xa2 != Ma2 )
% 1.40/1.60 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.60 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.60 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.60 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % vebt_member.pelims(3)
% 1.40/1.60 thf(fact_1042_vebt__member_Opelims_I2_J,axiom,
% 1.40/1.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.60 ( ( vEBT_vebt_member @ X @ Xa2 )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.60 => ( ! [A5: $o,B5: $o] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 1.40/1.60 => ~ ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.60 => A5 )
% 1.40/1.60 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.60 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.60 => B5 )
% 1.40/1.60 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 1.40/1.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 1.40/1.60 => ~ ( ( Xa2 != Mi2 )
% 1.40/1.60 => ( ( Xa2 != Ma2 )
% 1.40/1.60 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.60 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 1.40/1.60 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.60 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 1.40/1.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % vebt_member.pelims(2)
% 1.40/1.60 thf(fact_1043_diff__Suc__Suc,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 1.40/1.60 = ( minus_minus_nat @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_Suc_Suc
% 1.40/1.60 thf(fact_1044_Suc__diff__diff,axiom,
% 1.40/1.60 ! [M: nat,N: nat,K: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 1.40/1.60 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_diff_diff
% 1.40/1.60 thf(fact_1045_diff__0__eq__0,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 1.40/1.60 = zero_zero_nat ) ).
% 1.40/1.60
% 1.40/1.60 % diff_0_eq_0
% 1.40/1.60 thf(fact_1046_diff__self__eq__0,axiom,
% 1.40/1.60 ! [M: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ M @ M )
% 1.40/1.60 = zero_zero_nat ) ).
% 1.40/1.60
% 1.40/1.60 % diff_self_eq_0
% 1.40/1.60 thf(fact_1047_diff__diff__cancel,axiom,
% 1.40/1.60 ! [I2: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ I2 @ N )
% 1.40/1.60 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 1.40/1.60 = I2 ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_diff_cancel
% 1.40/1.60 thf(fact_1048_diff__diff__left,axiom,
% 1.40/1.60 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 1.40/1.60 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_diff_left
% 1.40/1.60 thf(fact_1049_idiff__0,axiom,
% 1.40/1.60 ! [N: extended_enat] :
% 1.40/1.60 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 1.40/1.60 = zero_z5237406670263579293d_enat ) ).
% 1.40/1.60
% 1.40/1.60 % idiff_0
% 1.40/1.60 thf(fact_1050_idiff__0__right,axiom,
% 1.40/1.60 ! [N: extended_enat] :
% 1.40/1.60 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 1.40/1.60 = N ) ).
% 1.40/1.60
% 1.40/1.60 % idiff_0_right
% 1.40/1.60 thf(fact_1051_zero__less__diff,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 1.40/1.60 = ( ord_less_nat @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % zero_less_diff
% 1.40/1.60 thf(fact_1052_diff__is__0__eq_H,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.60 => ( ( minus_minus_nat @ M @ N )
% 1.40/1.60 = zero_zero_nat ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_is_0_eq'
% 1.40/1.60 thf(fact_1053_diff__is__0__eq,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( ( minus_minus_nat @ M @ N )
% 1.40/1.60 = zero_zero_nat )
% 1.40/1.60 = ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_is_0_eq
% 1.40/1.60 thf(fact_1054_Nat_Odiff__diff__right,axiom,
% 1.40/1.60 ! [K: nat,J: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ J )
% 1.40/1.60 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 1.40/1.60 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Nat.diff_diff_right
% 1.40/1.60 thf(fact_1055_Nat_Oadd__diff__assoc2,axiom,
% 1.40/1.60 ! [K: nat,J: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ J )
% 1.40/1.60 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 1.40/1.60 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Nat.add_diff_assoc2
% 1.40/1.60 thf(fact_1056_Nat_Oadd__diff__assoc,axiom,
% 1.40/1.60 ! [K: nat,J: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ J )
% 1.40/1.60 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 1.40/1.60 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Nat.add_diff_assoc
% 1.40/1.60 thf(fact_1057_diff__Suc__1,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 1.40/1.60 = N ) ).
% 1.40/1.60
% 1.40/1.60 % diff_Suc_1
% 1.40/1.60 thf(fact_1058_Suc__pred,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.60 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 1.40/1.60 = N ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_pred
% 1.40/1.60 thf(fact_1059_diff__Suc__diff__eq2,axiom,
% 1.40/1.60 ! [K: nat,J: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ J )
% 1.40/1.60 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 1.40/1.60 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_Suc_diff_eq2
% 1.40/1.60 thf(fact_1060_diff__Suc__diff__eq1,axiom,
% 1.40/1.60 ! [K: nat,J: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ J )
% 1.40/1.60 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 1.40/1.60 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_Suc_diff_eq1
% 1.40/1.60 thf(fact_1061_Suc__diff__1,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.60 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 1.40/1.60 = N ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_diff_1
% 1.40/1.60 thf(fact_1062_odd__Suc__minus__one,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.60 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 1.40/1.60 = N ) ) ).
% 1.40/1.60
% 1.40/1.60 % odd_Suc_minus_one
% 1.40/1.60 thf(fact_1063_even__diff__nat,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 1.40/1.60 = ( ( ord_less_nat @ M @ N )
% 1.40/1.60 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % even_diff_nat
% 1.40/1.60 thf(fact_1064_odd__two__times__div__two__nat,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.60 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.60 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % odd_two_times_div_two_nat
% 1.40/1.60 thf(fact_1065_dvd__antisym,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( dvd_dvd_nat @ M @ N )
% 1.40/1.60 => ( ( dvd_dvd_nat @ N @ M )
% 1.40/1.60 => ( M = N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % dvd_antisym
% 1.40/1.60 thf(fact_1066_dvd__diff__nat,axiom,
% 1.40/1.60 ! [K: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( dvd_dvd_nat @ K @ M )
% 1.40/1.60 => ( ( dvd_dvd_nat @ K @ N )
% 1.40/1.60 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % dvd_diff_nat
% 1.40/1.60 thf(fact_1067_zero__induct__lemma,axiom,
% 1.40/1.60 ! [P: nat > $o,K: nat,I2: nat] :
% 1.40/1.60 ( ( P @ K )
% 1.40/1.60 => ( ! [N4: nat] :
% 1.40/1.60 ( ( P @ ( suc @ N4 ) )
% 1.40/1.60 => ( P @ N4 ) )
% 1.40/1.60 => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zero_induct_lemma
% 1.40/1.60 thf(fact_1068_minus__nat_Odiff__0,axiom,
% 1.40/1.60 ! [M: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 1.40/1.60 = M ) ).
% 1.40/1.60
% 1.40/1.60 % minus_nat.diff_0
% 1.40/1.60 thf(fact_1069_diffs0__imp__equal,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( ( minus_minus_nat @ M @ N )
% 1.40/1.60 = zero_zero_nat )
% 1.40/1.60 => ( ( ( minus_minus_nat @ N @ M )
% 1.40/1.60 = zero_zero_nat )
% 1.40/1.60 => ( M = N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diffs0_imp_equal
% 1.40/1.60 thf(fact_1070_less__imp__diff__less,axiom,
% 1.40/1.60 ! [J: nat,K: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_nat @ J @ K )
% 1.40/1.60 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 1.40/1.60
% 1.40/1.60 % less_imp_diff_less
% 1.40/1.60 thf(fact_1071_diff__less__mono2,axiom,
% 1.40/1.60 ! [M: nat,N: nat,L2: nat] :
% 1.40/1.60 ( ( ord_less_nat @ M @ N )
% 1.40/1.60 => ( ( ord_less_nat @ M @ L2 )
% 1.40/1.60 => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_less_mono2
% 1.40/1.60 thf(fact_1072_dvd__minus__self,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 1.40/1.60 = ( ( ord_less_nat @ N @ M )
% 1.40/1.60 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % dvd_minus_self
% 1.40/1.60 thf(fact_1073_diff__le__mono2,axiom,
% 1.40/1.60 ! [M: nat,N: nat,L2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.60 => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_le_mono2
% 1.40/1.60 thf(fact_1074_le__diff__iff_H,axiom,
% 1.40/1.60 ! [A: nat,C: nat,B: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ A @ C )
% 1.40/1.60 => ( ( ord_less_eq_nat @ B @ C )
% 1.40/1.60 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 1.40/1.60 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % le_diff_iff'
% 1.40/1.60 thf(fact_1075_diff__le__self,axiom,
% 1.40/1.60 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 1.40/1.60
% 1.40/1.60 % diff_le_self
% 1.40/1.60 thf(fact_1076_diff__le__mono,axiom,
% 1.40/1.60 ! [M: nat,N: nat,L2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.60 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_le_mono
% 1.40/1.60 thf(fact_1077_Nat_Odiff__diff__eq,axiom,
% 1.40/1.60 ! [K: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ M )
% 1.40/1.60 => ( ( ord_less_eq_nat @ K @ N )
% 1.40/1.60 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 1.40/1.60 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Nat.diff_diff_eq
% 1.40/1.60 thf(fact_1078_le__diff__iff,axiom,
% 1.40/1.60 ! [K: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ M )
% 1.40/1.60 => ( ( ord_less_eq_nat @ K @ N )
% 1.40/1.60 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 1.40/1.60 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % le_diff_iff
% 1.40/1.60 thf(fact_1079_eq__diff__iff,axiom,
% 1.40/1.60 ! [K: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ M )
% 1.40/1.60 => ( ( ord_less_eq_nat @ K @ N )
% 1.40/1.60 => ( ( ( minus_minus_nat @ M @ K )
% 1.40/1.60 = ( minus_minus_nat @ N @ K ) )
% 1.40/1.60 = ( M = N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % eq_diff_iff
% 1.40/1.60 thf(fact_1080_dvd__diffD,axiom,
% 1.40/1.60 ! [K: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 1.40/1.60 => ( ( dvd_dvd_nat @ K @ N )
% 1.40/1.60 => ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.60 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % dvd_diffD
% 1.40/1.60 thf(fact_1081_dvd__diffD1,axiom,
% 1.40/1.60 ! [K: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 1.40/1.60 => ( ( dvd_dvd_nat @ K @ M )
% 1.40/1.60 => ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.60 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % dvd_diffD1
% 1.40/1.60 thf(fact_1082_less__eq__dvd__minus,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.60 => ( ( dvd_dvd_nat @ M @ N )
% 1.40/1.60 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % less_eq_dvd_minus
% 1.40/1.60 thf(fact_1083_diff__add__inverse2,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 1.40/1.60 = M ) ).
% 1.40/1.60
% 1.40/1.60 % diff_add_inverse2
% 1.40/1.60 thf(fact_1084_diff__add__inverse,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 1.40/1.60 = M ) ).
% 1.40/1.60
% 1.40/1.60 % diff_add_inverse
% 1.40/1.60 thf(fact_1085_diff__cancel2,axiom,
% 1.40/1.60 ! [M: nat,K: nat,N: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 1.40/1.60 = ( minus_minus_nat @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_cancel2
% 1.40/1.60 thf(fact_1086_Nat_Odiff__cancel,axiom,
% 1.40/1.60 ! [K: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 1.40/1.60 = ( minus_minus_nat @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % Nat.diff_cancel
% 1.40/1.60 thf(fact_1087_diff__mult__distrib,axiom,
% 1.40/1.60 ! [M: nat,N: nat,K: nat] :
% 1.40/1.60 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 1.40/1.60 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_mult_distrib
% 1.40/1.60 thf(fact_1088_diff__mult__distrib2,axiom,
% 1.40/1.60 ! [K: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 1.40/1.60 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_mult_distrib2
% 1.40/1.60 thf(fact_1089_bezout1__nat,axiom,
% 1.40/1.60 ! [A: nat,B: nat] :
% 1.40/1.60 ? [D3: nat,X5: nat,Y3: nat] :
% 1.40/1.60 ( ( dvd_dvd_nat @ D3 @ A )
% 1.40/1.60 & ( dvd_dvd_nat @ D3 @ B )
% 1.40/1.60 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X5 ) @ ( times_times_nat @ B @ Y3 ) )
% 1.40/1.60 = D3 )
% 1.40/1.60 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X5 ) @ ( times_times_nat @ A @ Y3 ) )
% 1.40/1.60 = D3 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bezout1_nat
% 1.40/1.60 thf(fact_1090_diff__less__Suc,axiom,
% 1.40/1.60 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_less_Suc
% 1.40/1.60 thf(fact_1091_Suc__diff__Suc,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_nat @ N @ M )
% 1.40/1.60 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 1.40/1.60 = ( minus_minus_nat @ M @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_diff_Suc
% 1.40/1.60 thf(fact_1092_diff__less,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.60 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.60 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_less
% 1.40/1.60 thf(fact_1093_Suc__diff__le,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.60 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 1.40/1.60 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_diff_le
% 1.40/1.60 thf(fact_1094_diff__less__mono,axiom,
% 1.40/1.60 ! [A: nat,B: nat,C: nat] :
% 1.40/1.60 ( ( ord_less_nat @ A @ B )
% 1.40/1.60 => ( ( ord_less_eq_nat @ C @ A )
% 1.40/1.60 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_less_mono
% 1.40/1.60 thf(fact_1095_less__diff__iff,axiom,
% 1.40/1.60 ! [K: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ M )
% 1.40/1.60 => ( ( ord_less_eq_nat @ K @ N )
% 1.40/1.60 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 1.40/1.60 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % less_diff_iff
% 1.40/1.60 thf(fact_1096_diff__add__0,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 1.40/1.60 = zero_zero_nat ) ).
% 1.40/1.60
% 1.40/1.60 % diff_add_0
% 1.40/1.60 thf(fact_1097_add__diff__inverse__nat,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ~ ( ord_less_nat @ M @ N )
% 1.40/1.60 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 1.40/1.60 = M ) ) ).
% 1.40/1.60
% 1.40/1.60 % add_diff_inverse_nat
% 1.40/1.60 thf(fact_1098_less__diff__conv,axiom,
% 1.40/1.60 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.60 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 1.40/1.60 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 1.40/1.60
% 1.40/1.60 % less_diff_conv
% 1.40/1.60 thf(fact_1099_Nat_Ole__imp__diff__is__add,axiom,
% 1.40/1.60 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.60 => ( ( ( minus_minus_nat @ J @ I2 )
% 1.40/1.60 = K )
% 1.40/1.60 = ( J
% 1.40/1.60 = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Nat.le_imp_diff_is_add
% 1.40/1.60 thf(fact_1100_Nat_Odiff__add__assoc2,axiom,
% 1.40/1.60 ! [K: nat,J: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ J )
% 1.40/1.60 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 1.40/1.60 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Nat.diff_add_assoc2
% 1.40/1.60 thf(fact_1101_Nat_Odiff__add__assoc,axiom,
% 1.40/1.60 ! [K: nat,J: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ J )
% 1.40/1.60 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 1.40/1.60 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Nat.diff_add_assoc
% 1.40/1.60 thf(fact_1102_Nat_Ole__diff__conv2,axiom,
% 1.40/1.60 ! [K: nat,J: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ J )
% 1.40/1.60 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 1.40/1.60 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Nat.le_diff_conv2
% 1.40/1.60 thf(fact_1103_le__diff__conv,axiom,
% 1.40/1.60 ! [J: nat,K: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 1.40/1.60 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % le_diff_conv
% 1.40/1.60 thf(fact_1104_diff__Suc__eq__diff__pred,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 1.40/1.60 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_Suc_eq_diff_pred
% 1.40/1.60 thf(fact_1105_mod__if,axiom,
% 1.40/1.60 ( modulo_modulo_nat
% 1.40/1.60 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N2 ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mod_if
% 1.40/1.60 thf(fact_1106_mod__geq,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ~ ( ord_less_nat @ M @ N )
% 1.40/1.60 => ( ( modulo_modulo_nat @ M @ N )
% 1.40/1.60 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mod_geq
% 1.40/1.60 thf(fact_1107_le__mod__geq,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.60 => ( ( modulo_modulo_nat @ M @ N )
% 1.40/1.60 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % le_mod_geq
% 1.40/1.60 thf(fact_1108_mod__eq__dvd__iff__nat,axiom,
% 1.40/1.60 ! [N: nat,M: nat,Q2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.60 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 1.40/1.60 = ( modulo_modulo_nat @ N @ Q2 ) )
% 1.40/1.60 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mod_eq_dvd_iff_nat
% 1.40/1.60 thf(fact_1109_nat__minus__add__max,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 1.40/1.60 = ( ord_max_nat @ N @ M ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_minus_add_max
% 1.40/1.60 thf(fact_1110_add__diff__assoc__enat,axiom,
% 1.40/1.60 ! [Z: extended_enat,Y2: extended_enat,X: extended_enat] :
% 1.40/1.60 ( ( ord_le2932123472753598470d_enat @ Z @ Y2 )
% 1.40/1.60 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y2 @ Z ) )
% 1.40/1.60 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y2 ) @ Z ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % add_diff_assoc_enat
% 1.40/1.60 thf(fact_1111_diff__Suc__less,axiom,
% 1.40/1.60 ! [N: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.60 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_Suc_less
% 1.40/1.60 thf(fact_1112_nat__diff__split__asm,axiom,
% 1.40/1.60 ! [P: nat > $o,A: nat,B: nat] :
% 1.40/1.60 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 1.40/1.60 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 1.40/1.60 & ~ ( P @ zero_zero_nat ) )
% 1.40/1.60 | ? [D2: nat] :
% 1.40/1.60 ( ( A
% 1.40/1.60 = ( plus_plus_nat @ B @ D2 ) )
% 1.40/1.60 & ~ ( P @ D2 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_diff_split_asm
% 1.40/1.60 thf(fact_1113_nat__diff__split,axiom,
% 1.40/1.60 ! [P: nat > $o,A: nat,B: nat] :
% 1.40/1.60 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 1.40/1.60 = ( ( ( ord_less_nat @ A @ B )
% 1.40/1.60 => ( P @ zero_zero_nat ) )
% 1.40/1.60 & ! [D2: nat] :
% 1.40/1.60 ( ( A
% 1.40/1.60 = ( plus_plus_nat @ B @ D2 ) )
% 1.40/1.60 => ( P @ D2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_diff_split
% 1.40/1.60 thf(fact_1114_less__diff__conv2,axiom,
% 1.40/1.60 ! [K: nat,J: nat,I2: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ K @ J )
% 1.40/1.60 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 1.40/1.60 = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % less_diff_conv2
% 1.40/1.60 thf(fact_1115_nat__diff__add__eq2,axiom,
% 1.40/1.60 ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.60 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 1.40/1.60 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_diff_add_eq2
% 1.40/1.60 thf(fact_1116_nat__diff__add__eq1,axiom,
% 1.40/1.60 ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ J @ I2 )
% 1.40/1.60 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 1.40/1.60 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_diff_add_eq1
% 1.40/1.60 thf(fact_1117_nat__le__add__iff2,axiom,
% 1.40/1.60 ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.60 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 1.40/1.60 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_le_add_iff2
% 1.40/1.60 thf(fact_1118_nat__le__add__iff1,axiom,
% 1.40/1.60 ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ J @ I2 )
% 1.40/1.60 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 1.40/1.60 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_le_add_iff1
% 1.40/1.60 thf(fact_1119_nat__eq__add__iff2,axiom,
% 1.40/1.60 ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.60 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 1.40/1.60 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 1.40/1.60 = ( M
% 1.40/1.60 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_eq_add_iff2
% 1.40/1.60 thf(fact_1120_nat__eq__add__iff1,axiom,
% 1.40/1.60 ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ J @ I2 )
% 1.40/1.60 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 1.40/1.60 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 1.40/1.60 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
% 1.40/1.60 = N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_eq_add_iff1
% 1.40/1.60 thf(fact_1121_dvd__minus__add,axiom,
% 1.40/1.60 ! [Q2: nat,N: nat,R2: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ Q2 @ N )
% 1.40/1.60 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R2 @ M ) )
% 1.40/1.60 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 1.40/1.60 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q2 ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % dvd_minus_add
% 1.40/1.60 thf(fact_1122_mod__nat__eqI,axiom,
% 1.40/1.60 ! [R2: nat,N: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_nat @ R2 @ N )
% 1.40/1.60 => ( ( ord_less_eq_nat @ R2 @ M )
% 1.40/1.60 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 1.40/1.60 => ( ( modulo_modulo_nat @ M @ N )
% 1.40/1.60 = R2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mod_nat_eqI
% 1.40/1.60 thf(fact_1123_modulo__nat__def,axiom,
% 1.40/1.60 ( modulo_modulo_nat
% 1.40/1.60 = ( ^ [M6: nat,N2: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N2 ) @ N2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % modulo_nat_def
% 1.40/1.60 thf(fact_1124_Suc__diff__eq__diff__pred,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.60 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 1.40/1.60 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_diff_eq_diff_pred
% 1.40/1.60 thf(fact_1125_Suc__pred_H,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.60 => ( N
% 1.40/1.60 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_pred'
% 1.40/1.60 thf(fact_1126_div__if,axiom,
% 1.40/1.60 ( divide_divide_nat
% 1.40/1.60 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.60 ( if_nat
% 1.40/1.60 @ ( ( ord_less_nat @ M6 @ N2 )
% 1.40/1.60 | ( N2 = zero_zero_nat ) )
% 1.40/1.60 @ zero_zero_nat
% 1.40/1.60 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % div_if
% 1.40/1.60 thf(fact_1127_div__geq,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.60 => ( ~ ( ord_less_nat @ M @ N )
% 1.40/1.60 => ( ( divide_divide_nat @ M @ N )
% 1.40/1.60 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % div_geq
% 1.40/1.60 thf(fact_1128_add__eq__if,axiom,
% 1.40/1.60 ( plus_plus_nat
% 1.40/1.60 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % add_eq_if
% 1.40/1.60 thf(fact_1129_nat__less__add__iff2,axiom,
% 1.40/1.60 ! [I2: nat,J: nat,U: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.60 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 1.40/1.60 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_less_add_iff2
% 1.40/1.60 thf(fact_1130_nat__less__add__iff1,axiom,
% 1.40/1.60 ! [J: nat,I2: nat,U: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ J @ I2 )
% 1.40/1.60 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 1.40/1.60 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_less_add_iff1
% 1.40/1.60 thf(fact_1131_mult__eq__if,axiom,
% 1.40/1.60 ( times_times_nat
% 1.40/1.60 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mult_eq_if
% 1.40/1.60 thf(fact_1132_diff__le__diff__pow,axiom,
% 1.40/1.60 ! [K: nat,M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 1.40/1.60 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_le_diff_pow
% 1.40/1.60 thf(fact_1133_le__div__geq,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.60 => ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.60 => ( ( divide_divide_nat @ M @ N )
% 1.40/1.60 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % le_div_geq
% 1.40/1.60 thf(fact_1134_list__decode_Ocases,axiom,
% 1.40/1.60 ! [X: nat] :
% 1.40/1.60 ( ( X != zero_zero_nat )
% 1.40/1.60 => ~ ! [N4: nat] :
% 1.40/1.60 ( X
% 1.40/1.60 != ( suc @ N4 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % list_decode.cases
% 1.40/1.60 thf(fact_1135_even__mod__4__div__2,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 1.40/1.60 = ( suc @ zero_zero_nat ) )
% 1.40/1.60 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % even_mod_4_div_2
% 1.40/1.60 thf(fact_1136_int__power__div__base,axiom,
% 1.40/1.60 ! [M: nat,K: int] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.60 => ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.60 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 1.40/1.60 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_power_div_base
% 1.40/1.60 thf(fact_1137_vebt__buildup_Osimps_I3_J,axiom,
% 1.40/1.60 ! [Va2: nat] :
% 1.40/1.60 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 1.40/1.60 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 1.40/1.60 = ( 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 ) ) ) ) ) ) )
% 1.40/1.60 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 1.40/1.60 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 1.40/1.60 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % vebt_buildup.simps(3)
% 1.40/1.60 thf(fact_1138_real__average__minus__first,axiom,
% 1.40/1.60 ! [A: real,B: real] :
% 1.40/1.60 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 1.40/1.60 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_average_minus_first
% 1.40/1.60 thf(fact_1139_real__average__minus__second,axiom,
% 1.40/1.60 ! [B: real,A: real] :
% 1.40/1.60 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 1.40/1.60 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_average_minus_second
% 1.40/1.60 thf(fact_1140_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 1.40/1.60 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 1.40/1.60 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 1.40/1.60 = Y2 )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.60 => ( ! [A5: $o,B5: $o] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.60 => ( ( Y2
% 1.40/1.60 = ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.60 => A5 )
% 1.40/1.60 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.60 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.60 => B5 )
% 1.40/1.60 & ( Xa2 = one_one_nat ) ) ) ) )
% 1.40/1.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 1.40/1.60 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 1.40/1.60 => ( ~ Y2
% 1.40/1.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa2 ) ) ) )
% 1.40/1.60 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 1.40/1.60 => ( ( Y2
% 1.40/1.60 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( 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 ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 1.40/1.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % VEBT_internal.naive_member.pelims(1)
% 1.40/1.60 thf(fact_1141_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 1.40/1.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.60 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.60 => ( ! [A5: $o,B5: $o] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 1.40/1.60 => ~ ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.60 => A5 )
% 1.40/1.60 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.60 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.60 => B5 )
% 1.40/1.60 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 1.40/1.60 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) )
% 1.40/1.60 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( 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 ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % VEBT_internal.naive_member.pelims(2)
% 1.40/1.60 thf(fact_1142_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 1.40/1.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.60 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.60 => ( ! [A5: $o,B5: $o] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Leaf @ A5 @ B5 ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 1.40/1.60 => ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.60 => A5 )
% 1.40/1.60 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.60 => ( ( ( Xa2 = one_one_nat )
% 1.40/1.60 => B5 )
% 1.40/1.60 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 1.40/1.60 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 1.40/1.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa2 ) ) )
% 1.40/1.60 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S2 ) @ Xa2 ) )
% 1.40/1.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( 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 ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % VEBT_internal.naive_member.pelims(3)
% 1.40/1.60 thf(fact_1143_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 1.40/1.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.60 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.60 => ( ! [Uu: $o,Uv: $o] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Leaf @ Uu @ Uv ) )
% 1.40/1.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) )
% 1.40/1.60 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 1.40/1.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) @ Xa2 ) ) )
% 1.40/1.60 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 1.40/1.60 => ( ( 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 ) )
% 1.40/1.60 => ( ( Xa2 = Mi2 )
% 1.40/1.60 | ( Xa2 = Ma2 ) ) ) )
% 1.40/1.60 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 1.40/1.60 => ( ( Xa2 = Mi2 )
% 1.40/1.60 | ( Xa2 = Ma2 )
% 1.40/1.60 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( 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 ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 1.40/1.60 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) )
% 1.40/1.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( 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 ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % VEBT_internal.membermima.pelims(3)
% 1.40/1.60 thf(fact_1144_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 1.40/1.60 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 1.40/1.60 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 1.40/1.60 = Y2 )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.60 => ( ! [Uu: $o,Uv: $o] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Leaf @ Uu @ Uv ) )
% 1.40/1.60 => ( ~ Y2
% 1.40/1.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) ) )
% 1.40/1.60 => ( ! [Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) )
% 1.40/1.60 => ( ~ Y2
% 1.40/1.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy2 ) @ Xa2 ) ) ) )
% 1.40/1.60 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 1.40/1.60 => ( ( Y2
% 1.40/1.60 = ( ( Xa2 = Mi2 )
% 1.40/1.60 | ( Xa2 = Ma2 ) ) )
% 1.40/1.60 => ~ ( 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 ) ) ) )
% 1.40/1.60 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 1.40/1.60 => ( ( Y2
% 1.40/1.60 = ( ( Xa2 = Mi2 )
% 1.40/1.60 | ( Xa2 = Ma2 )
% 1.40/1.60 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( 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 ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 1.40/1.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 1.40/1.60 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 1.40/1.60 => ( ( Y2
% 1.40/1.60 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( 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 ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 1.40/1.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % VEBT_internal.membermima.pelims(1)
% 1.40/1.60 thf(fact_1145_diff__commute,axiom,
% 1.40/1.60 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 1.40/1.60 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_commute
% 1.40/1.60 thf(fact_1146_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 1.40/1.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.60 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.60 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 1.40/1.60 => ( ( 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 ) )
% 1.40/1.60 => ~ ( ( Xa2 = Mi2 )
% 1.40/1.60 | ( Xa2 = Ma2 ) ) ) )
% 1.40/1.60 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 1.40/1.60 => ~ ( ( Xa2 = Mi2 )
% 1.40/1.60 | ( Xa2 = Ma2 )
% 1.40/1.60 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( 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 ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 1.40/1.60 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 1.40/1.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa2 ) )
% 1.40/1.60 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 1.40/1.60 => ( 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 ) ) ) ) ) )
% 1.40/1.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % VEBT_internal.membermima.pelims(2)
% 1.40/1.60 thf(fact_1147_inrange,axiom,
% 1.40/1.60 ! [T: vEBT_VEBT,N: nat] :
% 1.40/1.60 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.60 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % inrange
% 1.40/1.60 thf(fact_1148_Bolzano,axiom,
% 1.40/1.60 ! [A: real,B: real,P: real > real > $o] :
% 1.40/1.60 ( ( ord_less_eq_real @ A @ B )
% 1.40/1.60 => ( ! [A5: real,B5: real,C2: real] :
% 1.40/1.60 ( ( P @ A5 @ B5 )
% 1.40/1.60 => ( ( P @ B5 @ C2 )
% 1.40/1.60 => ( ( ord_less_eq_real @ A5 @ B5 )
% 1.40/1.60 => ( ( ord_less_eq_real @ B5 @ C2 )
% 1.40/1.60 => ( P @ A5 @ C2 ) ) ) ) )
% 1.40/1.60 => ( ! [X5: real] :
% 1.40/1.60 ( ( ord_less_eq_real @ A @ X5 )
% 1.40/1.60 => ( ( ord_less_eq_real @ X5 @ B )
% 1.40/1.60 => ? [D4: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ D4 )
% 1.40/1.60 & ! [A5: real,B5: real] :
% 1.40/1.60 ( ( ( ord_less_eq_real @ A5 @ X5 )
% 1.40/1.60 & ( ord_less_eq_real @ X5 @ B5 )
% 1.40/1.60 & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D4 ) )
% 1.40/1.60 => ( P @ A5 @ B5 ) ) ) ) )
% 1.40/1.60 => ( P @ A @ B ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Bolzano
% 1.40/1.60 thf(fact_1149_triangle__def,axiom,
% 1.40/1.60 ( nat_triangle
% 1.40/1.60 = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % triangle_def
% 1.40/1.60 thf(fact_1150_vebt__buildup_Opelims,axiom,
% 1.40/1.60 ! [X: nat,Y2: vEBT_VEBT] :
% 1.40/1.60 ( ( ( vEBT_vebt_buildup @ X )
% 1.40/1.60 = Y2 )
% 1.40/1.60 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 1.40/1.60 => ( ( ( X = zero_zero_nat )
% 1.40/1.60 => ( ( Y2
% 1.40/1.60 = ( vEBT_Leaf @ $false @ $false ) )
% 1.40/1.60 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 1.40/1.60 => ( ( ( X
% 1.40/1.60 = ( suc @ zero_zero_nat ) )
% 1.40/1.60 => ( ( Y2
% 1.40/1.60 = ( vEBT_Leaf @ $false @ $false ) )
% 1.40/1.60 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 1.40/1.60 => ~ ! [Va: nat] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( suc @ ( suc @ Va ) ) )
% 1.40/1.60 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 1.40/1.60 => ( Y2
% 1.40/1.60 = ( 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 ) ) ) ) ) ) )
% 1.40/1.60 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 1.40/1.60 => ( Y2
% 1.40/1.60 = ( 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 ) ) ) ) ) ) ) ) )
% 1.40/1.60 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % vebt_buildup.pelims
% 1.40/1.60 thf(fact_1151_real__add__minus__iff,axiom,
% 1.40/1.60 ! [X: real,A: real] :
% 1.40/1.60 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 1.40/1.60 = zero_zero_real )
% 1.40/1.60 = ( X = A ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_add_minus_iff
% 1.40/1.60 thf(fact_1152_triangle__Suc,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( nat_triangle @ ( suc @ N ) )
% 1.40/1.60 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % triangle_Suc
% 1.40/1.60 thf(fact_1153_signed__take__bit__Suc__minus__bit0,axiom,
% 1.40/1.60 ! [N: nat,K: num] :
% 1.40/1.60 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 1.40/1.60 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_Suc_minus_bit0
% 1.40/1.60 thf(fact_1154_signed__take__bit__minus,axiom,
% 1.40/1.60 ! [N: nat,K: int] :
% 1.40/1.60 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 1.40/1.60 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_minus
% 1.40/1.60 thf(fact_1155_all__nat__less,axiom,
% 1.40/1.60 ! [N: nat,P: nat > $o] :
% 1.40/1.60 ( ( ! [M6: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ M6 @ N )
% 1.40/1.60 => ( P @ M6 ) ) )
% 1.40/1.60 = ( ! [X4: nat] :
% 1.40/1.60 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 1.40/1.60 => ( P @ X4 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % all_nat_less
% 1.40/1.60 thf(fact_1156_ex__nat__less,axiom,
% 1.40/1.60 ! [N: nat,P: nat > $o] :
% 1.40/1.60 ( ( ? [M6: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ M6 @ N )
% 1.40/1.60 & ( P @ M6 ) ) )
% 1.40/1.60 = ( ? [X4: nat] :
% 1.40/1.60 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 1.40/1.60 & ( P @ X4 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ex_nat_less
% 1.40/1.60 thf(fact_1157_real__minus__mult__self__le,axiom,
% 1.40/1.60 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_minus_mult_self_le
% 1.40/1.60 thf(fact_1158_zmult__eq__1__iff,axiom,
% 1.40/1.60 ! [M: int,N: int] :
% 1.40/1.60 ( ( ( times_times_int @ M @ N )
% 1.40/1.60 = one_one_int )
% 1.40/1.60 = ( ( ( M = one_one_int )
% 1.40/1.60 & ( N = one_one_int ) )
% 1.40/1.60 | ( ( M
% 1.40/1.60 = ( uminus_uminus_int @ one_one_int ) )
% 1.40/1.60 & ( N
% 1.40/1.60 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zmult_eq_1_iff
% 1.40/1.60 thf(fact_1159_pos__zmult__eq__1__iff__lemma,axiom,
% 1.40/1.60 ! [M: int,N: int] :
% 1.40/1.60 ( ( ( times_times_int @ M @ N )
% 1.40/1.60 = one_one_int )
% 1.40/1.60 => ( ( M = one_one_int )
% 1.40/1.60 | ( M
% 1.40/1.60 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % pos_zmult_eq_1_iff_lemma
% 1.40/1.60 thf(fact_1160_minus__real__def,axiom,
% 1.40/1.60 ( minus_minus_real
% 1.40/1.60 = ( ^ [X4: real,Y4: real] : ( plus_plus_real @ X4 @ ( uminus_uminus_real @ Y4 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % minus_real_def
% 1.40/1.60 thf(fact_1161_real__0__less__add__iff,axiom,
% 1.40/1.60 ! [X: real,Y2: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y2 ) )
% 1.40/1.60 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y2 ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_0_less_add_iff
% 1.40/1.60 thf(fact_1162_real__add__less__0__iff,axiom,
% 1.40/1.60 ! [X: real,Y2: real] :
% 1.40/1.60 ( ( ord_less_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 1.40/1.60 = ( ord_less_real @ Y2 @ ( uminus_uminus_real @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_add_less_0_iff
% 1.40/1.60 thf(fact_1163_real__add__le__0__iff,axiom,
% 1.40/1.60 ! [X: real,Y2: real] :
% 1.40/1.60 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y2 ) @ zero_zero_real )
% 1.40/1.60 = ( ord_less_eq_real @ Y2 @ ( uminus_uminus_real @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_add_le_0_iff
% 1.40/1.60 thf(fact_1164_real__0__le__add__iff,axiom,
% 1.40/1.60 ! [X: real,Y2: real] :
% 1.40/1.60 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y2 ) )
% 1.40/1.60 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y2 ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_0_le_add_iff
% 1.40/1.60 thf(fact_1165_verit__less__mono__div__int2,axiom,
% 1.40/1.60 ! [A2: int,B2: int,N: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ A2 @ B2 )
% 1.40/1.60 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 1.40/1.60 => ( ord_less_eq_int @ ( divide_divide_int @ B2 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % verit_less_mono_div_int2
% 1.40/1.60 thf(fact_1166_div__eq__minus1,axiom,
% 1.40/1.60 ! [B: int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.60 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 1.40/1.60 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % div_eq_minus1
% 1.40/1.60 thf(fact_1167_realpow__square__minus__le,axiom,
% 1.40/1.60 ! [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 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % realpow_square_minus_le
% 1.40/1.60 thf(fact_1168_minus__mod__int__eq,axiom,
% 1.40/1.60 ! [L2: int,K: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 1.40/1.60 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 1.40/1.60 = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % minus_mod_int_eq
% 1.40/1.60 thf(fact_1169_zmod__minus1,axiom,
% 1.40/1.60 ! [B: int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.60 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 1.40/1.60 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zmod_minus1
% 1.40/1.60 thf(fact_1170_zdiv__zminus2__eq__if,axiom,
% 1.40/1.60 ! [B: int,A: int] :
% 1.40/1.60 ( ( B != zero_zero_int )
% 1.40/1.60 => ( ( ( ( modulo_modulo_int @ A @ B )
% 1.40/1.60 = zero_zero_int )
% 1.40/1.60 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 1.40/1.60 & ( ( ( modulo_modulo_int @ A @ B )
% 1.40/1.60 != zero_zero_int )
% 1.40/1.60 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 1.40/1.60 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zdiv_zminus2_eq_if
% 1.40/1.60 thf(fact_1171_zdiv__zminus1__eq__if,axiom,
% 1.40/1.60 ! [B: int,A: int] :
% 1.40/1.60 ( ( B != zero_zero_int )
% 1.40/1.60 => ( ( ( ( modulo_modulo_int @ A @ B )
% 1.40/1.60 = zero_zero_int )
% 1.40/1.60 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 1.40/1.60 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 1.40/1.60 & ( ( ( modulo_modulo_int @ A @ B )
% 1.40/1.60 != zero_zero_int )
% 1.40/1.60 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 1.40/1.60 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zdiv_zminus1_eq_if
% 1.40/1.60 thf(fact_1172_zminus1__lemma,axiom,
% 1.40/1.60 ! [A: int,B: int,Q2: int,R2: int] :
% 1.40/1.60 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 1.40/1.60 => ( ( B != zero_zero_int )
% 1.40/1.60 => ( 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 ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zminus1_lemma
% 1.40/1.60 thf(fact_1173_minus__1__div__exp__eq__int,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.60 = ( uminus_uminus_int @ one_one_int ) ) ).
% 1.40/1.60
% 1.40/1.60 % minus_1_div_exp_eq_int
% 1.40/1.60 thf(fact_1174_div__pos__neg__trivial,axiom,
% 1.40/1.60 ! [K: int,L2: int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.60 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 1.40/1.60 => ( ( divide_divide_int @ K @ L2 )
% 1.40/1.60 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % div_pos_neg_trivial
% 1.40/1.60 thf(fact_1175_signed__take__bit__int__less__eq__self__iff,axiom,
% 1.40/1.60 ! [N: nat,K: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 1.40/1.60 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_int_less_eq_self_iff
% 1.40/1.60 thf(fact_1176_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 1.40/1.60 ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_int_greater_eq_minus_exp
% 1.40/1.60 thf(fact_1177_signed__take__bit__int__greater__self__iff,axiom,
% 1.40/1.60 ! [K: int,N: nat] :
% 1.40/1.60 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 1.40/1.60 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_int_greater_self_iff
% 1.40/1.60 thf(fact_1178_int__bit__induct,axiom,
% 1.40/1.60 ! [P: int > $o,K: int] :
% 1.40/1.60 ( ( P @ zero_zero_int )
% 1.40/1.60 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 1.40/1.60 => ( ! [K2: int] :
% 1.40/1.60 ( ( P @ K2 )
% 1.40/1.60 => ( ( K2 != zero_zero_int )
% 1.40/1.60 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.60 => ( ! [K2: int] :
% 1.40/1.60 ( ( P @ K2 )
% 1.40/1.60 => ( ( K2
% 1.40/1.60 != ( uminus_uminus_int @ one_one_int ) )
% 1.40/1.60 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 1.40/1.60 => ( P @ K ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_bit_induct
% 1.40/1.60 thf(fact_1179_signed__take__bit__int__eq__self,axiom,
% 1.40/1.60 ! [N: nat,K: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 1.40/1.60 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.60 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 1.40/1.60 = K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_int_eq_self
% 1.40/1.60 thf(fact_1180_signed__take__bit__int__eq__self__iff,axiom,
% 1.40/1.60 ! [N: nat,K: int] :
% 1.40/1.60 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 1.40/1.60 = K )
% 1.40/1.60 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 1.40/1.60 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_int_eq_self_iff
% 1.40/1.60 thf(fact_1181_signed__take__bit__int__greater__eq,axiom,
% 1.40/1.60 ! [K: int,N: nat] :
% 1.40/1.60 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 1.40/1.60 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_int_greater_eq
% 1.40/1.60 thf(fact_1182_signed__take__bit__Suc__minus__bit1,axiom,
% 1.40/1.60 ! [N: nat,K: num] :
% 1.40/1.60 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 1.40/1.60 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_Suc_minus_bit1
% 1.40/1.60 thf(fact_1183_set__decode__0,axiom,
% 1.40/1.60 ! [X: nat] :
% 1.40/1.60 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 1.40/1.60 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % set_decode_0
% 1.40/1.60 thf(fact_1184_set__decode__Suc,axiom,
% 1.40/1.60 ! [N: nat,X: nat] :
% 1.40/1.60 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 1.40/1.60 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % set_decode_Suc
% 1.40/1.60 thf(fact_1185_semiring__norm_I90_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( ( bit1 @ M )
% 1.40/1.60 = ( bit1 @ N ) )
% 1.40/1.60 = ( M = N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(90)
% 1.40/1.60 thf(fact_1186_semiring__norm_I89_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( bit1 @ M )
% 1.40/1.60 != ( bit0 @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(89)
% 1.40/1.60 thf(fact_1187_semiring__norm_I88_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( bit0 @ M )
% 1.40/1.60 != ( bit1 @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(88)
% 1.40/1.60 thf(fact_1188_semiring__norm_I86_J,axiom,
% 1.40/1.60 ! [M: num] :
% 1.40/1.60 ( ( bit1 @ M )
% 1.40/1.60 != one ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(86)
% 1.40/1.60 thf(fact_1189_semiring__norm_I84_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( one
% 1.40/1.60 != ( bit1 @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(84)
% 1.40/1.60 thf(fact_1190_semiring__norm_I73_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 1.40/1.60 = ( ord_less_eq_num @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(73)
% 1.40/1.60 thf(fact_1191_semiring__norm_I80_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 1.40/1.60 = ( ord_less_num @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(80)
% 1.40/1.60 thf(fact_1192_Suc__0__mod__eq,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.60 = ( zero_n2687167440665602831ol_nat
% 1.40/1.60 @ ( N
% 1.40/1.60 != ( suc @ zero_zero_nat ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_0_mod_eq
% 1.40/1.60 thf(fact_1193_semiring__norm_I7_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 1.40/1.60 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(7)
% 1.40/1.60 thf(fact_1194_semiring__norm_I9_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 1.40/1.60 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(9)
% 1.40/1.60 thf(fact_1195_semiring__norm_I14_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 1.40/1.60 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(14)
% 1.40/1.60 thf(fact_1196_semiring__norm_I15_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 1.40/1.60 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(15)
% 1.40/1.60 thf(fact_1197_semiring__norm_I72_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 1.40/1.60 = ( ord_less_eq_num @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(72)
% 1.40/1.60 thf(fact_1198_semiring__norm_I81_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 1.40/1.60 = ( ord_less_num @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(81)
% 1.40/1.60 thf(fact_1199_semiring__norm_I70_J,axiom,
% 1.40/1.60 ! [M: num] :
% 1.40/1.60 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(70)
% 1.40/1.60 thf(fact_1200_semiring__norm_I77_J,axiom,
% 1.40/1.60 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(77)
% 1.40/1.60 thf(fact_1201_zdiv__numeral__Bit1,axiom,
% 1.40/1.60 ! [V: num,W: num] :
% 1.40/1.60 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 1.40/1.60 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zdiv_numeral_Bit1
% 1.40/1.60 thf(fact_1202_semiring__norm_I10_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 1.40/1.60 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(10)
% 1.40/1.60 thf(fact_1203_semiring__norm_I8_J,axiom,
% 1.40/1.60 ! [M: num] :
% 1.40/1.60 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 1.40/1.60 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(8)
% 1.40/1.60 thf(fact_1204_semiring__norm_I5_J,axiom,
% 1.40/1.60 ! [M: num] :
% 1.40/1.60 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 1.40/1.60 = ( bit1 @ M ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(5)
% 1.40/1.60 thf(fact_1205_semiring__norm_I4_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 1.40/1.60 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(4)
% 1.40/1.60 thf(fact_1206_semiring__norm_I3_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 1.40/1.60 = ( bit1 @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(3)
% 1.40/1.60 thf(fact_1207_semiring__norm_I16_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 1.40/1.60 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(16)
% 1.40/1.60 thf(fact_1208_semiring__norm_I74_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 1.40/1.60 = ( ord_less_num @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(74)
% 1.40/1.60 thf(fact_1209_semiring__norm_I79_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 1.40/1.60 = ( ord_less_eq_num @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(79)
% 1.40/1.60 thf(fact_1210_div__Suc__eq__div__add3,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 1.40/1.60 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % div_Suc_eq_div_add3
% 1.40/1.60 thf(fact_1211_Suc__div__eq__add3__div__numeral,axiom,
% 1.40/1.60 ! [M: nat,V: num] :
% 1.40/1.60 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 1.40/1.60 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_div_eq_add3_div_numeral
% 1.40/1.60 thf(fact_1212_mod__Suc__eq__mod__add3,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 1.40/1.60 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mod_Suc_eq_mod_add3
% 1.40/1.60 thf(fact_1213_Suc__mod__eq__add3__mod__numeral,axiom,
% 1.40/1.60 ! [M: nat,V: num] :
% 1.40/1.60 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 1.40/1.60 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_mod_eq_add3_mod_numeral
% 1.40/1.60 thf(fact_1214_zmod__numeral__Bit1,axiom,
% 1.40/1.60 ! [V: num,W: num] :
% 1.40/1.60 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 1.40/1.60 = ( 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 ) ) ).
% 1.40/1.60
% 1.40/1.60 % zmod_numeral_Bit1
% 1.40/1.60 thf(fact_1215_signed__take__bit__Suc__bit1,axiom,
% 1.40/1.60 ! [N: nat,K: num] :
% 1.40/1.60 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 1.40/1.60 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_Suc_bit1
% 1.40/1.60 thf(fact_1216_verit__eq__simplify_I14_J,axiom,
% 1.40/1.60 ! [X23: num,X32: num] :
% 1.40/1.60 ( ( bit0 @ X23 )
% 1.40/1.60 != ( bit1 @ X32 ) ) ).
% 1.40/1.60
% 1.40/1.60 % verit_eq_simplify(14)
% 1.40/1.60 thf(fact_1217_verit__eq__simplify_I12_J,axiom,
% 1.40/1.60 ! [X32: num] :
% 1.40/1.60 ( one
% 1.40/1.60 != ( bit1 @ X32 ) ) ).
% 1.40/1.60
% 1.40/1.60 % verit_eq_simplify(12)
% 1.40/1.60 thf(fact_1218_xor__num_Ocases,axiom,
% 1.40/1.60 ! [X: product_prod_num_num] :
% 1.40/1.60 ( ( X
% 1.40/1.60 != ( product_Pair_num_num @ one @ one ) )
% 1.40/1.60 => ( ! [N4: num] :
% 1.40/1.60 ( X
% 1.40/1.60 != ( product_Pair_num_num @ one @ ( bit0 @ N4 ) ) )
% 1.40/1.60 => ( ! [N4: num] :
% 1.40/1.60 ( X
% 1.40/1.60 != ( product_Pair_num_num @ one @ ( bit1 @ N4 ) ) )
% 1.40/1.60 => ( ! [M5: num] :
% 1.40/1.60 ( X
% 1.40/1.60 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 1.40/1.60 => ( ! [M5: num,N4: num] :
% 1.40/1.60 ( X
% 1.40/1.60 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N4 ) ) )
% 1.40/1.60 => ( ! [M5: num,N4: num] :
% 1.40/1.60 ( X
% 1.40/1.60 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N4 ) ) )
% 1.40/1.60 => ( ! [M5: num] :
% 1.40/1.60 ( X
% 1.40/1.60 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 1.40/1.60 => ( ! [M5: num,N4: num] :
% 1.40/1.60 ( X
% 1.40/1.60 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N4 ) ) )
% 1.40/1.60 => ~ ! [M5: num,N4: num] :
% 1.40/1.60 ( X
% 1.40/1.60 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N4 ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % xor_num.cases
% 1.40/1.60 thf(fact_1219_num_Oexhaust,axiom,
% 1.40/1.60 ! [Y2: num] :
% 1.40/1.60 ( ( Y2 != one )
% 1.40/1.60 => ( ! [X24: num] :
% 1.40/1.60 ( Y2
% 1.40/1.60 != ( bit0 @ X24 ) )
% 1.40/1.60 => ~ ! [X33: num] :
% 1.40/1.60 ( Y2
% 1.40/1.60 != ( bit1 @ X33 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % num.exhaust
% 1.40/1.60 thf(fact_1220_eval__nat__numeral_I3_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 1.40/1.60 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % eval_nat_numeral(3)
% 1.40/1.60 thf(fact_1221_bset_I1_J,axiom,
% 1.40/1.60 ! [D5: int,B2: set_int,P: int > $o,Q: int > $o] :
% 1.40/1.60 ( ! [X5: int] :
% 1.40/1.60 ( ! [Xa: int] :
% 1.40/1.60 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb: int] :
% 1.40/1.60 ( ( member_int @ Xb @ B2 )
% 1.40/1.60 => ( X5
% 1.40/1.60 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 1.40/1.60 => ( ( P @ X5 )
% 1.40/1.60 => ( P @ ( minus_minus_int @ X5 @ D5 ) ) ) )
% 1.40/1.60 => ( ! [X5: int] :
% 1.40/1.60 ( ! [Xa: int] :
% 1.40/1.60 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb: int] :
% 1.40/1.60 ( ( member_int @ Xb @ B2 )
% 1.40/1.60 => ( X5
% 1.40/1.60 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 1.40/1.60 => ( ( Q @ X5 )
% 1.40/1.60 => ( Q @ ( minus_minus_int @ X5 @ D5 ) ) ) )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ B2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ( P @ X3 )
% 1.40/1.60 & ( Q @ X3 ) )
% 1.40/1.60 => ( ( P @ ( minus_minus_int @ X3 @ D5 ) )
% 1.40/1.60 & ( Q @ ( minus_minus_int @ X3 @ D5 ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bset(1)
% 1.40/1.60 thf(fact_1222_bset_I2_J,axiom,
% 1.40/1.60 ! [D5: int,B2: set_int,P: int > $o,Q: int > $o] :
% 1.40/1.60 ( ! [X5: int] :
% 1.40/1.60 ( ! [Xa: int] :
% 1.40/1.60 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb: int] :
% 1.40/1.60 ( ( member_int @ Xb @ B2 )
% 1.40/1.60 => ( X5
% 1.40/1.60 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 1.40/1.60 => ( ( P @ X5 )
% 1.40/1.60 => ( P @ ( minus_minus_int @ X5 @ D5 ) ) ) )
% 1.40/1.60 => ( ! [X5: int] :
% 1.40/1.60 ( ! [Xa: int] :
% 1.40/1.60 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb: int] :
% 1.40/1.60 ( ( member_int @ Xb @ B2 )
% 1.40/1.60 => ( X5
% 1.40/1.60 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 1.40/1.60 => ( ( Q @ X5 )
% 1.40/1.60 => ( Q @ ( minus_minus_int @ X5 @ D5 ) ) ) )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ B2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ( P @ X3 )
% 1.40/1.60 | ( Q @ X3 ) )
% 1.40/1.60 => ( ( P @ ( minus_minus_int @ X3 @ D5 ) )
% 1.40/1.60 | ( Q @ ( minus_minus_int @ X3 @ D5 ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bset(2)
% 1.40/1.60 thf(fact_1223_aset_I1_J,axiom,
% 1.40/1.60 ! [D5: int,A2: set_int,P: int > $o,Q: int > $o] :
% 1.40/1.60 ( ! [X5: int] :
% 1.40/1.60 ( ! [Xa: int] :
% 1.40/1.60 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb: int] :
% 1.40/1.60 ( ( member_int @ Xb @ A2 )
% 1.40/1.60 => ( X5
% 1.40/1.60 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 1.40/1.60 => ( ( P @ X5 )
% 1.40/1.60 => ( P @ ( plus_plus_int @ X5 @ D5 ) ) ) )
% 1.40/1.60 => ( ! [X5: int] :
% 1.40/1.60 ( ! [Xa: int] :
% 1.40/1.60 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb: int] :
% 1.40/1.60 ( ( member_int @ Xb @ A2 )
% 1.40/1.60 => ( X5
% 1.40/1.60 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 1.40/1.60 => ( ( Q @ X5 )
% 1.40/1.60 => ( Q @ ( plus_plus_int @ X5 @ D5 ) ) ) )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ A2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ( P @ X3 )
% 1.40/1.60 & ( Q @ X3 ) )
% 1.40/1.60 => ( ( P @ ( plus_plus_int @ X3 @ D5 ) )
% 1.40/1.60 & ( Q @ ( plus_plus_int @ X3 @ D5 ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % aset(1)
% 1.40/1.60 thf(fact_1224_aset_I2_J,axiom,
% 1.40/1.60 ! [D5: int,A2: set_int,P: int > $o,Q: int > $o] :
% 1.40/1.60 ( ! [X5: int] :
% 1.40/1.60 ( ! [Xa: int] :
% 1.40/1.60 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb: int] :
% 1.40/1.60 ( ( member_int @ Xb @ A2 )
% 1.40/1.60 => ( X5
% 1.40/1.60 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 1.40/1.60 => ( ( P @ X5 )
% 1.40/1.60 => ( P @ ( plus_plus_int @ X5 @ D5 ) ) ) )
% 1.40/1.60 => ( ! [X5: int] :
% 1.40/1.60 ( ! [Xa: int] :
% 1.40/1.60 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb: int] :
% 1.40/1.60 ( ( member_int @ Xb @ A2 )
% 1.40/1.60 => ( X5
% 1.40/1.60 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 1.40/1.60 => ( ( Q @ X5 )
% 1.40/1.60 => ( Q @ ( plus_plus_int @ X5 @ D5 ) ) ) )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ A2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ( P @ X3 )
% 1.40/1.60 | ( Q @ X3 ) )
% 1.40/1.60 => ( ( P @ ( plus_plus_int @ X3 @ D5 ) )
% 1.40/1.60 | ( Q @ ( plus_plus_int @ X3 @ D5 ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % aset(2)
% 1.40/1.60 thf(fact_1225_subset__decode__imp__le,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 1.40/1.60 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % subset_decode_imp_le
% 1.40/1.60 thf(fact_1226_numeral__3__eq__3,axiom,
% 1.40/1.60 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 1.40/1.60 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % numeral_3_eq_3
% 1.40/1.60 thf(fact_1227_Suc3__eq__add__3,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 1.40/1.60 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc3_eq_add_3
% 1.40/1.60 thf(fact_1228_bset_I9_J,axiom,
% 1.40/1.60 ! [D: int,D5: int,B2: set_int,T: int] :
% 1.40/1.60 ( ( dvd_dvd_int @ D @ D5 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ B2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T ) )
% 1.40/1.60 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X3 @ D5 ) @ T ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bset(9)
% 1.40/1.60 thf(fact_1229_bset_I10_J,axiom,
% 1.40/1.60 ! [D: int,D5: int,B2: set_int,T: int] :
% 1.40/1.60 ( ( dvd_dvd_int @ D @ D5 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ B2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T ) )
% 1.40/1.60 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X3 @ D5 ) @ T ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bset(10)
% 1.40/1.60 thf(fact_1230_aset_I9_J,axiom,
% 1.40/1.60 ! [D: int,D5: int,A2: set_int,T: int] :
% 1.40/1.60 ( ( dvd_dvd_int @ D @ D5 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ A2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T ) )
% 1.40/1.60 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X3 @ D5 ) @ T ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % aset(9)
% 1.40/1.60 thf(fact_1231_aset_I10_J,axiom,
% 1.40/1.60 ! [D: int,D5: int,A2: set_int,T: int] :
% 1.40/1.60 ( ( dvd_dvd_int @ D @ D5 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ A2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T ) )
% 1.40/1.60 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X3 @ D5 ) @ T ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % aset(10)
% 1.40/1.60 thf(fact_1232_num_Osize_I6_J,axiom,
% 1.40/1.60 ! [X32: num] :
% 1.40/1.60 ( ( size_size_num @ ( bit1 @ X32 ) )
% 1.40/1.60 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % num.size(6)
% 1.40/1.60 thf(fact_1233_periodic__finite__ex,axiom,
% 1.40/1.60 ! [D: int,P: int > $o] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D )
% 1.40/1.60 => ( ! [X5: int,K2: int] :
% 1.40/1.60 ( ( P @ X5 )
% 1.40/1.60 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 1.40/1.60 => ( ( ? [X2: int] : ( P @ X2 ) )
% 1.40/1.60 = ( ? [X4: int] :
% 1.40/1.60 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 1.40/1.60 & ( P @ X4 ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % periodic_finite_ex
% 1.40/1.60 thf(fact_1234_bset_I3_J,axiom,
% 1.40/1.60 ! [D5: int,T: int,B2: set_int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ B2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( X3 = T )
% 1.40/1.60 => ( ( minus_minus_int @ X3 @ D5 )
% 1.40/1.60 = T ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bset(3)
% 1.40/1.60 thf(fact_1235_bset_I4_J,axiom,
% 1.40/1.60 ! [D5: int,T: int,B2: set_int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ( ( member_int @ T @ B2 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ B2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( X3 != T )
% 1.40/1.60 => ( ( minus_minus_int @ X3 @ D5 )
% 1.40/1.60 != T ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bset(4)
% 1.40/1.60 thf(fact_1236_bset_I5_J,axiom,
% 1.40/1.60 ! [D5: int,B2: set_int,T: int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ B2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ord_less_int @ X3 @ T )
% 1.40/1.60 => ( ord_less_int @ ( minus_minus_int @ X3 @ D5 ) @ T ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bset(5)
% 1.40/1.60 thf(fact_1237_bset_I7_J,axiom,
% 1.40/1.60 ! [D5: int,T: int,B2: set_int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ( ( member_int @ T @ B2 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ B2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ord_less_int @ T @ X3 )
% 1.40/1.60 => ( ord_less_int @ T @ ( minus_minus_int @ X3 @ D5 ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bset(7)
% 1.40/1.60 thf(fact_1238_aset_I3_J,axiom,
% 1.40/1.60 ! [D5: int,T: int,A2: set_int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ A2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( X3 = T )
% 1.40/1.60 => ( ( plus_plus_int @ X3 @ D5 )
% 1.40/1.60 = T ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % aset(3)
% 1.40/1.60 thf(fact_1239_aset_I4_J,axiom,
% 1.40/1.60 ! [D5: int,T: int,A2: set_int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ( ( member_int @ T @ A2 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ A2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( X3 != T )
% 1.40/1.60 => ( ( plus_plus_int @ X3 @ D5 )
% 1.40/1.60 != T ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % aset(4)
% 1.40/1.60 thf(fact_1240_aset_I5_J,axiom,
% 1.40/1.60 ! [D5: int,T: int,A2: set_int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ( ( member_int @ T @ A2 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ A2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ord_less_int @ X3 @ T )
% 1.40/1.60 => ( ord_less_int @ ( plus_plus_int @ X3 @ D5 ) @ T ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % aset(5)
% 1.40/1.60 thf(fact_1241_aset_I7_J,axiom,
% 1.40/1.60 ! [D5: int,A2: set_int,T: int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ A2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ord_less_int @ T @ X3 )
% 1.40/1.60 => ( ord_less_int @ T @ ( plus_plus_int @ X3 @ D5 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % aset(7)
% 1.40/1.60 thf(fact_1242_Suc__div__eq__add3__div,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 1.40/1.60 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_div_eq_add3_div
% 1.40/1.60 thf(fact_1243_Suc__mod__eq__add3__mod,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 1.40/1.60 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_mod_eq_add3_mod
% 1.40/1.60 thf(fact_1244_aset_I8_J,axiom,
% 1.40/1.60 ! [D5: int,A2: set_int,T: int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ A2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ord_less_eq_int @ T @ X3 )
% 1.40/1.60 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X3 @ D5 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % aset(8)
% 1.40/1.60 thf(fact_1245_aset_I6_J,axiom,
% 1.40/1.60 ! [D5: int,T: int,A2: set_int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ A2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ord_less_eq_int @ X3 @ T )
% 1.40/1.60 => ( ord_less_eq_int @ ( plus_plus_int @ X3 @ D5 ) @ T ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % aset(6)
% 1.40/1.60 thf(fact_1246_bset_I8_J,axiom,
% 1.40/1.60 ! [D5: int,T: int,B2: set_int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B2 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ B2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ord_less_eq_int @ T @ X3 )
% 1.40/1.60 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X3 @ D5 ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bset(8)
% 1.40/1.60 thf(fact_1247_bset_I6_J,axiom,
% 1.40/1.60 ! [D5: int,B2: set_int,T: int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ! [X3: int] :
% 1.40/1.60 ( ! [Xa3: int] :
% 1.40/1.60 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb2: int] :
% 1.40/1.60 ( ( member_int @ Xb2 @ B2 )
% 1.40/1.60 => ( X3
% 1.40/1.60 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 1.40/1.60 => ( ( ord_less_eq_int @ X3 @ T )
% 1.40/1.60 => ( ord_less_eq_int @ ( minus_minus_int @ X3 @ D5 ) @ T ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % bset(6)
% 1.40/1.60 thf(fact_1248_cpmi,axiom,
% 1.40/1.60 ! [D5: int,P: int > $o,P3: int > $o,B2: set_int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ( ? [Z4: int] :
% 1.40/1.60 ! [X5: int] :
% 1.40/1.60 ( ( ord_less_int @ X5 @ Z4 )
% 1.40/1.60 => ( ( P @ X5 )
% 1.40/1.60 = ( P3 @ X5 ) ) )
% 1.40/1.60 => ( ! [X5: int] :
% 1.40/1.60 ( ! [Xa: int] :
% 1.40/1.60 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb: int] :
% 1.40/1.60 ( ( member_int @ Xb @ B2 )
% 1.40/1.60 => ( X5
% 1.40/1.60 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 1.40/1.60 => ( ( P @ X5 )
% 1.40/1.60 => ( P @ ( minus_minus_int @ X5 @ D5 ) ) ) )
% 1.40/1.60 => ( ! [X5: int,K2: int] :
% 1.40/1.60 ( ( P3 @ X5 )
% 1.40/1.60 = ( P3 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 1.40/1.60 => ( ( ? [X2: int] : ( P @ X2 ) )
% 1.40/1.60 = ( ? [X4: int] :
% 1.40/1.60 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 & ( P3 @ X4 ) )
% 1.40/1.60 | ? [X4: int] :
% 1.40/1.60 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 & ? [Y4: int] :
% 1.40/1.60 ( ( member_int @ Y4 @ B2 )
% 1.40/1.60 & ( P @ ( plus_plus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % cpmi
% 1.40/1.60 thf(fact_1249_cppi,axiom,
% 1.40/1.60 ! [D5: int,P: int > $o,P3: int > $o,A2: set_int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ D5 )
% 1.40/1.60 => ( ? [Z4: int] :
% 1.40/1.60 ! [X5: int] :
% 1.40/1.60 ( ( ord_less_int @ Z4 @ X5 )
% 1.40/1.60 => ( ( P @ X5 )
% 1.40/1.60 = ( P3 @ X5 ) ) )
% 1.40/1.60 => ( ! [X5: int] :
% 1.40/1.60 ( ! [Xa: int] :
% 1.40/1.60 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 => ! [Xb: int] :
% 1.40/1.60 ( ( member_int @ Xb @ A2 )
% 1.40/1.60 => ( X5
% 1.40/1.60 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 1.40/1.60 => ( ( P @ X5 )
% 1.40/1.60 => ( P @ ( plus_plus_int @ X5 @ D5 ) ) ) )
% 1.40/1.60 => ( ! [X5: int,K2: int] :
% 1.40/1.60 ( ( P3 @ X5 )
% 1.40/1.60 = ( P3 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D5 ) ) ) )
% 1.40/1.60 => ( ( ? [X2: int] : ( P @ X2 ) )
% 1.40/1.60 = ( ? [X4: int] :
% 1.40/1.60 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 & ( P3 @ X4 ) )
% 1.40/1.60 | ? [X4: int] :
% 1.40/1.60 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D5 ) )
% 1.40/1.60 & ? [Y4: int] :
% 1.40/1.60 ( ( member_int @ Y4 @ A2 )
% 1.40/1.60 & ( P @ ( minus_minus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % cppi
% 1.40/1.60 thf(fact_1250_odd__mod__4__div__2,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 1.40/1.60 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 1.40/1.60 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % odd_mod_4_div_2
% 1.40/1.60 thf(fact_1251_set__decode__def,axiom,
% 1.40/1.60 ( nat_set_decode
% 1.40/1.60 = ( ^ [X4: nat] :
% 1.40/1.60 ( collect_nat
% 1.40/1.60 @ ^ [N2: nat] :
% 1.40/1.60 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % set_decode_def
% 1.40/1.60 thf(fact_1252_mod__exhaust__less__4,axiom,
% 1.40/1.60 ! [M: nat] :
% 1.40/1.60 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 1.40/1.60 = zero_zero_nat )
% 1.40/1.60 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 1.40/1.60 = one_one_nat )
% 1.40/1.60 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 1.40/1.60 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.60 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 1.40/1.60 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mod_exhaust_less_4
% 1.40/1.60 thf(fact_1253_signed__take__bit__numeral__minus__bit1,axiom,
% 1.40/1.60 ! [L2: num,K: num] :
% 1.40/1.60 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 1.40/1.60 = ( 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 ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_numeral_minus_bit1
% 1.40/1.60 thf(fact_1254_signed__take__bit__numeral__bit1,axiom,
% 1.40/1.60 ! [L2: num,K: num] :
% 1.40/1.60 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 1.40/1.60 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_numeral_bit1
% 1.40/1.60 thf(fact_1255_pred__numeral__simps_I1_J,axiom,
% 1.40/1.60 ( ( pred_numeral @ one )
% 1.40/1.60 = zero_zero_nat ) ).
% 1.40/1.60
% 1.40/1.60 % pred_numeral_simps(1)
% 1.40/1.60 thf(fact_1256_Suc__eq__numeral,axiom,
% 1.40/1.60 ! [N: nat,K: num] :
% 1.40/1.60 ( ( ( suc @ N )
% 1.40/1.60 = ( numeral_numeral_nat @ K ) )
% 1.40/1.60 = ( N
% 1.40/1.60 = ( pred_numeral @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_eq_numeral
% 1.40/1.60 thf(fact_1257_eq__numeral__Suc,axiom,
% 1.40/1.60 ! [K: num,N: nat] :
% 1.40/1.60 ( ( ( numeral_numeral_nat @ K )
% 1.40/1.60 = ( suc @ N ) )
% 1.40/1.60 = ( ( pred_numeral @ K )
% 1.40/1.60 = N ) ) ).
% 1.40/1.60
% 1.40/1.60 % eq_numeral_Suc
% 1.40/1.60 thf(fact_1258_less__numeral__Suc,axiom,
% 1.40/1.60 ! [K: num,N: nat] :
% 1.40/1.60 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 1.40/1.60 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % less_numeral_Suc
% 1.40/1.60 thf(fact_1259_less__Suc__numeral,axiom,
% 1.40/1.60 ! [N: nat,K: num] :
% 1.40/1.60 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 1.40/1.60 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % less_Suc_numeral
% 1.40/1.60 thf(fact_1260_pred__numeral__simps_I3_J,axiom,
% 1.40/1.60 ! [K: num] :
% 1.40/1.60 ( ( pred_numeral @ ( bit1 @ K ) )
% 1.40/1.60 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % pred_numeral_simps(3)
% 1.40/1.60 thf(fact_1261_le__numeral__Suc,axiom,
% 1.40/1.60 ! [K: num,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 1.40/1.60 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % le_numeral_Suc
% 1.40/1.60 thf(fact_1262_le__Suc__numeral,axiom,
% 1.40/1.60 ! [N: nat,K: num] :
% 1.40/1.60 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 1.40/1.60 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % le_Suc_numeral
% 1.40/1.60 thf(fact_1263_diff__numeral__Suc,axiom,
% 1.40/1.60 ! [K: num,N: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 1.40/1.60 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_numeral_Suc
% 1.40/1.60 thf(fact_1264_diff__Suc__numeral,axiom,
% 1.40/1.60 ! [N: nat,K: num] :
% 1.40/1.60 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 1.40/1.60 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % diff_Suc_numeral
% 1.40/1.60 thf(fact_1265_max__numeral__Suc,axiom,
% 1.40/1.60 ! [K: num,N: nat] :
% 1.40/1.60 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 1.40/1.60 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % max_numeral_Suc
% 1.40/1.60 thf(fact_1266_max__Suc__numeral,axiom,
% 1.40/1.60 ! [N: nat,K: num] :
% 1.40/1.60 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 1.40/1.60 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % max_Suc_numeral
% 1.40/1.60 thf(fact_1267_signed__take__bit__numeral__bit0,axiom,
% 1.40/1.60 ! [L2: num,K: num] :
% 1.40/1.60 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 1.40/1.60 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_numeral_bit0
% 1.40/1.60 thf(fact_1268_signed__take__bit__numeral__minus__bit0,axiom,
% 1.40/1.60 ! [L2: num,K: num] :
% 1.40/1.60 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 1.40/1.60 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % signed_take_bit_numeral_minus_bit0
% 1.40/1.60 thf(fact_1269_numeral__eq__Suc,axiom,
% 1.40/1.60 ( numeral_numeral_nat
% 1.40/1.60 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % numeral_eq_Suc
% 1.40/1.60 thf(fact_1270_pred__numeral__def,axiom,
% 1.40/1.60 ( pred_numeral
% 1.40/1.60 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % pred_numeral_def
% 1.40/1.60 thf(fact_1271_divmod__int__def,axiom,
% 1.40/1.60 ( unique5052692396658037445od_int
% 1.40/1.60 = ( ^ [M6: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % divmod_int_def
% 1.40/1.60 thf(fact_1272_divmod_H__nat__def,axiom,
% 1.40/1.60 ( unique5055182867167087721od_nat
% 1.40/1.60 = ( ^ [M6: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % divmod'_nat_def
% 1.40/1.60 thf(fact_1273_eq__diff__eq_H,axiom,
% 1.40/1.60 ! [X: real,Y2: real,Z: real] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( minus_minus_real @ Y2 @ Z ) )
% 1.40/1.60 = ( Y2
% 1.40/1.60 = ( plus_plus_real @ X @ Z ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % eq_diff_eq'
% 1.40/1.60 thf(fact_1274_one__div__minus__numeral,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % one_div_minus_numeral
% 1.40/1.60 thf(fact_1275_minus__one__div__numeral,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % minus_one_div_numeral
% 1.40/1.60 thf(fact_1276_numeral__div__minus__numeral,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % numeral_div_minus_numeral
% 1.40/1.60 thf(fact_1277_minus__numeral__div__numeral,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % minus_numeral_div_numeral
% 1.40/1.60 thf(fact_1278_Divides_Oadjust__div__eq,axiom,
% 1.40/1.60 ! [Q2: int,R2: int] :
% 1.40/1.60 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 1.40/1.60 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Divides.adjust_div_eq
% 1.40/1.60 thf(fact_1279_divmod__BitM__2__eq,axiom,
% 1.40/1.60 ! [M: num] :
% 1.40/1.60 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 1.40/1.60 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 1.40/1.60
% 1.40/1.60 % divmod_BitM_2_eq
% 1.40/1.60 thf(fact_1280_Sum__Icc__int,axiom,
% 1.40/1.60 ! [M: int,N: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ M @ N )
% 1.40/1.60 => ( ( groups4538972089207619220nt_int
% 1.40/1.60 @ ^ [X4: int] : X4
% 1.40/1.60 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 1.40/1.60 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Sum_Icc_int
% 1.40/1.60 thf(fact_1281_pred__numeral__simps_I2_J,axiom,
% 1.40/1.60 ! [K: num] :
% 1.40/1.60 ( ( pred_numeral @ ( bit0 @ K ) )
% 1.40/1.60 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % pred_numeral_simps(2)
% 1.40/1.60 thf(fact_1282_semiring__norm_I26_J,axiom,
% 1.40/1.60 ( ( bitM @ one )
% 1.40/1.60 = one ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(26)
% 1.40/1.60 thf(fact_1283_semiring__norm_I27_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( bitM @ ( bit0 @ N ) )
% 1.40/1.60 = ( bit1 @ ( bitM @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(27)
% 1.40/1.60 thf(fact_1284_semiring__norm_I28_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( bitM @ ( bit1 @ N ) )
% 1.40/1.60 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % semiring_norm(28)
% 1.40/1.60 thf(fact_1285_real__of__int__div4,axiom,
% 1.40/1.60 ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_int_div4
% 1.40/1.60 thf(fact_1286_real__of__int__div,axiom,
% 1.40/1.60 ! [D: int,N: int] :
% 1.40/1.60 ( ( dvd_dvd_int @ D @ N )
% 1.40/1.60 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 1.40/1.60 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_int_div
% 1.40/1.60 thf(fact_1287_eval__nat__numeral_I2_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 1.40/1.60 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % eval_nat_numeral(2)
% 1.40/1.60 thf(fact_1288_one__plus__BitM,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 1.40/1.60 = ( bit0 @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % one_plus_BitM
% 1.40/1.60 thf(fact_1289_BitM__plus__one,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 1.40/1.60 = ( bit0 @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % BitM_plus_one
% 1.40/1.60 thf(fact_1290_int__le__real__less,axiom,
% 1.40/1.60 ( ord_less_eq_int
% 1.40/1.60 = ( ^ [N2: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_le_real_less
% 1.40/1.60 thf(fact_1291_int__less__real__le,axiom,
% 1.40/1.60 ( ord_less_int
% 1.40/1.60 = ( ^ [N2: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_less_real_le
% 1.40/1.60 thf(fact_1292_real__of__int__div__aux,axiom,
% 1.40/1.60 ! [X: int,D: int] :
% 1.40/1.60 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 1.40/1.60 = ( 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 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_int_div_aux
% 1.40/1.60 thf(fact_1293_real__of__int__div2,axiom,
% 1.40/1.60 ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_int_div2
% 1.40/1.60 thf(fact_1294_real__of__int__div3,axiom,
% 1.40/1.60 ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_int_div3
% 1.40/1.60 thf(fact_1295_divmod__step__nat__def,axiom,
% 1.40/1.60 ( unique5026877609467782581ep_nat
% 1.40/1.60 = ( ^ [L: num] :
% 1.40/1.60 ( produc2626176000494625587at_nat
% 1.40/1.60 @ ^ [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 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % divmod_step_nat_def
% 1.40/1.60 thf(fact_1296_divmod__step__int__def,axiom,
% 1.40/1.60 ( unique5024387138958732305ep_int
% 1.40/1.60 = ( ^ [L: num] :
% 1.40/1.60 ( produc4245557441103728435nt_int
% 1.40/1.60 @ ^ [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 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % divmod_step_int_def
% 1.40/1.60 thf(fact_1297_divmod__nat__if,axiom,
% 1.40/1.60 ( divmod_nat
% 1.40/1.60 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.60 ( if_Pro6206227464963214023at_nat
% 1.40/1.60 @ ( ( N2 = zero_zero_nat )
% 1.40/1.60 | ( ord_less_nat @ M6 @ N2 ) )
% 1.40/1.60 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 1.40/1.60 @ ( produc2626176000494625587at_nat
% 1.40/1.60 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 1.40/1.60 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N2 ) @ N2 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % divmod_nat_if
% 1.40/1.60 thf(fact_1298_mask__nat__positive__iff,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 1.40/1.60 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % mask_nat_positive_iff
% 1.40/1.60 thf(fact_1299_less__eq__mask,axiom,
% 1.40/1.60 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % less_eq_mask
% 1.40/1.60 thf(fact_1300_mask__nonnegative__int,axiom,
% 1.40/1.60 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % mask_nonnegative_int
% 1.40/1.60 thf(fact_1301_not__mask__negative__int,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 1.40/1.60
% 1.40/1.60 % not_mask_negative_int
% 1.40/1.60 thf(fact_1302_less__mask,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.60 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % less_mask
% 1.40/1.60 thf(fact_1303_Suc__mask__eq__exp,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 1.40/1.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_mask_eq_exp
% 1.40/1.60 thf(fact_1304_mask__nat__less__exp,axiom,
% 1.40/1.60 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % mask_nat_less_exp
% 1.40/1.60 thf(fact_1305_mask__nat__def,axiom,
% 1.40/1.60 ( bit_se2002935070580805687sk_nat
% 1.40/1.60 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mask_nat_def
% 1.40/1.60 thf(fact_1306_mask__half__int,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 1.40/1.60 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mask_half_int
% 1.40/1.60 thf(fact_1307_exists__least__lemma,axiom,
% 1.40/1.60 ! [P: nat > $o] :
% 1.40/1.60 ( ~ ( P @ zero_zero_nat )
% 1.40/1.60 => ( ? [X_1: nat] : ( P @ X_1 )
% 1.40/1.60 => ? [N4: nat] :
% 1.40/1.60 ( ~ ( P @ N4 )
% 1.40/1.60 & ( P @ ( suc @ N4 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % exists_least_lemma
% 1.40/1.60 thf(fact_1308_mask__int__def,axiom,
% 1.40/1.60 ( bit_se2000444600071755411sk_int
% 1.40/1.60 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mask_int_def
% 1.40/1.60 thf(fact_1309_divmod__nat__def,axiom,
% 1.40/1.60 ( divmod_nat
% 1.40/1.60 = ( ^ [M6: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N2 ) @ ( modulo_modulo_nat @ M6 @ N2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % divmod_nat_def
% 1.40/1.60 thf(fact_1310_mask__eq__sum__exp__nat,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 1.40/1.60 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.60 @ ( collect_nat
% 1.40/1.60 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % mask_eq_sum_exp_nat
% 1.40/1.60 thf(fact_1311_gauss__sum__nat,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( groups3542108847815614940at_nat
% 1.40/1.60 @ ^ [X4: nat] : X4
% 1.40/1.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 1.40/1.60 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % gauss_sum_nat
% 1.40/1.60 thf(fact_1312_arith__series__nat,axiom,
% 1.40/1.60 ! [A: nat,D: nat,N: nat] :
% 1.40/1.60 ( ( groups3542108847815614940at_nat
% 1.40/1.60 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I4 @ D ) )
% 1.40/1.60 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 1.40/1.60 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % arith_series_nat
% 1.40/1.60 thf(fact_1313_Sum__Icc__nat,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( groups3542108847815614940at_nat
% 1.40/1.60 @ ^ [X4: nat] : X4
% 1.40/1.60 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 1.40/1.60 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Sum_Icc_nat
% 1.40/1.60 thf(fact_1314_or__int__unfold,axiom,
% 1.40/1.60 ( bit_se1409905431419307370or_int
% 1.40/1.60 = ( ^ [K3: int,L: int] :
% 1.40/1.60 ( if_int
% 1.40/1.60 @ ( ( K3
% 1.40/1.60 = ( uminus_uminus_int @ one_one_int ) )
% 1.40/1.60 | ( L
% 1.40/1.60 = ( uminus_uminus_int @ one_one_int ) ) )
% 1.40/1.60 @ ( uminus_uminus_int @ one_one_int )
% 1.40/1.60 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_int_unfold
% 1.40/1.60 thf(fact_1315_int__eq__iff__numeral,axiom,
% 1.40/1.60 ! [M: nat,V: num] :
% 1.40/1.60 ( ( ( semiri1314217659103216013at_int @ M )
% 1.40/1.60 = ( numeral_numeral_int @ V ) )
% 1.40/1.60 = ( M
% 1.40/1.60 = ( numeral_numeral_nat @ V ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_eq_iff_numeral
% 1.40/1.60 thf(fact_1316_negative__zle,axiom,
% 1.40/1.60 ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 1.40/1.60
% 1.40/1.60 % negative_zle
% 1.40/1.60 thf(fact_1317_negative__zless,axiom,
% 1.40/1.60 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 1.40/1.60
% 1.40/1.60 % negative_zless
% 1.40/1.60 thf(fact_1318_or__nonnegative__int__iff,axiom,
% 1.40/1.60 ! [K: int,L2: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 1.40/1.60 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.60 & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_nonnegative_int_iff
% 1.40/1.60 thf(fact_1319_or__negative__int__iff,axiom,
% 1.40/1.60 ! [K: int,L2: int] :
% 1.40/1.60 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 1.40/1.60 = ( ( ord_less_int @ K @ zero_zero_int )
% 1.40/1.60 | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_negative_int_iff
% 1.40/1.60 thf(fact_1320_real__of__nat__less__numeral__iff,axiom,
% 1.40/1.60 ! [N: nat,W: num] :
% 1.40/1.60 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 1.40/1.60 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_nat_less_numeral_iff
% 1.40/1.60 thf(fact_1321_numeral__less__real__of__nat__iff,axiom,
% 1.40/1.60 ! [W: num,N: nat] :
% 1.40/1.60 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 1.40/1.60 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % numeral_less_real_of_nat_iff
% 1.40/1.60 thf(fact_1322_numeral__le__real__of__nat__iff,axiom,
% 1.40/1.60 ! [N: num,M: nat] :
% 1.40/1.60 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 1.40/1.60 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 1.40/1.60
% 1.40/1.60 % numeral_le_real_of_nat_iff
% 1.40/1.60 thf(fact_1323_or__minus__numerals_I6_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 1.40/1.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_minus_numerals(6)
% 1.40/1.60 thf(fact_1324_or__minus__numerals_I2_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_minus_numerals(2)
% 1.40/1.60 thf(fact_1325_or__greater__eq,axiom,
% 1.40/1.60 ! [L2: int,K: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 1.40/1.60 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_greater_eq
% 1.40/1.60 thf(fact_1326_OR__lower,axiom,
% 1.40/1.60 ! [X: int,Y2: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.60 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.60 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % OR_lower
% 1.40/1.60 thf(fact_1327_int__ops_I3_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 1.40/1.60 = ( numeral_numeral_int @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_ops(3)
% 1.40/1.60 thf(fact_1328_nat__int__comparison_I2_J,axiom,
% 1.40/1.60 ( ord_less_nat
% 1.40/1.60 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_int_comparison(2)
% 1.40/1.60 thf(fact_1329_int__cases,axiom,
% 1.40/1.60 ! [Z: int] :
% 1.40/1.60 ( ! [N4: nat] :
% 1.40/1.60 ( Z
% 1.40/1.60 != ( semiri1314217659103216013at_int @ N4 ) )
% 1.40/1.60 => ~ ! [N4: nat] :
% 1.40/1.60 ( Z
% 1.40/1.60 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_cases
% 1.40/1.60 thf(fact_1330_int__of__nat__induct,axiom,
% 1.40/1.60 ! [P: int > $o,Z: int] :
% 1.40/1.60 ( ! [N4: nat] : ( P @ ( semiri1314217659103216013at_int @ N4 ) )
% 1.40/1.60 => ( ! [N4: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) )
% 1.40/1.60 => ( P @ Z ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_of_nat_induct
% 1.40/1.60 thf(fact_1331_nat__int__comparison_I3_J,axiom,
% 1.40/1.60 ( ord_less_eq_nat
% 1.40/1.60 = ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_int_comparison(3)
% 1.40/1.60 thf(fact_1332_zle__int,axiom,
% 1.40/1.60 ! [M: nat,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 1.40/1.60 = ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.60
% 1.40/1.60 % zle_int
% 1.40/1.60 thf(fact_1333_zero__le__imp__eq__int,axiom,
% 1.40/1.60 ! [K: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.60 => ? [N4: nat] :
% 1.40/1.60 ( K
% 1.40/1.60 = ( semiri1314217659103216013at_int @ N4 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zero_le_imp_eq_int
% 1.40/1.60 thf(fact_1334_nonneg__int__cases,axiom,
% 1.40/1.60 ! [K: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.60 => ~ ! [N4: nat] :
% 1.40/1.60 ( K
% 1.40/1.60 != ( semiri1314217659103216013at_int @ N4 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nonneg_int_cases
% 1.40/1.60 thf(fact_1335_int__ops_I5_J,axiom,
% 1.40/1.60 ! [A: nat,B: nat] :
% 1.40/1.60 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 1.40/1.60 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_ops(5)
% 1.40/1.60 thf(fact_1336_int__plus,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 1.40/1.60 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_plus
% 1.40/1.60 thf(fact_1337_zadd__int__left,axiom,
% 1.40/1.60 ! [M: nat,N: nat,Z: int] :
% 1.40/1.60 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 1.40/1.60 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 1.40/1.60
% 1.40/1.60 % zadd_int_left
% 1.40/1.60 thf(fact_1338_int__ops_I7_J,axiom,
% 1.40/1.60 ! [A: nat,B: nat] :
% 1.40/1.60 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 1.40/1.60 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_ops(7)
% 1.40/1.60 thf(fact_1339_int__ops_I2_J,axiom,
% 1.40/1.60 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 1.40/1.60 = one_one_int ) ).
% 1.40/1.60
% 1.40/1.60 % int_ops(2)
% 1.40/1.60 thf(fact_1340_zle__iff__zadd,axiom,
% 1.40/1.60 ( ord_less_eq_int
% 1.40/1.60 = ( ^ [W3: int,Z5: int] :
% 1.40/1.60 ? [N2: nat] :
% 1.40/1.60 ( Z5
% 1.40/1.60 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zle_iff_zadd
% 1.40/1.60 thf(fact_1341_zdiv__int,axiom,
% 1.40/1.60 ! [A: nat,B: nat] :
% 1.40/1.60 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 1.40/1.60 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zdiv_int
% 1.40/1.60 thf(fact_1342_nat__less__as__int,axiom,
% 1.40/1.60 ( ord_less_nat
% 1.40/1.60 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_less_as_int
% 1.40/1.60 thf(fact_1343_nat__leq__as__int,axiom,
% 1.40/1.60 ( ord_less_eq_nat
% 1.40/1.60 = ( ^ [A4: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_leq_as_int
% 1.40/1.60 thf(fact_1344_reals__Archimedean3,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ! [Y: real] :
% 1.40/1.60 ? [N4: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % reals_Archimedean3
% 1.40/1.60 thf(fact_1345_int__cases4,axiom,
% 1.40/1.60 ! [M: int] :
% 1.40/1.60 ( ! [N4: nat] :
% 1.40/1.60 ( M
% 1.40/1.60 != ( semiri1314217659103216013at_int @ N4 ) )
% 1.40/1.60 => ~ ! [N4: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 1.40/1.60 => ( M
% 1.40/1.60 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_cases4
% 1.40/1.60 thf(fact_1346_real__of__nat__div4,axiom,
% 1.40/1.60 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_nat_div4
% 1.40/1.60 thf(fact_1347_int__zle__neg,axiom,
% 1.40/1.60 ! [N: nat,M: nat] :
% 1.40/1.60 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 1.40/1.60 = ( ( N = zero_zero_nat )
% 1.40/1.60 & ( M = zero_zero_nat ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_zle_neg
% 1.40/1.60 thf(fact_1348_int__Suc,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 1.40/1.60 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_Suc
% 1.40/1.60 thf(fact_1349_int__ops_I4_J,axiom,
% 1.40/1.60 ! [A: nat] :
% 1.40/1.60 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 1.40/1.60 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_ops(4)
% 1.40/1.60 thf(fact_1350_zless__iff__Suc__zadd,axiom,
% 1.40/1.60 ( ord_less_int
% 1.40/1.60 = ( ^ [W3: int,Z5: int] :
% 1.40/1.60 ? [N2: nat] :
% 1.40/1.60 ( Z5
% 1.40/1.60 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zless_iff_Suc_zadd
% 1.40/1.60 thf(fact_1351_nonpos__int__cases,axiom,
% 1.40/1.60 ! [K: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 1.40/1.60 => ~ ! [N4: nat] :
% 1.40/1.60 ( K
% 1.40/1.60 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nonpos_int_cases
% 1.40/1.60 thf(fact_1352_negative__zle__0,axiom,
% 1.40/1.60 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 1.40/1.60
% 1.40/1.60 % negative_zle_0
% 1.40/1.60 thf(fact_1353_real__of__nat__div,axiom,
% 1.40/1.60 ! [D: nat,N: nat] :
% 1.40/1.60 ( ( dvd_dvd_nat @ D @ N )
% 1.40/1.60 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 1.40/1.60 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_nat_div
% 1.40/1.60 thf(fact_1354_pos__int__cases,axiom,
% 1.40/1.60 ! [K: int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.60 => ~ ! [N4: nat] :
% 1.40/1.60 ( ( K
% 1.40/1.60 = ( semiri1314217659103216013at_int @ N4 ) )
% 1.40/1.60 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % pos_int_cases
% 1.40/1.60 thf(fact_1355_zero__less__imp__eq__int,axiom,
% 1.40/1.60 ! [K: int] :
% 1.40/1.60 ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.60 => ? [N4: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 1.40/1.60 & ( K
% 1.40/1.60 = ( semiri1314217659103216013at_int @ N4 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zero_less_imp_eq_int
% 1.40/1.60 thf(fact_1356_int__cases3,axiom,
% 1.40/1.60 ! [K: int] :
% 1.40/1.60 ( ( K != zero_zero_int )
% 1.40/1.60 => ( ! [N4: nat] :
% 1.40/1.60 ( ( K
% 1.40/1.60 = ( semiri1314217659103216013at_int @ N4 ) )
% 1.40/1.60 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) )
% 1.40/1.60 => ~ ! [N4: nat] :
% 1.40/1.60 ( ( K
% 1.40/1.60 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N4 ) ) )
% 1.40/1.60 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % int_cases3
% 1.40/1.60 thf(fact_1357_nat__less__real__le,axiom,
% 1.40/1.60 ( ord_less_nat
% 1.40/1.60 = ( ^ [N2: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_less_real_le
% 1.40/1.60 thf(fact_1358_nat__le__real__less,axiom,
% 1.40/1.60 ( ord_less_eq_nat
% 1.40/1.60 = ( ^ [N2: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % nat_le_real_less
% 1.40/1.60 thf(fact_1359_zmult__zless__mono2__lemma,axiom,
% 1.40/1.60 ! [I2: int,J: int,K: nat] :
% 1.40/1.60 ( ( ord_less_int @ I2 @ J )
% 1.40/1.60 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.60 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zmult_zless_mono2_lemma
% 1.40/1.60 thf(fact_1360_not__zle__0__negative,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % not_zle_0_negative
% 1.40/1.60 thf(fact_1361_negD,axiom,
% 1.40/1.60 ! [X: int] :
% 1.40/1.60 ( ( ord_less_int @ X @ zero_zero_int )
% 1.40/1.60 => ? [N4: nat] :
% 1.40/1.60 ( X
% 1.40/1.60 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % negD
% 1.40/1.60 thf(fact_1362_negative__zless__0,axiom,
% 1.40/1.60 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 1.40/1.60
% 1.40/1.60 % negative_zless_0
% 1.40/1.60 thf(fact_1363_real__of__nat__div__aux,axiom,
% 1.40/1.60 ! [X: nat,D: nat] :
% 1.40/1.60 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 1.40/1.60 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_nat_div_aux
% 1.40/1.60 thf(fact_1364_real__archimedian__rdiv__eq__0,axiom,
% 1.40/1.60 ! [X: real,C: real] :
% 1.40/1.60 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 1.40/1.60 => ( ! [M5: nat] :
% 1.40/1.60 ( ( ord_less_nat @ zero_zero_nat @ M5 )
% 1.40/1.60 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ X ) @ C ) )
% 1.40/1.60 => ( X = zero_zero_real ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_archimedian_rdiv_eq_0
% 1.40/1.60 thf(fact_1365_neg__int__cases,axiom,
% 1.40/1.60 ! [K: int] :
% 1.40/1.60 ( ( ord_less_int @ K @ zero_zero_int )
% 1.40/1.60 => ~ ! [N4: nat] :
% 1.40/1.60 ( ( K
% 1.40/1.60 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N4 ) ) )
% 1.40/1.60 => ~ ( ord_less_nat @ zero_zero_nat @ N4 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % neg_int_cases
% 1.40/1.60 thf(fact_1366_zdiff__int__split,axiom,
% 1.40/1.60 ! [P: int > $o,X: nat,Y2: nat] :
% 1.40/1.60 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y2 ) ) )
% 1.40/1.60 = ( ( ( ord_less_eq_nat @ Y2 @ X )
% 1.40/1.60 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) )
% 1.40/1.60 & ( ( ord_less_nat @ X @ Y2 )
% 1.40/1.60 => ( P @ zero_zero_int ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % zdiff_int_split
% 1.40/1.60 thf(fact_1367_real__of__nat__div2,axiom,
% 1.40/1.60 ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_nat_div2
% 1.40/1.60 thf(fact_1368_real__of__nat__div3,axiom,
% 1.40/1.60 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 1.40/1.60
% 1.40/1.60 % real_of_nat_div3
% 1.40/1.60 thf(fact_1369_linear__plus__1__le__power,axiom,
% 1.40/1.60 ! [X: real,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % linear_plus_1_le_power
% 1.40/1.60 thf(fact_1370_Bernoulli__inequality,axiom,
% 1.40/1.60 ! [X: real,N: nat] :
% 1.40/1.60 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.60 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Bernoulli_inequality
% 1.40/1.60 thf(fact_1371_OR__upper,axiom,
% 1.40/1.60 ! [X: int,N: nat,Y2: int] :
% 1.40/1.60 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.60 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.60 => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.60 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % OR_upper
% 1.40/1.60 thf(fact_1372_or__int__rec,axiom,
% 1.40/1.60 ( bit_se1409905431419307370or_int
% 1.40/1.60 = ( ^ [K3: int,L: int] :
% 1.40/1.60 ( plus_plus_int
% 1.40/1.60 @ ( zero_n2684676970156552555ol_int
% 1.40/1.60 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 1.40/1.60 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 1.40/1.60 @ ( 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 ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_int_rec
% 1.40/1.60 thf(fact_1373_Bernoulli__inequality__even,axiom,
% 1.40/1.60 ! [N: nat,X: real] :
% 1.40/1.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.60 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Bernoulli_inequality_even
% 1.40/1.60 thf(fact_1374_or__minus__numerals_I1_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_minus_numerals(1)
% 1.40/1.60 thf(fact_1375_or__minus__numerals_I5_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 1.40/1.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_minus_numerals(5)
% 1.40/1.60 thf(fact_1376_or__nat__numerals_I4_J,axiom,
% 1.40/1.60 ! [X: num] :
% 1.40/1.60 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 1.40/1.60 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_nat_numerals(4)
% 1.40/1.60 thf(fact_1377_or__nat__numerals_I2_J,axiom,
% 1.40/1.60 ! [Y2: num] :
% 1.40/1.60 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 1.40/1.60 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_nat_numerals(2)
% 1.40/1.60 thf(fact_1378_or__nat__numerals_I3_J,axiom,
% 1.40/1.60 ! [X: num] :
% 1.40/1.60 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 1.40/1.60 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_nat_numerals(3)
% 1.40/1.60 thf(fact_1379_or__nat__numerals_I1_J,axiom,
% 1.40/1.60 ! [Y2: num] :
% 1.40/1.60 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 1.40/1.60 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_nat_numerals(1)
% 1.40/1.60 thf(fact_1380_or__minus__numerals_I8_J,axiom,
% 1.40/1.60 ! [N: num,M: num] :
% 1.40/1.60 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_minus_numerals(8)
% 1.40/1.60 thf(fact_1381_or__minus__numerals_I4_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_minus_numerals(4)
% 1.40/1.60 thf(fact_1382_or__minus__numerals_I7_J,axiom,
% 1.40/1.60 ! [N: num,M: num] :
% 1.40/1.60 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_minus_numerals(7)
% 1.40/1.60 thf(fact_1383_or__minus__numerals_I3_J,axiom,
% 1.40/1.60 ! [M: num,N: num] :
% 1.40/1.60 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 1.40/1.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_minus_numerals(3)
% 1.40/1.60 thf(fact_1384_or__not__num__neg_Osimps_I1_J,axiom,
% 1.40/1.60 ( ( bit_or_not_num_neg @ one @ one )
% 1.40/1.60 = one ) ).
% 1.40/1.60
% 1.40/1.60 % or_not_num_neg.simps(1)
% 1.40/1.60 thf(fact_1385_or__not__num__neg_Osimps_I4_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 1.40/1.60 = ( bit0 @ one ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_not_num_neg.simps(4)
% 1.40/1.60 thf(fact_1386_or__not__num__neg_Osimps_I6_J,axiom,
% 1.40/1.60 ! [N: num,M: num] :
% 1.40/1.60 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 1.40/1.60 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_not_num_neg.simps(6)
% 1.40/1.60 thf(fact_1387_or__not__num__neg_Osimps_I7_J,axiom,
% 1.40/1.60 ! [N: num] :
% 1.40/1.60 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 1.40/1.60 = one ) ).
% 1.40/1.60
% 1.40/1.60 % or_not_num_neg.simps(7)
% 1.40/1.60 thf(fact_1388_or__not__num__neg_Osimps_I3_J,axiom,
% 1.40/1.60 ! [M: num] :
% 1.40/1.60 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 1.40/1.60 = ( bit1 @ M ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_not_num_neg.simps(3)
% 1.40/1.60 thf(fact_1389_or__not__num__neg_Osimps_I5_J,axiom,
% 1.40/1.60 ! [N: num,M: num] :
% 1.40/1.60 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 1.40/1.60 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_not_num_neg.simps(5)
% 1.40/1.60 thf(fact_1390_or__not__num__neg_Osimps_I9_J,axiom,
% 1.40/1.60 ! [N: num,M: num] :
% 1.40/1.60 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 1.40/1.60 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_not_num_neg.simps(9)
% 1.40/1.60 thf(fact_1391_or__not__num__neg_Osimps_I2_J,axiom,
% 1.40/1.60 ! [M: num] :
% 1.40/1.60 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 1.40/1.60 = ( bit1 @ M ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_not_num_neg.simps(2)
% 1.40/1.60 thf(fact_1392_or__not__num__neg_Osimps_I8_J,axiom,
% 1.40/1.60 ! [N: num,M: num] :
% 1.40/1.60 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 1.40/1.60 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_not_num_neg.simps(8)
% 1.40/1.60 thf(fact_1393_or__not__num__neg_Oelims,axiom,
% 1.40/1.60 ! [X: num,Xa2: num,Y2: num] :
% 1.40/1.60 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 1.40/1.60 = Y2 )
% 1.40/1.60 => ( ( ( X = one )
% 1.40/1.60 => ( ( Xa2 = one )
% 1.40/1.60 => ( Y2 != one ) ) )
% 1.40/1.60 => ( ( ( X = one )
% 1.40/1.60 => ! [M5: num] :
% 1.40/1.60 ( ( Xa2
% 1.40/1.60 = ( bit0 @ M5 ) )
% 1.40/1.60 => ( Y2
% 1.40/1.60 != ( bit1 @ M5 ) ) ) )
% 1.40/1.60 => ( ( ( X = one )
% 1.40/1.60 => ! [M5: num] :
% 1.40/1.60 ( ( Xa2
% 1.40/1.60 = ( bit1 @ M5 ) )
% 1.40/1.60 => ( Y2
% 1.40/1.60 != ( bit1 @ M5 ) ) ) )
% 1.40/1.60 => ( ( ? [N4: num] :
% 1.40/1.60 ( X
% 1.40/1.60 = ( bit0 @ N4 ) )
% 1.40/1.60 => ( ( Xa2 = one )
% 1.40/1.60 => ( Y2
% 1.40/1.60 != ( bit0 @ one ) ) ) )
% 1.40/1.60 => ( ! [N4: num] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( bit0 @ N4 ) )
% 1.40/1.60 => ! [M5: num] :
% 1.40/1.60 ( ( Xa2
% 1.40/1.60 = ( bit0 @ M5 ) )
% 1.40/1.60 => ( Y2
% 1.40/1.60 != ( bitM @ ( bit_or_not_num_neg @ N4 @ M5 ) ) ) ) )
% 1.40/1.60 => ( ! [N4: num] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( bit0 @ N4 ) )
% 1.40/1.60 => ! [M5: num] :
% 1.40/1.60 ( ( Xa2
% 1.40/1.60 = ( bit1 @ M5 ) )
% 1.40/1.60 => ( Y2
% 1.40/1.60 != ( bit0 @ ( bit_or_not_num_neg @ N4 @ M5 ) ) ) ) )
% 1.40/1.60 => ( ( ? [N4: num] :
% 1.40/1.60 ( X
% 1.40/1.60 = ( bit1 @ N4 ) )
% 1.40/1.60 => ( ( Xa2 = one )
% 1.40/1.60 => ( Y2 != one ) ) )
% 1.40/1.60 => ( ! [N4: num] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( bit1 @ N4 ) )
% 1.40/1.60 => ! [M5: num] :
% 1.40/1.60 ( ( Xa2
% 1.40/1.60 = ( bit0 @ M5 ) )
% 1.40/1.60 => ( Y2
% 1.40/1.60 != ( bitM @ ( bit_or_not_num_neg @ N4 @ M5 ) ) ) ) )
% 1.40/1.60 => ~ ! [N4: num] :
% 1.40/1.60 ( ( X
% 1.40/1.60 = ( bit1 @ N4 ) )
% 1.40/1.60 => ! [M5: num] :
% 1.40/1.60 ( ( Xa2
% 1.40/1.60 = ( bit1 @ M5 ) )
% 1.40/1.60 => ( Y2
% 1.40/1.60 != ( bitM @ ( bit_or_not_num_neg @ N4 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_not_num_neg.elims
% 1.40/1.60 thf(fact_1394_Suc__0__or__eq,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.60 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % Suc_0_or_eq
% 1.40/1.60 thf(fact_1395_or__Suc__0__eq,axiom,
% 1.40/1.60 ! [N: nat] :
% 1.40/1.60 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 1.40/1.60 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_Suc_0_eq
% 1.40/1.60 thf(fact_1396_or__nat__rec,axiom,
% 1.40/1.60 ( bit_se1412395901928357646or_nat
% 1.40/1.60 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.60 ( plus_plus_nat
% 1.40/1.60 @ ( zero_n2687167440665602831ol_nat
% 1.40/1.60 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 1.40/1.60 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 1.40/1.60 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_nat_rec
% 1.40/1.60 thf(fact_1397_or__nat__unfold,axiom,
% 1.40/1.60 ( bit_se1412395901928357646or_nat
% 1.40/1.60 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % or_nat_unfold
% 1.40/1.60 thf(fact_1398_ln__one__minus__pos__lower__bound,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.60 => ( 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 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_one_minus_pos_lower_bound
% 1.40/1.60 thf(fact_1399_ln__le__cancel__iff,axiom,
% 1.40/1.60 ! [X: real,Y2: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 1.40/1.60 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) )
% 1.40/1.60 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_le_cancel_iff
% 1.40/1.60 thf(fact_1400_ln__eq__zero__iff,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ( ln_ln_real @ X )
% 1.40/1.60 = zero_zero_real )
% 1.40/1.60 = ( X = one_one_real ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_eq_zero_iff
% 1.40/1.60 thf(fact_1401_ln__gt__zero__iff,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 1.40/1.60 = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_gt_zero_iff
% 1.40/1.60 thf(fact_1402_ln__less__zero__iff,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 1.40/1.60 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_less_zero_iff
% 1.40/1.60 thf(fact_1403_ln__ge__zero__iff,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 1.40/1.60 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_ge_zero_iff
% 1.40/1.60 thf(fact_1404_ln__le__zero__iff,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 1.40/1.60 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_le_zero_iff
% 1.40/1.60 thf(fact_1405_ln__bound,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_bound
% 1.40/1.60 thf(fact_1406_ln__gt__zero,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.60 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_gt_zero
% 1.40/1.60 thf(fact_1407_ln__less__zero,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.60 => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_less_zero
% 1.40/1.60 thf(fact_1408_ln__gt__zero__imp__gt__one,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 1.40/1.60 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_gt_zero_imp_gt_one
% 1.40/1.60 thf(fact_1409_ln__ge__zero,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_eq_real @ one_one_real @ X )
% 1.40/1.60 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_ge_zero
% 1.40/1.60 thf(fact_1410_ln__ge__zero__imp__ge__one,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 1.40/1.60 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_ge_zero_imp_ge_one
% 1.40/1.60 thf(fact_1411_ln__add__one__self__le__self,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_add_one_self_le_self
% 1.40/1.60 thf(fact_1412_ln__mult,axiom,
% 1.40/1.60 ! [X: real,Y2: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 1.40/1.60 => ( ( ln_ln_real @ ( times_times_real @ X @ Y2 ) )
% 1.40/1.60 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_mult
% 1.40/1.60 thf(fact_1413_ln__eq__minus__one,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ( ln_ln_real @ X )
% 1.40/1.60 = ( minus_minus_real @ X @ one_one_real ) )
% 1.40/1.60 => ( X = one_one_real ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_eq_minus_one
% 1.40/1.60 thf(fact_1414_ln__2__less__1,axiom,
% 1.40/1.60 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 1.40/1.60
% 1.40/1.60 % ln_2_less_1
% 1.40/1.60 thf(fact_1415_ln__le__minus__one,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_le_minus_one
% 1.40/1.60 thf(fact_1416_ln__diff__le,axiom,
% 1.40/1.60 ! [X: real,Y2: real] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 1.40/1.60 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y2 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y2 ) @ Y2 ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_diff_le
% 1.40/1.60 thf(fact_1417_ln__add__one__self__le__self2,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.60 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_add_one_self_le_self2
% 1.40/1.60 thf(fact_1418_ln__realpow,axiom,
% 1.40/1.60 ! [X: real,N: nat] :
% 1.40/1.60 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 1.40/1.60 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 1.40/1.60
% 1.40/1.60 % ln_realpow
% 1.40/1.60 thf(fact_1419_ln__one__minus__pos__upper__bound,axiom,
% 1.40/1.60 ! [X: real] :
% 1.40/1.60 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.60 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.60 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % ln_one_minus_pos_upper_bound
% 1.40/1.61 thf(fact_1420_sums__if_H,axiom,
% 1.40/1.61 ! [G: nat > real,X: real] :
% 1.40/1.61 ( ( sums_real @ G @ X )
% 1.40/1.61 => ( sums_real
% 1.40/1.61 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % sums_if'
% 1.40/1.61 thf(fact_1421_sums__if,axiom,
% 1.40/1.61 ! [G: nat > real,X: real,F: nat > real,Y2: real] :
% 1.40/1.61 ( ( sums_real @ G @ X )
% 1.40/1.61 => ( ( sums_real @ F @ Y2 )
% 1.40/1.61 => ( sums_real
% 1.40/1.61 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( F @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 @ ( plus_plus_real @ X @ Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sums_if
% 1.40/1.61 thf(fact_1422_sum__split__even__odd,axiom,
% 1.40/1.61 ! [F: nat > real,G: nat > real,N: nat] :
% 1.40/1.61 ( ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( F @ I4 ) @ ( G @ I4 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [I4: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ one_one_nat ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sum_split_even_odd
% 1.40/1.61 thf(fact_1423_ln__one__plus__pos__lower__bound,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.61 => ( 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 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % ln_one_plus_pos_lower_bound
% 1.40/1.61 thf(fact_1424_power__half__series,axiom,
% 1.40/1.61 ( sums_real
% 1.40/1.61 @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 1.40/1.61 @ one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % power_half_series
% 1.40/1.61 thf(fact_1425_prod__int__plus__eq,axiom,
% 1.40/1.61 ! [I2: nat,J: nat] :
% 1.40/1.61 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 1.40/1.61 = ( groups1705073143266064639nt_int
% 1.40/1.61 @ ^ [X4: int] : X4
% 1.40/1.61 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % prod_int_plus_eq
% 1.40/1.61 thf(fact_1426_sumr__cos__zero__one,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 1.40/1.61 = one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % sumr_cos_zero_one
% 1.40/1.61 thf(fact_1427_ln__series,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.61 => ( ( ln_ln_real @ X )
% 1.40/1.61 = ( suminf_real
% 1.40/1.61 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % ln_series
% 1.40/1.61 thf(fact_1428_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 1.40/1.61 => ( 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 ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 1.40/1.61 thf(fact_1429_tanh__ln__real,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 1.40/1.61 = ( 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 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tanh_ln_real
% 1.40/1.61 thf(fact_1430_abs__ln__one__plus__x__minus__x__bound,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( 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 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % abs_ln_one_plus_x_minus_x_bound
% 1.40/1.61 thf(fact_1431_tanh__real__le__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % tanh_real_le_iff
% 1.40/1.61 thf(fact_1432_tanh__real__nonpos__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 1.40/1.61 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % tanh_real_nonpos_iff
% 1.40/1.61 thf(fact_1433_tanh__real__nonneg__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 1.40/1.61 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % tanh_real_nonneg_iff
% 1.40/1.61 thf(fact_1434_cos__coeff__0,axiom,
% 1.40/1.61 ( ( cos_coeff @ zero_zero_nat )
% 1.40/1.61 = one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % cos_coeff_0
% 1.40/1.61 thf(fact_1435_artanh__minus__real,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 1.40/1.61 = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % artanh_minus_real
% 1.40/1.61 thf(fact_1436_tanh__real__lt__1,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % tanh_real_lt_1
% 1.40/1.61 thf(fact_1437_abs__real__def,axiom,
% 1.40/1.61 ( abs_abs_real
% 1.40/1.61 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % abs_real_def
% 1.40/1.61 thf(fact_1438_sin__bound__lemma,axiom,
% 1.40/1.61 ! [X: real,Y2: real,U: real,V: real] :
% 1.40/1.61 ( ( X = Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 1.40/1.61 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y2 ) ) @ V ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_bound_lemma
% 1.40/1.61 thf(fact_1439_tanh__real__gt__neg1,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % tanh_real_gt_neg1
% 1.40/1.61 thf(fact_1440_lemma__interval,axiom,
% 1.40/1.61 ! [A: real,X: real,B: real] :
% 1.40/1.61 ( ( ord_less_real @ A @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ B )
% 1.40/1.61 => ? [D3: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ D3 )
% 1.40/1.61 & ! [Y: real] :
% 1.40/1.61 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y ) ) @ D3 )
% 1.40/1.61 => ( ( ord_less_eq_real @ A @ Y )
% 1.40/1.61 & ( ord_less_eq_real @ Y @ B ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % lemma_interval
% 1.40/1.61 thf(fact_1441_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.61 => ( 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 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 1.40/1.61 thf(fact_1442_monoseq__arctan__series,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( topolo6980174941875973593q_real
% 1.40/1.61 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % monoseq_arctan_series
% 1.40/1.61 thf(fact_1443_arctan__series,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( ( arctan @ X )
% 1.40/1.61 = ( suminf_real
% 1.40/1.61 @ ^ [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 ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_series
% 1.40/1.61 thf(fact_1444_pi__series,axiom,
% 1.40/1.61 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = ( suminf_real
% 1.40/1.61 @ ^ [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 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % pi_series
% 1.40/1.61 thf(fact_1445_summable__arctan__series,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( summable_real
% 1.40/1.61 @ ^ [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 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % summable_arctan_series
% 1.40/1.61 thf(fact_1446_zdvd1__eq,axiom,
% 1.40/1.61 ! [X: int] :
% 1.40/1.61 ( ( dvd_dvd_int @ X @ one_one_int )
% 1.40/1.61 = ( ( abs_abs_int @ X )
% 1.40/1.61 = one_one_int ) ) ).
% 1.40/1.61
% 1.40/1.61 % zdvd1_eq
% 1.40/1.61 thf(fact_1447_zabs__less__one__iff,axiom,
% 1.40/1.61 ! [Z: int] :
% 1.40/1.61 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 1.40/1.61 = ( Z = zero_zero_int ) ) ).
% 1.40/1.61
% 1.40/1.61 % zabs_less_one_iff
% 1.40/1.61 thf(fact_1448_arctan__le__zero__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 1.40/1.61 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_le_zero_iff
% 1.40/1.61 thf(fact_1449_zero__le__arctan__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 1.40/1.61 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % zero_le_arctan_iff
% 1.40/1.61 thf(fact_1450_arctan__monotone_H,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ X @ Y2 )
% 1.40/1.61 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_monotone'
% 1.40/1.61 thf(fact_1451_arctan__le__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_le_iff
% 1.40/1.61 thf(fact_1452_abs__zmult__eq__1,axiom,
% 1.40/1.61 ! [M: int,N: int] :
% 1.40/1.61 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 1.40/1.61 = one_one_int )
% 1.40/1.61 => ( ( abs_abs_int @ M )
% 1.40/1.61 = one_one_int ) ) ).
% 1.40/1.61
% 1.40/1.61 % abs_zmult_eq_1
% 1.40/1.61 thf(fact_1453_pi__ge__zero,axiom,
% 1.40/1.61 ord_less_eq_real @ zero_zero_real @ pi ).
% 1.40/1.61
% 1.40/1.61 % pi_ge_zero
% 1.40/1.61 thf(fact_1454_arctan__ubound,axiom,
% 1.40/1.61 ! [Y2: real] : ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_ubound
% 1.40/1.61 thf(fact_1455_arctan__one,axiom,
% 1.40/1.61 ( ( arctan @ one_one_real )
% 1.40/1.61 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_one
% 1.40/1.61 thf(fact_1456_arctan__bounded,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 1.40/1.61 & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_bounded
% 1.40/1.61 thf(fact_1457_arctan__lbound,axiom,
% 1.40/1.61 ! [Y2: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_lbound
% 1.40/1.61 thf(fact_1458_dvd__imp__le__int,axiom,
% 1.40/1.61 ! [I2: int,D: int] :
% 1.40/1.61 ( ( I2 != zero_zero_int )
% 1.40/1.61 => ( ( dvd_dvd_int @ D @ I2 )
% 1.40/1.61 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % dvd_imp_le_int
% 1.40/1.61 thf(fact_1459_abs__mod__less,axiom,
% 1.40/1.61 ! [L2: int,K: int] :
% 1.40/1.61 ( ( L2 != zero_zero_int )
% 1.40/1.61 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % abs_mod_less
% 1.40/1.61 thf(fact_1460_summable__rabs__comparison__test,axiom,
% 1.40/1.61 ! [F: nat > real,G: nat > real] :
% 1.40/1.61 ( ? [N5: nat] :
% 1.40/1.61 ! [N4: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ N5 @ N4 )
% 1.40/1.61 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N4 ) ) @ ( G @ N4 ) ) )
% 1.40/1.61 => ( ( summable_real @ G )
% 1.40/1.61 => ( summable_real
% 1.40/1.61 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % summable_rabs_comparison_test
% 1.40/1.61 thf(fact_1461_summable__rabs,axiom,
% 1.40/1.61 ! [F: nat > real] :
% 1.40/1.61 ( ( summable_real
% 1.40/1.61 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 1.40/1.61 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 1.40/1.61 @ ( suminf_real
% 1.40/1.61 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % summable_rabs
% 1.40/1.61 thf(fact_1462_machin__Euler,axiom,
% 1.40/1.61 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 1.40/1.61 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % machin_Euler
% 1.40/1.61 thf(fact_1463_machin,axiom,
% 1.40/1.61 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % machin
% 1.40/1.61 thf(fact_1464_pi__less__4,axiom,
% 1.40/1.61 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % pi_less_4
% 1.40/1.61 thf(fact_1465_pi__ge__two,axiom,
% 1.40/1.61 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 1.40/1.61
% 1.40/1.61 % pi_ge_two
% 1.40/1.61 thf(fact_1466_zdvd__mult__cancel1,axiom,
% 1.40/1.61 ! [M: int,N: int] :
% 1.40/1.61 ( ( M != zero_zero_int )
% 1.40/1.61 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 1.40/1.61 = ( ( abs_abs_int @ N )
% 1.40/1.61 = one_one_int ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % zdvd_mult_cancel1
% 1.40/1.61 thf(fact_1467_pi__half__neq__two,axiom,
% 1.40/1.61 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.61 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % pi_half_neq_two
% 1.40/1.61 thf(fact_1468_even__abs__add__iff,axiom,
% 1.40/1.61 ! [K: int,L2: int] :
% 1.40/1.61 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 1.40/1.61 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % even_abs_add_iff
% 1.40/1.61 thf(fact_1469_even__add__abs__iff,axiom,
% 1.40/1.61 ! [K: int,L2: int] :
% 1.40/1.61 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 1.40/1.61 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % even_add_abs_iff
% 1.40/1.61 thf(fact_1470_pi__half__neq__zero,axiom,
% 1.40/1.61 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.61 != zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % pi_half_neq_zero
% 1.40/1.61 thf(fact_1471_pi__half__less__two,axiom,
% 1.40/1.61 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 1.40/1.61
% 1.40/1.61 % pi_half_less_two
% 1.40/1.61 thf(fact_1472_pi__half__le__two,axiom,
% 1.40/1.61 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 1.40/1.61
% 1.40/1.61 % pi_half_le_two
% 1.40/1.61 thf(fact_1473_monoseq__realpow,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.61 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % monoseq_realpow
% 1.40/1.61 thf(fact_1474_summable__power__series,axiom,
% 1.40/1.61 ! [F: nat > real,Z: real] :
% 1.40/1.61 ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 1.40/1.61 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 1.40/1.61 => ( ( ord_less_real @ Z @ one_one_real )
% 1.40/1.61 => ( summable_real
% 1.40/1.61 @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z @ I4 ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % summable_power_series
% 1.40/1.61 thf(fact_1475_nat__intermed__int__val,axiom,
% 1.40/1.61 ! [M: nat,N: nat,F: nat > int,K: int] :
% 1.40/1.61 ( ! [I3: nat] :
% 1.40/1.61 ( ( ( ord_less_eq_nat @ M @ I3 )
% 1.40/1.61 & ( ord_less_nat @ I3 @ N ) )
% 1.40/1.61 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 1.40/1.61 => ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.61 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 1.40/1.61 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 1.40/1.61 => ? [I3: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ M @ I3 )
% 1.40/1.61 & ( ord_less_eq_nat @ I3 @ N )
% 1.40/1.61 & ( ( F @ I3 )
% 1.40/1.61 = K ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % nat_intermed_int_val
% 1.40/1.61 thf(fact_1476_incr__lemma,axiom,
% 1.40/1.61 ! [D: int,Z: int,X: int] :
% 1.40/1.61 ( ( ord_less_int @ zero_zero_int @ D )
% 1.40/1.61 => ( 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 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % incr_lemma
% 1.40/1.61 thf(fact_1477_decr__lemma,axiom,
% 1.40/1.61 ! [D: int,X: int,Z: int] :
% 1.40/1.61 ( ( ord_less_int @ zero_zero_int @ D )
% 1.40/1.61 => ( 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 ) ) ).
% 1.40/1.61
% 1.40/1.61 % decr_lemma
% 1.40/1.61 thf(fact_1478_pi__half__gt__zero,axiom,
% 1.40/1.61 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % pi_half_gt_zero
% 1.40/1.61 thf(fact_1479_pi__half__ge__zero,axiom,
% 1.40/1.61 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % pi_half_ge_zero
% 1.40/1.61 thf(fact_1480_m2pi__less__pi,axiom,
% 1.40/1.61 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 1.40/1.61
% 1.40/1.61 % m2pi_less_pi
% 1.40/1.61 thf(fact_1481_nat__ivt__aux,axiom,
% 1.40/1.61 ! [N: nat,F: nat > int,K: int] :
% 1.40/1.61 ( ! [I3: nat] :
% 1.40/1.61 ( ( ord_less_nat @ I3 @ N )
% 1.40/1.61 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 1.40/1.61 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 1.40/1.61 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 1.40/1.61 => ? [I3: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ I3 @ N )
% 1.40/1.61 & ( ( F @ I3 )
% 1.40/1.61 = K ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % nat_ivt_aux
% 1.40/1.61 thf(fact_1482_complex__mod__minus__le__complex__mod,axiom,
% 1.40/1.61 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % complex_mod_minus_le_complex_mod
% 1.40/1.61 thf(fact_1483_minus__pi__half__less__zero,axiom,
% 1.40/1.61 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 1.40/1.61
% 1.40/1.61 % minus_pi_half_less_zero
% 1.40/1.61 thf(fact_1484_complex__mod__triangle__ineq2,axiom,
% 1.40/1.61 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 1.40/1.61
% 1.40/1.61 % complex_mod_triangle_ineq2
% 1.40/1.61 thf(fact_1485_nat0__intermed__int__val,axiom,
% 1.40/1.61 ! [N: nat,F: nat > int,K: int] :
% 1.40/1.61 ( ! [I3: nat] :
% 1.40/1.61 ( ( ord_less_nat @ I3 @ N )
% 1.40/1.61 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 1.40/1.61 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 1.40/1.61 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 1.40/1.61 => ? [I3: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ I3 @ N )
% 1.40/1.61 & ( ( F @ I3 )
% 1.40/1.61 = K ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % nat0_intermed_int_val
% 1.40/1.61 thf(fact_1486_sum__nth__roots,axiom,
% 1.40/1.61 ! [N: nat,C: complex] :
% 1.40/1.61 ( ( ord_less_nat @ one_one_nat @ N )
% 1.40/1.61 => ( ( groups7754918857620584856omplex
% 1.40/1.61 @ ^ [X4: complex] : X4
% 1.40/1.61 @ ( collect_complex
% 1.40/1.61 @ ^ [Z5: complex] :
% 1.40/1.61 ( ( power_power_complex @ Z5 @ N )
% 1.40/1.61 = C ) ) )
% 1.40/1.61 = zero_zero_complex ) ) ).
% 1.40/1.61
% 1.40/1.61 % sum_nth_roots
% 1.40/1.61 thf(fact_1487_sum__roots__unity,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( ord_less_nat @ one_one_nat @ N )
% 1.40/1.61 => ( ( groups7754918857620584856omplex
% 1.40/1.61 @ ^ [X4: complex] : X4
% 1.40/1.61 @ ( collect_complex
% 1.40/1.61 @ ^ [Z5: complex] :
% 1.40/1.61 ( ( power_power_complex @ Z5 @ N )
% 1.40/1.61 = one_one_complex ) ) )
% 1.40/1.61 = zero_zero_complex ) ) ).
% 1.40/1.61
% 1.40/1.61 % sum_roots_unity
% 1.40/1.61 thf(fact_1488_arctan__add,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 1.40/1.61 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y2 ) )
% 1.40/1.61 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y2 ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_add
% 1.40/1.61 thf(fact_1489_sum__pos__lt__pair,axiom,
% 1.40/1.61 ! [F: nat > real,K: nat] :
% 1.40/1.61 ( ( summable_real @ F )
% 1.40/1.61 => ( ! [D3: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) @ one_one_nat ) ) ) ) )
% 1.40/1.61 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sum_pos_lt_pair
% 1.40/1.61 thf(fact_1490_arctan__double,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 1.40/1.61 = ( 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 ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_double
% 1.40/1.61 thf(fact_1491_sin__cos__npi,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_cos_npi
% 1.40/1.61 thf(fact_1492_cos__pi__eq__zero,axiom,
% 1.40/1.61 ! [M: nat] :
% 1.40/1.61 ( ( 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 ) ) ) )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % cos_pi_eq_zero
% 1.40/1.61 thf(fact_1493_cos__pi,axiom,
% 1.40/1.61 ( ( cos_real @ pi )
% 1.40/1.61 = ( uminus_uminus_real @ one_one_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_pi
% 1.40/1.61 thf(fact_1494_cos__periodic__pi2,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 1.40/1.61 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_periodic_pi2
% 1.40/1.61 thf(fact_1495_cos__periodic__pi,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 1.40/1.61 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_periodic_pi
% 1.40/1.61 thf(fact_1496_sin__periodic__pi2,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 1.40/1.61 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_periodic_pi2
% 1.40/1.61 thf(fact_1497_sin__periodic__pi,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 1.40/1.61 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_periodic_pi
% 1.40/1.61 thf(fact_1498_sin__npi2,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % sin_npi2
% 1.40/1.61 thf(fact_1499_sin__npi,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % sin_npi
% 1.40/1.61 thf(fact_1500_sin__npi__int,axiom,
% 1.40/1.61 ! [N: int] :
% 1.40/1.61 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % sin_npi_int
% 1.40/1.61 thf(fact_1501_cos__pi__half,axiom,
% 1.40/1.61 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % cos_pi_half
% 1.40/1.61 thf(fact_1502_sin__two__pi,axiom,
% 1.40/1.61 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % sin_two_pi
% 1.40/1.61 thf(fact_1503_sin__pi__half,axiom,
% 1.40/1.61 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % sin_pi_half
% 1.40/1.61 thf(fact_1504_cos__two__pi,axiom,
% 1.40/1.61 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 1.40/1.61 = one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % cos_two_pi
% 1.40/1.61 thf(fact_1505_cos__periodic,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 1.40/1.61 = ( cos_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_periodic
% 1.40/1.61 thf(fact_1506_sin__periodic,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 1.40/1.61 = ( sin_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_periodic
% 1.40/1.61 thf(fact_1507_cos__2pi__minus,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 1.40/1.61 = ( cos_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_2pi_minus
% 1.40/1.61 thf(fact_1508_cos__npi2,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 1.40/1.61 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_npi2
% 1.40/1.61 thf(fact_1509_cos__npi,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 1.40/1.61 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_npi
% 1.40/1.61 thf(fact_1510_sin__2npi,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % sin_2npi
% 1.40/1.61 thf(fact_1511_cos__2npi,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 1.40/1.61 = one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % cos_2npi
% 1.40/1.61 thf(fact_1512_sin__2pi__minus,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 1.40/1.61 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_2pi_minus
% 1.40/1.61 thf(fact_1513_sin__int__2pin,axiom,
% 1.40/1.61 ! [N: int] :
% 1.40/1.61 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % sin_int_2pin
% 1.40/1.61 thf(fact_1514_cos__int__2pin,axiom,
% 1.40/1.61 ! [N: int] :
% 1.40/1.61 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 1.40/1.61 = one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % cos_int_2pin
% 1.40/1.61 thf(fact_1515_cos__3over2__pi,axiom,
% 1.40/1.61 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % cos_3over2_pi
% 1.40/1.61 thf(fact_1516_sin__3over2__pi,axiom,
% 1.40/1.61 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 1.40/1.61 = ( uminus_uminus_real @ one_one_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_3over2_pi
% 1.40/1.61 thf(fact_1517_cos__npi__int,axiom,
% 1.40/1.61 ! [N: int] :
% 1.40/1.61 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 1.40/1.61 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 1.40/1.61 = one_one_real ) )
% 1.40/1.61 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 1.40/1.61 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 1.40/1.61 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_npi_int
% 1.40/1.61 thf(fact_1518_polar__Ex,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ? [R3: real,A5: real] :
% 1.40/1.61 ( ( X
% 1.40/1.61 = ( times_times_real @ R3 @ ( cos_real @ A5 ) ) )
% 1.40/1.61 & ( Y2
% 1.40/1.61 = ( times_times_real @ R3 @ ( sin_real @ A5 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % polar_Ex
% 1.40/1.61 thf(fact_1519_sin__zero__abs__cos__one,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( sin_real @ X )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 => ( ( abs_abs_real @ ( cos_real @ X ) )
% 1.40/1.61 = one_one_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_zero_abs_cos_one
% 1.40/1.61 thf(fact_1520_sincos__principal__value,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ? [Y3: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 1.40/1.61 & ( ord_less_eq_real @ Y3 @ pi )
% 1.40/1.61 & ( ( sin_real @ Y3 )
% 1.40/1.61 = ( sin_real @ X ) )
% 1.40/1.61 & ( ( cos_real @ Y3 )
% 1.40/1.61 = ( cos_real @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sincos_principal_value
% 1.40/1.61 thf(fact_1521_sin__x__le__x,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_x_le_x
% 1.40/1.61 thf(fact_1522_sin__le__one,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % sin_le_one
% 1.40/1.61 thf(fact_1523_cos__le__one,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % cos_le_one
% 1.40/1.61 thf(fact_1524_abs__sin__x__le__abs__x,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % abs_sin_x_le_abs_x
% 1.40/1.61 thf(fact_1525_sin__cos__le1,axiom,
% 1.40/1.61 ! [X: real,Y2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) @ one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % sin_cos_le1
% 1.40/1.61 thf(fact_1526_sin__x__ge__neg__x,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_x_ge_neg_x
% 1.40/1.61 thf(fact_1527_sin__ge__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ pi )
% 1.40/1.61 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_ge_zero
% 1.40/1.61 thf(fact_1528_sin__ge__minus__one,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_ge_minus_one
% 1.40/1.61 thf(fact_1529_cos__monotone__0__pi__le,axiom,
% 1.40/1.61 ! [Y2: real,X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ pi )
% 1.40/1.61 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_monotone_0_pi_le
% 1.40/1.61 thf(fact_1530_cos__mono__le__eq,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ pi )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ pi )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_mono_le_eq
% 1.40/1.61 thf(fact_1531_cos__inj__pi,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ pi )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ pi )
% 1.40/1.61 => ( ( ( cos_real @ X )
% 1.40/1.61 = ( cos_real @ Y2 ) )
% 1.40/1.61 => ( X = Y2 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_inj_pi
% 1.40/1.61 thf(fact_1532_cos__ge__minus__one,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_ge_minus_one
% 1.40/1.61 thf(fact_1533_abs__sin__le__one,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % abs_sin_le_one
% 1.40/1.61 thf(fact_1534_abs__cos__le__one,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % abs_cos_le_one
% 1.40/1.61 thf(fact_1535_cos__two__neq__zero,axiom,
% 1.40/1.61 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.61 != zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % cos_two_neq_zero
% 1.40/1.61 thf(fact_1536_cos__monotone__0__pi,axiom,
% 1.40/1.61 ! [Y2: real,X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ pi )
% 1.40/1.61 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_monotone_0_pi
% 1.40/1.61 thf(fact_1537_cos__mono__less__eq,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ pi )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ pi )
% 1.40/1.61 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y2 ) )
% 1.40/1.61 = ( ord_less_real @ Y2 @ X ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_mono_less_eq
% 1.40/1.61 thf(fact_1538_cos__monotone__minus__pi__0_H,axiom,
% 1.40/1.61 ! [Y2: real,X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 1.40/1.61 => ( ord_less_eq_real @ ( cos_real @ Y2 ) @ ( cos_real @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_monotone_minus_pi_0'
% 1.40/1.61 thf(fact_1539_sin__zero__iff__int2,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( sin_real @ X )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 = ( ? [I4: int] :
% 1.40/1.61 ( X
% 1.40/1.61 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ pi ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_zero_iff_int2
% 1.40/1.61 thf(fact_1540_sincos__total__pi,axiom,
% 1.40/1.61 ! [Y2: real,X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = one_one_real )
% 1.40/1.61 => ? [T3: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 1.40/1.61 & ( ord_less_eq_real @ T3 @ pi )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( cos_real @ T3 ) )
% 1.40/1.61 & ( Y2
% 1.40/1.61 = ( sin_real @ T3 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sincos_total_pi
% 1.40/1.61 thf(fact_1541_sin__expansion__lemma,axiom,
% 1.40/1.61 ! [X: real,M: nat] :
% 1.40/1.61 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_expansion_lemma
% 1.40/1.61 thf(fact_1542_cos__expansion__lemma,axiom,
% 1.40/1.61 ! [X: real,M: nat] :
% 1.40/1.61 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_expansion_lemma
% 1.40/1.61 thf(fact_1543_sin__gt__zero__02,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.61 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_gt_zero_02
% 1.40/1.61 thf(fact_1544_cos__two__less__zero,axiom,
% 1.40/1.61 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 1.40/1.61
% 1.40/1.61 % cos_two_less_zero
% 1.40/1.61 thf(fact_1545_cos__two__le__zero,axiom,
% 1.40/1.61 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 1.40/1.61
% 1.40/1.61 % cos_two_le_zero
% 1.40/1.61 thf(fact_1546_cos__is__zero,axiom,
% 1.40/1.61 ? [X5: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 1.40/1.61 & ( ord_less_eq_real @ X5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.61 & ( ( cos_real @ X5 )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 & ! [Y: real] :
% 1.40/1.61 ( ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 1.40/1.61 & ( ord_less_eq_real @ Y @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.61 & ( ( cos_real @ Y )
% 1.40/1.61 = zero_zero_real ) )
% 1.40/1.61 => ( Y = X5 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_is_zero
% 1.40/1.61 thf(fact_1547_cos__monotone__minus__pi__0,axiom,
% 1.40/1.61 ! [Y2: real,X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 1.40/1.61 => ( ord_less_real @ ( cos_real @ Y2 ) @ ( cos_real @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_monotone_minus_pi_0
% 1.40/1.61 thf(fact_1548_cos__total,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ? [X5: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 1.40/1.61 & ( ord_less_eq_real @ X5 @ pi )
% 1.40/1.61 & ( ( cos_real @ X5 )
% 1.40/1.61 = Y2 )
% 1.40/1.61 & ! [Y: real] :
% 1.40/1.61 ( ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 1.40/1.61 & ( ord_less_eq_real @ Y @ pi )
% 1.40/1.61 & ( ( cos_real @ Y )
% 1.40/1.61 = Y2 ) )
% 1.40/1.61 => ( Y = X5 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_total
% 1.40/1.61 thf(fact_1549_sincos__total__pi__half,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = one_one_real )
% 1.40/1.61 => ? [T3: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 1.40/1.61 & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( cos_real @ T3 ) )
% 1.40/1.61 & ( Y2
% 1.40/1.61 = ( sin_real @ T3 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sincos_total_pi_half
% 1.40/1.61 thf(fact_1550_sincos__total__2pi__le,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = one_one_real )
% 1.40/1.61 => ? [T3: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 1.40/1.61 & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( cos_real @ T3 ) )
% 1.40/1.61 & ( Y2
% 1.40/1.61 = ( sin_real @ T3 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sincos_total_2pi_le
% 1.40/1.61 thf(fact_1551_sincos__total__2pi,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = one_one_real )
% 1.40/1.61 => ~ ! [T3: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 1.40/1.61 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 1.40/1.61 => ( ( X
% 1.40/1.61 = ( cos_real @ T3 ) )
% 1.40/1.61 => ( Y2
% 1.40/1.61 != ( sin_real @ T3 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sincos_total_2pi
% 1.40/1.61 thf(fact_1552_sin__pi__divide__n__ge__0,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( N != zero_zero_nat )
% 1.40/1.61 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_pi_divide_n_ge_0
% 1.40/1.61 thf(fact_1553_sin__gt__zero2,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_gt_zero2
% 1.40/1.61 thf(fact_1554_sin__lt__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ pi @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 1.40/1.61 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_lt_zero
% 1.40/1.61 thf(fact_1555_cos__double__less__one,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.61 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_double_less_one
% 1.40/1.61 thf(fact_1556_sin__30,axiom,
% 1.40/1.61 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 1.40/1.61 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_30
% 1.40/1.61 thf(fact_1557_cos__gt__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_gt_zero
% 1.40/1.61 thf(fact_1558_sin__inj__pi,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ( sin_real @ X )
% 1.40/1.61 = ( sin_real @ Y2 ) )
% 1.40/1.61 => ( X = Y2 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_inj_pi
% 1.40/1.61 thf(fact_1559_sin__mono__le__eq,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_mono_le_eq
% 1.40/1.61 thf(fact_1560_sin__monotone__2pi__le,axiom,
% 1.40/1.61 ! [Y2: real,X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_eq_real @ ( sin_real @ Y2 ) @ ( sin_real @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_monotone_2pi_le
% 1.40/1.61 thf(fact_1561_cos__60,axiom,
% 1.40/1.61 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 1.40/1.61 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_60
% 1.40/1.61 thf(fact_1562_cos__one__2pi__int,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( cos_real @ X )
% 1.40/1.61 = one_one_real )
% 1.40/1.61 = ( ? [X4: int] :
% 1.40/1.61 ( X
% 1.40/1.61 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_one_2pi_int
% 1.40/1.61 thf(fact_1563_sin__le__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ pi @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 1.40/1.61 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_le_zero
% 1.40/1.61 thf(fact_1564_sin__less__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ zero_zero_real )
% 1.40/1.61 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_less_zero
% 1.40/1.61 thf(fact_1565_sin__mono__less__eq,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y2 ) )
% 1.40/1.61 = ( ord_less_real @ X @ Y2 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_mono_less_eq
% 1.40/1.61 thf(fact_1566_sin__monotone__2pi,axiom,
% 1.40/1.61 ! [Y2: real,X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_real @ ( sin_real @ Y2 ) @ ( sin_real @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_monotone_2pi
% 1.40/1.61 thf(fact_1567_sin__total,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ? [X5: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 1.40/1.61 & ( ord_less_eq_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 & ( ( sin_real @ X5 )
% 1.40/1.61 = Y2 )
% 1.40/1.61 & ! [Y: real] :
% 1.40/1.61 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 1.40/1.61 & ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 & ( ( sin_real @ Y )
% 1.40/1.61 = Y2 ) )
% 1.40/1.61 => ( Y = X5 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_total
% 1.40/1.61 thf(fact_1568_cos__gt__zero__pi,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_gt_zero_pi
% 1.40/1.61 thf(fact_1569_cos__ge__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_ge_zero
% 1.40/1.61 thf(fact_1570_cos__one__2pi,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( cos_real @ X )
% 1.40/1.61 = one_one_real )
% 1.40/1.61 = ( ? [X4: nat] :
% 1.40/1.61 ( X
% 1.40/1.61 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 1.40/1.61 | ? [X4: nat] :
% 1.40/1.61 ( X
% 1.40/1.61 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_one_2pi
% 1.40/1.61 thf(fact_1571_sin__pi__divide__n__gt__0,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.61 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_pi_divide_n_gt_0
% 1.40/1.61 thf(fact_1572_sin__zero__iff__int,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( sin_real @ X )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 = ( ? [I4: int] :
% 1.40/1.61 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_zero_iff_int
% 1.40/1.61 thf(fact_1573_cos__zero__iff__int,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( cos_real @ X )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 = ( ? [I4: int] :
% 1.40/1.61 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_zero_iff_int
% 1.40/1.61 thf(fact_1574_sin__zero__lemma,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ( sin_real @ X )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 => ? [N4: nat] :
% 1.40/1.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_zero_lemma
% 1.40/1.61 thf(fact_1575_sin__zero__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( sin_real @ X )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 = ( ? [N2: nat] :
% 1.40/1.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.61 | ? [N2: nat] :
% 1.40/1.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_zero_iff
% 1.40/1.61 thf(fact_1576_cos__zero__lemma,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ( cos_real @ X )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 => ? [N4: nat] :
% 1.40/1.61 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_zero_lemma
% 1.40/1.61 thf(fact_1577_cos__zero__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( cos_real @ X )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 = ( ? [N2: nat] :
% 1.40/1.61 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.61 | ? [N2: nat] :
% 1.40/1.61 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 1.40/1.61 & ( X
% 1.40/1.61 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_zero_iff
% 1.40/1.61 thf(fact_1578_Maclaurin__cos__expansion2,axiom,
% 1.40/1.61 ! [X: real,N: nat] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.61 => ? [T3: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ T3 )
% 1.40/1.61 & ( ord_less_real @ T3 @ X )
% 1.40/1.61 & ( ( cos_real @ X )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_cos_expansion2
% 1.40/1.61 thf(fact_1579_Maclaurin__minus__cos__expansion,axiom,
% 1.40/1.61 ! [N: nat,X: real] :
% 1.40/1.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.61 => ( ( ord_less_real @ X @ zero_zero_real )
% 1.40/1.61 => ? [T3: real] :
% 1.40/1.61 ( ( ord_less_real @ X @ T3 )
% 1.40/1.61 & ( ord_less_real @ T3 @ zero_zero_real )
% 1.40/1.61 & ( ( cos_real @ X )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_minus_cos_expansion
% 1.40/1.61 thf(fact_1580_Maclaurin__cos__expansion,axiom,
% 1.40/1.61 ! [X: real,N: nat] :
% 1.40/1.61 ? [T3: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 1.40/1.61 & ( ( cos_real @ X )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_cos_expansion
% 1.40/1.61 thf(fact_1581_sin__paired,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( sums_real
% 1.40/1.61 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 1.40/1.61 @ ( sin_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_paired
% 1.40/1.61 thf(fact_1582_tan__periodic__pi,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 1.40/1.61 = ( tan_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_periodic_pi
% 1.40/1.61 thf(fact_1583_tan__npi,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % tan_npi
% 1.40/1.61 thf(fact_1584_tan__periodic__n,axiom,
% 1.40/1.61 ! [X: real,N: num] :
% 1.40/1.61 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 1.40/1.61 = ( tan_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_periodic_n
% 1.40/1.61 thf(fact_1585_tan__periodic__nat,axiom,
% 1.40/1.61 ! [X: real,N: nat] :
% 1.40/1.61 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 1.40/1.61 = ( tan_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_periodic_nat
% 1.40/1.61 thf(fact_1586_tan__periodic__int,axiom,
% 1.40/1.61 ! [X: real,I2: int] :
% 1.40/1.61 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 1.40/1.61 = ( tan_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_periodic_int
% 1.40/1.61 thf(fact_1587_tan__periodic,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 1.40/1.61 = ( tan_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_periodic
% 1.40/1.61 thf(fact_1588_square__fact__le__2__fact,axiom,
% 1.40/1.61 ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % square_fact_le_2_fact
% 1.40/1.61 thf(fact_1589_tan__45,axiom,
% 1.40/1.61 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 = one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % tan_45
% 1.40/1.61 thf(fact_1590_lemma__tan__total,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ? [X5: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X5 )
% 1.40/1.61 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 & ( ord_less_real @ Y2 @ ( tan_real @ X5 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % lemma_tan_total
% 1.40/1.61 thf(fact_1591_tan__gt__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_gt_zero
% 1.40/1.61 thf(fact_1592_lemma__tan__total1,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ? [X5: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 1.40/1.61 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 & ( ( tan_real @ X5 )
% 1.40/1.61 = Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % lemma_tan_total1
% 1.40/1.61 thf(fact_1593_tan__mono__lt__eq,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 1.40/1.61 = ( ord_less_real @ X @ Y2 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_mono_lt_eq
% 1.40/1.61 thf(fact_1594_tan__monotone_H,axiom,
% 1.40/1.61 ! [Y2: real,X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ X )
% 1.40/1.61 = ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_monotone'
% 1.40/1.61 thf(fact_1595_tan__monotone,axiom,
% 1.40/1.61 ! [Y2: real,X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_real @ ( tan_real @ Y2 ) @ ( tan_real @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_monotone
% 1.40/1.61 thf(fact_1596_tan__total,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ? [X5: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 1.40/1.61 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 & ( ( tan_real @ X5 )
% 1.40/1.61 = Y2 )
% 1.40/1.61 & ! [Y: real] :
% 1.40/1.61 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 1.40/1.61 & ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 & ( ( tan_real @ Y )
% 1.40/1.61 = Y2 ) )
% 1.40/1.61 => ( Y = X5 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_total
% 1.40/1.61 thf(fact_1597_tan__minus__45,axiom,
% 1.40/1.61 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.61 = ( uminus_uminus_real @ one_one_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_minus_45
% 1.40/1.61 thf(fact_1598_tan__inverse,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y2 ) )
% 1.40/1.61 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_inverse
% 1.40/1.61 thf(fact_1599_tan__pos__pi2__le,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_pos_pi2_le
% 1.40/1.61 thf(fact_1600_tan__total__pos,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ? [X5: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 1.40/1.61 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 & ( ( tan_real @ X5 )
% 1.40/1.61 = Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_total_pos
% 1.40/1.61 thf(fact_1601_tan__less__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ zero_zero_real )
% 1.40/1.61 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_less_zero
% 1.40/1.61 thf(fact_1602_tan__mono__le__eq,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_mono_le_eq
% 1.40/1.61 thf(fact_1603_tan__mono__le,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_mono_le
% 1.40/1.61 thf(fact_1604_tan__bound__pi2,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_bound_pi2
% 1.40/1.61 thf(fact_1605_arctan__unique,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ( tan_real @ X )
% 1.40/1.61 = Y2 )
% 1.40/1.61 => ( ( arctan @ Y2 )
% 1.40/1.61 = X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_unique
% 1.40/1.61 thf(fact_1606_arctan__tan,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( arctan @ ( tan_real @ X ) )
% 1.40/1.61 = X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_tan
% 1.40/1.61 thf(fact_1607_arctan,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y2 ) )
% 1.40/1.61 & ( ord_less_real @ ( arctan @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 & ( ( tan_real @ ( arctan @ Y2 ) )
% 1.40/1.61 = Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan
% 1.40/1.61 thf(fact_1608_Maclaurin__lemma,axiom,
% 1.40/1.61 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ H2 )
% 1.40/1.61 => ? [B6: real] :
% 1.40/1.61 ( ( F @ H2 )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( times_times_real @ B6 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_lemma
% 1.40/1.61 thf(fact_1609_tan__total__pi4,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ? [Z3: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 1.40/1.61 & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 & ( ( tan_real @ Z3 )
% 1.40/1.61 = X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_total_pi4
% 1.40/1.61 thf(fact_1610_cos__coeff__def,axiom,
% 1.40/1.61 ( cos_coeff
% 1.40/1.61 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_coeff_def
% 1.40/1.61 thf(fact_1611_cos__paired,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( sums_real
% 1.40/1.61 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 1.40/1.61 @ ( cos_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_paired
% 1.40/1.61 thf(fact_1612_Maclaurin__sin__expansion3,axiom,
% 1.40/1.61 ! [N: nat,X: real] :
% 1.40/1.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ? [T3: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ T3 )
% 1.40/1.61 & ( ord_less_real @ T3 @ X )
% 1.40/1.61 & ( ( sin_real @ X )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_sin_expansion3
% 1.40/1.61 thf(fact_1613_Maclaurin__sin__expansion4,axiom,
% 1.40/1.61 ! [X: real,N: nat] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ? [T3: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ T3 )
% 1.40/1.61 & ( ord_less_eq_real @ T3 @ X )
% 1.40/1.61 & ( ( sin_real @ X )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_sin_expansion4
% 1.40/1.61 thf(fact_1614_Maclaurin__sin__expansion2,axiom,
% 1.40/1.61 ! [X: real,N: nat] :
% 1.40/1.61 ? [T3: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 1.40/1.61 & ( ( sin_real @ X )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_sin_expansion2
% 1.40/1.61 thf(fact_1615_Maclaurin__sin__expansion,axiom,
% 1.40/1.61 ! [X: real,N: nat] :
% 1.40/1.61 ? [T3: real] :
% 1.40/1.61 ( ( sin_real @ X )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_sin_expansion
% 1.40/1.61 thf(fact_1616_sin__coeff__def,axiom,
% 1.40/1.61 ( sin_coeff
% 1.40/1.61 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_coeff_def
% 1.40/1.61 thf(fact_1617_fact__ge__self,axiom,
% 1.40/1.61 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % fact_ge_self
% 1.40/1.61 thf(fact_1618_fact__mono__nat,axiom,
% 1.40/1.61 ! [M: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.61 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % fact_mono_nat
% 1.40/1.61 thf(fact_1619_fact__less__mono__nat,axiom,
% 1.40/1.61 ! [M: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.61 => ( ( ord_less_nat @ M @ N )
% 1.40/1.61 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % fact_less_mono_nat
% 1.40/1.61 thf(fact_1620_fact__ge__Suc__0__nat,axiom,
% 1.40/1.61 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % fact_ge_Suc_0_nat
% 1.40/1.61 thf(fact_1621_dvd__fact,axiom,
% 1.40/1.61 ! [M: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 1.40/1.61 => ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.61 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % dvd_fact
% 1.40/1.61 thf(fact_1622_fact__diff__Suc,axiom,
% 1.40/1.61 ! [N: nat,M: nat] :
% 1.40/1.61 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 1.40/1.61 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 1.40/1.61 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % fact_diff_Suc
% 1.40/1.61 thf(fact_1623_fact__div__fact__le__pow,axiom,
% 1.40/1.61 ! [R2: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ R2 @ N )
% 1.40/1.61 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % fact_div_fact_le_pow
% 1.40/1.61 thf(fact_1624_fact__eq__fact__times,axiom,
% 1.40/1.61 ! [N: nat,M: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.61 => ( ( semiri1408675320244567234ct_nat @ M )
% 1.40/1.61 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 1.40/1.61 @ ( groups708209901874060359at_nat
% 1.40/1.61 @ ^ [X4: nat] : X4
% 1.40/1.61 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % fact_eq_fact_times
% 1.40/1.61 thf(fact_1625_fact__div__fact,axiom,
% 1.40/1.61 ! [N: nat,M: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.61 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 1.40/1.61 = ( groups708209901874060359at_nat
% 1.40/1.61 @ ^ [X4: nat] : X4
% 1.40/1.61 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % fact_div_fact
% 1.40/1.61 thf(fact_1626_sin__coeff__Suc,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( sin_coeff @ ( suc @ N ) )
% 1.40/1.61 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_coeff_Suc
% 1.40/1.61 thf(fact_1627_cos__coeff__Suc,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( cos_coeff @ ( suc @ N ) )
% 1.40/1.61 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_coeff_Suc
% 1.40/1.61 thf(fact_1628_sin__tan,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( sin_real @ X )
% 1.40/1.61 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_tan
% 1.40/1.61 thf(fact_1629_cos__tan,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( cos_real @ X )
% 1.40/1.61 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_tan
% 1.40/1.61 thf(fact_1630_complex__unimodular__polar,axiom,
% 1.40/1.61 ! [Z: complex] :
% 1.40/1.61 ( ( ( real_V1022390504157884413omplex @ Z )
% 1.40/1.61 = one_one_real )
% 1.40/1.61 => ~ ! [T3: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 1.40/1.61 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 1.40/1.61 => ( Z
% 1.40/1.61 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % complex_unimodular_polar
% 1.40/1.61 thf(fact_1631_Maclaurin__exp__lt,axiom,
% 1.40/1.61 ! [X: real,N: nat] :
% 1.40/1.61 ( ( X != zero_zero_real )
% 1.40/1.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.61 => ? [T3: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 1.40/1.61 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 1.40/1.61 & ( ( exp_real @ X )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_exp_lt
% 1.40/1.61 thf(fact_1632_binomial__code,axiom,
% 1.40/1.61 ( binomial
% 1.40/1.61 = ( ^ [N2: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K3 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_code
% 1.40/1.61 thf(fact_1633_real__sqrt__eq__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ( sqrt @ X )
% 1.40/1.61 = ( sqrt @ Y2 ) )
% 1.40/1.61 = ( X = Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_eq_iff
% 1.40/1.61 thf(fact_1634_real__sqrt__zero,axiom,
% 1.40/1.61 ( ( sqrt @ zero_zero_real )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_zero
% 1.40/1.61 thf(fact_1635_real__sqrt__eq__zero__cancel__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( sqrt @ X )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 = ( X = zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_eq_zero_cancel_iff
% 1.40/1.61 thf(fact_1636_real__sqrt__less__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) )
% 1.40/1.61 = ( ord_less_real @ X @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_less_iff
% 1.40/1.61 thf(fact_1637_real__sqrt__le__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_le_iff
% 1.40/1.61 thf(fact_1638_binomial__Suc__n,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( binomial @ ( suc @ N ) @ N )
% 1.40/1.61 = ( suc @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_Suc_n
% 1.40/1.61 thf(fact_1639_real__sqrt__one,axiom,
% 1.40/1.61 ( ( sqrt @ one_one_real )
% 1.40/1.61 = one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_one
% 1.40/1.61 thf(fact_1640_real__sqrt__eq__1__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( sqrt @ X )
% 1.40/1.61 = one_one_real )
% 1.40/1.61 = ( X = one_one_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_eq_1_iff
% 1.40/1.61 thf(fact_1641_exp__le__cancel__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_le_cancel_iff
% 1.40/1.61 thf(fact_1642_binomial__n__n,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( binomial @ N @ N )
% 1.40/1.61 = one_one_nat ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_n_n
% 1.40/1.61 thf(fact_1643_real__sqrt__gt__0__iff,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 1.40/1.61 = ( ord_less_real @ zero_zero_real @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_gt_0_iff
% 1.40/1.61 thf(fact_1644_real__sqrt__lt__0__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 1.40/1.61 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_lt_0_iff
% 1.40/1.61 thf(fact_1645_binomial__0__Suc,axiom,
% 1.40/1.61 ! [K: nat] :
% 1.40/1.61 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 1.40/1.61 = zero_zero_nat ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_0_Suc
% 1.40/1.61 thf(fact_1646_binomial__1,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 1.40/1.61 = N ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_1
% 1.40/1.61 thf(fact_1647_real__sqrt__le__0__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 1.40/1.61 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_le_0_iff
% 1.40/1.61 thf(fact_1648_real__sqrt__ge__0__iff,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_ge_0_iff
% 1.40/1.61 thf(fact_1649_binomial__eq__0__iff,axiom,
% 1.40/1.61 ! [N: nat,K: nat] :
% 1.40/1.61 ( ( ( binomial @ N @ K )
% 1.40/1.61 = zero_zero_nat )
% 1.40/1.61 = ( ord_less_nat @ N @ K ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_eq_0_iff
% 1.40/1.61 thf(fact_1650_real__sqrt__gt__1__iff,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y2 ) )
% 1.40/1.61 = ( ord_less_real @ one_one_real @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_gt_1_iff
% 1.40/1.61 thf(fact_1651_real__sqrt__lt__1__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 1.40/1.61 = ( ord_less_real @ X @ one_one_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_lt_1_iff
% 1.40/1.61 thf(fact_1652_binomial__Suc__Suc,axiom,
% 1.40/1.61 ! [N: nat,K: nat] :
% 1.40/1.61 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 1.40/1.61 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_Suc_Suc
% 1.40/1.61 thf(fact_1653_real__sqrt__le__1__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 1.40/1.61 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_le_1_iff
% 1.40/1.61 thf(fact_1654_real__sqrt__ge__1__iff,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_ge_1_iff
% 1.40/1.61 thf(fact_1655_binomial__n__0,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( binomial @ N @ zero_zero_nat )
% 1.40/1.61 = one_one_nat ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_n_0
% 1.40/1.61 thf(fact_1656_exp__eq__one__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( exp_real @ X )
% 1.40/1.61 = one_one_real )
% 1.40/1.61 = ( X = zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_eq_one_iff
% 1.40/1.61 thf(fact_1657_real__sqrt__mult__self,axiom,
% 1.40/1.61 ! [A: real] :
% 1.40/1.61 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 1.40/1.61 = ( abs_abs_real @ A ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_mult_self
% 1.40/1.61 thf(fact_1658_real__sqrt__abs2,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 1.40/1.61 = ( abs_abs_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_abs2
% 1.40/1.61 thf(fact_1659_real__sqrt__four,axiom,
% 1.40/1.61 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_four
% 1.40/1.61 thf(fact_1660_zero__less__binomial__iff,axiom,
% 1.40/1.61 ! [N: nat,K: nat] :
% 1.40/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 1.40/1.61 = ( ord_less_eq_nat @ K @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % zero_less_binomial_iff
% 1.40/1.61 thf(fact_1661_one__less__exp__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 1.40/1.61 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % one_less_exp_iff
% 1.40/1.61 thf(fact_1662_exp__less__one__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 1.40/1.61 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_less_one_iff
% 1.40/1.61 thf(fact_1663_one__le__exp__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 1.40/1.61 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % one_le_exp_iff
% 1.40/1.61 thf(fact_1664_exp__le__one__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 1.40/1.61 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_le_one_iff
% 1.40/1.61 thf(fact_1665_norm__cos__sin,axiom,
% 1.40/1.61 ! [T: real] :
% 1.40/1.61 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 1.40/1.61 = one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % norm_cos_sin
% 1.40/1.61 thf(fact_1666_real__sqrt__abs,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = ( abs_abs_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_abs
% 1.40/1.61 thf(fact_1667_real__sqrt__pow2__iff,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.61 = X )
% 1.40/1.61 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_pow2_iff
% 1.40/1.61 thf(fact_1668_real__sqrt__pow2,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.61 = X ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_pow2
% 1.40/1.61 thf(fact_1669_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 1.40/1.61 ! [X: real,Y2: real,Xa2: real,Ya: real] :
% 1.40/1.61 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.61 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_sum_squares_mult_squared_eq
% 1.40/1.61 thf(fact_1670_real__sqrt__power,axiom,
% 1.40/1.61 ! [X: real,K: nat] :
% 1.40/1.61 ( ( sqrt @ ( power_power_real @ X @ K ) )
% 1.40/1.61 = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_power
% 1.40/1.61 thf(fact_1671_choose__one,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( binomial @ N @ one_one_nat )
% 1.40/1.61 = N ) ).
% 1.40/1.61
% 1.40/1.61 % choose_one
% 1.40/1.61 thf(fact_1672_real__sqrt__le__mono,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ X @ Y2 )
% 1.40/1.61 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_le_mono
% 1.40/1.61 thf(fact_1673_real__sqrt__less__mono,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ X @ Y2 )
% 1.40/1.61 => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_less_mono
% 1.40/1.61 thf(fact_1674_real__sqrt__minus,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 1.40/1.61 = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_minus
% 1.40/1.61 thf(fact_1675_real__sqrt__mult,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( sqrt @ ( times_times_real @ X @ Y2 ) )
% 1.40/1.61 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_mult
% 1.40/1.61 thf(fact_1676_real__sqrt__divide,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( sqrt @ ( divide_divide_real @ X @ Y2 ) )
% 1.40/1.61 = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_divide
% 1.40/1.61 thf(fact_1677_binomial__eq__0,axiom,
% 1.40/1.61 ! [N: nat,K: nat] :
% 1.40/1.61 ( ( ord_less_nat @ N @ K )
% 1.40/1.61 => ( ( binomial @ N @ K )
% 1.40/1.61 = zero_zero_nat ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_eq_0
% 1.40/1.61 thf(fact_1678_Suc__times__binomial,axiom,
% 1.40/1.61 ! [K: nat,N: nat] :
% 1.40/1.61 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 1.40/1.61 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Suc_times_binomial
% 1.40/1.61 thf(fact_1679_Suc__times__binomial__eq,axiom,
% 1.40/1.61 ! [N: nat,K: nat] :
% 1.40/1.61 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 1.40/1.61 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Suc_times_binomial_eq
% 1.40/1.61 thf(fact_1680_real__sqrt__gt__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_gt_zero
% 1.40/1.61 thf(fact_1681_binomial__symmetric,axiom,
% 1.40/1.61 ! [K: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ K @ N )
% 1.40/1.61 => ( ( binomial @ N @ K )
% 1.40/1.61 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_symmetric
% 1.40/1.61 thf(fact_1682_real__sqrt__eq__zero__cancel,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ( sqrt @ X )
% 1.40/1.61 = zero_zero_real )
% 1.40/1.61 => ( X = zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_eq_zero_cancel
% 1.40/1.61 thf(fact_1683_real__sqrt__ge__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_ge_zero
% 1.40/1.61 thf(fact_1684_exp__ge__zero,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_ge_zero
% 1.40/1.61 thf(fact_1685_not__exp__le__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % not_exp_le_zero
% 1.40/1.61 thf(fact_1686_choose__mult__lemma,axiom,
% 1.40/1.61 ! [M: nat,R2: nat,K: nat] :
% 1.40/1.61 ( ( 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 ) )
% 1.40/1.61 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % choose_mult_lemma
% 1.40/1.61 thf(fact_1687_real__sqrt__ge__one,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ one_one_real @ X )
% 1.40/1.61 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_ge_one
% 1.40/1.61 thf(fact_1688_binomial__le__pow,axiom,
% 1.40/1.61 ! [R2: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ R2 @ N )
% 1.40/1.61 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_le_pow
% 1.40/1.61 thf(fact_1689_Complex__eq__numeral,axiom,
% 1.40/1.61 ! [A: real,B: real,W: num] :
% 1.40/1.61 ( ( ( complex2 @ A @ B )
% 1.40/1.61 = ( numera6690914467698888265omplex @ W ) )
% 1.40/1.61 = ( ( A
% 1.40/1.61 = ( numeral_numeral_real @ W ) )
% 1.40/1.61 & ( B = zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Complex_eq_numeral
% 1.40/1.61 thf(fact_1690_complex__add,axiom,
% 1.40/1.61 ! [A: real,B: real,C: real,D: real] :
% 1.40/1.61 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 1.40/1.61 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % complex_add
% 1.40/1.61 thf(fact_1691_zero__less__binomial,axiom,
% 1.40/1.61 ! [K: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ K @ N )
% 1.40/1.61 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % zero_less_binomial
% 1.40/1.61 thf(fact_1692_Suc__times__binomial__add,axiom,
% 1.40/1.61 ! [A: nat,B: nat] :
% 1.40/1.61 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 1.40/1.61 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Suc_times_binomial_add
% 1.40/1.61 thf(fact_1693_complex__norm,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y2 ) )
% 1.40/1.61 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % complex_norm
% 1.40/1.61 thf(fact_1694_choose__mult,axiom,
% 1.40/1.61 ! [K: nat,M: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ K @ M )
% 1.40/1.61 => ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.61 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 1.40/1.61 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % choose_mult
% 1.40/1.61 thf(fact_1695_binomial__fact__lemma,axiom,
% 1.40/1.61 ! [K: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ K @ N )
% 1.40/1.61 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 1.40/1.61 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_fact_lemma
% 1.40/1.61 thf(fact_1696_binomial__Suc__Suc__eq__times,axiom,
% 1.40/1.61 ! [N: nat,K: nat] :
% 1.40/1.61 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 1.40/1.61 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_Suc_Suc_eq_times
% 1.40/1.61 thf(fact_1697_exp__gt__one,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_gt_one
% 1.40/1.61 thf(fact_1698_real__div__sqrt,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 1.40/1.61 = ( sqrt @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_div_sqrt
% 1.40/1.61 thf(fact_1699_binomial__absorb__comp,axiom,
% 1.40/1.61 ! [N: nat,K: nat] :
% 1.40/1.61 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 1.40/1.61 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_absorb_comp
% 1.40/1.61 thf(fact_1700_sqrt__add__le__add__sqrt,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y2 ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sqrt_add_le_add_sqrt
% 1.40/1.61 thf(fact_1701_exp__ge__add__one__self,axiom,
% 1.40/1.61 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_ge_add_one_self
% 1.40/1.61 thf(fact_1702_le__real__sqrt__sumsq,axiom,
% 1.40/1.61 ! [X: real,Y2: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y2 @ Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % le_real_sqrt_sumsq
% 1.40/1.61 thf(fact_1703_Complex__eq__neg__numeral,axiom,
% 1.40/1.61 ! [A: real,B: real,W: num] :
% 1.40/1.61 ( ( ( complex2 @ A @ B )
% 1.40/1.61 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 1.40/1.61 = ( ( A
% 1.40/1.61 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 1.40/1.61 & ( B = zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Complex_eq_neg_numeral
% 1.40/1.61 thf(fact_1704_complex__mult,axiom,
% 1.40/1.61 ! [A: real,B: real,C: real,D: real] :
% 1.40/1.61 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 1.40/1.61 = ( 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 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % complex_mult
% 1.40/1.61 thf(fact_1705_one__complex_Ocode,axiom,
% 1.40/1.61 ( one_one_complex
% 1.40/1.61 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % one_complex.code
% 1.40/1.61 thf(fact_1706_Complex__eq__1,axiom,
% 1.40/1.61 ! [A: real,B: real] :
% 1.40/1.61 ( ( ( complex2 @ A @ B )
% 1.40/1.61 = one_one_complex )
% 1.40/1.61 = ( ( A = one_one_real )
% 1.40/1.61 & ( B = zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Complex_eq_1
% 1.40/1.61 thf(fact_1707_sqrt2__less__2,axiom,
% 1.40/1.61 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 1.40/1.61
% 1.40/1.61 % sqrt2_less_2
% 1.40/1.61 thf(fact_1708_binomial__absorption,axiom,
% 1.40/1.61 ! [K: nat,N: nat] :
% 1.40/1.61 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 1.40/1.61 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_absorption
% 1.40/1.61 thf(fact_1709_binomial__altdef__nat,axiom,
% 1.40/1.61 ! [K: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ K @ N )
% 1.40/1.61 => ( ( binomial @ N @ K )
% 1.40/1.61 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_altdef_nat
% 1.40/1.61 thf(fact_1710_exp__ge__add__one__self__aux,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_ge_add_one_self_aux
% 1.40/1.61 thf(fact_1711_lemma__exp__total,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ one_one_real @ Y2 )
% 1.40/1.61 => ? [X5: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 1.40/1.61 & ( ord_less_eq_real @ X5 @ ( minus_minus_real @ Y2 @ one_one_real ) )
% 1.40/1.61 & ( ( exp_real @ X5 )
% 1.40/1.61 = Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % lemma_exp_total
% 1.40/1.61 thf(fact_1712_ln__ge__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ ( ln_ln_real @ X ) )
% 1.40/1.61 = ( ord_less_eq_real @ ( exp_real @ Y2 ) @ X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % ln_ge_iff
% 1.40/1.61 thf(fact_1713_ln__x__over__x__mono,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ Y2 )
% 1.40/1.61 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y2 ) @ Y2 ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % ln_x_over_x_mono
% 1.40/1.61 thf(fact_1714_Complex__eq__neg__1,axiom,
% 1.40/1.61 ! [A: real,B: real] :
% 1.40/1.61 ( ( ( complex2 @ A @ B )
% 1.40/1.61 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 1.40/1.61 = ( ( A
% 1.40/1.61 = ( uminus_uminus_real @ one_one_real ) )
% 1.40/1.61 & ( B = zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Complex_eq_neg_1
% 1.40/1.61 thf(fact_1715_binomial__maximum_H,axiom,
% 1.40/1.61 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_maximum'
% 1.40/1.61 thf(fact_1716_binomial__mono,axiom,
% 1.40/1.61 ! [K: nat,K4: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ K @ K4 )
% 1.40/1.61 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) @ N )
% 1.40/1.61 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K4 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_mono
% 1.40/1.61 thf(fact_1717_binomial__antimono,axiom,
% 1.40/1.61 ! [K: nat,K4: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ K @ K4 )
% 1.40/1.61 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 1.40/1.61 => ( ( ord_less_eq_nat @ K4 @ N )
% 1.40/1.61 => ( ord_less_eq_nat @ ( binomial @ N @ K4 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_antimono
% 1.40/1.61 thf(fact_1718_binomial__maximum,axiom,
% 1.40/1.61 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_maximum
% 1.40/1.61 thf(fact_1719_binomial__le__pow2,axiom,
% 1.40/1.61 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_le_pow2
% 1.40/1.61 thf(fact_1720_real__less__rsqrt,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 1.40/1.61 => ( ord_less_real @ X @ ( sqrt @ Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_less_rsqrt
% 1.40/1.61 thf(fact_1721_choose__reduce__nat,axiom,
% 1.40/1.61 ! [N: nat,K: nat] :
% 1.40/1.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.61 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.61 => ( ( binomial @ N @ K )
% 1.40/1.61 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % choose_reduce_nat
% 1.40/1.61 thf(fact_1722_real__le__rsqrt,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 )
% 1.40/1.61 => ( ord_less_eq_real @ X @ ( sqrt @ Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_le_rsqrt
% 1.40/1.61 thf(fact_1723_sqrt__le__D,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y2 )
% 1.40/1.61 => ( ord_less_eq_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sqrt_le_D
% 1.40/1.61 thf(fact_1724_times__binomial__minus1__eq,axiom,
% 1.40/1.61 ! [K: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.61 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 1.40/1.61 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % times_binomial_minus1_eq
% 1.40/1.61 thf(fact_1725_exp__le,axiom,
% 1.40/1.61 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_le
% 1.40/1.61 thf(fact_1726_binomial__less__binomial__Suc,axiom,
% 1.40/1.61 ! [K: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_less_binomial_Suc
% 1.40/1.61 thf(fact_1727_binomial__strict__antimono,axiom,
% 1.40/1.61 ! [K: nat,K4: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_nat @ K @ K4 )
% 1.40/1.61 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 1.40/1.61 => ( ( ord_less_eq_nat @ K4 @ N )
% 1.40/1.61 => ( ord_less_nat @ ( binomial @ N @ K4 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_strict_antimono
% 1.40/1.61 thf(fact_1728_binomial__strict__mono,axiom,
% 1.40/1.61 ! [K: nat,K4: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_nat @ K @ K4 )
% 1.40/1.61 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) @ N )
% 1.40/1.61 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K4 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_strict_mono
% 1.40/1.61 thf(fact_1729_central__binomial__odd,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.61 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % central_binomial_odd
% 1.40/1.61 thf(fact_1730_binomial__addition__formula,axiom,
% 1.40/1.61 ! [N: nat,K: nat] :
% 1.40/1.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.61 => ( ( binomial @ N @ ( suc @ K ) )
% 1.40/1.61 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_addition_formula
% 1.40/1.61 thf(fact_1731_real__sqrt__unique,axiom,
% 1.40/1.61 ! [Y2: real,X: real] :
% 1.40/1.61 ( ( ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.61 = X )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( sqrt @ X )
% 1.40/1.61 = Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_unique
% 1.40/1.61 thf(fact_1732_real__le__lsqrt,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_le_lsqrt
% 1.40/1.61 thf(fact_1733_lemma__real__divide__sqrt__less,axiom,
% 1.40/1.61 ! [U: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ U )
% 1.40/1.61 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 1.40/1.61
% 1.40/1.61 % lemma_real_divide_sqrt_less
% 1.40/1.61 thf(fact_1734_real__sqrt__sum__squares__eq__cancel2,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 = Y2 )
% 1.40/1.61 => ( X = zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_sum_squares_eq_cancel2
% 1.40/1.61 thf(fact_1735_real__sqrt__sum__squares__eq__cancel,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 = X )
% 1.40/1.61 => ( Y2 = zero_zero_real ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_sum_squares_eq_cancel
% 1.40/1.61 thf(fact_1736_exp__half__le2,axiom,
% 1.40/1.61 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_half_le2
% 1.40/1.61 thf(fact_1737_real__sqrt__sum__squares__triangle__ineq,axiom,
% 1.40/1.61 ! [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 ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_sum_squares_triangle_ineq
% 1.40/1.61 thf(fact_1738_real__sqrt__sum__squares__ge2,axiom,
% 1.40/1.61 ! [Y2: real,X: real] : ( ord_less_eq_real @ Y2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_sum_squares_ge2
% 1.40/1.61 thf(fact_1739_real__sqrt__sum__squares__ge1,axiom,
% 1.40/1.61 ! [X: real,Y2: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_sum_squares_ge1
% 1.40/1.61 thf(fact_1740_sqrt__ge__absD,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y2 ) )
% 1.40/1.61 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % sqrt_ge_absD
% 1.40/1.61 thf(fact_1741_cos__45,axiom,
% 1.40/1.61 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_45
% 1.40/1.61 thf(fact_1742_sin__45,axiom,
% 1.40/1.61 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_45
% 1.40/1.61 thf(fact_1743_tan__60,axiom,
% 1.40/1.61 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 1.40/1.61 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_60
% 1.40/1.61 thf(fact_1744_choose__two,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.61 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % choose_two
% 1.40/1.61 thf(fact_1745_real__less__lsqrt,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ X @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_real @ ( sqrt @ X ) @ Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_less_lsqrt
% 1.40/1.61 thf(fact_1746_sqrt__sum__squares__le__sum,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sqrt_sum_squares_le_sum
% 1.40/1.61 thf(fact_1747_sqrt__even__pow2,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.61 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.61 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sqrt_even_pow2
% 1.40/1.61 thf(fact_1748_real__sqrt__ge__abs1,axiom,
% 1.40/1.61 ! [X: real,Y2: 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 @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_ge_abs1
% 1.40/1.61 thf(fact_1749_real__sqrt__ge__abs2,axiom,
% 1.40/1.61 ! [Y2: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_ge_abs2
% 1.40/1.61 thf(fact_1750_sqrt__sum__squares__le__sum__abs,axiom,
% 1.40/1.61 ! [X: real,Y2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sqrt_sum_squares_le_sum_abs
% 1.40/1.61 thf(fact_1751_ln__sqrt,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 1.40/1.61 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % ln_sqrt
% 1.40/1.61 thf(fact_1752_cos__30,axiom,
% 1.40/1.61 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 1.40/1.61 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_30
% 1.40/1.61 thf(fact_1753_sin__60,axiom,
% 1.40/1.61 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 1.40/1.61 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_60
% 1.40/1.61 thf(fact_1754_arsinh__real__aux,axiom,
% 1.40/1.61 ! [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 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arsinh_real_aux
% 1.40/1.61 thf(fact_1755_exp__bound,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.61 => ( 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 ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_bound
% 1.40/1.61 thf(fact_1756_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 1.40/1.61 ! [X: real,Y2: 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 @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_sum_squares_mult_ge_zero
% 1.40/1.61 thf(fact_1757_real__sqrt__power__even,axiom,
% 1.40/1.61 ! [N: nat,X: real] :
% 1.40/1.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 1.40/1.61 = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_power_even
% 1.40/1.61 thf(fact_1758_arith__geo__mean__sqrt,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y2 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arith_geo_mean_sqrt
% 1.40/1.61 thf(fact_1759_tan__30,axiom,
% 1.40/1.61 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 1.40/1.61 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tan_30
% 1.40/1.61 thf(fact_1760_real__exp__bound__lemma,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_exp_bound_lemma
% 1.40/1.61 thf(fact_1761_cos__x__y__le__one,axiom,
% 1.40/1.61 ! [X: real,Y2: 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 @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % cos_x_y_le_one
% 1.40/1.61 thf(fact_1762_real__sqrt__sum__squares__less,axiom,
% 1.40/1.61 ! [X: real,U: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 => ( ( ord_less_real @ ( abs_abs_real @ Y2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 1.40/1.61 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % real_sqrt_sum_squares_less
% 1.40/1.61 thf(fact_1763_arcosh__real__def,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ one_one_real @ X )
% 1.40/1.61 => ( ( arcosh_real @ X )
% 1.40/1.61 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcosh_real_def
% 1.40/1.61 thf(fact_1764_exp__ge__one__plus__x__over__n__power__n,axiom,
% 1.40/1.61 ! [N: nat,X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 1.40/1.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.61 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_ge_one_plus_x_over_n_power_n
% 1.40/1.61 thf(fact_1765_exp__ge__one__minus__x__over__n__power__n,axiom,
% 1.40/1.61 ! [X: real,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 1.40/1.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.61 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_ge_one_minus_x_over_n_power_n
% 1.40/1.61 thf(fact_1766_cos__arctan,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( cos_real @ ( arctan @ X ) )
% 1.40/1.61 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_arctan
% 1.40/1.61 thf(fact_1767_sin__arctan,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( sin_real @ ( arctan @ X ) )
% 1.40/1.61 = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_arctan
% 1.40/1.61 thf(fact_1768_Maclaurin__exp__le,axiom,
% 1.40/1.61 ! [X: real,N: nat] :
% 1.40/1.61 ? [T3: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 1.40/1.61 & ( ( exp_real @ X )
% 1.40/1.61 = ( plus_plus_real
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.61 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_exp_le
% 1.40/1.61 thf(fact_1769_sqrt__sum__squares__half__less,axiom,
% 1.40/1.61 ! [X: real,U: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sqrt_sum_squares_half_less
% 1.40/1.61 thf(fact_1770_exp__lower__Taylor__quadratic,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( 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 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % exp_lower_Taylor_quadratic
% 1.40/1.61 thf(fact_1771_sin__cos__sqrt,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 1.40/1.61 => ( ( sin_real @ X )
% 1.40/1.61 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_cos_sqrt
% 1.40/1.61 thf(fact_1772_arctan__half,axiom,
% 1.40/1.61 ( arctan
% 1.40/1.61 = ( ^ [X4: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X4 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arctan_half
% 1.40/1.61 thf(fact_1773_tanh__real__altdef,axiom,
% 1.40/1.61 ( tanh_real
% 1.40/1.61 = ( ^ [X4: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % tanh_real_altdef
% 1.40/1.61 thf(fact_1774_central__binomial__lower__bound,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.61 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % central_binomial_lower_bound
% 1.40/1.61 thf(fact_1775_arsinh__real__def,axiom,
% 1.40/1.61 ( arsinh_real
% 1.40/1.61 = ( ^ [X4: real] : ( ln_ln_real @ ( plus_plus_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arsinh_real_def
% 1.40/1.61 thf(fact_1776_cos__arcsin,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.61 => ( ( cos_real @ ( arcsin @ X ) )
% 1.40/1.61 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_arcsin
% 1.40/1.61 thf(fact_1777_sin__arccos__abs,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 1.40/1.61 => ( ( sin_real @ ( arccos @ Y2 ) )
% 1.40/1.61 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_arccos_abs
% 1.40/1.61 thf(fact_1778_arccos__1,axiom,
% 1.40/1.61 ( ( arccos @ one_one_real )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_1
% 1.40/1.61 thf(fact_1779_arccos__minus__1,axiom,
% 1.40/1.61 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 1.40/1.61 = pi ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_minus_1
% 1.40/1.61 thf(fact_1780_cos__arccos,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ( cos_real @ ( arccos @ Y2 ) )
% 1.40/1.61 = Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_arccos
% 1.40/1.61 thf(fact_1781_sin__arcsin,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ( sin_real @ ( arcsin @ Y2 ) )
% 1.40/1.61 = Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_arcsin
% 1.40/1.61 thf(fact_1782_arccos__0,axiom,
% 1.40/1.61 ( ( arccos @ zero_zero_real )
% 1.40/1.61 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_0
% 1.40/1.61 thf(fact_1783_arcsin__1,axiom,
% 1.40/1.61 ( ( arcsin @ one_one_real )
% 1.40/1.61 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_1
% 1.40/1.61 thf(fact_1784_arcsin__minus__1,axiom,
% 1.40/1.61 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 1.40/1.61 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_minus_1
% 1.40/1.61 thf(fact_1785_lessThan__Suc__atMost,axiom,
% 1.40/1.61 ! [K: nat] :
% 1.40/1.61 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 1.40/1.61 = ( set_ord_atMost_nat @ K ) ) ).
% 1.40/1.61
% 1.40/1.61 % lessThan_Suc_atMost
% 1.40/1.61 thf(fact_1786_arccos__le__arccos,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( arccos @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_le_arccos
% 1.40/1.61 thf(fact_1787_sum__choose__upper,axiom,
% 1.40/1.61 ! [M: nat,N: nat] :
% 1.40/1.61 ( ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 1.40/1.61 @ ( set_ord_atMost_nat @ N ) )
% 1.40/1.61 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sum_choose_upper
% 1.40/1.61 thf(fact_1788_arccos__le__mono,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_le_mono
% 1.40/1.61 thf(fact_1789_arccos__eq__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 & ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real ) )
% 1.40/1.61 => ( ( ( arccos @ X )
% 1.40/1.61 = ( arccos @ Y2 ) )
% 1.40/1.61 = ( X = Y2 ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_eq_iff
% 1.40/1.61 thf(fact_1790_arcsin__le__arcsin,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_le_arcsin
% 1.40/1.61 thf(fact_1791_arcsin__minus,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.61 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 1.40/1.61 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_minus
% 1.40/1.61 thf(fact_1792_arcsin__le__mono,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_le_mono
% 1.40/1.61 thf(fact_1793_arcsin__eq__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 1.40/1.61 => ( ( ( arcsin @ X )
% 1.40/1.61 = ( arcsin @ Y2 ) )
% 1.40/1.61 = ( X = Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_eq_iff
% 1.40/1.61 thf(fact_1794_sum__choose__lower,axiom,
% 1.40/1.61 ! [R2: nat,N: nat] :
% 1.40/1.61 ( ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 1.40/1.61 @ ( set_ord_atMost_nat @ N ) )
% 1.40/1.61 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N ) ) @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % sum_choose_lower
% 1.40/1.61 thf(fact_1795_choose__rising__sum_I2_J,axiom,
% 1.40/1.61 ! [N: nat,M: nat] :
% 1.40/1.61 ( ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 1.40/1.61 @ ( set_ord_atMost_nat @ M ) )
% 1.40/1.61 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 1.40/1.61
% 1.40/1.61 % choose_rising_sum(2)
% 1.40/1.61 thf(fact_1796_choose__rising__sum_I1_J,axiom,
% 1.40/1.61 ! [N: nat,M: nat] :
% 1.40/1.61 ( ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 1.40/1.61 @ ( set_ord_atMost_nat @ M ) )
% 1.40/1.61 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % choose_rising_sum(1)
% 1.40/1.61 thf(fact_1797_arccos__lbound,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_lbound
% 1.40/1.61 thf(fact_1798_arccos__less__arccos,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ord_less_real @ ( arccos @ Y2 ) @ ( arccos @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_less_arccos
% 1.40/1.61 thf(fact_1799_arccos__less__mono,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 1.40/1.61 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y2 ) )
% 1.40/1.61 = ( ord_less_real @ Y2 @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_less_mono
% 1.40/1.61 thf(fact_1800_arccos__ubound,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_ubound
% 1.40/1.61 thf(fact_1801_arccos__cos,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ pi )
% 1.40/1.61 => ( ( arccos @ ( cos_real @ X ) )
% 1.40/1.61 = X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_cos
% 1.40/1.61 thf(fact_1802_arcsin__less__arcsin,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_less_arcsin
% 1.40/1.61 thf(fact_1803_arcsin__less__mono,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 1.40/1.61 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y2 ) )
% 1.40/1.61 = ( ord_less_real @ X @ Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_less_mono
% 1.40/1.61 thf(fact_1804_cos__arccos__abs,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ Y2 ) @ one_one_real )
% 1.40/1.61 => ( ( cos_real @ ( arccos @ Y2 ) )
% 1.40/1.61 = Y2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_arccos_abs
% 1.40/1.61 thf(fact_1805_arccos__cos__eq__abs,axiom,
% 1.40/1.61 ! [Theta: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 1.40/1.61 => ( ( arccos @ ( cos_real @ Theta ) )
% 1.40/1.61 = ( abs_abs_real @ Theta ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_cos_eq_abs
% 1.40/1.61 thf(fact_1806_sum__choose__diagonal,axiom,
% 1.40/1.61 ! [M: nat,N: nat] :
% 1.40/1.61 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.61 => ( ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 1.40/1.61 @ ( set_ord_atMost_nat @ M ) )
% 1.40/1.61 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sum_choose_diagonal
% 1.40/1.61 thf(fact_1807_vandermonde,axiom,
% 1.40/1.61 ! [M: nat,N: nat,R2: nat] :
% 1.40/1.61 ( ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 1.40/1.61 @ ( set_ord_atMost_nat @ R2 ) )
% 1.40/1.61 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % vandermonde
% 1.40/1.61 thf(fact_1808_arccos__lt__bounded,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 1.40/1.61 & ( ord_less_real @ ( arccos @ Y2 ) @ pi ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_lt_bounded
% 1.40/1.61 thf(fact_1809_arccos__bounded,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 1.40/1.61 & ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_bounded
% 1.40/1.61 thf(fact_1810_sin__arccos__nonzero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.61 => ( ( sin_real @ ( arccos @ X ) )
% 1.40/1.61 != zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_arccos_nonzero
% 1.40/1.61 thf(fact_1811_arccos__cos2,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 1.40/1.61 => ( ( arccos @ ( cos_real @ X ) )
% 1.40/1.61 = ( uminus_uminus_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_cos2
% 1.40/1.61 thf(fact_1812_arccos__minus,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.61 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 1.40/1.61 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_minus
% 1.40/1.61 thf(fact_1813_cos__arcsin__nonzero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.61 => ( ( cos_real @ ( arcsin @ X ) )
% 1.40/1.61 != zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cos_arcsin_nonzero
% 1.40/1.61 thf(fact_1814_choose__row__sum,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 1.40/1.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % choose_row_sum
% 1.40/1.61 thf(fact_1815_binomial,axiom,
% 1.40/1.61 ! [A: nat,B: nat,N: nat] :
% 1.40/1.61 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 1.40/1.61 = ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 1.40/1.61 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial
% 1.40/1.61 thf(fact_1816_arccos,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y2 ) )
% 1.40/1.61 & ( ord_less_eq_real @ ( arccos @ Y2 ) @ pi )
% 1.40/1.61 & ( ( cos_real @ ( arccos @ Y2 ) )
% 1.40/1.61 = Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos
% 1.40/1.61 thf(fact_1817_arccos__minus__abs,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.61 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 1.40/1.61 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_minus_abs
% 1.40/1.61 thf(fact_1818_polynomial__product__nat,axiom,
% 1.40/1.61 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 1.40/1.61 ( ! [I3: nat] :
% 1.40/1.61 ( ( ord_less_nat @ M @ I3 )
% 1.40/1.61 => ( ( A @ I3 )
% 1.40/1.61 = zero_zero_nat ) )
% 1.40/1.61 => ( ! [J2: nat] :
% 1.40/1.61 ( ( ord_less_nat @ N @ J2 )
% 1.40/1.61 => ( ( B @ J2 )
% 1.40/1.61 = zero_zero_nat ) )
% 1.40/1.61 => ( ( times_times_nat
% 1.40/1.61 @ ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( power_power_nat @ X @ I4 ) )
% 1.40/1.61 @ ( set_ord_atMost_nat @ M ) )
% 1.40/1.61 @ ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 1.40/1.61 @ ( set_ord_atMost_nat @ N ) ) )
% 1.40/1.61 = ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [R5: nat] :
% 1.40/1.61 ( times_times_nat
% 1.40/1.61 @ ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 1.40/1.61 @ ( set_ord_atMost_nat @ R5 ) )
% 1.40/1.61 @ ( power_power_nat @ X @ R5 ) )
% 1.40/1.61 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % polynomial_product_nat
% 1.40/1.61 thf(fact_1819_choose__square__sum,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.61 @ ( set_ord_atMost_nat @ N ) )
% 1.40/1.61 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % choose_square_sum
% 1.40/1.61 thf(fact_1820_arccos__le__pi2,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ord_less_eq_real @ ( arccos @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_le_pi2
% 1.40/1.61 thf(fact_1821_binomial__r__part__sum,axiom,
% 1.40/1.61 ! [M: nat] :
% 1.40/1.61 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 1.40/1.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % binomial_r_part_sum
% 1.40/1.61 thf(fact_1822_choose__linear__sum,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( groups3542108847815614940at_nat
% 1.40/1.61 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 1.40/1.61 @ ( set_ord_atMost_nat @ N ) )
% 1.40/1.61 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % choose_linear_sum
% 1.40/1.61 thf(fact_1823_arcsin__lt__bounded,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 1.40/1.61 & ( ord_less_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_lt_bounded
% 1.40/1.61 thf(fact_1824_arcsin__lbound,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_lbound
% 1.40/1.61 thf(fact_1825_arcsin__ubound,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_ubound
% 1.40/1.61 thf(fact_1826_arcsin__bounded,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 1.40/1.61 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_bounded
% 1.40/1.61 thf(fact_1827_arcsin__sin,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( arcsin @ ( sin_real @ X ) )
% 1.40/1.61 = X ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_sin
% 1.40/1.61 thf(fact_1828_arcsin,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 1.40/1.61 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 & ( ( sin_real @ ( arcsin @ Y2 ) )
% 1.40/1.61 = Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin
% 1.40/1.61 thf(fact_1829_arcsin__pi,axiom,
% 1.40/1.61 ! [Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y2 ) )
% 1.40/1.61 & ( ord_less_eq_real @ ( arcsin @ Y2 ) @ pi )
% 1.40/1.61 & ( ( sin_real @ ( arcsin @ Y2 ) )
% 1.40/1.61 = Y2 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_pi
% 1.40/1.61 thf(fact_1830_arcsin__le__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y2 )
% 1.40/1.61 = ( ord_less_eq_real @ X @ ( sin_real @ Y2 ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arcsin_le_iff
% 1.40/1.61 thf(fact_1831_le__arcsin__iff,axiom,
% 1.40/1.61 ! [X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.61 => ( ( ord_less_eq_real @ Y2 @ ( arcsin @ X ) )
% 1.40/1.61 = ( ord_less_eq_real @ ( sin_real @ Y2 ) @ X ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % le_arcsin_iff
% 1.40/1.61 thf(fact_1832_arccos__cos__eq__abs__2pi,axiom,
% 1.40/1.61 ! [Theta: real] :
% 1.40/1.61 ~ ! [K2: int] :
% 1.40/1.61 ( ( arccos @ ( cos_real @ Theta ) )
% 1.40/1.61 != ( 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 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % arccos_cos_eq_abs_2pi
% 1.40/1.61 thf(fact_1833_sin__arccos,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.61 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.61 => ( ( sin_real @ ( arccos @ X ) )
% 1.40/1.61 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % sin_arccos
% 1.40/1.61 thf(fact_1834_of__nat__id,axiom,
% 1.40/1.61 ( semiri1316708129612266289at_nat
% 1.40/1.61 = ( ^ [N2: nat] : N2 ) ) ).
% 1.40/1.61
% 1.40/1.61 % of_nat_id
% 1.40/1.61 thf(fact_1835_real__scaleR__def,axiom,
% 1.40/1.61 real_V1485227260804924795R_real = times_times_real ).
% 1.40/1.61
% 1.40/1.61 % real_scaleR_def
% 1.40/1.61 thf(fact_1836_complex__scaleR,axiom,
% 1.40/1.61 ! [R2: real,A: real,B: real] :
% 1.40/1.61 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B ) )
% 1.40/1.61 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % complex_scaleR
% 1.40/1.61 thf(fact_1837_Maclaurin__sin__bound,axiom,
% 1.40/1.61 ! [X: real,N: nat] :
% 1.40/1.61 ( ord_less_eq_real
% 1.40/1.61 @ ( abs_abs_real
% 1.40/1.61 @ ( minus_minus_real @ ( sin_real @ X )
% 1.40/1.61 @ ( groups6591440286371151544t_real
% 1.40/1.61 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.61 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 1.40/1.61 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % Maclaurin_sin_bound
% 1.40/1.61 thf(fact_1838_cot__less__zero,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 1.40/1.61 => ( ( ord_less_real @ X @ zero_zero_real )
% 1.40/1.61 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % cot_less_zero
% 1.40/1.61 thf(fact_1839_i__even__power,axiom,
% 1.40/1.61 ! [N: nat] :
% 1.40/1.61 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.61 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 1.40/1.61
% 1.40/1.61 % i_even_power
% 1.40/1.61 thf(fact_1840_log__base__10__eq1,axiom,
% 1.40/1.61 ! [X: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.61 = ( 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 ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % log_base_10_eq1
% 1.40/1.61 thf(fact_1841_log__one,axiom,
% 1.40/1.61 ! [A: real] :
% 1.40/1.61 ( ( log @ A @ one_one_real )
% 1.40/1.61 = zero_zero_real ) ).
% 1.40/1.61
% 1.40/1.61 % log_one
% 1.40/1.61 thf(fact_1842_norm__ii,axiom,
% 1.40/1.61 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 1.40/1.61 = one_one_real ) ).
% 1.40/1.61
% 1.40/1.61 % norm_ii
% 1.40/1.61 thf(fact_1843_complex__i__mult__minus,axiom,
% 1.40/1.61 ! [X: complex] :
% 1.40/1.61 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 1.40/1.61 = ( uminus1482373934393186551omplex @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % complex_i_mult_minus
% 1.40/1.61 thf(fact_1844_divide__i,axiom,
% 1.40/1.61 ! [X: complex] :
% 1.40/1.61 ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 1.40/1.61 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 1.40/1.61
% 1.40/1.61 % divide_i
% 1.40/1.61 thf(fact_1845_log__eq__one,axiom,
% 1.40/1.61 ! [A: real] :
% 1.40/1.61 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.61 => ( ( A != one_one_real )
% 1.40/1.61 => ( ( log @ A @ A )
% 1.40/1.61 = one_one_real ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % log_eq_one
% 1.40/1.61 thf(fact_1846_log__less__cancel__iff,axiom,
% 1.40/1.61 ! [A: real,X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) )
% 1.40/1.61 = ( ord_less_real @ X @ Y2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % log_less_cancel_iff
% 1.40/1.61 thf(fact_1847_log__less__one__cancel__iff,axiom,
% 1.40/1.61 ! [A: real,X: real] :
% 1.40/1.61 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 1.40/1.61 = ( ord_less_real @ X @ A ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % log_less_one_cancel_iff
% 1.40/1.61 thf(fact_1848_one__less__log__cancel__iff,axiom,
% 1.40/1.61 ! [A: real,X: real] :
% 1.40/1.61 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 1.40/1.61 = ( ord_less_real @ A @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % one_less_log_cancel_iff
% 1.40/1.61 thf(fact_1849_log__less__zero__cancel__iff,axiom,
% 1.40/1.61 ! [A: real,X: real] :
% 1.40/1.61 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 1.40/1.61 = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % log_less_zero_cancel_iff
% 1.40/1.61 thf(fact_1850_zero__less__log__cancel__iff,axiom,
% 1.40/1.61 ! [A: real,X: real] :
% 1.40/1.61 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 1.40/1.61 = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % zero_less_log_cancel_iff
% 1.40/1.61 thf(fact_1851_i__squared,axiom,
% 1.40/1.61 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 1.40/1.61 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 1.40/1.61
% 1.40/1.61 % i_squared
% 1.40/1.61 thf(fact_1852_divide__numeral__i,axiom,
% 1.40/1.61 ! [Z: complex,N: num] :
% 1.40/1.61 ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 1.40/1.61 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % divide_numeral_i
% 1.40/1.61 thf(fact_1853_log__le__cancel__iff,axiom,
% 1.40/1.61 ! [A: real,X: real,Y2: real] :
% 1.40/1.61 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.61 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 1.40/1.61 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) )
% 1.40/1.61 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ) ).
% 1.40/1.61
% 1.40/1.61 % log_le_cancel_iff
% 1.40/1.62 thf(fact_1854_log__le__one__cancel__iff,axiom,
% 1.40/1.62 ! [A: real,X: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 1.40/1.62 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_le_one_cancel_iff
% 1.40/1.62 thf(fact_1855_one__le__log__cancel__iff,axiom,
% 1.40/1.62 ! [A: real,X: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 1.40/1.62 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % one_le_log_cancel_iff
% 1.40/1.62 thf(fact_1856_log__le__zero__cancel__iff,axiom,
% 1.40/1.62 ! [A: real,X: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 1.40/1.62 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_le_zero_cancel_iff
% 1.40/1.62 thf(fact_1857_zero__le__log__cancel__iff,axiom,
% 1.40/1.62 ! [A: real,X: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 1.40/1.62 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % zero_le_log_cancel_iff
% 1.40/1.62 thf(fact_1858_cot__npi,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 1.40/1.62 = zero_zero_real ) ).
% 1.40/1.62
% 1.40/1.62 % cot_npi
% 1.40/1.62 thf(fact_1859_log__pow__cancel,axiom,
% 1.40/1.62 ! [A: real,B: nat] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( A != one_one_real )
% 1.40/1.62 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 1.40/1.62 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_pow_cancel
% 1.40/1.62 thf(fact_1860_cot__periodic,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 1.40/1.62 = ( cot_real @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % cot_periodic
% 1.40/1.62 thf(fact_1861_power2__i,axiom,
% 1.40/1.62 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.62 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 1.40/1.62
% 1.40/1.62 % power2_i
% 1.40/1.62 thf(fact_1862_real__sqrt__inverse,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 1.40/1.62 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % real_sqrt_inverse
% 1.40/1.62 thf(fact_1863_complex__i__not__one,axiom,
% 1.40/1.62 imaginary_unit != one_one_complex ).
% 1.40/1.62
% 1.40/1.62 % complex_i_not_one
% 1.40/1.62 thf(fact_1864_complex__i__not__numeral,axiom,
% 1.40/1.62 ! [W: num] :
% 1.40/1.62 ( imaginary_unit
% 1.40/1.62 != ( numera6690914467698888265omplex @ W ) ) ).
% 1.40/1.62
% 1.40/1.62 % complex_i_not_numeral
% 1.40/1.62 thf(fact_1865_log__inverse,axiom,
% 1.40/1.62 ! [A: real,X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( A != one_one_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 1.40/1.62 = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_inverse
% 1.40/1.62 thf(fact_1866_divide__real__def,axiom,
% 1.40/1.62 ( divide_divide_real
% 1.40/1.62 = ( ^ [X4: real,Y4: real] : ( times_times_real @ X4 @ ( inverse_inverse_real @ Y4 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % divide_real_def
% 1.40/1.62 thf(fact_1867_i__times__eq__iff,axiom,
% 1.40/1.62 ! [W: complex,Z: complex] :
% 1.40/1.62 ( ( ( times_times_complex @ imaginary_unit @ W )
% 1.40/1.62 = Z )
% 1.40/1.62 = ( W
% 1.40/1.62 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % i_times_eq_iff
% 1.40/1.62 thf(fact_1868_complex__i__not__neg__numeral,axiom,
% 1.40/1.62 ! [W: num] :
% 1.40/1.62 ( imaginary_unit
% 1.40/1.62 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % complex_i_not_neg_numeral
% 1.40/1.62 thf(fact_1869_log__ln,axiom,
% 1.40/1.62 ( ln_ln_real
% 1.40/1.62 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_ln
% 1.40/1.62 thf(fact_1870_Complex__eq__i,axiom,
% 1.40/1.62 ! [X: real,Y2: real] :
% 1.40/1.62 ( ( ( complex2 @ X @ Y2 )
% 1.40/1.62 = imaginary_unit )
% 1.40/1.62 = ( ( X = zero_zero_real )
% 1.40/1.62 & ( Y2 = one_one_real ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Complex_eq_i
% 1.40/1.62 thf(fact_1871_imaginary__unit_Ocode,axiom,
% 1.40/1.62 ( imaginary_unit
% 1.40/1.62 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 1.40/1.62
% 1.40/1.62 % imaginary_unit.code
% 1.40/1.62 thf(fact_1872_Complex__mult__i,axiom,
% 1.40/1.62 ! [A: real,B: real] :
% 1.40/1.62 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 1.40/1.62 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 1.40/1.62
% 1.40/1.62 % Complex_mult_i
% 1.40/1.62 thf(fact_1873_i__mult__Complex,axiom,
% 1.40/1.62 ! [A: real,B: real] :
% 1.40/1.62 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 1.40/1.62 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 1.40/1.62
% 1.40/1.62 % i_mult_Complex
% 1.40/1.62 thf(fact_1874_log__base__change,axiom,
% 1.40/1.62 ! [A: real,B: real,X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( A != one_one_real )
% 1.40/1.62 => ( ( log @ B @ X )
% 1.40/1.62 = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_base_change
% 1.40/1.62 thf(fact_1875_less__log__of__power,axiom,
% 1.40/1.62 ! [B: real,N: nat,M: real] :
% 1.40/1.62 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 1.40/1.62 => ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % less_log_of_power
% 1.40/1.62 thf(fact_1876_log__of__power__eq,axiom,
% 1.40/1.62 ! [M: nat,B: real,N: nat] :
% 1.40/1.62 ( ( ( semiri5074537144036343181t_real @ M )
% 1.40/1.62 = ( power_power_real @ B @ N ) )
% 1.40/1.62 => ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( semiri5074537144036343181t_real @ N )
% 1.40/1.62 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_of_power_eq
% 1.40/1.62 thf(fact_1877_forall__pos__mono__1,axiom,
% 1.40/1.62 ! [P: real > $o,E: real] :
% 1.40/1.62 ( ! [D3: real,E2: real] :
% 1.40/1.62 ( ( ord_less_real @ D3 @ E2 )
% 1.40/1.62 => ( ( P @ D3 )
% 1.40/1.62 => ( P @ E2 ) ) )
% 1.40/1.62 => ( ! [N4: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ E )
% 1.40/1.62 => ( P @ E ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % forall_pos_mono_1
% 1.40/1.62 thf(fact_1878_real__arch__inverse,axiom,
% 1.40/1.62 ! [E: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ E )
% 1.40/1.62 = ( ? [N2: nat] :
% 1.40/1.62 ( ( N2 != zero_zero_nat )
% 1.40/1.62 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 1.40/1.62 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % real_arch_inverse
% 1.40/1.62 thf(fact_1879_forall__pos__mono,axiom,
% 1.40/1.62 ! [P: real > $o,E: real] :
% 1.40/1.62 ( ! [D3: real,E2: real] :
% 1.40/1.62 ( ( ord_less_real @ D3 @ E2 )
% 1.40/1.62 => ( ( P @ D3 )
% 1.40/1.62 => ( P @ E2 ) ) )
% 1.40/1.62 => ( ! [N4: nat] :
% 1.40/1.62 ( ( N4 != zero_zero_nat )
% 1.40/1.62 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) ) )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ E )
% 1.40/1.62 => ( P @ E ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % forall_pos_mono
% 1.40/1.62 thf(fact_1880_sqrt__divide__self__eq,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 1.40/1.62 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % sqrt_divide_self_eq
% 1.40/1.62 thf(fact_1881_log__mult,axiom,
% 1.40/1.62 ! [A: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( A != one_one_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 1.40/1.62 => ( ( log @ A @ ( times_times_real @ X @ Y2 ) )
% 1.40/1.62 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_mult
% 1.40/1.62 thf(fact_1882_log__divide,axiom,
% 1.40/1.62 ! [A: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( A != one_one_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 1.40/1.62 => ( ( log @ A @ ( divide_divide_real @ X @ Y2 ) )
% 1.40/1.62 = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y2 ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_divide
% 1.40/1.62 thf(fact_1883_le__log__of__power,axiom,
% 1.40/1.62 ! [B: real,N: nat,M: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 1.40/1.62 => ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % le_log_of_power
% 1.40/1.62 thf(fact_1884_log__base__pow,axiom,
% 1.40/1.62 ! [A: real,N: nat,X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 1.40/1.62 = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_base_pow
% 1.40/1.62 thf(fact_1885_log__nat__power,axiom,
% 1.40/1.62 ! [X: real,B: real,N: nat] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 1.40/1.62 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_nat_power
% 1.40/1.62 thf(fact_1886_log2__of__power__eq,axiom,
% 1.40/1.62 ! [M: nat,N: nat] :
% 1.40/1.62 ( ( M
% 1.40/1.62 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.62 => ( ( semiri5074537144036343181t_real @ N )
% 1.40/1.62 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log2_of_power_eq
% 1.40/1.62 thf(fact_1887_log__of__power__less,axiom,
% 1.40/1.62 ! [M: nat,B: real,N: nat] :
% 1.40/1.62 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 1.40/1.62 => ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.62 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_of_power_less
% 1.40/1.62 thf(fact_1888_log__eq__div__ln__mult__log,axiom,
% 1.40/1.62 ! [A: real,B: real,X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( A != one_one_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ B )
% 1.40/1.62 => ( ( B != one_one_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( log @ A @ X )
% 1.40/1.62 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_eq_div_ln_mult_log
% 1.40/1.62 thf(fact_1889_exp__plus__inverse__exp,axiom,
% 1.40/1.62 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % exp_plus_inverse_exp
% 1.40/1.62 thf(fact_1890_log__of__power__le,axiom,
% 1.40/1.62 ! [M: nat,B: real,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 1.40/1.62 => ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.62 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_of_power_le
% 1.40/1.62 thf(fact_1891_plus__inverse__ge__2,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % plus_inverse_ge_2
% 1.40/1.62 thf(fact_1892_real__inv__sqrt__pow2,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.62 = ( inverse_inverse_real @ X ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % real_inv_sqrt_pow2
% 1.40/1.62 thf(fact_1893_tan__cot,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 1.40/1.62 = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % tan_cot
% 1.40/1.62 thf(fact_1894_less__log2__of__power,axiom,
% 1.40/1.62 ! [N: nat,M: nat] :
% 1.40/1.62 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 1.40/1.62 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % less_log2_of_power
% 1.40/1.62 thf(fact_1895_le__log2__of__power,axiom,
% 1.40/1.62 ! [N: nat,M: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 1.40/1.62 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % le_log2_of_power
% 1.40/1.62 thf(fact_1896_real__le__x__sinh,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( 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 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % real_le_x_sinh
% 1.40/1.62 thf(fact_1897_real__le__abs__sinh,axiom,
% 1.40/1.62 ! [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 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % real_le_abs_sinh
% 1.40/1.62 thf(fact_1898_log2__of__power__less,axiom,
% 1.40/1.62 ! [M: nat,N: nat] :
% 1.40/1.62 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.62 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.62 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log2_of_power_less
% 1.40/1.62 thf(fact_1899_cot__gt__zero,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.62 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % cot_gt_zero
% 1.40/1.62 thf(fact_1900_log2__of__power__le,axiom,
% 1.40/1.62 ! [M: nat,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.62 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.62 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log2_of_power_le
% 1.40/1.62 thf(fact_1901_log__base__10__eq2,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 1.40/1.62 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_base_10_eq2
% 1.40/1.62 thf(fact_1902_tan__cot_H,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 1.40/1.62 = ( cot_real @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % tan_cot'
% 1.40/1.62 thf(fact_1903_Arg__minus__ii,axiom,
% 1.40/1.62 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 1.40/1.62 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Arg_minus_ii
% 1.40/1.62 thf(fact_1904_ceiling__log__nat__eq__powr__iff,axiom,
% 1.40/1.62 ! [B: nat,K: nat,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 1.40/1.62 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.62 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 1.40/1.62 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 1.40/1.62 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 1.40/1.62 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ceiling_log_nat_eq_powr_iff
% 1.40/1.62 thf(fact_1905_Arg__ii,axiom,
% 1.40/1.62 ( ( arg @ imaginary_unit )
% 1.40/1.62 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Arg_ii
% 1.40/1.62 thf(fact_1906_sinh__real__le__iff,axiom,
% 1.40/1.62 ! [X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y2 ) )
% 1.40/1.62 = ( ord_less_eq_real @ X @ Y2 ) ) ).
% 1.40/1.62
% 1.40/1.62 % sinh_real_le_iff
% 1.40/1.62 thf(fact_1907_sinh__real__nonneg__iff,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 1.40/1.62 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % sinh_real_nonneg_iff
% 1.40/1.62 thf(fact_1908_sinh__real__nonpos__iff,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 1.40/1.62 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 1.40/1.62
% 1.40/1.62 % sinh_real_nonpos_iff
% 1.40/1.62 thf(fact_1909_ceiling__divide__eq__div__numeral,axiom,
% 1.40/1.62 ! [A: num,B: num] :
% 1.40/1.62 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 1.40/1.62 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ceiling_divide_eq_div_numeral
% 1.40/1.62 thf(fact_1910_ceiling__minus__divide__eq__div__numeral,axiom,
% 1.40/1.62 ! [A: num,B: num] :
% 1.40/1.62 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 1.40/1.62 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ceiling_minus_divide_eq_div_numeral
% 1.40/1.62 thf(fact_1911_divide__complex__def,axiom,
% 1.40/1.62 ( divide1717551699836669952omplex
% 1.40/1.62 = ( ^ [X4: complex,Y4: complex] : ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ Y4 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % divide_complex_def
% 1.40/1.62 thf(fact_1912_Arg__bounded,axiom,
% 1.40/1.62 ! [Z: complex] :
% 1.40/1.62 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 1.40/1.62 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 1.40/1.62
% 1.40/1.62 % Arg_bounded
% 1.40/1.62 thf(fact_1913_complex__inverse,axiom,
% 1.40/1.62 ! [A: real,B: real] :
% 1.40/1.62 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 1.40/1.62 = ( 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 ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % complex_inverse
% 1.40/1.62 thf(fact_1914_sinh__ln__real,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 1.40/1.62 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % sinh_ln_real
% 1.40/1.62 thf(fact_1915_ceiling__log__nat__eq__if,axiom,
% 1.40/1.62 ! [B: nat,N: nat,K: nat] :
% 1.40/1.62 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 1.40/1.62 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 1.40/1.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 1.40/1.62 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 1.40/1.62 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ceiling_log_nat_eq_if
% 1.40/1.62 thf(fact_1916_ceiling__log2__div2,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.62 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 1.40/1.62 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ceiling_log2_div2
% 1.40/1.62 thf(fact_1917_cis__minus__pi__half,axiom,
% 1.40/1.62 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 1.40/1.62 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 1.40/1.62
% 1.40/1.62 % cis_minus_pi_half
% 1.40/1.62 thf(fact_1918_ceiling__log__eq__powr__iff,axiom,
% 1.40/1.62 ! [X: real,B: real,K: nat] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 1.40/1.62 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 1.40/1.62 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 1.40/1.62 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ceiling_log_eq_powr_iff
% 1.40/1.62 thf(fact_1919_floor__log__nat__eq__powr__iff,axiom,
% 1.40/1.62 ! [B: nat,K: nat,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 1.40/1.62 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 1.40/1.62 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 1.40/1.62 = ( semiri1314217659103216013at_int @ N ) )
% 1.40/1.62 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 1.40/1.62 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_log_nat_eq_powr_iff
% 1.40/1.62 thf(fact_1920_powr__nonneg__iff,axiom,
% 1.40/1.62 ! [A: real,X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 1.40/1.62 = ( A = zero_zero_real ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_nonneg_iff
% 1.40/1.62 thf(fact_1921_powr__less__cancel__iff,axiom,
% 1.40/1.62 ! [X: real,A: real,B: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 1.40/1.62 = ( ord_less_real @ A @ B ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_less_cancel_iff
% 1.40/1.62 thf(fact_1922_norm__cis,axiom,
% 1.40/1.62 ! [A: real] :
% 1.40/1.62 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 1.40/1.62 = one_one_real ) ).
% 1.40/1.62
% 1.40/1.62 % norm_cis
% 1.40/1.62 thf(fact_1923_cis__zero,axiom,
% 1.40/1.62 ( ( cis @ zero_zero_real )
% 1.40/1.62 = one_one_complex ) ).
% 1.40/1.62
% 1.40/1.62 % cis_zero
% 1.40/1.62 thf(fact_1924_powr__eq__one__iff,axiom,
% 1.40/1.62 ! [A: real,X: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ A )
% 1.40/1.62 => ( ( ( powr_real @ A @ X )
% 1.40/1.62 = one_one_real )
% 1.40/1.62 = ( X = zero_zero_real ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_eq_one_iff
% 1.40/1.62 thf(fact_1925_powr__one,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( powr_real @ X @ one_one_real )
% 1.40/1.62 = X ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_one
% 1.40/1.62 thf(fact_1926_powr__one__gt__zero__iff,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ( powr_real @ X @ one_one_real )
% 1.40/1.62 = X )
% 1.40/1.62 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_one_gt_zero_iff
% 1.40/1.62 thf(fact_1927_powr__le__cancel__iff,axiom,
% 1.40/1.62 ! [X: real,A: real,B: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 1.40/1.62 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_le_cancel_iff
% 1.40/1.62 thf(fact_1928_numeral__powr__numeral__real,axiom,
% 1.40/1.62 ! [M: num,N: num] :
% 1.40/1.62 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 1.40/1.62 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % numeral_powr_numeral_real
% 1.40/1.62 thf(fact_1929_cis__pi,axiom,
% 1.40/1.62 ( ( cis @ pi )
% 1.40/1.62 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 1.40/1.62
% 1.40/1.62 % cis_pi
% 1.40/1.62 thf(fact_1930_log__powr__cancel,axiom,
% 1.40/1.62 ! [A: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( A != one_one_real )
% 1.40/1.62 => ( ( log @ A @ ( powr_real @ A @ Y2 ) )
% 1.40/1.62 = Y2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_powr_cancel
% 1.40/1.62 thf(fact_1931_powr__log__cancel,axiom,
% 1.40/1.62 ! [A: real,X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( A != one_one_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( powr_real @ A @ ( log @ A @ X ) )
% 1.40/1.62 = X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_log_cancel
% 1.40/1.62 thf(fact_1932_floor__divide__eq__div__numeral,axiom,
% 1.40/1.62 ! [A: num,B: num] :
% 1.40/1.62 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 1.40/1.62 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_divide_eq_div_numeral
% 1.40/1.62 thf(fact_1933_powr__numeral,axiom,
% 1.40/1.62 ! [X: real,N: num] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 1.40/1.62 = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_numeral
% 1.40/1.62 thf(fact_1934_cis__pi__half,axiom,
% 1.40/1.62 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.62 = imaginary_unit ) ).
% 1.40/1.62
% 1.40/1.62 % cis_pi_half
% 1.40/1.62 thf(fact_1935_floor__one__divide__eq__div__numeral,axiom,
% 1.40/1.62 ! [B: num] :
% 1.40/1.62 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 1.40/1.62 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_one_divide_eq_div_numeral
% 1.40/1.62 thf(fact_1936_cis__2pi,axiom,
% 1.40/1.62 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 1.40/1.62 = one_one_complex ) ).
% 1.40/1.62
% 1.40/1.62 % cis_2pi
% 1.40/1.62 thf(fact_1937_floor__minus__divide__eq__div__numeral,axiom,
% 1.40/1.62 ! [A: num,B: num] :
% 1.40/1.62 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 1.40/1.62 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_minus_divide_eq_div_numeral
% 1.40/1.62 thf(fact_1938_square__powr__half,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.62 = ( abs_abs_real @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % square_powr_half
% 1.40/1.62 thf(fact_1939_floor__minus__one__divide__eq__div__numeral,axiom,
% 1.40/1.62 ! [B: num] :
% 1.40/1.62 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 1.40/1.62 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_minus_one_divide_eq_div_numeral
% 1.40/1.62 thf(fact_1940_sinh__le__cosh__real,axiom,
% 1.40/1.62 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % sinh_le_cosh_real
% 1.40/1.62 thf(fact_1941_powr__powr,axiom,
% 1.40/1.62 ! [X: real,A: real,B: real] :
% 1.40/1.62 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 1.40/1.62 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_powr
% 1.40/1.62 thf(fact_1942_powr__ge__pzero,axiom,
% 1.40/1.62 ! [X: real,Y2: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y2 ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_ge_pzero
% 1.40/1.62 thf(fact_1943_powr__mono2,axiom,
% 1.40/1.62 ! [A: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ X @ Y2 )
% 1.40/1.62 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_mono2
% 1.40/1.62 thf(fact_1944_powr__less__cancel,axiom,
% 1.40/1.62 ! [X: real,A: real,B: real] :
% 1.40/1.62 ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 1.40/1.62 => ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.62 => ( ord_less_real @ A @ B ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_less_cancel
% 1.40/1.62 thf(fact_1945_powr__less__mono,axiom,
% 1.40/1.62 ! [A: real,B: real,X: real] :
% 1.40/1.62 ( ( ord_less_real @ A @ B )
% 1.40/1.62 => ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.62 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_less_mono
% 1.40/1.62 thf(fact_1946_powr__mono,axiom,
% 1.40/1.62 ! [A: real,B: real,X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ A @ B )
% 1.40/1.62 => ( ( ord_less_eq_real @ one_one_real @ X )
% 1.40/1.62 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_mono
% 1.40/1.62 thf(fact_1947_cosh__real__nonpos__le__iff,axiom,
% 1.40/1.62 ! [X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 1.40/1.62 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 1.40/1.62 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 1.40/1.62 = ( ord_less_eq_real @ Y2 @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % cosh_real_nonpos_le_iff
% 1.40/1.62 thf(fact_1948_cosh__real__nonneg__le__iff,axiom,
% 1.40/1.62 ! [X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.62 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 1.40/1.62 = ( ord_less_eq_real @ X @ Y2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % cosh_real_nonneg_le_iff
% 1.40/1.62 thf(fact_1949_cosh__real__nonneg,axiom,
% 1.40/1.62 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % cosh_real_nonneg
% 1.40/1.62 thf(fact_1950_cosh__real__ge__1,axiom,
% 1.40/1.62 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % cosh_real_ge_1
% 1.40/1.62 thf(fact_1951_cis__mult,axiom,
% 1.40/1.62 ! [A: real,B: real] :
% 1.40/1.62 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 1.40/1.62 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % cis_mult
% 1.40/1.62 thf(fact_1952_powr__less__mono2,axiom,
% 1.40/1.62 ! [A: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ X @ Y2 )
% 1.40/1.62 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_less_mono2
% 1.40/1.62 thf(fact_1953_powr__mono2_H,axiom,
% 1.40/1.62 ! [A: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ X @ Y2 )
% 1.40/1.62 => ( ord_less_eq_real @ ( powr_real @ Y2 @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_mono2'
% 1.40/1.62 thf(fact_1954_powr__inj,axiom,
% 1.40/1.62 ! [A: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( A != one_one_real )
% 1.40/1.62 => ( ( ( powr_real @ A @ X )
% 1.40/1.62 = ( powr_real @ A @ Y2 ) )
% 1.40/1.62 = ( X = Y2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_inj
% 1.40/1.62 thf(fact_1955_gr__one__powr,axiom,
% 1.40/1.62 ! [X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ Y2 )
% 1.40/1.62 => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % gr_one_powr
% 1.40/1.62 thf(fact_1956_powr__le1,axiom,
% 1.40/1.62 ! [A: real,X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.62 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_le1
% 1.40/1.62 thf(fact_1957_powr__mono__both,axiom,
% 1.40/1.62 ! [A: real,B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ( ord_less_eq_real @ A @ B )
% 1.40/1.62 => ( ( ord_less_eq_real @ one_one_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ X @ Y2 )
% 1.40/1.62 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ B ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_mono_both
% 1.40/1.62 thf(fact_1958_ge__one__powr__ge__zero,axiom,
% 1.40/1.62 ! [X: real,A: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ one_one_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ge_one_powr_ge_zero
% 1.40/1.62 thf(fact_1959_powr__divide,axiom,
% 1.40/1.62 ! [X: real,Y2: real,A: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.62 => ( ( powr_real @ ( divide_divide_real @ X @ Y2 ) @ A )
% 1.40/1.62 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_divide
% 1.40/1.62 thf(fact_1960_powr__mult,axiom,
% 1.40/1.62 ! [X: real,Y2: real,A: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.62 => ( ( powr_real @ ( times_times_real @ X @ Y2 ) @ A )
% 1.40/1.62 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y2 @ A ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_mult
% 1.40/1.62 thf(fact_1961_inverse__powr,axiom,
% 1.40/1.62 ! [Y2: real,A: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.62 => ( ( powr_real @ ( inverse_inverse_real @ Y2 ) @ A )
% 1.40/1.62 = ( inverse_inverse_real @ ( powr_real @ Y2 @ A ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % inverse_powr
% 1.40/1.62 thf(fact_1962_divide__powr__uminus,axiom,
% 1.40/1.62 ! [A: real,B: real,C: real] :
% 1.40/1.62 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 1.40/1.62 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % divide_powr_uminus
% 1.40/1.62 thf(fact_1963_ln__powr,axiom,
% 1.40/1.62 ! [X: real,Y2: real] :
% 1.40/1.62 ( ( X != zero_zero_real )
% 1.40/1.62 => ( ( ln_ln_real @ ( powr_real @ X @ Y2 ) )
% 1.40/1.62 = ( times_times_real @ Y2 @ ( ln_ln_real @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ln_powr
% 1.40/1.62 thf(fact_1964_log__powr,axiom,
% 1.40/1.62 ! [X: real,B: real,Y2: real] :
% 1.40/1.62 ( ( X != zero_zero_real )
% 1.40/1.62 => ( ( log @ B @ ( powr_real @ X @ Y2 ) )
% 1.40/1.62 = ( times_times_real @ Y2 @ ( log @ B @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_powr
% 1.40/1.62 thf(fact_1965_cosh__real__nonpos__less__iff,axiom,
% 1.40/1.62 ! [X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 1.40/1.62 => ( ( ord_less_eq_real @ Y2 @ zero_zero_real )
% 1.40/1.62 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 1.40/1.62 = ( ord_less_real @ Y2 @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % cosh_real_nonpos_less_iff
% 1.40/1.62 thf(fact_1966_cosh__real__nonneg__less__iff,axiom,
% 1.40/1.62 ! [X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.62 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) )
% 1.40/1.62 = ( ord_less_real @ X @ Y2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % cosh_real_nonneg_less_iff
% 1.40/1.62 thf(fact_1967_cosh__real__strict__mono,axiom,
% 1.40/1.62 ! [X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ X @ Y2 )
% 1.40/1.62 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % cosh_real_strict_mono
% 1.40/1.62 thf(fact_1968_arcosh__cosh__real,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 1.40/1.62 = X ) ) ).
% 1.40/1.62
% 1.40/1.62 % arcosh_cosh_real
% 1.40/1.62 thf(fact_1969_floor__log__eq__powr__iff,axiom,
% 1.40/1.62 ! [X: real,B: real,K: int] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 1.40/1.62 = K )
% 1.40/1.62 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 1.40/1.62 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_log_eq_powr_iff
% 1.40/1.62 thf(fact_1970_powr__realpow,axiom,
% 1.40/1.62 ! [X: real,N: nat] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 1.40/1.62 = ( power_power_real @ X @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_realpow
% 1.40/1.62 thf(fact_1971_less__log__iff,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ Y2 @ ( log @ B @ X ) )
% 1.40/1.62 = ( ord_less_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % less_log_iff
% 1.40/1.62 thf(fact_1972_log__less__iff,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ ( log @ B @ X ) @ Y2 )
% 1.40/1.62 = ( ord_less_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_less_iff
% 1.40/1.62 thf(fact_1973_less__powr__iff,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ X @ ( powr_real @ B @ Y2 ) )
% 1.40/1.62 = ( ord_less_real @ ( log @ B @ X ) @ Y2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % less_powr_iff
% 1.40/1.62 thf(fact_1974_powr__less__iff,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ ( powr_real @ B @ Y2 ) @ X )
% 1.40/1.62 = ( ord_less_real @ Y2 @ ( log @ B @ X ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_less_iff
% 1.40/1.62 thf(fact_1975_real__of__int__floor__add__one__gt,axiom,
% 1.40/1.62 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 1.40/1.62
% 1.40/1.62 % real_of_int_floor_add_one_gt
% 1.40/1.62 thf(fact_1976_floor__eq,axiom,
% 1.40/1.62 ! [N: int,X: real] :
% 1.40/1.62 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 1.40/1.62 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 1.40/1.62 => ( ( archim6058952711729229775r_real @ X )
% 1.40/1.62 = N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_eq
% 1.40/1.62 thf(fact_1977_real__of__int__floor__add__one__ge,axiom,
% 1.40/1.62 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 1.40/1.62
% 1.40/1.62 % real_of_int_floor_add_one_ge
% 1.40/1.62 thf(fact_1978_real__of__int__floor__gt__diff__one,axiom,
% 1.40/1.62 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % real_of_int_floor_gt_diff_one
% 1.40/1.62 thf(fact_1979_real__of__int__floor__ge__diff__one,axiom,
% 1.40/1.62 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % real_of_int_floor_ge_diff_one
% 1.40/1.62 thf(fact_1980_DeMoivre,axiom,
% 1.40/1.62 ! [A: real,N: nat] :
% 1.40/1.62 ( ( power_power_complex @ ( cis @ A ) @ N )
% 1.40/1.62 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % DeMoivre
% 1.40/1.62 thf(fact_1981_powr__neg__one,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 1.40/1.62 = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_neg_one
% 1.40/1.62 thf(fact_1982_powr__mult__base,axiom,
% 1.40/1.62 ! [X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( times_times_real @ X @ ( powr_real @ X @ Y2 ) )
% 1.40/1.62 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_mult_base
% 1.40/1.62 thf(fact_1983_powr__le__iff,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X )
% 1.40/1.62 = ( ord_less_eq_real @ Y2 @ ( log @ B @ X ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_le_iff
% 1.40/1.62 thf(fact_1984_le__powr__iff,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y2 ) )
% 1.40/1.62 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % le_powr_iff
% 1.40/1.62 thf(fact_1985_log__le__iff,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y2 )
% 1.40/1.62 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_le_iff
% 1.40/1.62 thf(fact_1986_le__log__iff,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ Y2 @ ( log @ B @ X ) )
% 1.40/1.62 = ( ord_less_eq_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % le_log_iff
% 1.40/1.62 thf(fact_1987_floor__eq2,axiom,
% 1.40/1.62 ! [N: int,X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 1.40/1.62 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 1.40/1.62 => ( ( archim6058952711729229775r_real @ X )
% 1.40/1.62 = N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_eq2
% 1.40/1.62 thf(fact_1988_floor__divide__real__eq__div,axiom,
% 1.40/1.62 ! [B: int,A: real] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 1.40/1.62 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 1.40/1.62 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_divide_real_eq_div
% 1.40/1.62 thf(fact_1989_ln__powr__bound,axiom,
% 1.40/1.62 ! [X: real,A: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ one_one_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ln_powr_bound
% 1.40/1.62 thf(fact_1990_ln__powr__bound2,axiom,
% 1.40/1.62 ! [X: real,A: real] :
% 1.40/1.62 ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.62 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ln_powr_bound2
% 1.40/1.62 thf(fact_1991_add__log__eq__powr,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ B )
% 1.40/1.62 => ( ( B != one_one_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( plus_plus_real @ Y2 @ ( log @ B @ X ) )
% 1.40/1.62 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % add_log_eq_powr
% 1.40/1.62 thf(fact_1992_log__add__eq__powr,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ B )
% 1.40/1.62 => ( ( B != one_one_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y2 )
% 1.40/1.62 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y2 ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_add_eq_powr
% 1.40/1.62 thf(fact_1993_minus__log__eq__powr,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ B )
% 1.40/1.62 => ( ( B != one_one_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( minus_minus_real @ Y2 @ ( log @ B @ X ) )
% 1.40/1.62 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y2 ) @ X ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % minus_log_eq_powr
% 1.40/1.62 thf(fact_1994_log__minus__eq__powr,axiom,
% 1.40/1.62 ! [B: real,X: real,Y2: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ B )
% 1.40/1.62 => ( ( B != one_one_real )
% 1.40/1.62 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y2 )
% 1.40/1.62 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y2 ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % log_minus_eq_powr
% 1.40/1.62 thf(fact_1995_powr__half__sqrt,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.62 = ( sqrt @ X ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_half_sqrt
% 1.40/1.62 thf(fact_1996_powr__neg__numeral,axiom,
% 1.40/1.62 ! [X: real,N: num] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 1.40/1.62 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_neg_numeral
% 1.40/1.62 thf(fact_1997_cosh__ln__real,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 1.40/1.62 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % cosh_ln_real
% 1.40/1.62 thf(fact_1998_floor__log2__div2,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.62 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 1.40/1.62 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_log2_div2
% 1.40/1.62 thf(fact_1999_floor__log__nat__eq__if,axiom,
% 1.40/1.62 ! [B: nat,N: nat,K: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 1.40/1.62 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 1.40/1.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 1.40/1.62 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 1.40/1.62 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_log_nat_eq_if
% 1.40/1.62 thf(fact_2000_bij__betw__roots__unity,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.62 => ( bij_betw_nat_complex
% 1.40/1.62 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 1.40/1.62 @ ( set_ord_lessThan_nat @ N )
% 1.40/1.62 @ ( collect_complex
% 1.40/1.62 @ ^ [Z5: complex] :
% 1.40/1.62 ( ( power_power_complex @ Z5 @ N )
% 1.40/1.62 = one_one_complex ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bij_betw_roots_unity
% 1.40/1.62 thf(fact_2001_exp__pi__i_H,axiom,
% 1.40/1.62 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 1.40/1.62 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 1.40/1.62
% 1.40/1.62 % exp_pi_i'
% 1.40/1.62 thf(fact_2002_exp__pi__i,axiom,
% 1.40/1.62 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 1.40/1.62 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 1.40/1.62
% 1.40/1.62 % exp_pi_i
% 1.40/1.62 thf(fact_2003_exp__two__pi__i_H,axiom,
% 1.40/1.62 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 1.40/1.62 = one_one_complex ) ).
% 1.40/1.62
% 1.40/1.62 % exp_two_pi_i'
% 1.40/1.62 thf(fact_2004_exp__two__pi__i,axiom,
% 1.40/1.62 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 1.40/1.62 = one_one_complex ) ).
% 1.40/1.62
% 1.40/1.62 % exp_two_pi_i
% 1.40/1.62 thf(fact_2005_complex__exp__exists,axiom,
% 1.40/1.62 ! [Z: complex] :
% 1.40/1.62 ? [A5: complex,R3: real] :
% 1.40/1.62 ( Z
% 1.40/1.62 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( exp_complex @ A5 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % complex_exp_exists
% 1.40/1.62 thf(fact_2006_complex__of__real__mult__Complex,axiom,
% 1.40/1.62 ! [R2: real,X: real,Y2: real] :
% 1.40/1.62 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y2 ) )
% 1.40/1.62 = ( complex2 @ ( times_times_real @ R2 @ X ) @ ( times_times_real @ R2 @ Y2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % complex_of_real_mult_Complex
% 1.40/1.62 thf(fact_2007_Complex__mult__complex__of__real,axiom,
% 1.40/1.62 ! [X: real,Y2: real,R2: real] :
% 1.40/1.62 ( ( times_times_complex @ ( complex2 @ X @ Y2 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 1.40/1.62 = ( complex2 @ ( times_times_real @ X @ R2 ) @ ( times_times_real @ Y2 @ R2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Complex_mult_complex_of_real
% 1.40/1.62 thf(fact_2008_Complex__add__complex__of__real,axiom,
% 1.40/1.62 ! [X: real,Y2: real,R2: real] :
% 1.40/1.62 ( ( plus_plus_complex @ ( complex2 @ X @ Y2 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 1.40/1.62 = ( complex2 @ ( plus_plus_real @ X @ R2 ) @ Y2 ) ) ).
% 1.40/1.62
% 1.40/1.62 % Complex_add_complex_of_real
% 1.40/1.62 thf(fact_2009_complex__of__real__add__Complex,axiom,
% 1.40/1.62 ! [R2: real,X: real,Y2: real] :
% 1.40/1.62 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y2 ) )
% 1.40/1.62 = ( complex2 @ ( plus_plus_real @ R2 @ X ) @ Y2 ) ) ).
% 1.40/1.62
% 1.40/1.62 % complex_of_real_add_Complex
% 1.40/1.62 thf(fact_2010_cis__conv__exp,axiom,
% 1.40/1.62 ( cis
% 1.40/1.62 = ( ^ [B4: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % cis_conv_exp
% 1.40/1.62 thf(fact_2011_complex__of__real__i,axiom,
% 1.40/1.62 ! [R2: real] :
% 1.40/1.62 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 1.40/1.62 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 1.40/1.62
% 1.40/1.62 % complex_of_real_i
% 1.40/1.62 thf(fact_2012_i__complex__of__real,axiom,
% 1.40/1.62 ! [R2: real] :
% 1.40/1.62 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 1.40/1.62 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 1.40/1.62
% 1.40/1.62 % i_complex_of_real
% 1.40/1.62 thf(fact_2013_Complex__eq,axiom,
% 1.40/1.62 ( complex2
% 1.40/1.62 = ( ^ [A4: real,B4: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A4 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Complex_eq
% 1.40/1.62 thf(fact_2014_complex__split__polar,axiom,
% 1.40/1.62 ! [Z: complex] :
% 1.40/1.62 ? [R3: real,A5: real] :
% 1.40/1.62 ( Z
% 1.40/1.62 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A5 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A5 ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % complex_split_polar
% 1.40/1.62 thf(fact_2015_cmod__unit__one,axiom,
% 1.40/1.62 ! [A: real] :
% 1.40/1.62 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 1.40/1.62 = one_one_real ) ).
% 1.40/1.62
% 1.40/1.62 % cmod_unit_one
% 1.40/1.62 thf(fact_2016_cmod__complex__polar,axiom,
% 1.40/1.62 ! [R2: real,A: real] :
% 1.40/1.62 ( ( 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 ) ) ) ) ) )
% 1.40/1.62 = ( abs_abs_real @ R2 ) ) ).
% 1.40/1.62
% 1.40/1.62 % cmod_complex_polar
% 1.40/1.62 thf(fact_2017_csqrt__ii,axiom,
% 1.40/1.62 ( ( csqrt @ imaginary_unit )
% 1.40/1.62 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % csqrt_ii
% 1.40/1.62 thf(fact_2018_arctan__def,axiom,
% 1.40/1.62 ( arctan
% 1.40/1.62 = ( ^ [Y4: real] :
% 1.40/1.62 ( the_real
% 1.40/1.62 @ ^ [X4: real] :
% 1.40/1.62 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 1.40/1.62 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.62 & ( ( tan_real @ X4 )
% 1.40/1.62 = Y4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % arctan_def
% 1.40/1.62 thf(fact_2019_arcsin__def,axiom,
% 1.40/1.62 ( arcsin
% 1.40/1.62 = ( ^ [Y4: real] :
% 1.40/1.62 ( the_real
% 1.40/1.62 @ ^ [X4: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 1.40/1.62 & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.62 & ( ( sin_real @ X4 )
% 1.40/1.62 = Y4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % arcsin_def
% 1.40/1.62 thf(fact_2020_modulo__int__unfold,axiom,
% 1.40/1.62 ! [L2: int,K: int,N: nat,M: nat] :
% 1.40/1.62 ( ( ( ( ( sgn_sgn_int @ L2 )
% 1.40/1.62 = zero_zero_int )
% 1.40/1.62 | ( ( sgn_sgn_int @ K )
% 1.40/1.62 = zero_zero_int )
% 1.40/1.62 | ( N = zero_zero_nat ) )
% 1.40/1.62 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 1.40/1.62 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 1.40/1.62 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 1.40/1.62 = zero_zero_int )
% 1.40/1.62 | ( ( sgn_sgn_int @ K )
% 1.40/1.62 = zero_zero_int )
% 1.40/1.62 | ( N = zero_zero_nat ) )
% 1.40/1.62 => ( ( ( ( sgn_sgn_int @ K )
% 1.40/1.62 = ( sgn_sgn_int @ L2 ) )
% 1.40/1.62 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 1.40/1.62 = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 1.40/1.62 & ( ( ( sgn_sgn_int @ K )
% 1.40/1.62 != ( sgn_sgn_int @ L2 ) )
% 1.40/1.62 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 1.40/1.62 = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 1.40/1.62 @ ( minus_minus_int
% 1.40/1.62 @ ( semiri1314217659103216013at_int
% 1.40/1.62 @ ( times_times_nat @ N
% 1.40/1.62 @ ( zero_n2687167440665602831ol_nat
% 1.40/1.62 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 1.40/1.62 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % modulo_int_unfold
% 1.40/1.62 thf(fact_2021_csqrt__1,axiom,
% 1.40/1.62 ( ( csqrt @ one_one_complex )
% 1.40/1.62 = one_one_complex ) ).
% 1.40/1.62
% 1.40/1.62 % csqrt_1
% 1.40/1.62 thf(fact_2022_csqrt__eq__1,axiom,
% 1.40/1.62 ! [Z: complex] :
% 1.40/1.62 ( ( ( csqrt @ Z )
% 1.40/1.62 = one_one_complex )
% 1.40/1.62 = ( Z = one_one_complex ) ) ).
% 1.40/1.62
% 1.40/1.62 % csqrt_eq_1
% 1.40/1.62 thf(fact_2023_sgn__mult__dvd__iff,axiom,
% 1.40/1.62 ! [R2: int,L2: int,K: int] :
% 1.40/1.62 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L2 ) @ K )
% 1.40/1.62 = ( ( dvd_dvd_int @ L2 @ K )
% 1.40/1.62 & ( ( R2 = zero_zero_int )
% 1.40/1.62 => ( K = zero_zero_int ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % sgn_mult_dvd_iff
% 1.40/1.62 thf(fact_2024_mult__sgn__dvd__iff,axiom,
% 1.40/1.62 ! [L2: int,R2: int,K: int] :
% 1.40/1.62 ( ( dvd_dvd_int @ ( times_times_int @ L2 @ ( sgn_sgn_int @ R2 ) ) @ K )
% 1.40/1.62 = ( ( dvd_dvd_int @ L2 @ K )
% 1.40/1.62 & ( ( R2 = zero_zero_int )
% 1.40/1.62 => ( K = zero_zero_int ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % mult_sgn_dvd_iff
% 1.40/1.62 thf(fact_2025_dvd__sgn__mult__iff,axiom,
% 1.40/1.62 ! [L2: int,R2: int,K: int] :
% 1.40/1.62 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 1.40/1.62 = ( ( dvd_dvd_int @ L2 @ K )
% 1.40/1.62 | ( R2 = zero_zero_int ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % dvd_sgn_mult_iff
% 1.40/1.62 thf(fact_2026_dvd__mult__sgn__iff,axiom,
% 1.40/1.62 ! [L2: int,K: int,R2: int] :
% 1.40/1.62 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 1.40/1.62 = ( ( dvd_dvd_int @ L2 @ K )
% 1.40/1.62 | ( R2 = zero_zero_int ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % dvd_mult_sgn_iff
% 1.40/1.62 thf(fact_2027_power2__csqrt,axiom,
% 1.40/1.62 ! [Z: complex] :
% 1.40/1.62 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.62 = Z ) ).
% 1.40/1.62
% 1.40/1.62 % power2_csqrt
% 1.40/1.62 thf(fact_2028_int__sgnE,axiom,
% 1.40/1.62 ! [K: int] :
% 1.40/1.62 ~ ! [N4: nat,L3: int] :
% 1.40/1.62 ( K
% 1.40/1.62 != ( times_times_int @ ( sgn_sgn_int @ L3 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % int_sgnE
% 1.40/1.62 thf(fact_2029_sgn__mod,axiom,
% 1.40/1.62 ! [L2: int,K: int] :
% 1.40/1.62 ( ( L2 != zero_zero_int )
% 1.40/1.62 => ( ~ ( dvd_dvd_int @ L2 @ K )
% 1.40/1.62 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 1.40/1.62 = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % sgn_mod
% 1.40/1.62 thf(fact_2030_ln__neg__is__const,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 1.40/1.62 => ( ( ln_ln_real @ X )
% 1.40/1.62 = ( the_real
% 1.40/1.62 @ ^ [X4: real] : $false ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ln_neg_is_const
% 1.40/1.62 thf(fact_2031_zsgn__def,axiom,
% 1.40/1.62 ( sgn_sgn_int
% 1.40/1.62 = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % zsgn_def
% 1.40/1.62 thf(fact_2032_div__sgn__abs__cancel,axiom,
% 1.40/1.62 ! [V: int,K: int,L2: int] :
% 1.40/1.62 ( ( V != zero_zero_int )
% 1.40/1.62 => ( ( 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 ) ) )
% 1.40/1.62 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % div_sgn_abs_cancel
% 1.40/1.62 thf(fact_2033_div__dvd__sgn__abs,axiom,
% 1.40/1.62 ! [L2: int,K: int] :
% 1.40/1.62 ( ( dvd_dvd_int @ L2 @ K )
% 1.40/1.62 => ( ( divide_divide_int @ K @ L2 )
% 1.40/1.62 = ( 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 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % div_dvd_sgn_abs
% 1.40/1.62 thf(fact_2034_of__real__sqrt,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 1.40/1.62 = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % of_real_sqrt
% 1.40/1.62 thf(fact_2035_arccos__def,axiom,
% 1.40/1.62 ( arccos
% 1.40/1.62 = ( ^ [Y4: real] :
% 1.40/1.62 ( the_real
% 1.40/1.62 @ ^ [X4: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 1.40/1.62 & ( ord_less_eq_real @ X4 @ pi )
% 1.40/1.62 & ( ( cos_real @ X4 )
% 1.40/1.62 = Y4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % arccos_def
% 1.40/1.62 thf(fact_2036_eucl__rel__int__remainderI,axiom,
% 1.40/1.62 ! [R2: int,L2: int,K: int,Q2: int] :
% 1.40/1.62 ( ( ( sgn_sgn_int @ R2 )
% 1.40/1.62 = ( sgn_sgn_int @ L2 ) )
% 1.40/1.62 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L2 ) )
% 1.40/1.62 => ( ( K
% 1.40/1.62 = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R2 ) )
% 1.40/1.62 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % eucl_rel_int_remainderI
% 1.40/1.62 thf(fact_2037_eucl__rel__int_Ocases,axiom,
% 1.40/1.62 ! [A1: int,A22: int,A32: product_prod_int_int] :
% 1.40/1.62 ( ( eucl_rel_int @ A1 @ A22 @ A32 )
% 1.40/1.62 => ( ( ( A22 = zero_zero_int )
% 1.40/1.62 => ( A32
% 1.40/1.62 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 1.40/1.62 => ( ! [Q3: int] :
% 1.40/1.62 ( ( A32
% 1.40/1.62 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 1.40/1.62 => ( ( A22 != zero_zero_int )
% 1.40/1.62 => ( A1
% 1.40/1.62 != ( times_times_int @ Q3 @ A22 ) ) ) )
% 1.40/1.62 => ~ ! [R3: int,Q3: int] :
% 1.40/1.62 ( ( A32
% 1.40/1.62 = ( product_Pair_int_int @ Q3 @ R3 ) )
% 1.40/1.62 => ( ( ( sgn_sgn_int @ R3 )
% 1.40/1.62 = ( sgn_sgn_int @ A22 ) )
% 1.40/1.62 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A22 ) )
% 1.40/1.62 => ( A1
% 1.40/1.62 != ( plus_plus_int @ ( times_times_int @ Q3 @ A22 ) @ R3 ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % eucl_rel_int.cases
% 1.40/1.62 thf(fact_2038_eucl__rel__int_Osimps,axiom,
% 1.40/1.62 ( eucl_rel_int
% 1.40/1.62 = ( ^ [A12: int,A23: int,A33: product_prod_int_int] :
% 1.40/1.62 ( ? [K3: int] :
% 1.40/1.62 ( ( A12 = K3 )
% 1.40/1.62 & ( A23 = zero_zero_int )
% 1.40/1.62 & ( A33
% 1.40/1.62 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 1.40/1.62 | ? [L: int,K3: int,Q4: int] :
% 1.40/1.62 ( ( A12 = K3 )
% 1.40/1.62 & ( A23 = L )
% 1.40/1.62 & ( A33
% 1.40/1.62 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 1.40/1.62 & ( L != zero_zero_int )
% 1.40/1.62 & ( K3
% 1.40/1.62 = ( times_times_int @ Q4 @ L ) ) )
% 1.40/1.62 | ? [R5: int,L: int,K3: int,Q4: int] :
% 1.40/1.62 ( ( A12 = K3 )
% 1.40/1.62 & ( A23 = L )
% 1.40/1.62 & ( A33
% 1.40/1.62 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 1.40/1.62 & ( ( sgn_sgn_int @ R5 )
% 1.40/1.62 = ( sgn_sgn_int @ L ) )
% 1.40/1.62 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 1.40/1.62 & ( K3
% 1.40/1.62 = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R5 ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % eucl_rel_int.simps
% 1.40/1.62 thf(fact_2039_pi__half,axiom,
% 1.40/1.62 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.62 = ( the_real
% 1.40/1.62 @ ^ [X4: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 1.40/1.62 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.62 & ( ( cos_real @ X4 )
% 1.40/1.62 = zero_zero_real ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % pi_half
% 1.40/1.62 thf(fact_2040_pi__def,axiom,
% 1.40/1.62 ( pi
% 1.40/1.62 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 1.40/1.62 @ ( the_real
% 1.40/1.62 @ ^ [X4: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 1.40/1.62 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 1.40/1.62 & ( ( cos_real @ X4 )
% 1.40/1.62 = zero_zero_real ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % pi_def
% 1.40/1.62 thf(fact_2041_divide__int__unfold,axiom,
% 1.40/1.62 ! [L2: int,K: int,N: nat,M: nat] :
% 1.40/1.62 ( ( ( ( ( sgn_sgn_int @ L2 )
% 1.40/1.62 = zero_zero_int )
% 1.40/1.62 | ( ( sgn_sgn_int @ K )
% 1.40/1.62 = zero_zero_int )
% 1.40/1.62 | ( N = zero_zero_nat ) )
% 1.40/1.62 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 1.40/1.62 = zero_zero_int ) )
% 1.40/1.62 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 1.40/1.62 = zero_zero_int )
% 1.40/1.62 | ( ( sgn_sgn_int @ K )
% 1.40/1.62 = zero_zero_int )
% 1.40/1.62 | ( N = zero_zero_nat ) )
% 1.40/1.62 => ( ( ( ( sgn_sgn_int @ K )
% 1.40/1.62 = ( sgn_sgn_int @ L2 ) )
% 1.40/1.62 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 1.40/1.62 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 1.40/1.62 & ( ( ( sgn_sgn_int @ K )
% 1.40/1.62 != ( sgn_sgn_int @ L2 ) )
% 1.40/1.62 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 1.40/1.62 = ( uminus_uminus_int
% 1.40/1.62 @ ( semiri1314217659103216013at_int
% 1.40/1.62 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 1.40/1.62 @ ( zero_n2687167440665602831ol_nat
% 1.40/1.62 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % divide_int_unfold
% 1.40/1.62 thf(fact_2042_modulo__int__def,axiom,
% 1.40/1.62 ( modulo_modulo_int
% 1.40/1.62 = ( ^ [K3: int,L: int] :
% 1.40/1.62 ( if_int @ ( L = zero_zero_int ) @ K3
% 1.40/1.62 @ ( if_int
% 1.40/1.62 @ ( ( sgn_sgn_int @ K3 )
% 1.40/1.62 = ( sgn_sgn_int @ L ) )
% 1.40/1.62 @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 1.40/1.62 @ ( times_times_int @ ( sgn_sgn_int @ L )
% 1.40/1.62 @ ( minus_minus_int
% 1.40/1.62 @ ( times_times_int @ ( abs_abs_int @ L )
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ~ ( dvd_dvd_int @ L @ K3 ) ) )
% 1.40/1.62 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % modulo_int_def
% 1.40/1.62 thf(fact_2043_divide__int__def,axiom,
% 1.40/1.62 ( divide_divide_int
% 1.40/1.62 = ( ^ [K3: int,L: int] :
% 1.40/1.62 ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 1.40/1.62 @ ( if_int
% 1.40/1.62 @ ( ( sgn_sgn_int @ K3 )
% 1.40/1.62 = ( sgn_sgn_int @ L ) )
% 1.40/1.62 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 1.40/1.62 @ ( uminus_uminus_int
% 1.40/1.62 @ ( semiri1314217659103216013at_int
% 1.40/1.62 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 1.40/1.62 @ ( zero_n2687167440665602831ol_nat
% 1.40/1.62 @ ~ ( dvd_dvd_int @ L @ K3 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % divide_int_def
% 1.40/1.62 thf(fact_2044_num_Osize__gen_I3_J,axiom,
% 1.40/1.62 ! [X32: num] :
% 1.40/1.62 ( ( size_num @ ( bit1 @ X32 ) )
% 1.40/1.62 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % num.size_gen(3)
% 1.40/1.62 thf(fact_2045_powr__int,axiom,
% 1.40/1.62 ! [X: real,I2: int] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 1.40/1.62 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 1.40/1.62 = ( power_power_real @ X @ ( nat2 @ I2 ) ) ) )
% 1.40/1.62 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 1.40/1.62 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I2 ) )
% 1.40/1.62 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_int
% 1.40/1.62 thf(fact_2046_sgn__le__0__iff,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 1.40/1.62 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 1.40/1.62
% 1.40/1.62 % sgn_le_0_iff
% 1.40/1.62 thf(fact_2047_zero__le__sgn__iff,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 1.40/1.62 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % zero_le_sgn_iff
% 1.40/1.62 thf(fact_2048_nat__numeral,axiom,
% 1.40/1.62 ! [K: num] :
% 1.40/1.62 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 1.40/1.62 = ( numeral_numeral_nat @ K ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_numeral
% 1.40/1.62 thf(fact_2049_nat__1,axiom,
% 1.40/1.62 ( ( nat2 @ one_one_int )
% 1.40/1.62 = ( suc @ zero_zero_nat ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_1
% 1.40/1.62 thf(fact_2050_nat__le__0,axiom,
% 1.40/1.62 ! [Z: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 1.40/1.62 => ( ( nat2 @ Z )
% 1.40/1.62 = zero_zero_nat ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_le_0
% 1.40/1.62 thf(fact_2051_nat__0__iff,axiom,
% 1.40/1.62 ! [I2: int] :
% 1.40/1.62 ( ( ( nat2 @ I2 )
% 1.40/1.62 = zero_zero_nat )
% 1.40/1.62 = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_0_iff
% 1.40/1.62 thf(fact_2052_zless__nat__conj,axiom,
% 1.40/1.62 ! [W: int,Z: int] :
% 1.40/1.62 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 1.40/1.62 = ( ( ord_less_int @ zero_zero_int @ Z )
% 1.40/1.62 & ( ord_less_int @ W @ Z ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % zless_nat_conj
% 1.40/1.62 thf(fact_2053_nat__neg__numeral,axiom,
% 1.40/1.62 ! [K: num] :
% 1.40/1.62 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 1.40/1.62 = zero_zero_nat ) ).
% 1.40/1.62
% 1.40/1.62 % nat_neg_numeral
% 1.40/1.62 thf(fact_2054_int__nat__eq,axiom,
% 1.40/1.62 ! [Z: int] :
% 1.40/1.62 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 1.40/1.62 = Z ) )
% 1.40/1.62 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 1.40/1.62 = zero_zero_int ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % int_nat_eq
% 1.40/1.62 thf(fact_2055_zero__less__nat__eq,axiom,
% 1.40/1.62 ! [Z: int] :
% 1.40/1.62 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 1.40/1.62 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 1.40/1.62
% 1.40/1.62 % zero_less_nat_eq
% 1.40/1.62 thf(fact_2056_diff__nat__numeral,axiom,
% 1.40/1.62 ! [V: num,V3: num] :
% 1.40/1.62 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 1.40/1.62 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % diff_nat_numeral
% 1.40/1.62 thf(fact_2057_numeral__power__eq__nat__cancel__iff,axiom,
% 1.40/1.62 ! [X: num,N: nat,Y2: int] :
% 1.40/1.62 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 1.40/1.62 = ( nat2 @ Y2 ) )
% 1.40/1.62 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 1.40/1.62 = Y2 ) ) ).
% 1.40/1.62
% 1.40/1.62 % numeral_power_eq_nat_cancel_iff
% 1.40/1.62 thf(fact_2058_nat__eq__numeral__power__cancel__iff,axiom,
% 1.40/1.62 ! [Y2: int,X: num,N: nat] :
% 1.40/1.62 ( ( ( nat2 @ Y2 )
% 1.40/1.62 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 1.40/1.62 = ( Y2
% 1.40/1.62 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_eq_numeral_power_cancel_iff
% 1.40/1.62 thf(fact_2059_nat__ceiling__le__eq,axiom,
% 1.40/1.62 ! [X: real,A: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 1.40/1.62 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_ceiling_le_eq
% 1.40/1.62 thf(fact_2060_one__less__nat__eq,axiom,
% 1.40/1.62 ! [Z: int] :
% 1.40/1.62 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 1.40/1.62 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 1.40/1.62
% 1.40/1.62 % one_less_nat_eq
% 1.40/1.62 thf(fact_2061_nat__numeral__diff__1,axiom,
% 1.40/1.62 ! [V: num] :
% 1.40/1.62 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 1.40/1.62 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_numeral_diff_1
% 1.40/1.62 thf(fact_2062_numeral__power__less__nat__cancel__iff,axiom,
% 1.40/1.62 ! [X: num,N: nat,A: int] :
% 1.40/1.62 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 1.40/1.62 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 1.40/1.62
% 1.40/1.62 % numeral_power_less_nat_cancel_iff
% 1.40/1.62 thf(fact_2063_nat__less__numeral__power__cancel__iff,axiom,
% 1.40/1.62 ! [A: int,X: num,N: nat] :
% 1.40/1.62 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 1.40/1.62 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_less_numeral_power_cancel_iff
% 1.40/1.62 thf(fact_2064_numeral__power__le__nat__cancel__iff,axiom,
% 1.40/1.62 ! [X: num,N: nat,A: int] :
% 1.40/1.62 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 1.40/1.62 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 1.40/1.62
% 1.40/1.62 % numeral_power_le_nat_cancel_iff
% 1.40/1.62 thf(fact_2065_nat__le__numeral__power__cancel__iff,axiom,
% 1.40/1.62 ! [A: int,X: num,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 1.40/1.62 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_le_numeral_power_cancel_iff
% 1.40/1.62 thf(fact_2066_nat__numeral__as__int,axiom,
% 1.40/1.62 ( numeral_numeral_nat
% 1.40/1.62 = ( ^ [I4: num] : ( nat2 @ ( numeral_numeral_int @ I4 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_numeral_as_int
% 1.40/1.62 thf(fact_2067_nat__mono,axiom,
% 1.40/1.62 ! [X: int,Y2: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ X @ Y2 )
% 1.40/1.62 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_mono
% 1.40/1.62 thf(fact_2068_eq__nat__nat__iff,axiom,
% 1.40/1.62 ! [Z: int,Z6: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 1.40/1.62 => ( ( ( nat2 @ Z )
% 1.40/1.62 = ( nat2 @ Z6 ) )
% 1.40/1.62 = ( Z = Z6 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % eq_nat_nat_iff
% 1.40/1.62 thf(fact_2069_all__nat,axiom,
% 1.40/1.62 ( ( ^ [P4: nat > $o] :
% 1.40/1.62 ! [X7: nat] : ( P4 @ X7 ) )
% 1.40/1.62 = ( ^ [P5: nat > $o] :
% 1.40/1.62 ! [X4: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 1.40/1.62 => ( P5 @ ( nat2 @ X4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % all_nat
% 1.40/1.62 thf(fact_2070_ex__nat,axiom,
% 1.40/1.62 ( ( ^ [P4: nat > $o] :
% 1.40/1.62 ? [X7: nat] : ( P4 @ X7 ) )
% 1.40/1.62 = ( ^ [P5: nat > $o] :
% 1.40/1.62 ? [X4: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 1.40/1.62 & ( P5 @ ( nat2 @ X4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % ex_nat
% 1.40/1.62 thf(fact_2071_nat__one__as__int,axiom,
% 1.40/1.62 ( one_one_nat
% 1.40/1.62 = ( nat2 @ one_one_int ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_one_as_int
% 1.40/1.62 thf(fact_2072_unset__bit__nat__def,axiom,
% 1.40/1.62 ( bit_se4205575877204974255it_nat
% 1.40/1.62 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % unset_bit_nat_def
% 1.40/1.62 thf(fact_2073_nat__mask__eq,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 1.40/1.62 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_mask_eq
% 1.40/1.62 thf(fact_2074_nat__mono__iff,axiom,
% 1.40/1.62 ! [Z: int,W: int] :
% 1.40/1.62 ( ( ord_less_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 1.40/1.62 = ( ord_less_int @ W @ Z ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_mono_iff
% 1.40/1.62 thf(fact_2075_zless__nat__eq__int__zless,axiom,
% 1.40/1.62 ! [M: nat,Z: int] :
% 1.40/1.62 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 1.40/1.62 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 1.40/1.62
% 1.40/1.62 % zless_nat_eq_int_zless
% 1.40/1.62 thf(fact_2076_nat__le__iff,axiom,
% 1.40/1.62 ! [X: int,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 1.40/1.62 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_le_iff
% 1.40/1.62 thf(fact_2077_nat__0__le,axiom,
% 1.40/1.62 ! [Z: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 1.40/1.62 = Z ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_0_le
% 1.40/1.62 thf(fact_2078_int__eq__iff,axiom,
% 1.40/1.62 ! [M: nat,Z: int] :
% 1.40/1.62 ( ( ( semiri1314217659103216013at_int @ M )
% 1.40/1.62 = Z )
% 1.40/1.62 = ( ( M
% 1.40/1.62 = ( nat2 @ Z ) )
% 1.40/1.62 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % int_eq_iff
% 1.40/1.62 thf(fact_2079_nat__int__add,axiom,
% 1.40/1.62 ! [A: nat,B: nat] :
% 1.40/1.62 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 1.40/1.62 = ( plus_plus_nat @ A @ B ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_int_add
% 1.40/1.62 thf(fact_2080_nat__abs__mult__distrib,axiom,
% 1.40/1.62 ! [W: int,Z: int] :
% 1.40/1.62 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 1.40/1.62 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_abs_mult_distrib
% 1.40/1.62 thf(fact_2081_nat__plus__as__int,axiom,
% 1.40/1.62 ( plus_plus_nat
% 1.40/1.62 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_plus_as_int
% 1.40/1.62 thf(fact_2082_or__nat__def,axiom,
% 1.40/1.62 ( bit_se1412395901928357646or_nat
% 1.40/1.62 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % or_nat_def
% 1.40/1.62 thf(fact_2083_nat__times__as__int,axiom,
% 1.40/1.62 ( times_times_nat
% 1.40/1.62 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_times_as_int
% 1.40/1.62 thf(fact_2084_real__nat__ceiling__ge,axiom,
% 1.40/1.62 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % real_nat_ceiling_ge
% 1.40/1.62 thf(fact_2085_nat__div__as__int,axiom,
% 1.40/1.62 ( divide_divide_nat
% 1.40/1.62 = ( ^ [A4: nat,B4: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_div_as_int
% 1.40/1.62 thf(fact_2086_sgn__real__def,axiom,
% 1.40/1.62 ( sgn_sgn_real
% 1.40/1.62 = ( ^ [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 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % sgn_real_def
% 1.40/1.62 thf(fact_2087_nat__less__eq__zless,axiom,
% 1.40/1.62 ! [W: int,Z: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 1.40/1.62 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 1.40/1.62 = ( ord_less_int @ W @ Z ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_less_eq_zless
% 1.40/1.62 thf(fact_2088_nat__le__eq__zle,axiom,
% 1.40/1.62 ! [W: int,Z: int] :
% 1.40/1.62 ( ( ( ord_less_int @ zero_zero_int @ W )
% 1.40/1.62 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 1.40/1.62 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 1.40/1.62 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_le_eq_zle
% 1.40/1.62 thf(fact_2089_nat__eq__iff2,axiom,
% 1.40/1.62 ! [M: nat,W: int] :
% 1.40/1.62 ( ( M
% 1.40/1.62 = ( nat2 @ W ) )
% 1.40/1.62 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 1.40/1.62 => ( W
% 1.40/1.62 = ( semiri1314217659103216013at_int @ M ) ) )
% 1.40/1.62 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 1.40/1.62 => ( M = zero_zero_nat ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_eq_iff2
% 1.40/1.62 thf(fact_2090_nat__eq__iff,axiom,
% 1.40/1.62 ! [W: int,M: nat] :
% 1.40/1.62 ( ( ( nat2 @ W )
% 1.40/1.62 = M )
% 1.40/1.62 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 1.40/1.62 => ( W
% 1.40/1.62 = ( semiri1314217659103216013at_int @ M ) ) )
% 1.40/1.62 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 1.40/1.62 => ( M = zero_zero_nat ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_eq_iff
% 1.40/1.62 thf(fact_2091_le__nat__iff,axiom,
% 1.40/1.62 ! [K: int,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.62 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 1.40/1.62 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % le_nat_iff
% 1.40/1.62 thf(fact_2092_nat__add__distrib,axiom,
% 1.40/1.62 ! [Z: int,Z6: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 1.40/1.62 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 1.40/1.62 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_add_distrib
% 1.40/1.62 thf(fact_2093_nat__mult__distrib,axiom,
% 1.40/1.62 ! [Z: int,Z6: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 1.40/1.62 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_mult_distrib
% 1.40/1.62 thf(fact_2094_Suc__as__int,axiom,
% 1.40/1.62 ( suc
% 1.40/1.62 = ( ^ [A4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ one_one_int ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Suc_as_int
% 1.40/1.62 thf(fact_2095_nat__diff__distrib,axiom,
% 1.40/1.62 ! [Z6: int,Z: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 1.40/1.62 => ( ( ord_less_eq_int @ Z6 @ Z )
% 1.40/1.62 => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 1.40/1.62 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_diff_distrib
% 1.40/1.62 thf(fact_2096_nat__diff__distrib_H,axiom,
% 1.40/1.62 ! [X: int,Y2: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.62 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.62 => ( ( nat2 @ ( minus_minus_int @ X @ Y2 ) )
% 1.40/1.62 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_diff_distrib'
% 1.40/1.62 thf(fact_2097_nat__abs__triangle__ineq,axiom,
% 1.40/1.62 ! [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 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_abs_triangle_ineq
% 1.40/1.62 thf(fact_2098_nat__div__distrib,axiom,
% 1.40/1.62 ! [X: int,Y2: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.62 => ( ( nat2 @ ( divide_divide_int @ X @ Y2 ) )
% 1.40/1.62 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_div_distrib
% 1.40/1.62 thf(fact_2099_nat__div__distrib_H,axiom,
% 1.40/1.62 ! [Y2: int,X: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.62 => ( ( nat2 @ ( divide_divide_int @ X @ Y2 ) )
% 1.40/1.62 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_div_distrib'
% 1.40/1.62 thf(fact_2100_nat__floor__neg,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 1.40/1.62 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 1.40/1.62 = zero_zero_nat ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_floor_neg
% 1.40/1.62 thf(fact_2101_nat__power__eq,axiom,
% 1.40/1.62 ! [Z: int,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 1.40/1.62 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_power_eq
% 1.40/1.62 thf(fact_2102_nat__mod__distrib,axiom,
% 1.40/1.62 ! [X: int,Y2: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.62 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.62 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y2 ) )
% 1.40/1.62 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_mod_distrib
% 1.40/1.62 thf(fact_2103_div__abs__eq__div__nat,axiom,
% 1.40/1.62 ! [K: int,L2: int] :
% 1.40/1.62 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 1.40/1.62 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % div_abs_eq_div_nat
% 1.40/1.62 thf(fact_2104_floor__eq3,axiom,
% 1.40/1.62 ! [N: nat,X: real] :
% 1.40/1.62 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 1.40/1.62 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 1.40/1.62 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 1.40/1.62 = N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_eq3
% 1.40/1.62 thf(fact_2105_le__nat__floor,axiom,
% 1.40/1.62 ! [X: nat,A: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 1.40/1.62 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % le_nat_floor
% 1.40/1.62 thf(fact_2106_nat__2,axiom,
% 1.40/1.62 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 1.40/1.62 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_2
% 1.40/1.62 thf(fact_2107_sgn__power__injE,axiom,
% 1.40/1.62 ! [A: real,N: nat,X: real,B: real] :
% 1.40/1.62 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 1.40/1.62 = X )
% 1.40/1.62 => ( ( X
% 1.40/1.62 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 1.40/1.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.62 => ( A = B ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % sgn_power_injE
% 1.40/1.62 thf(fact_2108_Suc__nat__eq__nat__zadd1,axiom,
% 1.40/1.62 ! [Z: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( ( suc @ ( nat2 @ Z ) )
% 1.40/1.62 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Suc_nat_eq_nat_zadd1
% 1.40/1.62 thf(fact_2109_nat__less__iff,axiom,
% 1.40/1.62 ! [W: int,M: nat] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 1.40/1.62 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 1.40/1.62 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_less_iff
% 1.40/1.62 thf(fact_2110_nat__mult__distrib__neg,axiom,
% 1.40/1.62 ! [Z: int,Z6: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 1.40/1.62 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 1.40/1.62 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_mult_distrib_neg
% 1.40/1.62 thf(fact_2111_nat__abs__int__diff,axiom,
% 1.40/1.62 ! [A: nat,B: nat] :
% 1.40/1.62 ( ( ( ord_less_eq_nat @ A @ B )
% 1.40/1.62 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 1.40/1.62 = ( minus_minus_nat @ B @ A ) ) )
% 1.40/1.62 & ( ~ ( ord_less_eq_nat @ A @ B )
% 1.40/1.62 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 1.40/1.62 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_abs_int_diff
% 1.40/1.62 thf(fact_2112_floor__eq4,axiom,
% 1.40/1.62 ! [N: nat,X: real] :
% 1.40/1.62 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 1.40/1.62 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 1.40/1.62 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 1.40/1.62 = N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % floor_eq4
% 1.40/1.62 thf(fact_2113_num_Osize__gen_I1_J,axiom,
% 1.40/1.62 ( ( size_num @ one )
% 1.40/1.62 = zero_zero_nat ) ).
% 1.40/1.62
% 1.40/1.62 % num.size_gen(1)
% 1.40/1.62 thf(fact_2114_nat__dvd__iff,axiom,
% 1.40/1.62 ! [Z: int,M: nat] :
% 1.40/1.62 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 1.40/1.62 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 1.40/1.62 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 1.40/1.62 => ( M = zero_zero_nat ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_dvd_iff
% 1.40/1.62 thf(fact_2115_cis__Arg__unique,axiom,
% 1.40/1.62 ! [Z: complex,X: real] :
% 1.40/1.62 ( ( ( sgn_sgn_complex @ Z )
% 1.40/1.62 = ( cis @ X ) )
% 1.40/1.62 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 1.40/1.62 => ( ( ord_less_eq_real @ X @ pi )
% 1.40/1.62 => ( ( arg @ Z )
% 1.40/1.62 = X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % cis_Arg_unique
% 1.40/1.62 thf(fact_2116_Arg__correct,axiom,
% 1.40/1.62 ! [Z: complex] :
% 1.40/1.62 ( ( Z != zero_zero_complex )
% 1.40/1.62 => ( ( ( sgn_sgn_complex @ Z )
% 1.40/1.62 = ( cis @ ( arg @ Z ) ) )
% 1.40/1.62 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 1.40/1.62 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Arg_correct
% 1.40/1.62 thf(fact_2117_even__nat__iff,axiom,
% 1.40/1.62 ! [K: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.62 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 1.40/1.62 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % even_nat_iff
% 1.40/1.62 thf(fact_2118_powr__real__of__int,axiom,
% 1.40/1.62 ! [X: real,N: int] :
% 1.40/1.62 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.62 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 1.40/1.62 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 1.40/1.62 = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 1.40/1.62 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 1.40/1.62 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 1.40/1.62 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % powr_real_of_int
% 1.40/1.62 thf(fact_2119_arctan__inverse,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( X != zero_zero_real )
% 1.40/1.62 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 1.40/1.62 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % arctan_inverse
% 1.40/1.62 thf(fact_2120_num_Osize__gen_I2_J,axiom,
% 1.40/1.62 ! [X23: num] :
% 1.40/1.62 ( ( size_num @ ( bit0 @ X23 ) )
% 1.40/1.62 = ( plus_plus_nat @ ( size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % num.size_gen(2)
% 1.40/1.62 thf(fact_2121_and__int__unfold,axiom,
% 1.40/1.62 ( bit_se725231765392027082nd_int
% 1.40/1.62 = ( ^ [K3: int,L: int] :
% 1.40/1.62 ( if_int
% 1.40/1.62 @ ( ( K3 = zero_zero_int )
% 1.40/1.62 | ( L = zero_zero_int ) )
% 1.40/1.62 @ zero_zero_int
% 1.40/1.62 @ ( if_int
% 1.40/1.62 @ ( K3
% 1.40/1.62 = ( uminus_uminus_int @ one_one_int ) )
% 1.40/1.62 @ L
% 1.40/1.62 @ ( if_int
% 1.40/1.62 @ ( L
% 1.40/1.62 = ( uminus_uminus_int @ one_one_int ) )
% 1.40/1.62 @ K3
% 1.40/1.62 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_int_unfold
% 1.40/1.62 thf(fact_2122_Arg__def,axiom,
% 1.40/1.62 ( arg
% 1.40/1.62 = ( ^ [Z5: complex] :
% 1.40/1.62 ( if_real @ ( Z5 = zero_zero_complex ) @ zero_zero_real
% 1.40/1.62 @ ( fChoice_real
% 1.40/1.62 @ ^ [A4: real] :
% 1.40/1.62 ( ( ( sgn_sgn_complex @ Z5 )
% 1.40/1.62 = ( cis @ A4 ) )
% 1.40/1.62 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 1.40/1.62 & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Arg_def
% 1.40/1.62 thf(fact_2123_buildup__gives__empty,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 1.40/1.62 = bot_bot_set_nat ) ).
% 1.40/1.62
% 1.40/1.62 % buildup_gives_empty
% 1.40/1.62 thf(fact_2124_concat__bit__of__zero__2,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 1.40/1.62 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 1.40/1.62
% 1.40/1.62 % concat_bit_of_zero_2
% 1.40/1.62 thf(fact_2125_and__nonnegative__int__iff,axiom,
% 1.40/1.62 ! [K: int,L2: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 1.40/1.62 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.62 | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_nonnegative_int_iff
% 1.40/1.62 thf(fact_2126_and__negative__int__iff,axiom,
% 1.40/1.62 ! [K: int,L2: int] :
% 1.40/1.62 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 1.40/1.62 = ( ( ord_less_int @ K @ zero_zero_int )
% 1.40/1.62 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_negative_int_iff
% 1.40/1.62 thf(fact_2127_take__bit__of__Suc__0,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 1.40/1.62 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_of_Suc_0
% 1.40/1.62 thf(fact_2128_and__minus__numerals_I2_J,axiom,
% 1.40/1.62 ! [N: num] :
% 1.40/1.62 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 1.40/1.62 = one_one_int ) ).
% 1.40/1.62
% 1.40/1.62 % and_minus_numerals(2)
% 1.40/1.62 thf(fact_2129_and__minus__numerals_I6_J,axiom,
% 1.40/1.62 ! [N: num] :
% 1.40/1.62 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 1.40/1.62 = one_one_int ) ).
% 1.40/1.62
% 1.40/1.62 % and_minus_numerals(6)
% 1.40/1.62 thf(fact_2130_and__minus__numerals_I5_J,axiom,
% 1.40/1.62 ! [N: num] :
% 1.40/1.62 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 1.40/1.62 = zero_zero_int ) ).
% 1.40/1.62
% 1.40/1.62 % and_minus_numerals(5)
% 1.40/1.62 thf(fact_2131_and__minus__numerals_I1_J,axiom,
% 1.40/1.62 ! [N: num] :
% 1.40/1.62 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 1.40/1.62 = zero_zero_int ) ).
% 1.40/1.62
% 1.40/1.62 % and_minus_numerals(1)
% 1.40/1.62 thf(fact_2132_nat__take__bit__eq,axiom,
% 1.40/1.62 ! [K: int,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.62 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 1.40/1.62 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % nat_take_bit_eq
% 1.40/1.62 thf(fact_2133_take__bit__nat__eq,axiom,
% 1.40/1.62 ! [K: int,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.62 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 1.40/1.62 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_nat_eq
% 1.40/1.62 thf(fact_2134_take__bit__tightened__less__eq__nat,axiom,
% 1.40/1.62 ! [M: nat,N: nat,Q2: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.62 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_tightened_less_eq_nat
% 1.40/1.62 thf(fact_2135_take__bit__nat__less__eq__self,axiom,
% 1.40/1.62 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_nat_less_eq_self
% 1.40/1.62 thf(fact_2136_take__bit__diff,axiom,
% 1.40/1.62 ! [N: nat,K: int,L2: int] :
% 1.40/1.62 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 1.40/1.62 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_diff
% 1.40/1.62 thf(fact_2137_take__bit__minus,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 1.40/1.62 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_minus
% 1.40/1.62 thf(fact_2138_take__bit__mult,axiom,
% 1.40/1.62 ! [N: nat,K: int,L2: int] :
% 1.40/1.62 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 1.40/1.62 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_mult
% 1.40/1.62 thf(fact_2139_concat__bit__take__bit__eq,axiom,
% 1.40/1.62 ! [N: nat,B: int] :
% 1.40/1.62 ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 1.40/1.62 = ( bit_concat_bit @ N @ B ) ) ).
% 1.40/1.62
% 1.40/1.62 % concat_bit_take_bit_eq
% 1.40/1.62 thf(fact_2140_concat__bit__eq__iff,axiom,
% 1.40/1.62 ! [N: nat,K: int,L2: int,R2: int,S: int] :
% 1.40/1.62 ( ( ( bit_concat_bit @ N @ K @ L2 )
% 1.40/1.62 = ( bit_concat_bit @ N @ R2 @ S ) )
% 1.40/1.62 = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 1.40/1.62 = ( bit_se2923211474154528505it_int @ N @ R2 ) )
% 1.40/1.62 & ( L2 = S ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % concat_bit_eq_iff
% 1.40/1.62 thf(fact_2141_AND__lower,axiom,
% 1.40/1.62 ! [X: int,Y2: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.62 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % AND_lower
% 1.40/1.62 thf(fact_2142_AND__upper1,axiom,
% 1.40/1.62 ! [X: int,Y2: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.62 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % AND_upper1
% 1.40/1.62 thf(fact_2143_AND__upper2,axiom,
% 1.40/1.62 ! [Y2: int,X: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.62 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Y2 ) ) ).
% 1.40/1.62
% 1.40/1.62 % AND_upper2
% 1.40/1.62 thf(fact_2144_AND__upper1_H,axiom,
% 1.40/1.62 ! [Y2: int,Z: int,Ya: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.62 => ( ( ord_less_eq_int @ Y2 @ Z )
% 1.40/1.62 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % AND_upper1'
% 1.40/1.62 thf(fact_2145_AND__upper2_H,axiom,
% 1.40/1.62 ! [Y2: int,Z: int,X: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.62 => ( ( ord_less_eq_int @ Y2 @ Z )
% 1.40/1.62 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Z ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % AND_upper2'
% 1.40/1.62 thf(fact_2146_take__bit__tightened__less__eq__int,axiom,
% 1.40/1.62 ! [M: nat,N: nat,K: int] :
% 1.40/1.62 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.62 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_tightened_less_eq_int
% 1.40/1.62 thf(fact_2147_take__bit__nonnegative,axiom,
% 1.40/1.62 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_nonnegative
% 1.40/1.62 thf(fact_2148_take__bit__int__less__eq__self__iff,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 1.40/1.62 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_int_less_eq_self_iff
% 1.40/1.62 thf(fact_2149_not__take__bit__negative,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 1.40/1.62
% 1.40/1.62 % not_take_bit_negative
% 1.40/1.62 thf(fact_2150_take__bit__int__greater__self__iff,axiom,
% 1.40/1.62 ! [K: int,N: nat] :
% 1.40/1.62 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 1.40/1.62 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_int_greater_self_iff
% 1.40/1.62 thf(fact_2151_plus__and__or,axiom,
% 1.40/1.62 ! [X: int,Y2: int] :
% 1.40/1.62 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ ( bit_se1409905431419307370or_int @ X @ Y2 ) )
% 1.40/1.62 = ( plus_plus_int @ X @ Y2 ) ) ).
% 1.40/1.62
% 1.40/1.62 % plus_and_or
% 1.40/1.62 thf(fact_2152_and__less__eq,axiom,
% 1.40/1.62 ! [L2: int,K: int] :
% 1.40/1.62 ( ( ord_less_int @ L2 @ zero_zero_int )
% 1.40/1.62 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_less_eq
% 1.40/1.62 thf(fact_2153_AND__upper1_H_H,axiom,
% 1.40/1.62 ! [Y2: int,Z: int,Ya: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.62 => ( ( ord_less_int @ Y2 @ Z )
% 1.40/1.62 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y2 @ Ya ) @ Z ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % AND_upper1''
% 1.40/1.62 thf(fact_2154_AND__upper2_H_H,axiom,
% 1.40/1.62 ! [Y2: int,Z: int,X: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.62 => ( ( ord_less_int @ Y2 @ Z )
% 1.40/1.62 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y2 ) @ Z ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % AND_upper2''
% 1.40/1.62 thf(fact_2155_take__bit__decr__eq,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 1.40/1.62 != zero_zero_int )
% 1.40/1.62 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 1.40/1.62 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_decr_eq
% 1.40/1.62 thf(fact_2156_even__and__iff__int,axiom,
% 1.40/1.62 ! [K: int,L2: int] :
% 1.40/1.62 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 1.40/1.62 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 1.40/1.62 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % even_and_iff_int
% 1.40/1.62 thf(fact_2157_take__bit__eq__mask__iff,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 1.40/1.62 = ( bit_se2000444600071755411sk_int @ N ) )
% 1.40/1.62 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 1.40/1.62 = zero_zero_int ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_eq_mask_iff
% 1.40/1.62 thf(fact_2158_take__bit__nat__eq__self,axiom,
% 1.40/1.62 ! [M: nat,N: nat] :
% 1.40/1.62 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.62 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 1.40/1.62 = M ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_nat_eq_self
% 1.40/1.62 thf(fact_2159_take__bit__nat__less__exp,axiom,
% 1.40/1.62 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_nat_less_exp
% 1.40/1.62 thf(fact_2160_take__bit__nat__eq__self__iff,axiom,
% 1.40/1.62 ! [N: nat,M: nat] :
% 1.40/1.62 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 1.40/1.62 = M )
% 1.40/1.62 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_nat_eq_self_iff
% 1.40/1.62 thf(fact_2161_take__bit__nat__def,axiom,
% 1.40/1.62 ( bit_se2925701944663578781it_nat
% 1.40/1.62 = ( ^ [N2: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_nat_def
% 1.40/1.62 thf(fact_2162_take__bit__int__less__exp,axiom,
% 1.40/1.62 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_int_less_exp
% 1.40/1.62 thf(fact_2163_take__bit__int__def,axiom,
% 1.40/1.62 ( bit_se2923211474154528505it_int
% 1.40/1.62 = ( ^ [N2: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_int_def
% 1.40/1.62 thf(fact_2164_take__bit__nat__less__self__iff,axiom,
% 1.40/1.62 ! [N: nat,M: nat] :
% 1.40/1.62 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 1.40/1.62 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_nat_less_self_iff
% 1.40/1.62 thf(fact_2165_take__bit__Suc__minus__bit0,axiom,
% 1.40/1.62 ! [N: nat,K: num] :
% 1.40/1.62 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 1.40/1.62 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_Suc_minus_bit0
% 1.40/1.62 thf(fact_2166_take__bit__int__greater__eq__self__iff,axiom,
% 1.40/1.62 ! [K: int,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 1.40/1.62 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_int_greater_eq_self_iff
% 1.40/1.62 thf(fact_2167_take__bit__int__less__self__iff,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 1.40/1.62 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_int_less_self_iff
% 1.40/1.62 thf(fact_2168_take__bit__int__eq__self__iff,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 1.40/1.62 = K )
% 1.40/1.62 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.62 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_int_eq_self_iff
% 1.40/1.62 thf(fact_2169_take__bit__int__eq__self,axiom,
% 1.40/1.62 ! [K: int,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.62 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.62 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 1.40/1.62 = K ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_int_eq_self
% 1.40/1.62 thf(fact_2170_take__bit__numeral__minus__bit0,axiom,
% 1.40/1.62 ! [L2: num,K: num] :
% 1.40/1.62 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 1.40/1.62 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_numeral_minus_bit0
% 1.40/1.62 thf(fact_2171_take__bit__incr__eq,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 1.40/1.62 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 1.40/1.62 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 1.40/1.62 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_incr_eq
% 1.40/1.62 thf(fact_2172_take__bit__int__less__eq,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 1.40/1.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.62 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_int_less_eq
% 1.40/1.62 thf(fact_2173_take__bit__int__greater__eq,axiom,
% 1.40/1.62 ! [K: int,N: nat] :
% 1.40/1.62 ( ( ord_less_int @ K @ zero_zero_int )
% 1.40/1.62 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_int_greater_eq
% 1.40/1.62 thf(fact_2174_signed__take__bit__eq__take__bit__shift,axiom,
% 1.40/1.62 ( bit_ri631733984087533419it_int
% 1.40/1.62 = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % signed_take_bit_eq_take_bit_shift
% 1.40/1.62 thf(fact_2175_and__int__rec,axiom,
% 1.40/1.62 ( bit_se725231765392027082nd_int
% 1.40/1.62 = ( ^ [K3: int,L: int] :
% 1.40/1.62 ( plus_plus_int
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 1.40/1.62 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 1.40/1.62 @ ( 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 ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_int_rec
% 1.40/1.62 thf(fact_2176_take__bit__eq__mask__iff__exp__dvd,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 1.40/1.62 = ( bit_se2000444600071755411sk_int @ N ) )
% 1.40/1.62 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_eq_mask_iff_exp_dvd
% 1.40/1.62 thf(fact_2177_take__bit__minus__small__eq,axiom,
% 1.40/1.62 ! [K: int,N: nat] :
% 1.40/1.62 ( ( ord_less_int @ zero_zero_int @ K )
% 1.40/1.62 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.62 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 1.40/1.62 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_minus_small_eq
% 1.40/1.62 thf(fact_2178_take__bit__numeral__minus__bit1,axiom,
% 1.40/1.62 ! [L2: num,K: num] :
% 1.40/1.62 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 1.40/1.62 = ( 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 ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_numeral_minus_bit1
% 1.40/1.62 thf(fact_2179_take__bit__Suc__minus__bit1,axiom,
% 1.40/1.62 ! [N: nat,K: num] :
% 1.40/1.62 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 1.40/1.62 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_Suc_minus_bit1
% 1.40/1.62 thf(fact_2180_cis__multiple__2pi,axiom,
% 1.40/1.62 ! [N: real] :
% 1.40/1.62 ( ( member_real @ N @ ring_1_Ints_real )
% 1.40/1.62 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 1.40/1.62 = one_one_complex ) ) ).
% 1.40/1.62
% 1.40/1.62 % cis_multiple_2pi
% 1.40/1.62 thf(fact_2181_pred__numeral__inc,axiom,
% 1.40/1.62 ! [K: num] :
% 1.40/1.62 ( ( pred_numeral @ ( inc @ K ) )
% 1.40/1.62 = ( numeral_numeral_nat @ K ) ) ).
% 1.40/1.62
% 1.40/1.62 % pred_numeral_inc
% 1.40/1.62 thf(fact_2182_and__nat__numerals_I1_J,axiom,
% 1.40/1.62 ! [Y2: num] :
% 1.40/1.62 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 1.40/1.62 = zero_zero_nat ) ).
% 1.40/1.62
% 1.40/1.62 % and_nat_numerals(1)
% 1.40/1.62 thf(fact_2183_and__nat__numerals_I3_J,axiom,
% 1.40/1.62 ! [X: num] :
% 1.40/1.62 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 1.40/1.62 = zero_zero_nat ) ).
% 1.40/1.62
% 1.40/1.62 % and_nat_numerals(3)
% 1.40/1.62 thf(fact_2184_and__nat__numerals_I2_J,axiom,
% 1.40/1.62 ! [Y2: num] :
% 1.40/1.62 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 1.40/1.62 = one_one_nat ) ).
% 1.40/1.62
% 1.40/1.62 % and_nat_numerals(2)
% 1.40/1.62 thf(fact_2185_and__nat__numerals_I4_J,axiom,
% 1.40/1.62 ! [X: num] :
% 1.40/1.62 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 1.40/1.62 = one_one_nat ) ).
% 1.40/1.62
% 1.40/1.62 % and_nat_numerals(4)
% 1.40/1.62 thf(fact_2186_and__Suc__0__eq,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 1.40/1.62 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_Suc_0_eq
% 1.40/1.62 thf(fact_2187_Suc__0__and__eq,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.62 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Suc_0_and_eq
% 1.40/1.62 thf(fact_2188_bot__enat__def,axiom,
% 1.40/1.62 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 1.40/1.62
% 1.40/1.62 % bot_enat_def
% 1.40/1.62 thf(fact_2189_bot__nat__def,axiom,
% 1.40/1.62 bot_bot_nat = zero_zero_nat ).
% 1.40/1.62
% 1.40/1.62 % bot_nat_def
% 1.40/1.62 thf(fact_2190_num__induct,axiom,
% 1.40/1.62 ! [P: num > $o,X: num] :
% 1.40/1.62 ( ( P @ one )
% 1.40/1.62 => ( ! [X5: num] :
% 1.40/1.62 ( ( P @ X5 )
% 1.40/1.62 => ( P @ ( inc @ X5 ) ) )
% 1.40/1.62 => ( P @ X ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % num_induct
% 1.40/1.62 thf(fact_2191_add__inc,axiom,
% 1.40/1.62 ! [X: num,Y2: num] :
% 1.40/1.62 ( ( plus_plus_num @ X @ ( inc @ Y2 ) )
% 1.40/1.62 = ( inc @ ( plus_plus_num @ X @ Y2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % add_inc
% 1.40/1.62 thf(fact_2192_inc_Osimps_I1_J,axiom,
% 1.40/1.62 ( ( inc @ one )
% 1.40/1.62 = ( bit0 @ one ) ) ).
% 1.40/1.62
% 1.40/1.62 % inc.simps(1)
% 1.40/1.62 thf(fact_2193_inc_Osimps_I2_J,axiom,
% 1.40/1.62 ! [X: num] :
% 1.40/1.62 ( ( inc @ ( bit0 @ X ) )
% 1.40/1.62 = ( bit1 @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % inc.simps(2)
% 1.40/1.62 thf(fact_2194_inc_Osimps_I3_J,axiom,
% 1.40/1.62 ! [X: num] :
% 1.40/1.62 ( ( inc @ ( bit1 @ X ) )
% 1.40/1.62 = ( bit0 @ ( inc @ X ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % inc.simps(3)
% 1.40/1.62 thf(fact_2195_add__One,axiom,
% 1.40/1.62 ! [X: num] :
% 1.40/1.62 ( ( plus_plus_num @ X @ one )
% 1.40/1.62 = ( inc @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % add_One
% 1.40/1.62 thf(fact_2196_inc__BitM__eq,axiom,
% 1.40/1.62 ! [N: num] :
% 1.40/1.62 ( ( inc @ ( bitM @ N ) )
% 1.40/1.62 = ( bit0 @ N ) ) ).
% 1.40/1.62
% 1.40/1.62 % inc_BitM_eq
% 1.40/1.62 thf(fact_2197_BitM__inc__eq,axiom,
% 1.40/1.62 ! [N: num] :
% 1.40/1.62 ( ( bitM @ ( inc @ N ) )
% 1.40/1.62 = ( bit1 @ N ) ) ).
% 1.40/1.62
% 1.40/1.62 % BitM_inc_eq
% 1.40/1.62 thf(fact_2198_and__nat__def,axiom,
% 1.40/1.62 ( bit_se727722235901077358nd_nat
% 1.40/1.62 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_nat_def
% 1.40/1.62 thf(fact_2199_mult__inc,axiom,
% 1.40/1.62 ! [X: num,Y2: num] :
% 1.40/1.62 ( ( times_times_num @ X @ ( inc @ Y2 ) )
% 1.40/1.62 = ( plus_plus_num @ ( times_times_num @ X @ Y2 ) @ X ) ) ).
% 1.40/1.62
% 1.40/1.62 % mult_inc
% 1.40/1.62 thf(fact_2200_sin__times__pi__eq__0,axiom,
% 1.40/1.62 ! [X: real] :
% 1.40/1.62 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 1.40/1.62 = zero_zero_real )
% 1.40/1.62 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 1.40/1.62
% 1.40/1.62 % sin_times_pi_eq_0
% 1.40/1.62 thf(fact_2201_sin__integer__2pi,axiom,
% 1.40/1.62 ! [N: real] :
% 1.40/1.62 ( ( member_real @ N @ ring_1_Ints_real )
% 1.40/1.62 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 1.40/1.62 = zero_zero_real ) ) ).
% 1.40/1.62
% 1.40/1.62 % sin_integer_2pi
% 1.40/1.62 thf(fact_2202_cos__integer__2pi,axiom,
% 1.40/1.62 ! [N: real] :
% 1.40/1.62 ( ( member_real @ N @ ring_1_Ints_real )
% 1.40/1.62 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 1.40/1.62 = one_one_real ) ) ).
% 1.40/1.62
% 1.40/1.62 % cos_integer_2pi
% 1.40/1.62 thf(fact_2203_and__nat__unfold,axiom,
% 1.40/1.62 ( bit_se727722235901077358nd_nat
% 1.40/1.62 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.62 ( if_nat
% 1.40/1.62 @ ( ( M6 = zero_zero_nat )
% 1.40/1.62 | ( N2 = zero_zero_nat ) )
% 1.40/1.62 @ zero_zero_nat
% 1.40/1.62 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_nat_unfold
% 1.40/1.62 thf(fact_2204_and__nat__rec,axiom,
% 1.40/1.62 ( bit_se727722235901077358nd_nat
% 1.40/1.62 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.62 ( plus_plus_nat
% 1.40/1.62 @ ( zero_n2687167440665602831ol_nat
% 1.40/1.62 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 1.40/1.62 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 1.40/1.62 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_nat_rec
% 1.40/1.62 thf(fact_2205_and__int_Osimps,axiom,
% 1.40/1.62 ( bit_se725231765392027082nd_int
% 1.40/1.62 = ( ^ [K3: int,L: int] :
% 1.40/1.62 ( if_int
% 1.40/1.62 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 1.40/1.62 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 1.40/1.62 @ ( uminus_uminus_int
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 1.40/1.62 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 1.40/1.62 @ ( plus_plus_int
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 1.40/1.62 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 1.40/1.62 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_int.simps
% 1.40/1.62 thf(fact_2206_and__int_Oelims,axiom,
% 1.40/1.62 ! [X: int,Xa2: int,Y2: int] :
% 1.40/1.62 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 1.40/1.62 = Y2 )
% 1.40/1.62 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 1.40/1.62 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 1.40/1.62 => ( Y2
% 1.40/1.62 = ( uminus_uminus_int
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 1.40/1.62 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 1.40/1.62 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 1.40/1.62 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 1.40/1.62 => ( Y2
% 1.40/1.62 = ( plus_plus_int
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 1.40/1.62 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 1.40/1.62 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_int.elims
% 1.40/1.62 thf(fact_2207_signed__take__bit__eq__take__bit__minus,axiom,
% 1.40/1.62 ( bit_ri631733984087533419it_int
% 1.40/1.62 = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % signed_take_bit_eq_take_bit_minus
% 1.40/1.62 thf(fact_2208_take__bit__Suc__from__most,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 1.40/1.62 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % take_bit_Suc_from_most
% 1.40/1.62 thf(fact_2209_signed__take__bit__nonnegative__iff,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 1.40/1.62 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % signed_take_bit_nonnegative_iff
% 1.40/1.62 thf(fact_2210_signed__take__bit__negative__iff,axiom,
% 1.40/1.62 ! [N: nat,K: int] :
% 1.40/1.62 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 1.40/1.62 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 1.40/1.62
% 1.40/1.62 % signed_take_bit_negative_iff
% 1.40/1.62 thf(fact_2211_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 1.40/1.62 ! [W: num,N: nat] :
% 1.40/1.62 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 1.40/1.62 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_minus_numeral_Bit0_Suc_iff
% 1.40/1.62 thf(fact_2212_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 1.40/1.62 ! [W: num,N: nat] :
% 1.40/1.62 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 1.40/1.62 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_minus_numeral_Bit1_Suc_iff
% 1.40/1.62 thf(fact_2213_bit__minus__numeral__int_I1_J,axiom,
% 1.40/1.62 ! [W: num,N: num] :
% 1.40/1.62 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 1.40/1.62 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_minus_numeral_int(1)
% 1.40/1.62 thf(fact_2214_bit__minus__numeral__int_I2_J,axiom,
% 1.40/1.62 ! [W: num,N: num] :
% 1.40/1.62 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 1.40/1.62 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_minus_numeral_int(2)
% 1.40/1.62 thf(fact_2215_bit__and__int__iff,axiom,
% 1.40/1.62 ! [K: int,L2: int,N: nat] :
% 1.40/1.62 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N )
% 1.40/1.62 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 1.40/1.62 & ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_and_int_iff
% 1.40/1.62 thf(fact_2216_bit__or__int__iff,axiom,
% 1.40/1.62 ! [K: int,L2: int,N: nat] :
% 1.40/1.62 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N )
% 1.40/1.62 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 1.40/1.62 | ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_or_int_iff
% 1.40/1.62 thf(fact_2217_bit__not__int__iff_H,axiom,
% 1.40/1.62 ! [K: int,N: nat] :
% 1.40/1.62 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 1.40/1.62 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_not_int_iff'
% 1.40/1.62 thf(fact_2218_bit__imp__take__bit__positive,axiom,
% 1.40/1.62 ! [N: nat,M: nat,K: int] :
% 1.40/1.62 ( ( ord_less_nat @ N @ M )
% 1.40/1.62 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 1.40/1.62 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_imp_take_bit_positive
% 1.40/1.62 thf(fact_2219_bit__concat__bit__iff,axiom,
% 1.40/1.62 ! [M: nat,K: int,L2: int,N: nat] :
% 1.40/1.62 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 1.40/1.62 = ( ( ( ord_less_nat @ N @ M )
% 1.40/1.62 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 1.40/1.62 | ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.62 & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_concat_bit_iff
% 1.40/1.62 thf(fact_2220_atLeastAtMostPlus1__int__conv,axiom,
% 1.40/1.62 ! [M: int,N: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 1.40/1.62 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 1.40/1.62 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % atLeastAtMostPlus1_int_conv
% 1.40/1.62 thf(fact_2221_simp__from__to,axiom,
% 1.40/1.62 ( set_or1266510415728281911st_int
% 1.40/1.62 = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % simp_from_to
% 1.40/1.62 thf(fact_2222_signed__take__bit__eq__concat__bit,axiom,
% 1.40/1.62 ( bit_ri631733984087533419it_int
% 1.40/1.62 = ( ^ [N2: nat,K3: int] : ( bit_concat_bit @ N2 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % signed_take_bit_eq_concat_bit
% 1.40/1.62 thf(fact_2223_int__bit__bound,axiom,
% 1.40/1.62 ! [K: int] :
% 1.40/1.62 ~ ! [N4: nat] :
% 1.40/1.62 ( ! [M3: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ N4 @ M3 )
% 1.40/1.62 => ( ( bit_se1146084159140164899it_int @ K @ M3 )
% 1.40/1.62 = ( bit_se1146084159140164899it_int @ K @ N4 ) ) )
% 1.40/1.62 => ~ ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 1.40/1.62 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N4 @ one_one_nat ) )
% 1.40/1.62 = ( ~ ( bit_se1146084159140164899it_int @ K @ N4 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % int_bit_bound
% 1.40/1.62 thf(fact_2224_bit__int__def,axiom,
% 1.40/1.62 ( bit_se1146084159140164899it_int
% 1.40/1.62 = ( ^ [K3: int,N2: nat] :
% 1.40/1.62 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_int_def
% 1.40/1.62 thf(fact_2225_set__bit__eq,axiom,
% 1.40/1.62 ( bit_se7879613467334960850it_int
% 1.40/1.62 = ( ^ [N2: nat,K3: int] :
% 1.40/1.62 ( plus_plus_int @ K3
% 1.40/1.62 @ ( times_times_int
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N2 ) )
% 1.40/1.62 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % set_bit_eq
% 1.40/1.62 thf(fact_2226_unset__bit__eq,axiom,
% 1.40/1.62 ( bit_se4203085406695923979it_int
% 1.40/1.62 = ( ^ [N2: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % unset_bit_eq
% 1.40/1.62 thf(fact_2227_and__int_Opelims,axiom,
% 1.40/1.62 ! [X: int,Xa2: int,Y2: int] :
% 1.40/1.62 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 1.40/1.62 = Y2 )
% 1.40/1.62 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 1.40/1.62 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 1.40/1.62 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 1.40/1.62 => ( Y2
% 1.40/1.62 = ( uminus_uminus_int
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 1.40/1.62 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 1.40/1.62 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 1.40/1.62 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 1.40/1.62 => ( Y2
% 1.40/1.62 = ( plus_plus_int
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 1.40/1.62 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 1.40/1.62 @ ( 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 ) ) ) ) ) ) ) ) )
% 1.40/1.62 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_int.pelims
% 1.40/1.62 thf(fact_2228_and__int_Opsimps,axiom,
% 1.40/1.62 ! [K: int,L2: int] :
% 1.40/1.62 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 1.40/1.62 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 1.40/1.62 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 1.40/1.62 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 1.40/1.62 = ( uminus_uminus_int
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 1.40/1.62 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 1.40/1.62 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 1.40/1.62 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 1.40/1.62 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 1.40/1.62 = ( plus_plus_int
% 1.40/1.62 @ ( zero_n2684676970156552555ol_int
% 1.40/1.62 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 1.40/1.62 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 1.40/1.62 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_int.psimps
% 1.40/1.62 thf(fact_2229_not__bit__Suc__0__Suc,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 1.40/1.62
% 1.40/1.62 % not_bit_Suc_0_Suc
% 1.40/1.62 thf(fact_2230_bit__Suc__0__iff,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.62 = ( N = zero_zero_nat ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_Suc_0_iff
% 1.40/1.62 thf(fact_2231_lessThan__Suc,axiom,
% 1.40/1.62 ! [K: nat] :
% 1.40/1.62 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 1.40/1.62 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % lessThan_Suc
% 1.40/1.62 thf(fact_2232_atMost__Suc,axiom,
% 1.40/1.62 ! [K: nat] :
% 1.40/1.62 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 1.40/1.62 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % atMost_Suc
% 1.40/1.62 thf(fact_2233_not__bit__Suc__0__numeral,axiom,
% 1.40/1.62 ! [N: num] :
% 1.40/1.62 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 1.40/1.62
% 1.40/1.62 % not_bit_Suc_0_numeral
% 1.40/1.62 thf(fact_2234_atLeast0__atMost__Suc,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 1.40/1.62 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % atLeast0_atMost_Suc
% 1.40/1.62 thf(fact_2235_atLeastAtMost__insertL,axiom,
% 1.40/1.62 ! [M: nat,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.62 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 1.40/1.62 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % atLeastAtMost_insertL
% 1.40/1.62 thf(fact_2236_atLeastAtMostSuc__conv,axiom,
% 1.40/1.62 ! [M: nat,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 1.40/1.62 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 1.40/1.62 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % atLeastAtMostSuc_conv
% 1.40/1.62 thf(fact_2237_Icc__eq__insert__lb__nat,axiom,
% 1.40/1.62 ! [M: nat,N: nat] :
% 1.40/1.62 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.62 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 1.40/1.62 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Icc_eq_insert_lb_nat
% 1.40/1.62 thf(fact_2238_lessThan__nat__numeral,axiom,
% 1.40/1.62 ! [K: num] :
% 1.40/1.62 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 1.40/1.62 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % lessThan_nat_numeral
% 1.40/1.62 thf(fact_2239_atMost__nat__numeral,axiom,
% 1.40/1.62 ! [K: num] :
% 1.40/1.62 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 1.40/1.62 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % atMost_nat_numeral
% 1.40/1.62 thf(fact_2240_bit__nat__iff,axiom,
% 1.40/1.62 ! [K: int,N: nat] :
% 1.40/1.62 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 1.40/1.62 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.62 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_nat_iff
% 1.40/1.62 thf(fact_2241_atLeast1__atMost__eq__remove0,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.62 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % atLeast1_atMost_eq_remove0
% 1.40/1.62 thf(fact_2242_bit__nat__def,axiom,
% 1.40/1.62 ( bit_se1148574629649215175it_nat
% 1.40/1.62 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.62 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % bit_nat_def
% 1.40/1.62 thf(fact_2243_set__decode__plus__power__2,axiom,
% 1.40/1.62 ! [N: nat,Z: nat] :
% 1.40/1.62 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 1.40/1.62 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 1.40/1.62 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % set_decode_plus_power_2
% 1.40/1.62 thf(fact_2244_and__int_Opinduct,axiom,
% 1.40/1.62 ! [A0: int,A1: int,P: int > int > $o] :
% 1.40/1.62 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 1.40/1.62 => ( ! [K2: int,L3: int] :
% 1.40/1.62 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L3 ) )
% 1.40/1.62 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 1.40/1.62 & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 1.40/1.62 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 1.40/1.62 => ( P @ K2 @ L3 ) ) )
% 1.40/1.62 => ( P @ A0 @ A1 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % and_int.pinduct
% 1.40/1.62 thf(fact_2245_upto_Opinduct,axiom,
% 1.40/1.62 ! [A0: int,A1: int,P: int > int > $o] :
% 1.40/1.62 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 1.40/1.62 => ( ! [I3: int,J2: int] :
% 1.40/1.62 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 1.40/1.62 => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 1.40/1.62 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 1.40/1.62 => ( P @ I3 @ J2 ) ) )
% 1.40/1.62 => ( P @ A0 @ A1 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % upto.pinduct
% 1.40/1.62 thf(fact_2246_or__not__num__neg_Opelims,axiom,
% 1.40/1.62 ! [X: num,Xa2: num,Y2: num] :
% 1.40/1.62 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 1.40/1.62 = Y2 )
% 1.40/1.62 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 1.40/1.62 => ( ( ( X = one )
% 1.40/1.62 => ( ( Xa2 = one )
% 1.40/1.62 => ( ( Y2 = one )
% 1.40/1.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 1.40/1.62 => ( ( ( X = one )
% 1.40/1.62 => ! [M5: num] :
% 1.40/1.62 ( ( Xa2
% 1.40/1.62 = ( bit0 @ M5 ) )
% 1.40/1.62 => ( ( Y2
% 1.40/1.62 = ( bit1 @ M5 ) )
% 1.40/1.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M5 ) ) ) ) ) )
% 1.40/1.62 => ( ( ( X = one )
% 1.40/1.62 => ! [M5: num] :
% 1.40/1.62 ( ( Xa2
% 1.40/1.62 = ( bit1 @ M5 ) )
% 1.40/1.62 => ( ( Y2
% 1.40/1.62 = ( bit1 @ M5 ) )
% 1.40/1.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M5 ) ) ) ) ) )
% 1.40/1.62 => ( ! [N4: num] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( bit0 @ N4 ) )
% 1.40/1.62 => ( ( Xa2 = one )
% 1.40/1.62 => ( ( Y2
% 1.40/1.62 = ( bit0 @ one ) )
% 1.40/1.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N4 ) @ one ) ) ) ) )
% 1.40/1.62 => ( ! [N4: num] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( bit0 @ N4 ) )
% 1.40/1.62 => ! [M5: num] :
% 1.40/1.62 ( ( Xa2
% 1.40/1.62 = ( bit0 @ M5 ) )
% 1.40/1.62 => ( ( Y2
% 1.40/1.62 = ( bitM @ ( bit_or_not_num_neg @ N4 @ M5 ) ) )
% 1.40/1.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N4 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 1.40/1.62 => ( ! [N4: num] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( bit0 @ N4 ) )
% 1.40/1.62 => ! [M5: num] :
% 1.40/1.62 ( ( Xa2
% 1.40/1.62 = ( bit1 @ M5 ) )
% 1.40/1.62 => ( ( Y2
% 1.40/1.62 = ( bit0 @ ( bit_or_not_num_neg @ N4 @ M5 ) ) )
% 1.40/1.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N4 ) @ ( bit1 @ M5 ) ) ) ) ) )
% 1.40/1.62 => ( ! [N4: num] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( bit1 @ N4 ) )
% 1.40/1.62 => ( ( Xa2 = one )
% 1.40/1.62 => ( ( Y2 = one )
% 1.40/1.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N4 ) @ one ) ) ) ) )
% 1.40/1.62 => ( ! [N4: num] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( bit1 @ N4 ) )
% 1.40/1.62 => ! [M5: num] :
% 1.40/1.62 ( ( Xa2
% 1.40/1.62 = ( bit0 @ M5 ) )
% 1.40/1.62 => ( ( Y2
% 1.40/1.62 = ( bitM @ ( bit_or_not_num_neg @ N4 @ M5 ) ) )
% 1.40/1.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N4 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 1.40/1.62 => ~ ! [N4: num] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( bit1 @ N4 ) )
% 1.40/1.62 => ! [M5: num] :
% 1.40/1.62 ( ( Xa2
% 1.40/1.62 = ( bit1 @ M5 ) )
% 1.40/1.62 => ( ( Y2
% 1.40/1.62 = ( bitM @ ( bit_or_not_num_neg @ N4 @ M5 ) ) )
% 1.40/1.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N4 ) @ ( bit1 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % or_not_num_neg.pelims
% 1.40/1.62 thf(fact_2247_int__ge__less__than2__def,axiom,
% 1.40/1.62 ( int_ge_less_than2
% 1.40/1.62 = ( ^ [D2: int] :
% 1.40/1.62 ( collec213857154873943460nt_int
% 1.40/1.62 @ ( produc4947309494688390418_int_o
% 1.40/1.62 @ ^ [Z7: int,Z5: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ D2 @ Z5 )
% 1.40/1.62 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % int_ge_less_than2_def
% 1.40/1.62 thf(fact_2248_int__ge__less__than__def,axiom,
% 1.40/1.62 ( int_ge_less_than
% 1.40/1.62 = ( ^ [D2: int] :
% 1.40/1.62 ( collec213857154873943460nt_int
% 1.40/1.62 @ ( produc4947309494688390418_int_o
% 1.40/1.62 @ ^ [Z7: int,Z5: int] :
% 1.40/1.62 ( ( ord_less_eq_int @ D2 @ Z7 )
% 1.40/1.62 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % int_ge_less_than_def
% 1.40/1.62 thf(fact_2249_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 1.40/1.62 ! [X: vEBT_VEBT,Y2: $o] :
% 1.40/1.62 ( ( ( vEBT_VEBT_minNull @ X )
% 1.40/1.62 = Y2 )
% 1.40/1.62 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 1.40/1.62 => ( ( ( X
% 1.40/1.62 = ( vEBT_Leaf @ $false @ $false ) )
% 1.40/1.62 => ( Y2
% 1.40/1.62 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 1.40/1.62 => ( ! [Uv: $o] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( vEBT_Leaf @ $true @ Uv ) )
% 1.40/1.62 => ( ~ Y2
% 1.40/1.62 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv ) ) ) )
% 1.40/1.62 => ( ! [Uu: $o] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( vEBT_Leaf @ Uu @ $true ) )
% 1.40/1.62 => ( ~ Y2
% 1.40/1.62 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu @ $true ) ) ) )
% 1.40/1.62 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) )
% 1.40/1.62 => ( Y2
% 1.40/1.62 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) ) ) )
% 1.40/1.62 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 1.40/1.62 => ( ~ Y2
% 1.40/1.62 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % VEBT_internal.minNull.pelims(1)
% 1.40/1.62 thf(fact_2250_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 1.40/1.62 ! [X: vEBT_VEBT] :
% 1.40/1.62 ( ~ ( vEBT_VEBT_minNull @ X )
% 1.40/1.62 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 1.40/1.62 => ( ! [Uv: $o] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( vEBT_Leaf @ $true @ Uv ) )
% 1.40/1.62 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv ) ) )
% 1.40/1.62 => ( ! [Uu: $o] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( vEBT_Leaf @ Uu @ $true ) )
% 1.40/1.62 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu @ $true ) ) )
% 1.40/1.62 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 1.40/1.62 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % VEBT_internal.minNull.pelims(3)
% 1.40/1.62 thf(fact_2251_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 1.40/1.62 ! [X: vEBT_VEBT] :
% 1.40/1.62 ( ( vEBT_VEBT_minNull @ X )
% 1.40/1.62 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 1.40/1.62 => ( ( ( X
% 1.40/1.62 = ( vEBT_Leaf @ $false @ $false ) )
% 1.40/1.62 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 1.40/1.62 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 1.40/1.62 ( ( X
% 1.40/1.62 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) )
% 1.40/1.62 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy2 ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % VEBT_internal.minNull.pelims(2)
% 1.40/1.62 thf(fact_2252_xor__Suc__0__eq,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 1.40/1.62 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 1.40/1.62 @ ( zero_n2687167440665602831ol_nat
% 1.40/1.62 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % xor_Suc_0_eq
% 1.40/1.62 thf(fact_2253_Suc__0__xor__eq,axiom,
% 1.40/1.62 ! [N: nat] :
% 1.40/1.62 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.62 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 1.40/1.62 @ ( zero_n2687167440665602831ol_nat
% 1.40/1.62 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % Suc_0_xor_eq
% 1.40/1.62 thf(fact_2254_upto__aux__rec,axiom,
% 1.40/1.62 ( upto_aux
% 1.40/1.62 = ( ^ [I4: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % upto_aux_rec
% 1.40/1.62 thf(fact_2255_horner__sum__of__bool__2__less,axiom,
% 1.40/1.62 ! [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 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % horner_sum_of_bool_2_less
% 1.40/1.62 thf(fact_2256_xor__nat__numerals_I4_J,axiom,
% 1.40/1.62 ! [X: num] :
% 1.40/1.62 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 1.40/1.62 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % xor_nat_numerals(4)
% 1.40/1.62 thf(fact_2257_xor__nat__numerals_I3_J,axiom,
% 1.40/1.62 ! [X: num] :
% 1.40/1.62 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 1.40/1.62 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % xor_nat_numerals(3)
% 1.40/1.62 thf(fact_2258_xor__nat__numerals_I2_J,axiom,
% 1.40/1.62 ! [Y2: num] :
% 1.40/1.62 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) )
% 1.40/1.62 = ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % xor_nat_numerals(2)
% 1.40/1.62 thf(fact_2259_xor__nat__numerals_I1_J,axiom,
% 1.40/1.62 ! [Y2: num] :
% 1.40/1.62 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y2 ) ) )
% 1.40/1.62 = ( numeral_numeral_nat @ ( bit1 @ Y2 ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % xor_nat_numerals(1)
% 1.40/1.62 thf(fact_2260_xor__nat__unfold,axiom,
% 1.40/1.62 ( bit_se6528837805403552850or_nat
% 1.40/1.62 = ( ^ [M6: nat,N2: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = 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 @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % xor_nat_unfold
% 1.40/1.62 thf(fact_2261_xor__nat__rec,axiom,
% 1.40/1.62 ( bit_se6528837805403552850or_nat
% 1.40/1.62 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.62 ( plus_plus_nat
% 1.40/1.62 @ ( zero_n2687167440665602831ol_nat
% 1.40/1.62 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 1.40/1.62 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 1.40/1.62 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % xor_nat_rec
% 1.40/1.62 thf(fact_2262_upto_Opsimps,axiom,
% 1.40/1.62 ! [I2: int,J: int] :
% 1.40/1.62 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J ) )
% 1.40/1.62 => ( ( ( ord_less_eq_int @ I2 @ J )
% 1.40/1.62 => ( ( upto @ I2 @ J )
% 1.40/1.62 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) )
% 1.40/1.62 & ( ~ ( ord_less_eq_int @ I2 @ J )
% 1.40/1.62 => ( ( upto @ I2 @ J )
% 1.40/1.62 = nil_int ) ) ) ) ).
% 1.40/1.62
% 1.40/1.62 % upto.psimps
% 1.40/1.62 thf(fact_2263_upto_Opelims,axiom,
% 1.40/1.62 ! [X: int,Xa2: int,Y2: list_int] :
% 1.40/1.62 ( ( ( upto @ X @ Xa2 )
% 1.40/1.62 = Y2 )
% 1.40/1.62 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 1.40/1.63 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 1.40/1.63 => ( Y2
% 1.40/1.63 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 1.40/1.63 => ( Y2 = nil_int ) ) )
% 1.40/1.63 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto.pelims
% 1.40/1.63 thf(fact_2264_set__encode__def,axiom,
% 1.40/1.63 ( nat_set_encode
% 1.40/1.63 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % set_encode_def
% 1.40/1.63 thf(fact_2265_push__bit__nonnegative__int__iff,axiom,
% 1.40/1.63 ! [N: nat,K: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 1.40/1.63 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 1.40/1.63
% 1.40/1.63 % push_bit_nonnegative_int_iff
% 1.40/1.63 thf(fact_2266_push__bit__negative__int__iff,axiom,
% 1.40/1.63 ! [N: nat,K: int] :
% 1.40/1.63 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 1.40/1.63 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % push_bit_negative_int_iff
% 1.40/1.63 thf(fact_2267_concat__bit__of__zero__1,axiom,
% 1.40/1.63 ! [N: nat,L2: int] :
% 1.40/1.63 ( ( bit_concat_bit @ N @ zero_zero_int @ L2 )
% 1.40/1.63 = ( bit_se545348938243370406it_int @ N @ L2 ) ) ).
% 1.40/1.63
% 1.40/1.63 % concat_bit_of_zero_1
% 1.40/1.63 thf(fact_2268_xor__nonnegative__int__iff,axiom,
% 1.40/1.63 ! [K: int,L2: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 1.40/1.63 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 1.40/1.63 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % xor_nonnegative_int_iff
% 1.40/1.63 thf(fact_2269_xor__negative__int__iff,axiom,
% 1.40/1.63 ! [K: int,L2: int] :
% 1.40/1.63 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 1.40/1.63 = ( ( ord_less_int @ K @ zero_zero_int )
% 1.40/1.63 != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % xor_negative_int_iff
% 1.40/1.63 thf(fact_2270_upto__Nil,axiom,
% 1.40/1.63 ! [I2: int,J: int] :
% 1.40/1.63 ( ( ( upto @ I2 @ J )
% 1.40/1.63 = nil_int )
% 1.40/1.63 = ( ord_less_int @ J @ I2 ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_Nil
% 1.40/1.63 thf(fact_2271_upto__Nil2,axiom,
% 1.40/1.63 ! [I2: int,J: int] :
% 1.40/1.63 ( ( nil_int
% 1.40/1.63 = ( upto @ I2 @ J ) )
% 1.40/1.63 = ( ord_less_int @ J @ I2 ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_Nil2
% 1.40/1.63 thf(fact_2272_upto__empty,axiom,
% 1.40/1.63 ! [J: int,I2: int] :
% 1.40/1.63 ( ( ord_less_int @ J @ I2 )
% 1.40/1.63 => ( ( upto @ I2 @ J )
% 1.40/1.63 = nil_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_empty
% 1.40/1.63 thf(fact_2273_upto__single,axiom,
% 1.40/1.63 ! [I2: int] :
% 1.40/1.63 ( ( upto @ I2 @ I2 )
% 1.40/1.63 = ( cons_int @ I2 @ nil_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_single
% 1.40/1.63 thf(fact_2274_nth__upto,axiom,
% 1.40/1.63 ! [I2: int,K: nat,J: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 1.40/1.63 => ( ( nth_int @ ( upto @ I2 @ J ) @ K )
% 1.40/1.63 = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % nth_upto
% 1.40/1.63 thf(fact_2275_length__upto,axiom,
% 1.40/1.63 ! [I2: int,J: int] :
% 1.40/1.63 ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 1.40/1.63 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % length_upto
% 1.40/1.63 thf(fact_2276_push__bit__of__Suc__0,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 1.40/1.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % push_bit_of_Suc_0
% 1.40/1.63 thf(fact_2277_upto__rec__numeral_I1_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 = nil_int ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_rec_numeral(1)
% 1.40/1.63 thf(fact_2278_upto__rec__numeral_I2_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = nil_int ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_rec_numeral(2)
% 1.40/1.63 thf(fact_2279_upto__rec__numeral_I3_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 = nil_int ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_rec_numeral(3)
% 1.40/1.63 thf(fact_2280_upto__rec__numeral_I4_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = nil_int ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_rec_numeral(4)
% 1.40/1.63 thf(fact_2281_bit__xor__int__iff,axiom,
% 1.40/1.63 ! [K: int,L2: int,N: nat] :
% 1.40/1.63 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N )
% 1.40/1.63 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 1.40/1.63 != ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bit_xor_int_iff
% 1.40/1.63 thf(fact_2282_flip__bit__int__def,axiom,
% 1.40/1.63 ( bit_se2159334234014336723it_int
% 1.40/1.63 = ( ^ [N2: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % flip_bit_int_def
% 1.40/1.63 thf(fact_2283_atLeastAtMost__upto,axiom,
% 1.40/1.63 ( set_or1266510415728281911st_int
% 1.40/1.63 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ I4 @ J3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeastAtMost_upto
% 1.40/1.63 thf(fact_2284_push__bit__nat__eq,axiom,
% 1.40/1.63 ! [N: nat,K: int] :
% 1.40/1.63 ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 1.40/1.63 = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % push_bit_nat_eq
% 1.40/1.63 thf(fact_2285_upto__code,axiom,
% 1.40/1.63 ( upto
% 1.40/1.63 = ( ^ [I4: int,J3: int] : ( upto_aux @ I4 @ J3 @ nil_int ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_code
% 1.40/1.63 thf(fact_2286_upto__aux__def,axiom,
% 1.40/1.63 ( upto_aux
% 1.40/1.63 = ( ^ [I4: int,J3: int] : ( append_int @ ( upto @ I4 @ J3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_aux_def
% 1.40/1.63 thf(fact_2287_XOR__lower,axiom,
% 1.40/1.63 ! [X: int,Y2: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.63 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % XOR_lower
% 1.40/1.63 thf(fact_2288_set__bit__nat__def,axiom,
% 1.40/1.63 ( bit_se7882103937844011126it_nat
% 1.40/1.63 = ( ^ [M6: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % set_bit_nat_def
% 1.40/1.63 thf(fact_2289_flip__bit__nat__def,axiom,
% 1.40/1.63 ( bit_se2161824704523386999it_nat
% 1.40/1.63 = ( ^ [M6: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % flip_bit_nat_def
% 1.40/1.63 thf(fact_2290_bit__push__bit__iff__int,axiom,
% 1.40/1.63 ! [M: nat,K: int,N: nat] :
% 1.40/1.63 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 1.40/1.63 = ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.63 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bit_push_bit_iff_int
% 1.40/1.63 thf(fact_2291_xor__nat__def,axiom,
% 1.40/1.63 ( bit_se6528837805403552850or_nat
% 1.40/1.63 = ( ^ [M6: nat,N2: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % xor_nat_def
% 1.40/1.63 thf(fact_2292_bit__push__bit__iff__nat,axiom,
% 1.40/1.63 ! [M: nat,Q2: nat,N: nat] :
% 1.40/1.63 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 1.40/1.63 = ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.63 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bit_push_bit_iff_nat
% 1.40/1.63 thf(fact_2293_concat__bit__eq,axiom,
% 1.40/1.63 ( bit_concat_bit
% 1.40/1.63 = ( ^ [N2: nat,K3: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % concat_bit_eq
% 1.40/1.63 thf(fact_2294_upto__split2,axiom,
% 1.40/1.63 ! [I2: int,J: int,K: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ I2 @ J )
% 1.40/1.63 => ( ( ord_less_eq_int @ J @ K )
% 1.40/1.63 => ( ( upto @ I2 @ K )
% 1.40/1.63 = ( append_int @ ( upto @ I2 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_split2
% 1.40/1.63 thf(fact_2295_upto__split1,axiom,
% 1.40/1.63 ! [I2: int,J: int,K: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ I2 @ J )
% 1.40/1.63 => ( ( ord_less_eq_int @ J @ K )
% 1.40/1.63 => ( ( upto @ I2 @ K )
% 1.40/1.63 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_split1
% 1.40/1.63 thf(fact_2296_concat__bit__def,axiom,
% 1.40/1.63 ( bit_concat_bit
% 1.40/1.63 = ( ^ [N2: nat,K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % concat_bit_def
% 1.40/1.63 thf(fact_2297_set__bit__int__def,axiom,
% 1.40/1.63 ( bit_se7879613467334960850it_int
% 1.40/1.63 = ( ^ [N2: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % set_bit_int_def
% 1.40/1.63 thf(fact_2298_upto__rec1,axiom,
% 1.40/1.63 ! [I2: int,J: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ I2 @ J )
% 1.40/1.63 => ( ( upto @ I2 @ J )
% 1.40/1.63 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_rec1
% 1.40/1.63 thf(fact_2299_upto_Osimps,axiom,
% 1.40/1.63 ( upto
% 1.40/1.63 = ( ^ [I4: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I4 @ J3 ) @ ( cons_int @ I4 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto.simps
% 1.40/1.63 thf(fact_2300_upto_Oelims,axiom,
% 1.40/1.63 ! [X: int,Xa2: int,Y2: list_int] :
% 1.40/1.63 ( ( ( upto @ X @ Xa2 )
% 1.40/1.63 = Y2 )
% 1.40/1.63 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 1.40/1.63 => ( Y2
% 1.40/1.63 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 1.40/1.63 => ( Y2 = nil_int ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto.elims
% 1.40/1.63 thf(fact_2301_upto__rec2,axiom,
% 1.40/1.63 ! [I2: int,J: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ I2 @ J )
% 1.40/1.63 => ( ( upto @ I2 @ J )
% 1.40/1.63 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_rec2
% 1.40/1.63 thf(fact_2302_push__bit__int__def,axiom,
% 1.40/1.63 ( bit_se545348938243370406it_int
% 1.40/1.63 = ( ^ [N2: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % push_bit_int_def
% 1.40/1.63 thf(fact_2303_push__bit__nat__def,axiom,
% 1.40/1.63 ( bit_se547839408752420682it_nat
% 1.40/1.63 = ( ^ [N2: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % push_bit_nat_def
% 1.40/1.63 thf(fact_2304_upto__split3,axiom,
% 1.40/1.63 ! [I2: int,J: int,K: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ I2 @ J )
% 1.40/1.63 => ( ( ord_less_eq_int @ J @ K )
% 1.40/1.63 => ( ( upto @ I2 @ K )
% 1.40/1.63 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % upto_split3
% 1.40/1.63 thf(fact_2305_push__bit__minus__one,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 1.40/1.63 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % push_bit_minus_one
% 1.40/1.63 thf(fact_2306_XOR__upper,axiom,
% 1.40/1.63 ! [X: int,N: nat,Y2: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.63 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.63 => ( ( ord_less_int @ Y2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 1.40/1.63 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % XOR_upper
% 1.40/1.63 thf(fact_2307_xor__int__rec,axiom,
% 1.40/1.63 ( bit_se6526347334894502574or_int
% 1.40/1.63 = ( ^ [K3: int,L: int] :
% 1.40/1.63 ( plus_plus_int
% 1.40/1.63 @ ( zero_n2684676970156552555ol_int
% 1.40/1.63 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 1.40/1.63 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 1.40/1.63 @ ( 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 ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % xor_int_rec
% 1.40/1.63 thf(fact_2308_xor__int__unfold,axiom,
% 1.40/1.63 ( bit_se6526347334894502574or_int
% 1.40/1.63 = ( ^ [K3: int,L: int] :
% 1.40/1.63 ( if_int
% 1.40/1.63 @ ( K3
% 1.40/1.63 = ( uminus_uminus_int @ one_one_int ) )
% 1.40/1.63 @ ( bit_ri7919022796975470100ot_int @ L )
% 1.40/1.63 @ ( if_int
% 1.40/1.63 @ ( L
% 1.40/1.63 = ( uminus_uminus_int @ one_one_int ) )
% 1.40/1.63 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 1.40/1.63 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % xor_int_unfold
% 1.40/1.63 thf(fact_2309_set__encode__insert,axiom,
% 1.40/1.63 ! [A2: set_nat,N: nat] :
% 1.40/1.63 ( ( finite_finite_nat @ A2 )
% 1.40/1.63 => ( ~ ( member_nat @ N @ A2 )
% 1.40/1.63 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 1.40/1.63 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % set_encode_insert
% 1.40/1.63 thf(fact_2310_valid__eq,axiom,
% 1.40/1.63 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 1.40/1.63
% 1.40/1.63 % valid_eq
% 1.40/1.63 thf(fact_2311_valid__eq2,axiom,
% 1.40/1.63 ! [T: vEBT_VEBT,D: nat] :
% 1.40/1.63 ( ( vEBT_VEBT_valid @ T @ D )
% 1.40/1.63 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 1.40/1.63
% 1.40/1.63 % valid_eq2
% 1.40/1.63 thf(fact_2312_valid__eq1,axiom,
% 1.40/1.63 ! [T: vEBT_VEBT,D: nat] :
% 1.40/1.63 ( ( vEBT_invar_vebt @ T @ D )
% 1.40/1.63 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 1.40/1.63
% 1.40/1.63 % valid_eq1
% 1.40/1.63 thf(fact_2313_set__vebt__finite,axiom,
% 1.40/1.63 ! [T: vEBT_VEBT,N: nat] :
% 1.40/1.63 ( ( vEBT_invar_vebt @ T @ N )
% 1.40/1.63 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % set_vebt_finite
% 1.40/1.63 thf(fact_2314_not__negative__int__iff,axiom,
% 1.40/1.63 ! [K: int] :
% 1.40/1.63 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 1.40/1.63 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 1.40/1.63
% 1.40/1.63 % not_negative_int_iff
% 1.40/1.63 thf(fact_2315_not__nonnegative__int__iff,axiom,
% 1.40/1.63 ! [K: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 1.40/1.63 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % not_nonnegative_int_iff
% 1.40/1.63 thf(fact_2316_and__minus__minus__numerals,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % and_minus_minus_numerals
% 1.40/1.63 thf(fact_2317_or__minus__minus__numerals,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_minus_minus_numerals
% 1.40/1.63 thf(fact_2318_bit__not__int__iff,axiom,
% 1.40/1.63 ! [K: int,N: nat] :
% 1.40/1.63 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 1.40/1.63 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bit_not_int_iff
% 1.40/1.63 thf(fact_2319_finite__M__bounded__by__nat,axiom,
% 1.40/1.63 ! [P: nat > $o,I2: nat] :
% 1.40/1.63 ( finite_finite_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [K3: nat] :
% 1.40/1.63 ( ( P @ K3 )
% 1.40/1.63 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_M_bounded_by_nat
% 1.40/1.63 thf(fact_2320_finite__nat__set__iff__bounded,axiom,
% 1.40/1.63 ( finite_finite_nat
% 1.40/1.63 = ( ^ [N6: set_nat] :
% 1.40/1.63 ? [M6: nat] :
% 1.40/1.63 ! [X4: nat] :
% 1.40/1.63 ( ( member_nat @ X4 @ N6 )
% 1.40/1.63 => ( ord_less_nat @ X4 @ M6 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_nat_set_iff_bounded
% 1.40/1.63 thf(fact_2321_bounded__nat__set__is__finite,axiom,
% 1.40/1.63 ! [N3: set_nat,N: nat] :
% 1.40/1.63 ( ! [X5: nat] :
% 1.40/1.63 ( ( member_nat @ X5 @ N3 )
% 1.40/1.63 => ( ord_less_nat @ X5 @ N ) )
% 1.40/1.63 => ( finite_finite_nat @ N3 ) ) ).
% 1.40/1.63
% 1.40/1.63 % bounded_nat_set_is_finite
% 1.40/1.63 thf(fact_2322_finite__nat__set__iff__bounded__le,axiom,
% 1.40/1.63 ( finite_finite_nat
% 1.40/1.63 = ( ^ [N6: set_nat] :
% 1.40/1.63 ? [M6: nat] :
% 1.40/1.63 ! [X4: nat] :
% 1.40/1.63 ( ( member_nat @ X4 @ N6 )
% 1.40/1.63 => ( ord_less_eq_nat @ X4 @ M6 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_nat_set_iff_bounded_le
% 1.40/1.63 thf(fact_2323_finite__less__ub,axiom,
% 1.40/1.63 ! [F: nat > nat,U: nat] :
% 1.40/1.63 ( ! [N4: nat] : ( ord_less_eq_nat @ N4 @ ( F @ N4 ) )
% 1.40/1.63 => ( finite_finite_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_less_ub
% 1.40/1.63 thf(fact_2324_or__int__def,axiom,
% 1.40/1.63 ( bit_se1409905431419307370or_int
% 1.40/1.63 = ( ^ [K3: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_int_def
% 1.40/1.63 thf(fact_2325_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 1.40/1.63 ! [Uu2: $o,Uv2: $o,D: nat] :
% 1.40/1.63 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D )
% 1.40/1.63 = ( D = one_one_nat ) ) ).
% 1.40/1.63
% 1.40/1.63 % VEBT_internal.valid'.simps(1)
% 1.40/1.63 thf(fact_2326_not__int__def,axiom,
% 1.40/1.63 ( bit_ri7919022796975470100ot_int
% 1.40/1.63 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % not_int_def
% 1.40/1.63 thf(fact_2327_and__not__numerals_I1_J,axiom,
% 1.40/1.63 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 1.40/1.63 = zero_zero_int ) ).
% 1.40/1.63
% 1.40/1.63 % and_not_numerals(1)
% 1.40/1.63 thf(fact_2328_or__not__numerals_I1_J,axiom,
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 1.40/1.63 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_not_numerals(1)
% 1.40/1.63 thf(fact_2329_unset__bit__int__def,axiom,
% 1.40/1.63 ( bit_se4203085406695923979it_int
% 1.40/1.63 = ( ^ [N2: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % unset_bit_int_def
% 1.40/1.63 thf(fact_2330_xor__int__def,axiom,
% 1.40/1.63 ( bit_se6526347334894502574or_int
% 1.40/1.63 = ( ^ [K3: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % xor_int_def
% 1.40/1.63 thf(fact_2331_finite__divisors__nat,axiom,
% 1.40/1.63 ! [M: nat] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.63 => ( finite_finite_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_divisors_nat
% 1.40/1.63 thf(fact_2332_subset__eq__atLeast0__atMost__finite,axiom,
% 1.40/1.63 ! [N3: set_nat,N: nat] :
% 1.40/1.63 ( ( ord_less_eq_set_nat @ N3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 1.40/1.63 => ( finite_finite_nat @ N3 ) ) ).
% 1.40/1.63
% 1.40/1.63 % subset_eq_atLeast0_atMost_finite
% 1.40/1.63 thf(fact_2333_not__int__div__2,axiom,
% 1.40/1.63 ! [K: int] :
% 1.40/1.63 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 1.40/1.63 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % not_int_div_2
% 1.40/1.63 thf(fact_2334_even__not__iff__int,axiom,
% 1.40/1.63 ! [K: int] :
% 1.40/1.63 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 1.40/1.63 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % even_not_iff_int
% 1.40/1.63 thf(fact_2335_and__not__numerals_I2_J,axiom,
% 1.40/1.63 ! [N: num] :
% 1.40/1.63 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 1.40/1.63 = one_one_int ) ).
% 1.40/1.63
% 1.40/1.63 % and_not_numerals(2)
% 1.40/1.63 thf(fact_2336_and__not__numerals_I4_J,axiom,
% 1.40/1.63 ! [M: num] :
% 1.40/1.63 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 1.40/1.63 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % and_not_numerals(4)
% 1.40/1.63 thf(fact_2337_or__not__numerals_I4_J,axiom,
% 1.40/1.63 ! [M: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 1.40/1.63 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_not_numerals(4)
% 1.40/1.63 thf(fact_2338_or__not__numerals_I2_J,axiom,
% 1.40/1.63 ! [N: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 1.40/1.63 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_not_numerals(2)
% 1.40/1.63 thf(fact_2339_bit__minus__int__iff,axiom,
% 1.40/1.63 ! [K: int,N: nat] :
% 1.40/1.63 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 1.40/1.63 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % bit_minus_int_iff
% 1.40/1.63 thf(fact_2340_int__numeral__or__not__num__neg,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % int_numeral_or_not_num_neg
% 1.40/1.63 thf(fact_2341_int__numeral__not__or__num__neg,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % int_numeral_not_or_num_neg
% 1.40/1.63 thf(fact_2342_numeral__or__not__num__eq,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 1.40/1.63 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % numeral_or_not_num_eq
% 1.40/1.63 thf(fact_2343_and__not__numerals_I5_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 1.40/1.63 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % and_not_numerals(5)
% 1.40/1.63 thf(fact_2344_and__not__numerals_I7_J,axiom,
% 1.40/1.63 ! [M: num] :
% 1.40/1.63 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 1.40/1.63 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % and_not_numerals(7)
% 1.40/1.63 thf(fact_2345_or__not__numerals_I3_J,axiom,
% 1.40/1.63 ! [N: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 1.40/1.63 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_not_numerals(3)
% 1.40/1.63 thf(fact_2346_and__not__numerals_I3_J,axiom,
% 1.40/1.63 ! [N: num] :
% 1.40/1.63 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 1.40/1.63 = zero_zero_int ) ).
% 1.40/1.63
% 1.40/1.63 % and_not_numerals(3)
% 1.40/1.63 thf(fact_2347_or__not__numerals_I7_J,axiom,
% 1.40/1.63 ! [M: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 1.40/1.63 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_not_numerals(7)
% 1.40/1.63 thf(fact_2348_and__not__numerals_I6_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 1.40/1.63 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % and_not_numerals(6)
% 1.40/1.63 thf(fact_2349_and__not__numerals_I9_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 1.40/1.63 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % and_not_numerals(9)
% 1.40/1.63 thf(fact_2350_or__not__numerals_I6_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 1.40/1.63 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_not_numerals(6)
% 1.40/1.63 thf(fact_2351_even__set__encode__iff,axiom,
% 1.40/1.63 ! [A2: set_nat] :
% 1.40/1.63 ( ( finite_finite_nat @ A2 )
% 1.40/1.63 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 1.40/1.63 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % even_set_encode_iff
% 1.40/1.63 thf(fact_2352_or__not__numerals_I5_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 1.40/1.63 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_not_numerals(5)
% 1.40/1.63 thf(fact_2353_and__not__numerals_I8_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 1.40/1.63 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % and_not_numerals(8)
% 1.40/1.63 thf(fact_2354_or__not__numerals_I8_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 1.40/1.63 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_not_numerals(8)
% 1.40/1.63 thf(fact_2355_or__not__numerals_I9_J,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 1.40/1.63 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % or_not_numerals(9)
% 1.40/1.63 thf(fact_2356_not__int__rec,axiom,
% 1.40/1.63 ( bit_ri7919022796975470100ot_int
% 1.40/1.63 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % not_int_rec
% 1.40/1.63 thf(fact_2357_finite__Collect__le__nat,axiom,
% 1.40/1.63 ! [K: nat] :
% 1.40/1.63 ( finite_finite_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_Collect_le_nat
% 1.40/1.63 thf(fact_2358_finite__Collect__less__nat,axiom,
% 1.40/1.63 ! [K: nat] :
% 1.40/1.63 ( finite_finite_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_Collect_less_nat
% 1.40/1.63 thf(fact_2359_finite__interval__int1,axiom,
% 1.40/1.63 ! [A: int,B: int] :
% 1.40/1.63 ( finite_finite_int
% 1.40/1.63 @ ( collect_int
% 1.40/1.63 @ ^ [I4: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ A @ I4 )
% 1.40/1.63 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_interval_int1
% 1.40/1.63 thf(fact_2360_finite__interval__int2,axiom,
% 1.40/1.63 ! [A: int,B: int] :
% 1.40/1.63 ( finite_finite_int
% 1.40/1.63 @ ( collect_int
% 1.40/1.63 @ ^ [I4: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ A @ I4 )
% 1.40/1.63 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_interval_int2
% 1.40/1.63 thf(fact_2361_finite__interval__int3,axiom,
% 1.40/1.63 ! [A: int,B: int] :
% 1.40/1.63 ( finite_finite_int
% 1.40/1.63 @ ( collect_int
% 1.40/1.63 @ ^ [I4: int] :
% 1.40/1.63 ( ( ord_less_int @ A @ I4 )
% 1.40/1.63 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_interval_int3
% 1.40/1.63 thf(fact_2362_finite__nth__roots,axiom,
% 1.40/1.63 ! [N: nat,C: complex] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( finite3207457112153483333omplex
% 1.40/1.63 @ ( collect_complex
% 1.40/1.63 @ ^ [Z5: complex] :
% 1.40/1.63 ( ( power_power_complex @ Z5 @ N )
% 1.40/1.63 = C ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_nth_roots
% 1.40/1.63 thf(fact_2363_finite__nat__iff__bounded__le,axiom,
% 1.40/1.63 ( finite_finite_nat
% 1.40/1.63 = ( ^ [S4: set_nat] :
% 1.40/1.63 ? [K3: nat] : ( ord_less_eq_set_nat @ S4 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_nat_iff_bounded_le
% 1.40/1.63 thf(fact_2364_bij__betw__nth__root__unity,axiom,
% 1.40/1.63 ! [C: complex,N: nat] :
% 1.40/1.63 ( ( C != zero_zero_complex )
% 1.40/1.63 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 1.40/1.63 @ ( collect_complex
% 1.40/1.63 @ ^ [Z5: complex] :
% 1.40/1.63 ( ( power_power_complex @ Z5 @ N )
% 1.40/1.63 = one_one_complex ) )
% 1.40/1.63 @ ( collect_complex
% 1.40/1.63 @ ^ [Z5: complex] :
% 1.40/1.63 ( ( power_power_complex @ Z5 @ N )
% 1.40/1.63 = C ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bij_betw_nth_root_unity
% 1.40/1.63 thf(fact_2365_finite__nat__bounded,axiom,
% 1.40/1.63 ! [S3: set_nat] :
% 1.40/1.63 ( ( finite_finite_nat @ S3 )
% 1.40/1.63 => ? [K2: nat] : ( ord_less_eq_set_nat @ S3 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_nat_bounded
% 1.40/1.63 thf(fact_2366_real__root__zero,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( root @ N @ zero_zero_real )
% 1.40/1.63 = zero_zero_real ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_zero
% 1.40/1.63 thf(fact_2367_real__root__Suc__0,axiom,
% 1.40/1.63 ! [X: real] :
% 1.40/1.63 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 1.40/1.63 = X ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_Suc_0
% 1.40/1.63 thf(fact_2368_root__0,axiom,
% 1.40/1.63 ! [X: real] :
% 1.40/1.63 ( ( root @ zero_zero_nat @ X )
% 1.40/1.63 = zero_zero_real ) ).
% 1.40/1.63
% 1.40/1.63 % root_0
% 1.40/1.63 thf(fact_2369_real__root__eq__iff,axiom,
% 1.40/1.63 ! [N: nat,X: real,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ( root @ N @ X )
% 1.40/1.63 = ( root @ N @ Y2 ) )
% 1.40/1.63 = ( X = Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_eq_iff
% 1.40/1.63 thf(fact_2370_real__root__eq__0__iff,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ( root @ N @ X )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 = ( X = zero_zero_real ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_eq_0_iff
% 1.40/1.63 thf(fact_2371_real__root__less__iff,axiom,
% 1.40/1.63 ! [N: nat,X: real,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) )
% 1.40/1.63 = ( ord_less_real @ X @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_less_iff
% 1.40/1.63 thf(fact_2372_real__root__le__iff,axiom,
% 1.40/1.63 ! [N: nat,X: real,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) )
% 1.40/1.63 = ( ord_less_eq_real @ X @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_le_iff
% 1.40/1.63 thf(fact_2373_real__root__one,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( root @ N @ one_one_real )
% 1.40/1.63 = one_one_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_one
% 1.40/1.63 thf(fact_2374_real__root__eq__1__iff,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ( root @ N @ X )
% 1.40/1.63 = one_one_real )
% 1.40/1.63 = ( X = one_one_real ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_eq_1_iff
% 1.40/1.63 thf(fact_2375_real__root__lt__0__iff,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 1.40/1.63 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_lt_0_iff
% 1.40/1.63 thf(fact_2376_real__root__gt__0__iff,axiom,
% 1.40/1.63 ! [N: nat,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 1.40/1.63 = ( ord_less_real @ zero_zero_real @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_gt_0_iff
% 1.40/1.63 thf(fact_2377_real__root__ge__0__iff,axiom,
% 1.40/1.63 ! [N: nat,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y2 ) )
% 1.40/1.63 = ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_ge_0_iff
% 1.40/1.63 thf(fact_2378_real__root__le__0__iff,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 1.40/1.63 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_le_0_iff
% 1.40/1.63 thf(fact_2379_real__root__gt__1__iff,axiom,
% 1.40/1.63 ! [N: nat,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y2 ) )
% 1.40/1.63 = ( ord_less_real @ one_one_real @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_gt_1_iff
% 1.40/1.63 thf(fact_2380_real__root__lt__1__iff,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 1.40/1.63 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_lt_1_iff
% 1.40/1.63 thf(fact_2381_real__root__le__1__iff,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 1.40/1.63 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_le_1_iff
% 1.40/1.63 thf(fact_2382_real__root__ge__1__iff,axiom,
% 1.40/1.63 ! [N: nat,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y2 ) )
% 1.40/1.63 = ( ord_less_eq_real @ one_one_real @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_ge_1_iff
% 1.40/1.63 thf(fact_2383_real__root__pow__pos2,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.63 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 1.40/1.63 = X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_pow_pos2
% 1.40/1.63 thf(fact_2384_real__root__minus,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( root @ N @ ( uminus_uminus_real @ X ) )
% 1.40/1.63 = ( uminus_uminus_real @ ( root @ N @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_minus
% 1.40/1.63 thf(fact_2385_real__root__divide,axiom,
% 1.40/1.63 ! [N: nat,X: real,Y2: real] :
% 1.40/1.63 ( ( root @ N @ ( divide_divide_real @ X @ Y2 ) )
% 1.40/1.63 = ( divide_divide_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_divide
% 1.40/1.63 thf(fact_2386_real__root__commute,axiom,
% 1.40/1.63 ! [M: nat,N: nat,X: real] :
% 1.40/1.63 ( ( root @ M @ ( root @ N @ X ) )
% 1.40/1.63 = ( root @ N @ ( root @ M @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_commute
% 1.40/1.63 thf(fact_2387_real__root__mult__exp,axiom,
% 1.40/1.63 ! [M: nat,N: nat,X: real] :
% 1.40/1.63 ( ( root @ ( times_times_nat @ M @ N ) @ X )
% 1.40/1.63 = ( root @ M @ ( root @ N @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_mult_exp
% 1.40/1.63 thf(fact_2388_real__root__mult,axiom,
% 1.40/1.63 ! [N: nat,X: real,Y2: real] :
% 1.40/1.63 ( ( root @ N @ ( times_times_real @ X @ Y2 ) )
% 1.40/1.63 = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_mult
% 1.40/1.63 thf(fact_2389_real__root__inverse,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( root @ N @ ( inverse_inverse_real @ X ) )
% 1.40/1.63 = ( inverse_inverse_real @ ( root @ N @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_inverse
% 1.40/1.63 thf(fact_2390_real__root__pos__pos__le,axiom,
% 1.40/1.63 ! [X: real,N: nat] :
% 1.40/1.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.63 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_pos_pos_le
% 1.40/1.63 thf(fact_2391_real__root__less__mono,axiom,
% 1.40/1.63 ! [N: nat,X: real,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ X @ Y2 )
% 1.40/1.63 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_less_mono
% 1.40/1.63 thf(fact_2392_real__root__le__mono,axiom,
% 1.40/1.63 ! [N: nat,X: real,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_real @ X @ Y2 )
% 1.40/1.63 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_le_mono
% 1.40/1.63 thf(fact_2393_real__root__power,axiom,
% 1.40/1.63 ! [N: nat,X: real,K: nat] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 1.40/1.63 = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_power
% 1.40/1.63 thf(fact_2394_real__root__abs,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 1.40/1.63 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_abs
% 1.40/1.63 thf(fact_2395_sgn__root,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 1.40/1.63 = ( sgn_sgn_real @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % sgn_root
% 1.40/1.63 thf(fact_2396_real__root__gt__zero,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.63 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_gt_zero
% 1.40/1.63 thf(fact_2397_real__root__strict__decreasing,axiom,
% 1.40/1.63 ! [N: nat,N3: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_nat @ N @ N3 )
% 1.40/1.63 => ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.63 => ( ord_less_real @ ( root @ N3 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_strict_decreasing
% 1.40/1.63 thf(fact_2398_sqrt__def,axiom,
% 1.40/1.63 ( sqrt
% 1.40/1.63 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % sqrt_def
% 1.40/1.63 thf(fact_2399_root__abs__power,axiom,
% 1.40/1.63 ! [N: nat,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y2 @ N ) ) )
% 1.40/1.63 = ( abs_abs_real @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % root_abs_power
% 1.40/1.63 thf(fact_2400_real__root__pos__pos,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.63 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_pos_pos
% 1.40/1.63 thf(fact_2401_real__root__strict__increasing,axiom,
% 1.40/1.63 ! [N: nat,N3: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_nat @ N @ N3 )
% 1.40/1.63 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.63 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.63 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N3 @ X ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_strict_increasing
% 1.40/1.63 thf(fact_2402_real__root__decreasing,axiom,
% 1.40/1.63 ! [N: nat,N3: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_nat @ N @ N3 )
% 1.40/1.63 => ( ( ord_less_eq_real @ one_one_real @ X )
% 1.40/1.63 => ( ord_less_eq_real @ ( root @ N3 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_decreasing
% 1.40/1.63 thf(fact_2403_real__root__pow__pos,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.63 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 1.40/1.63 = X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_pow_pos
% 1.40/1.63 thf(fact_2404_real__root__pos__unique,axiom,
% 1.40/1.63 ! [N: nat,Y2: real,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 1.40/1.63 => ( ( ( power_power_real @ Y2 @ N )
% 1.40/1.63 = X )
% 1.40/1.63 => ( ( root @ N @ X )
% 1.40/1.63 = Y2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_pos_unique
% 1.40/1.63 thf(fact_2405_real__root__power__cancel,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.63 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 1.40/1.63 = X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_power_cancel
% 1.40/1.63 thf(fact_2406_odd__real__root__pow,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.63 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 1.40/1.63 = X ) ) ).
% 1.40/1.63
% 1.40/1.63 % odd_real_root_pow
% 1.40/1.63 thf(fact_2407_odd__real__root__unique,axiom,
% 1.40/1.63 ! [N: nat,Y2: real,X: real] :
% 1.40/1.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.63 => ( ( ( power_power_real @ Y2 @ N )
% 1.40/1.63 = X )
% 1.40/1.63 => ( ( root @ N @ X )
% 1.40/1.63 = Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % odd_real_root_unique
% 1.40/1.63 thf(fact_2408_odd__real__root__power__cancel,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.63 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 1.40/1.63 = X ) ) ).
% 1.40/1.63
% 1.40/1.63 % odd_real_root_power_cancel
% 1.40/1.63 thf(fact_2409_real__root__increasing,axiom,
% 1.40/1.63 ! [N: nat,N3: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_eq_nat @ N @ N3 )
% 1.40/1.63 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.63 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.63 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N3 @ X ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_root_increasing
% 1.40/1.63 thf(fact_2410_root__sgn__power,axiom,
% 1.40/1.63 ! [N: nat,Y2: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N ) ) )
% 1.40/1.63 = Y2 ) ) ).
% 1.40/1.63
% 1.40/1.63 % root_sgn_power
% 1.40/1.63 thf(fact_2411_sgn__power__root,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 1.40/1.63 = X ) ) ).
% 1.40/1.63
% 1.40/1.63 % sgn_power_root
% 1.40/1.63 thf(fact_2412_ln__root,axiom,
% 1.40/1.63 ! [N: nat,B: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ zero_zero_real @ B )
% 1.40/1.63 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 1.40/1.63 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % ln_root
% 1.40/1.63 thf(fact_2413_log__root,axiom,
% 1.40/1.63 ! [N: nat,A: real,B: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ zero_zero_real @ A )
% 1.40/1.63 => ( ( log @ B @ ( root @ N @ A ) )
% 1.40/1.63 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % log_root
% 1.40/1.63 thf(fact_2414_log__base__root,axiom,
% 1.40/1.63 ! [N: nat,B: real,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ zero_zero_real @ B )
% 1.40/1.63 => ( ( log @ ( root @ N @ B ) @ X )
% 1.40/1.63 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % log_base_root
% 1.40/1.63 thf(fact_2415_split__root,axiom,
% 1.40/1.63 ! [P: real > $o,N: nat,X: real] :
% 1.40/1.63 ( ( P @ ( root @ N @ X ) )
% 1.40/1.63 = ( ( ( N = zero_zero_nat )
% 1.40/1.63 => ( P @ zero_zero_real ) )
% 1.40/1.63 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ! [Y4: real] :
% 1.40/1.63 ( ( ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 1.40/1.63 = X )
% 1.40/1.63 => ( P @ Y4 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % split_root
% 1.40/1.63 thf(fact_2416_infinite__int__iff__unbounded__le,axiom,
% 1.40/1.63 ! [S3: set_int] :
% 1.40/1.63 ( ( ~ ( finite_finite_int @ S3 ) )
% 1.40/1.63 = ( ! [M6: int] :
% 1.40/1.63 ? [N2: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ M6 @ ( abs_abs_int @ N2 ) )
% 1.40/1.63 & ( member_int @ N2 @ S3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % infinite_int_iff_unbounded_le
% 1.40/1.63 thf(fact_2417_infinite__nat__iff__unbounded,axiom,
% 1.40/1.63 ! [S3: set_nat] :
% 1.40/1.63 ( ( ~ ( finite_finite_nat @ S3 ) )
% 1.40/1.63 = ( ! [M6: nat] :
% 1.40/1.63 ? [N2: nat] :
% 1.40/1.63 ( ( ord_less_nat @ M6 @ N2 )
% 1.40/1.63 & ( member_nat @ N2 @ S3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % infinite_nat_iff_unbounded
% 1.40/1.63 thf(fact_2418_unbounded__k__infinite,axiom,
% 1.40/1.63 ! [K: nat,S3: set_nat] :
% 1.40/1.63 ( ! [M5: nat] :
% 1.40/1.63 ( ( ord_less_nat @ K @ M5 )
% 1.40/1.63 => ? [N7: nat] :
% 1.40/1.63 ( ( ord_less_nat @ M5 @ N7 )
% 1.40/1.63 & ( member_nat @ N7 @ S3 ) ) )
% 1.40/1.63 => ~ ( finite_finite_nat @ S3 ) ) ).
% 1.40/1.63
% 1.40/1.63 % unbounded_k_infinite
% 1.40/1.63 thf(fact_2419_infinite__nat__iff__unbounded__le,axiom,
% 1.40/1.63 ! [S3: set_nat] :
% 1.40/1.63 ( ( ~ ( finite_finite_nat @ S3 ) )
% 1.40/1.63 = ( ! [M6: nat] :
% 1.40/1.63 ? [N2: nat] :
% 1.40/1.63 ( ( ord_less_eq_nat @ M6 @ N2 )
% 1.40/1.63 & ( member_nat @ N2 @ S3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % infinite_nat_iff_unbounded_le
% 1.40/1.63 thf(fact_2420_root__powr__inverse,axiom,
% 1.40/1.63 ! [N: nat,X: real] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.63 => ( ( root @ N @ X )
% 1.40/1.63 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % root_powr_inverse
% 1.40/1.63 thf(fact_2421_finite__nat__iff__bounded,axiom,
% 1.40/1.63 ( finite_finite_nat
% 1.40/1.63 = ( ^ [S4: set_nat] :
% 1.40/1.63 ? [K3: nat] : ( ord_less_eq_set_nat @ S4 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_nat_iff_bounded
% 1.40/1.63 thf(fact_2422_Sum__Ico__nat,axiom,
% 1.40/1.63 ! [M: nat,N: nat] :
% 1.40/1.63 ( ( groups3542108847815614940at_nat
% 1.40/1.63 @ ^ [X4: nat] : X4
% 1.40/1.63 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 1.40/1.63 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Sum_Ico_nat
% 1.40/1.63 thf(fact_2423_Cauchy__iff2,axiom,
% 1.40/1.63 ( topolo4055970368930404560y_real
% 1.40/1.63 = ( ^ [X2: nat > real] :
% 1.40/1.63 ! [J3: nat] :
% 1.40/1.63 ? [M8: nat] :
% 1.40/1.63 ! [M6: nat] :
% 1.40/1.63 ( ( ord_less_eq_nat @ M8 @ M6 )
% 1.40/1.63 => ! [N2: nat] :
% 1.40/1.63 ( ( ord_less_eq_nat @ M8 @ N2 )
% 1.40/1.63 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X2 @ M6 ) @ ( X2 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Cauchy_iff2
% 1.40/1.63 thf(fact_2424_sum__power2,axiom,
% 1.40/1.63 ! [K: nat] :
% 1.40/1.63 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 1.40/1.63 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 1.40/1.63
% 1.40/1.63 % sum_power2
% 1.40/1.63 thf(fact_2425_atLeastLessThan__singleton,axiom,
% 1.40/1.63 ! [M: nat] :
% 1.40/1.63 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 1.40/1.63 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeastLessThan_singleton
% 1.40/1.63 thf(fact_2426_ex__nat__less__eq,axiom,
% 1.40/1.63 ! [N: nat,P: nat > $o] :
% 1.40/1.63 ( ( ? [M6: nat] :
% 1.40/1.63 ( ( ord_less_nat @ M6 @ N )
% 1.40/1.63 & ( P @ M6 ) ) )
% 1.40/1.63 = ( ? [X4: nat] :
% 1.40/1.63 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 1.40/1.63 & ( P @ X4 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % ex_nat_less_eq
% 1.40/1.63 thf(fact_2427_all__nat__less__eq,axiom,
% 1.40/1.63 ! [N: nat,P: nat > $o] :
% 1.40/1.63 ( ( ! [M6: nat] :
% 1.40/1.63 ( ( ord_less_nat @ M6 @ N )
% 1.40/1.63 => ( P @ M6 ) ) )
% 1.40/1.63 = ( ! [X4: nat] :
% 1.40/1.63 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 1.40/1.63 => ( P @ X4 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % all_nat_less_eq
% 1.40/1.63 thf(fact_2428_atLeastLessThanSuc__atLeastAtMost,axiom,
% 1.40/1.63 ! [L2: nat,U: nat] :
% 1.40/1.63 ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 1.40/1.63 = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeastLessThanSuc_atLeastAtMost
% 1.40/1.63 thf(fact_2429_atLeast0__lessThan__Suc,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 1.40/1.63 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeast0_lessThan_Suc
% 1.40/1.63 thf(fact_2430_subset__eq__atLeast0__lessThan__finite,axiom,
% 1.40/1.63 ! [N3: set_nat,N: nat] :
% 1.40/1.63 ( ( ord_less_eq_set_nat @ N3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 1.40/1.63 => ( finite_finite_nat @ N3 ) ) ).
% 1.40/1.63
% 1.40/1.63 % subset_eq_atLeast0_lessThan_finite
% 1.40/1.63 thf(fact_2431_atLeastLessThanSuc,axiom,
% 1.40/1.63 ! [M: nat,N: nat] :
% 1.40/1.63 ( ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.63 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 1.40/1.63 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_eq_nat @ M @ N )
% 1.40/1.63 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 1.40/1.63 = bot_bot_set_nat ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeastLessThanSuc
% 1.40/1.63 thf(fact_2432_prod__Suc__Suc__fact,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 1.40/1.63 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % prod_Suc_Suc_fact
% 1.40/1.63 thf(fact_2433_prod__Suc__fact,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 1.40/1.63 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % prod_Suc_fact
% 1.40/1.63 thf(fact_2434_atLeastLessThan__nat__numeral,axiom,
% 1.40/1.63 ! [M: nat,K: num] :
% 1.40/1.63 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 1.40/1.63 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 1.40/1.63 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 1.40/1.63 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 1.40/1.63 = bot_bot_set_nat ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeastLessThan_nat_numeral
% 1.40/1.63 thf(fact_2435_atLeast1__lessThan__eq__remove0,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 1.40/1.63 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeast1_lessThan_eq_remove0
% 1.40/1.63 thf(fact_2436_Chebyshev__sum__upper__nat,axiom,
% 1.40/1.63 ! [N: nat,A: nat > nat,B: nat > nat] :
% 1.40/1.63 ( ! [I3: nat,J2: nat] :
% 1.40/1.63 ( ( ord_less_eq_nat @ I3 @ J2 )
% 1.40/1.63 => ( ( ord_less_nat @ J2 @ N )
% 1.40/1.63 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 1.40/1.63 => ( ! [I3: nat,J2: nat] :
% 1.40/1.63 ( ( ord_less_eq_nat @ I3 @ J2 )
% 1.40/1.63 => ( ( ord_less_nat @ J2 @ N )
% 1.40/1.63 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I3 ) ) ) )
% 1.40/1.63 => ( ord_less_eq_nat
% 1.40/1.63 @ ( times_times_nat @ N
% 1.40/1.63 @ ( groups3542108847815614940at_nat
% 1.40/1.63 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( B @ I4 ) )
% 1.40/1.63 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 1.40/1.63 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Chebyshev_sum_upper_nat
% 1.40/1.63 thf(fact_2437_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 1.40/1.63 ! [L2: int,U: int] :
% 1.40/1.63 ( ( set_or4662586982721622107an_int @ L2 @ ( plus_plus_int @ U @ one_one_int ) )
% 1.40/1.63 = ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeastLessThanPlusOne_atLeastAtMost_int
% 1.40/1.63 thf(fact_2438_atLeastLessThan__upto,axiom,
% 1.40/1.63 ( set_or4662586982721622107an_int
% 1.40/1.63 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeastLessThan_upto
% 1.40/1.63 thf(fact_2439_Code__Target__Int_Opositive__def,axiom,
% 1.40/1.63 code_Target_positive = numeral_numeral_int ).
% 1.40/1.63
% 1.40/1.63 % Code_Target_Int.positive_def
% 1.40/1.63 thf(fact_2440_divmod__step__integer__def,axiom,
% 1.40/1.63 ( unique4921790084139445826nteger
% 1.40/1.63 = ( ^ [L: num] :
% 1.40/1.63 ( produc6916734918728496179nteger
% 1.40/1.63 @ ^ [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 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % divmod_step_integer_def
% 1.40/1.63 thf(fact_2441_csqrt_Osimps_I1_J,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( re @ ( csqrt @ Z ) )
% 1.40/1.63 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % csqrt.simps(1)
% 1.40/1.63 thf(fact_2442_card__Collect__less__nat,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( finite_card_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 1.40/1.63 = N ) ).
% 1.40/1.63
% 1.40/1.63 % card_Collect_less_nat
% 1.40/1.63 thf(fact_2443_card__atMost,axiom,
% 1.40/1.63 ! [U: nat] :
% 1.40/1.63 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 1.40/1.63 = ( suc @ U ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_atMost
% 1.40/1.63 thf(fact_2444_card__Collect__le__nat,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( finite_card_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 1.40/1.63 = ( suc @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_Collect_le_nat
% 1.40/1.63 thf(fact_2445_card__atLeastAtMost,axiom,
% 1.40/1.63 ! [L2: nat,U: nat] :
% 1.40/1.63 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 1.40/1.63 = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_atLeastAtMost
% 1.40/1.63 thf(fact_2446_complex__Re__numeral,axiom,
% 1.40/1.63 ! [V: num] :
% 1.40/1.63 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 1.40/1.63 = ( numeral_numeral_real @ V ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_Re_numeral
% 1.40/1.63 thf(fact_2447_card__atLeastAtMost__int,axiom,
% 1.40/1.63 ! [L2: int,U: int] :
% 1.40/1.63 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 1.40/1.63 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_atLeastAtMost_int
% 1.40/1.63 thf(fact_2448_Re__divide__numeral,axiom,
% 1.40/1.63 ! [Z: complex,W: num] :
% 1.40/1.63 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 1.40/1.63 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_divide_numeral
% 1.40/1.63 thf(fact_2449_divmod__integer_H__def,axiom,
% 1.40/1.63 ( unique3479559517661332726nteger
% 1.40/1.63 = ( ^ [M6: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % divmod_integer'_def
% 1.40/1.63 thf(fact_2450_less__eq__integer__code_I1_J,axiom,
% 1.40/1.63 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 1.40/1.63
% 1.40/1.63 % less_eq_integer_code(1)
% 1.40/1.63 thf(fact_2451_times__integer__code_I1_J,axiom,
% 1.40/1.63 ! [K: code_integer] :
% 1.40/1.63 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 1.40/1.63 = zero_z3403309356797280102nteger ) ).
% 1.40/1.63
% 1.40/1.63 % times_integer_code(1)
% 1.40/1.63 thf(fact_2452_times__integer__code_I2_J,axiom,
% 1.40/1.63 ! [L2: code_integer] :
% 1.40/1.63 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L2 )
% 1.40/1.63 = zero_z3403309356797280102nteger ) ).
% 1.40/1.63
% 1.40/1.63 % times_integer_code(2)
% 1.40/1.63 thf(fact_2453_plus__integer__code_I2_J,axiom,
% 1.40/1.63 ! [L2: code_integer] :
% 1.40/1.63 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L2 )
% 1.40/1.63 = L2 ) ).
% 1.40/1.63
% 1.40/1.63 % plus_integer_code(2)
% 1.40/1.63 thf(fact_2454_plus__integer__code_I1_J,axiom,
% 1.40/1.63 ! [K: code_integer] :
% 1.40/1.63 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 1.40/1.63 = K ) ).
% 1.40/1.63
% 1.40/1.63 % plus_integer_code(1)
% 1.40/1.63 thf(fact_2455_sgn__integer__code,axiom,
% 1.40/1.63 ( sgn_sgn_Code_integer
% 1.40/1.63 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % sgn_integer_code
% 1.40/1.63 thf(fact_2456_complex__Re__le__cmod,axiom,
% 1.40/1.63 ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_Re_le_cmod
% 1.40/1.63 thf(fact_2457_one__complex_Osimps_I1_J,axiom,
% 1.40/1.63 ( ( re @ one_one_complex )
% 1.40/1.63 = one_one_real ) ).
% 1.40/1.63
% 1.40/1.63 % one_complex.simps(1)
% 1.40/1.63 thf(fact_2458_plus__complex_Osimps_I1_J,axiom,
% 1.40/1.63 ! [X: complex,Y2: complex] :
% 1.40/1.63 ( ( re @ ( plus_plus_complex @ X @ Y2 ) )
% 1.40/1.63 = ( plus_plus_real @ ( re @ X ) @ ( re @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % plus_complex.simps(1)
% 1.40/1.63 thf(fact_2459_scaleR__complex_Osimps_I1_J,axiom,
% 1.40/1.63 ! [R2: real,X: complex] :
% 1.40/1.63 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 1.40/1.63 = ( times_times_real @ R2 @ ( re @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % scaleR_complex.simps(1)
% 1.40/1.63 thf(fact_2460_abs__Re__le__cmod,axiom,
% 1.40/1.63 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 1.40/1.63
% 1.40/1.63 % abs_Re_le_cmod
% 1.40/1.63 thf(fact_2461_Re__csqrt,axiom,
% 1.40/1.63 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_csqrt
% 1.40/1.63 thf(fact_2462_card__less__Suc2,axiom,
% 1.40/1.63 ! [M7: set_nat,I2: nat] :
% 1.40/1.63 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 1.40/1.63 => ( ( finite_card_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [K3: nat] :
% 1.40/1.63 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 1.40/1.63 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 1.40/1.63 = ( finite_card_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [K3: nat] :
% 1.40/1.63 ( ( member_nat @ K3 @ M7 )
% 1.40/1.63 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_less_Suc2
% 1.40/1.63 thf(fact_2463_card__less__Suc,axiom,
% 1.40/1.63 ! [M7: set_nat,I2: nat] :
% 1.40/1.63 ( ( member_nat @ zero_zero_nat @ M7 )
% 1.40/1.63 => ( ( suc
% 1.40/1.63 @ ( finite_card_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [K3: nat] :
% 1.40/1.63 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 1.40/1.63 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 1.40/1.63 = ( finite_card_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [K3: nat] :
% 1.40/1.63 ( ( member_nat @ K3 @ M7 )
% 1.40/1.63 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_less_Suc
% 1.40/1.63 thf(fact_2464_card__less,axiom,
% 1.40/1.63 ! [M7: set_nat,I2: nat] :
% 1.40/1.63 ( ( member_nat @ zero_zero_nat @ M7 )
% 1.40/1.63 => ( ( finite_card_nat
% 1.40/1.63 @ ( collect_nat
% 1.40/1.63 @ ^ [K3: nat] :
% 1.40/1.63 ( ( member_nat @ K3 @ M7 )
% 1.40/1.63 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 1.40/1.63 != zero_zero_nat ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_less
% 1.40/1.63 thf(fact_2465_one__integer_Orsp,axiom,
% 1.40/1.63 one_one_int = one_one_int ).
% 1.40/1.63
% 1.40/1.63 % one_integer.rsp
% 1.40/1.63 thf(fact_2466_subset__card__intvl__is__intvl,axiom,
% 1.40/1.63 ! [A2: set_nat,K: nat] :
% 1.40/1.63 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 1.40/1.63 => ( A2
% 1.40/1.63 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % subset_card_intvl_is_intvl
% 1.40/1.63 thf(fact_2467_one__natural_Orsp,axiom,
% 1.40/1.63 one_one_nat = one_one_nat ).
% 1.40/1.63
% 1.40/1.63 % one_natural.rsp
% 1.40/1.63 thf(fact_2468_subset__eq__atLeast0__lessThan__card,axiom,
% 1.40/1.63 ! [N3: set_nat,N: nat] :
% 1.40/1.63 ( ( ord_less_eq_set_nat @ N3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 1.40/1.63 => ( ord_less_eq_nat @ ( finite_card_nat @ N3 ) @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % subset_eq_atLeast0_lessThan_card
% 1.40/1.63 thf(fact_2469_card__sum__le__nat__sum,axiom,
% 1.40/1.63 ! [S3: set_nat] :
% 1.40/1.63 ( ord_less_eq_nat
% 1.40/1.63 @ ( groups3542108847815614940at_nat
% 1.40/1.63 @ ^ [X4: nat] : X4
% 1.40/1.63 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 1.40/1.63 @ ( groups3542108847815614940at_nat
% 1.40/1.63 @ ^ [X4: nat] : X4
% 1.40/1.63 @ S3 ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_sum_le_nat_sum
% 1.40/1.63 thf(fact_2470_card__nth__roots,axiom,
% 1.40/1.63 ! [C: complex,N: nat] :
% 1.40/1.63 ( ( C != zero_zero_complex )
% 1.40/1.63 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( finite_card_complex
% 1.40/1.63 @ ( collect_complex
% 1.40/1.63 @ ^ [Z5: complex] :
% 1.40/1.63 ( ( power_power_complex @ Z5 @ N )
% 1.40/1.63 = C ) ) )
% 1.40/1.63 = N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_nth_roots
% 1.40/1.63 thf(fact_2471_card__roots__unity__eq,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( finite_card_complex
% 1.40/1.63 @ ( collect_complex
% 1.40/1.63 @ ^ [Z5: complex] :
% 1.40/1.63 ( ( power_power_complex @ Z5 @ N )
% 1.40/1.63 = one_one_complex ) ) )
% 1.40/1.63 = N ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_roots_unity_eq
% 1.40/1.63 thf(fact_2472_cmod__plus__Re__le__0__iff,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 1.40/1.63 = ( ( re @ Z )
% 1.40/1.63 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % cmod_plus_Re_le_0_iff
% 1.40/1.63 thf(fact_2473_cos__n__Re__cis__pow__n,axiom,
% 1.40/1.63 ! [N: nat,A: real] :
% 1.40/1.63 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 1.40/1.63 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % cos_n_Re_cis_pow_n
% 1.40/1.63 thf(fact_2474_csqrt_Ocode,axiom,
% 1.40/1.63 ( csqrt
% 1.40/1.63 = ( ^ [Z5: complex] :
% 1.40/1.63 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.63 @ ( times_times_real
% 1.40/1.63 @ ( if_real
% 1.40/1.63 @ ( ( im @ Z5 )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 @ one_one_real
% 1.40/1.63 @ ( sgn_sgn_real @ ( im @ Z5 ) ) )
% 1.40/1.63 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % csqrt.code
% 1.40/1.63 thf(fact_2475_csqrt_Osimps_I2_J,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( im @ ( csqrt @ Z ) )
% 1.40/1.63 = ( times_times_real
% 1.40/1.63 @ ( if_real
% 1.40/1.63 @ ( ( im @ Z )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 @ one_one_real
% 1.40/1.63 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 1.40/1.63 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % csqrt.simps(2)
% 1.40/1.63 thf(fact_2476_integer__of__int__code,axiom,
% 1.40/1.63 ( code_integer_of_int
% 1.40/1.63 = ( ^ [K3: int] :
% 1.40/1.63 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 1.40/1.63 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 1.40/1.63 @ ( if_Code_integer
% 1.40/1.63 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 1.40/1.63 = zero_zero_int )
% 1.40/1.63 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 1.40/1.63 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % integer_of_int_code
% 1.40/1.63 thf(fact_2477_Im__power__real,axiom,
% 1.40/1.63 ! [X: complex,N: nat] :
% 1.40/1.63 ( ( ( im @ X )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 => ( ( im @ ( power_power_complex @ X @ N ) )
% 1.40/1.63 = zero_zero_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_power_real
% 1.40/1.63 thf(fact_2478_complex__Im__numeral,axiom,
% 1.40/1.63 ! [V: num] :
% 1.40/1.63 ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 1.40/1.63 = zero_zero_real ) ).
% 1.40/1.63
% 1.40/1.63 % complex_Im_numeral
% 1.40/1.63 thf(fact_2479_Im__i__times,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 1.40/1.63 = ( re @ Z ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_i_times
% 1.40/1.63 thf(fact_2480_Re__power__real,axiom,
% 1.40/1.63 ! [X: complex,N: nat] :
% 1.40/1.63 ( ( ( im @ X )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 => ( ( re @ ( power_power_complex @ X @ N ) )
% 1.40/1.63 = ( power_power_real @ ( re @ X ) @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_power_real
% 1.40/1.63 thf(fact_2481_Re__i__times,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 1.40/1.63 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_i_times
% 1.40/1.63 thf(fact_2482_Im__divide__numeral,axiom,
% 1.40/1.63 ! [Z: complex,W: num] :
% 1.40/1.63 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 1.40/1.63 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_divide_numeral
% 1.40/1.63 thf(fact_2483_csqrt__of__real__nonneg,axiom,
% 1.40/1.63 ! [X: complex] :
% 1.40/1.63 ( ( ( im @ X )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 1.40/1.63 => ( ( csqrt @ X )
% 1.40/1.63 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % csqrt_of_real_nonneg
% 1.40/1.63 thf(fact_2484_csqrt__minus,axiom,
% 1.40/1.63 ! [X: complex] :
% 1.40/1.63 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 1.40/1.63 | ( ( ( im @ X )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 1.40/1.63 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 1.40/1.63 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % csqrt_minus
% 1.40/1.63 thf(fact_2485_csqrt__of__real__nonpos,axiom,
% 1.40/1.63 ! [X: complex] :
% 1.40/1.63 ( ( ( im @ X )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 1.40/1.63 => ( ( csqrt @ X )
% 1.40/1.63 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % csqrt_of_real_nonpos
% 1.40/1.63 thf(fact_2486_imaginary__unit_Osimps_I2_J,axiom,
% 1.40/1.63 ( ( im @ imaginary_unit )
% 1.40/1.63 = one_one_real ) ).
% 1.40/1.63
% 1.40/1.63 % imaginary_unit.simps(2)
% 1.40/1.63 thf(fact_2487_one__complex_Osimps_I2_J,axiom,
% 1.40/1.63 ( ( im @ one_one_complex )
% 1.40/1.63 = zero_zero_real ) ).
% 1.40/1.63
% 1.40/1.63 % one_complex.simps(2)
% 1.40/1.63 thf(fact_2488_plus__integer_Oabs__eq,axiom,
% 1.40/1.63 ! [Xa2: int,X: int] :
% 1.40/1.63 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 1.40/1.63 = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % plus_integer.abs_eq
% 1.40/1.63 thf(fact_2489_times__integer_Oabs__eq,axiom,
% 1.40/1.63 ! [Xa2: int,X: int] :
% 1.40/1.63 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 1.40/1.63 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % times_integer.abs_eq
% 1.40/1.63 thf(fact_2490_one__integer__def,axiom,
% 1.40/1.63 ( one_one_Code_integer
% 1.40/1.63 = ( code_integer_of_int @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % one_integer_def
% 1.40/1.63 thf(fact_2491_less__eq__integer_Oabs__eq,axiom,
% 1.40/1.63 ! [Xa2: int,X: int] :
% 1.40/1.63 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 1.40/1.63 = ( ord_less_eq_int @ Xa2 @ X ) ) ).
% 1.40/1.63
% 1.40/1.63 % less_eq_integer.abs_eq
% 1.40/1.63 thf(fact_2492_plus__complex_Osimps_I2_J,axiom,
% 1.40/1.63 ! [X: complex,Y2: complex] :
% 1.40/1.63 ( ( im @ ( plus_plus_complex @ X @ Y2 ) )
% 1.40/1.63 = ( plus_plus_real @ ( im @ X ) @ ( im @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % plus_complex.simps(2)
% 1.40/1.63 thf(fact_2493_scaleR__complex_Osimps_I2_J,axiom,
% 1.40/1.63 ! [R2: real,X: complex] :
% 1.40/1.63 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 1.40/1.63 = ( times_times_real @ R2 @ ( im @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % scaleR_complex.simps(2)
% 1.40/1.63 thf(fact_2494_abs__Im__le__cmod,axiom,
% 1.40/1.63 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 1.40/1.63
% 1.40/1.63 % abs_Im_le_cmod
% 1.40/1.63 thf(fact_2495_times__complex_Osimps_I2_J,axiom,
% 1.40/1.63 ! [X: complex,Y2: complex] :
% 1.40/1.63 ( ( im @ ( times_times_complex @ X @ Y2 ) )
% 1.40/1.63 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % times_complex.simps(2)
% 1.40/1.63 thf(fact_2496_cmod__Im__le__iff,axiom,
% 1.40/1.63 ! [X: complex,Y2: complex] :
% 1.40/1.63 ( ( ( re @ X )
% 1.40/1.63 = ( re @ Y2 ) )
% 1.40/1.63 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) )
% 1.40/1.63 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % cmod_Im_le_iff
% 1.40/1.63 thf(fact_2497_cmod__Re__le__iff,axiom,
% 1.40/1.63 ! [X: complex,Y2: complex] :
% 1.40/1.63 ( ( ( im @ X )
% 1.40/1.63 = ( im @ Y2 ) )
% 1.40/1.63 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y2 ) )
% 1.40/1.63 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % cmod_Re_le_iff
% 1.40/1.63 thf(fact_2498_times__complex_Osimps_I1_J,axiom,
% 1.40/1.63 ! [X: complex,Y2: complex] :
% 1.40/1.63 ( ( re @ ( times_times_complex @ X @ Y2 ) )
% 1.40/1.63 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % times_complex.simps(1)
% 1.40/1.63 thf(fact_2499_plus__complex_Ocode,axiom,
% 1.40/1.63 ( plus_plus_complex
% 1.40/1.63 = ( ^ [X4: complex,Y4: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X4 ) @ ( re @ Y4 ) ) @ ( plus_plus_real @ ( im @ X4 ) @ ( im @ Y4 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % plus_complex.code
% 1.40/1.63 thf(fact_2500_scaleR__complex_Ocode,axiom,
% 1.40/1.63 ( real_V2046097035970521341omplex
% 1.40/1.63 = ( ^ [R5: real,X4: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X4 ) ) @ ( times_times_real @ R5 @ ( im @ X4 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % scaleR_complex.code
% 1.40/1.63 thf(fact_2501_csqrt__principal,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 1.40/1.63 | ( ( ( re @ ( csqrt @ Z ) )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % csqrt_principal
% 1.40/1.63 thf(fact_2502_cmod__le,axiom,
% 1.40/1.63 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % cmod_le
% 1.40/1.63 thf(fact_2503_sin__n__Im__cis__pow__n,axiom,
% 1.40/1.63 ! [N: nat,A: real] :
% 1.40/1.63 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 1.40/1.63 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % sin_n_Im_cis_pow_n
% 1.40/1.63 thf(fact_2504_Re__exp,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( re @ ( exp_complex @ Z ) )
% 1.40/1.63 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_exp
% 1.40/1.63 thf(fact_2505_Im__exp,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( im @ ( exp_complex @ Z ) )
% 1.40/1.63 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_exp
% 1.40/1.63 thf(fact_2506_complex__eq,axiom,
% 1.40/1.63 ! [A: complex] :
% 1.40/1.63 ( A
% 1.40/1.63 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_eq
% 1.40/1.63 thf(fact_2507_times__complex_Ocode,axiom,
% 1.40/1.63 ( times_times_complex
% 1.40/1.63 = ( ^ [X4: complex,Y4: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( im @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y4 ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % times_complex.code
% 1.40/1.63 thf(fact_2508_exp__eq__polar,axiom,
% 1.40/1.63 ( exp_complex
% 1.40/1.63 = ( ^ [Z5: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z5 ) ) ) @ ( cis @ ( im @ Z5 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % exp_eq_polar
% 1.40/1.63 thf(fact_2509_cmod__power2,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.63 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % cmod_power2
% 1.40/1.63 thf(fact_2510_Im__power2,axiom,
% 1.40/1.63 ! [X: complex] :
% 1.40/1.63 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.63 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_power2
% 1.40/1.63 thf(fact_2511_Re__power2,axiom,
% 1.40/1.63 ! [X: complex] :
% 1.40/1.63 ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.63 = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_power2
% 1.40/1.63 thf(fact_2512_complex__eq__0,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( Z = zero_zero_complex )
% 1.40/1.63 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.63 = zero_zero_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_eq_0
% 1.40/1.63 thf(fact_2513_norm__complex__def,axiom,
% 1.40/1.63 ( real_V1022390504157884413omplex
% 1.40/1.63 = ( ^ [Z5: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % norm_complex_def
% 1.40/1.63 thf(fact_2514_inverse__complex_Osimps_I1_J,axiom,
% 1.40/1.63 ! [X: complex] :
% 1.40/1.63 ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 1.40/1.63 = ( 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 ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % inverse_complex.simps(1)
% 1.40/1.63 thf(fact_2515_complex__neq__0,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( Z != zero_zero_complex )
% 1.40/1.63 = ( 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 ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_neq_0
% 1.40/1.63 thf(fact_2516_Re__divide,axiom,
% 1.40/1.63 ! [X: complex,Y2: complex] :
% 1.40/1.63 ( ( re @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 1.40/1.63 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X ) @ ( 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 ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_divide
% 1.40/1.63 thf(fact_2517_csqrt__unique,axiom,
% 1.40/1.63 ! [W: complex,Z: complex] :
% 1.40/1.63 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 1.40/1.63 = Z )
% 1.40/1.63 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 1.40/1.63 | ( ( ( re @ W )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 1.40/1.63 => ( ( csqrt @ Z )
% 1.40/1.63 = W ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % csqrt_unique
% 1.40/1.63 thf(fact_2518_csqrt__square,axiom,
% 1.40/1.63 ! [B: complex] :
% 1.40/1.63 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 1.40/1.63 | ( ( ( re @ B )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 1.40/1.63 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.63 = B ) ) ).
% 1.40/1.63
% 1.40/1.63 % csqrt_square
% 1.40/1.63 thf(fact_2519_inverse__complex_Osimps_I2_J,axiom,
% 1.40/1.63 ! [X: complex] :
% 1.40/1.63 ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 1.40/1.63 = ( 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 ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % inverse_complex.simps(2)
% 1.40/1.63 thf(fact_2520_Im__divide,axiom,
% 1.40/1.63 ! [X: complex,Y2: complex] :
% 1.40/1.63 ( ( im @ ( divide1717551699836669952omplex @ X @ Y2 ) )
% 1.40/1.63 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( re @ X ) @ ( 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 ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_divide
% 1.40/1.63 thf(fact_2521_complex__abs__le__norm,axiom,
% 1.40/1.63 ! [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 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_abs_le_norm
% 1.40/1.63 thf(fact_2522_complex__unit__circle,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( Z != zero_zero_complex )
% 1.40/1.63 => ( ( 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 ) ) ) )
% 1.40/1.63 = one_one_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_unit_circle
% 1.40/1.63 thf(fact_2523_inverse__complex_Ocode,axiom,
% 1.40/1.63 ( invers8013647133539491842omplex
% 1.40/1.63 = ( ^ [X4: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X4 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X4 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % inverse_complex.code
% 1.40/1.63 thf(fact_2524_Complex__divide,axiom,
% 1.40/1.63 ( divide1717551699836669952omplex
% 1.40/1.63 = ( ^ [X4: complex,Y4: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( re @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Complex_divide
% 1.40/1.63 thf(fact_2525_Im__Reals__divide,axiom,
% 1.40/1.63 ! [R2: complex,Z: complex] :
% 1.40/1.63 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 1.40/1.63 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 1.40/1.63 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_Reals_divide
% 1.40/1.63 thf(fact_2526_real__eq__imaginary__iff,axiom,
% 1.40/1.63 ! [Y2: complex,X: complex] :
% 1.40/1.63 ( ( member_complex @ Y2 @ real_V2521375963428798218omplex )
% 1.40/1.63 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 1.40/1.63 => ( ( X
% 1.40/1.63 = ( times_times_complex @ imaginary_unit @ Y2 ) )
% 1.40/1.63 = ( ( X = zero_zero_complex )
% 1.40/1.63 & ( Y2 = zero_zero_complex ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % real_eq_imaginary_iff
% 1.40/1.63 thf(fact_2527_imaginary__eq__real__iff,axiom,
% 1.40/1.63 ! [Y2: complex,X: complex] :
% 1.40/1.63 ( ( member_complex @ Y2 @ real_V2521375963428798218omplex )
% 1.40/1.63 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 1.40/1.63 => ( ( ( times_times_complex @ imaginary_unit @ Y2 )
% 1.40/1.63 = X )
% 1.40/1.63 = ( ( X = zero_zero_complex )
% 1.40/1.63 & ( Y2 = zero_zero_complex ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % imaginary_eq_real_iff
% 1.40/1.63 thf(fact_2528_distinct__upto,axiom,
% 1.40/1.63 ! [I2: int,J: int] : ( distinct_int @ ( upto @ I2 @ J ) ) ).
% 1.40/1.63
% 1.40/1.63 % distinct_upto
% 1.40/1.63 thf(fact_2529_Re__Reals__divide,axiom,
% 1.40/1.63 ! [R2: complex,Z: complex] :
% 1.40/1.63 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 1.40/1.63 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 1.40/1.63 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_Reals_divide
% 1.40/1.63 thf(fact_2530_Code__Numeral_Opositive__def,axiom,
% 1.40/1.63 code_positive = numera6620942414471956472nteger ).
% 1.40/1.63
% 1.40/1.63 % Code_Numeral.positive_def
% 1.40/1.63 thf(fact_2531_complex__mult__cnj,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 1.40/1.63 = ( 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 ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_mult_cnj
% 1.40/1.63 thf(fact_2532_complex__cnj__mult,axiom,
% 1.40/1.63 ! [X: complex,Y2: complex] :
% 1.40/1.63 ( ( cnj @ ( times_times_complex @ X @ Y2 ) )
% 1.40/1.63 = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_cnj_mult
% 1.40/1.63 thf(fact_2533_complex__cnj__one,axiom,
% 1.40/1.63 ( ( cnj @ one_one_complex )
% 1.40/1.63 = one_one_complex ) ).
% 1.40/1.63
% 1.40/1.63 % complex_cnj_one
% 1.40/1.63 thf(fact_2534_complex__cnj__one__iff,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( ( cnj @ Z )
% 1.40/1.63 = one_one_complex )
% 1.40/1.63 = ( Z = one_one_complex ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_cnj_one_iff
% 1.40/1.63 thf(fact_2535_complex__cnj__power,axiom,
% 1.40/1.63 ! [X: complex,N: nat] :
% 1.40/1.63 ( ( cnj @ ( power_power_complex @ X @ N ) )
% 1.40/1.63 = ( power_power_complex @ ( cnj @ X ) @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_cnj_power
% 1.40/1.63 thf(fact_2536_complex__cnj__add,axiom,
% 1.40/1.63 ! [X: complex,Y2: complex] :
% 1.40/1.63 ( ( cnj @ ( plus_plus_complex @ X @ Y2 ) )
% 1.40/1.63 = ( plus_plus_complex @ ( cnj @ X ) @ ( cnj @ Y2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_cnj_add
% 1.40/1.63 thf(fact_2537_complex__cnj__numeral,axiom,
% 1.40/1.63 ! [W: num] :
% 1.40/1.63 ( ( cnj @ ( numera6690914467698888265omplex @ W ) )
% 1.40/1.63 = ( numera6690914467698888265omplex @ W ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_cnj_numeral
% 1.40/1.63 thf(fact_2538_complex__cnj__neg__numeral,axiom,
% 1.40/1.63 ! [W: num] :
% 1.40/1.63 ( ( cnj @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 1.40/1.63 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_cnj_neg_numeral
% 1.40/1.63 thf(fact_2539_complex__In__mult__cnj__zero,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 1.40/1.63 = zero_zero_real ) ).
% 1.40/1.63
% 1.40/1.63 % complex_In_mult_cnj_zero
% 1.40/1.63 thf(fact_2540_Re__complex__div__eq__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 1.40/1.63 = zero_zero_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_complex_div_eq_0
% 1.40/1.63 thf(fact_2541_Im__complex__div__eq__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 1.40/1.63 = zero_zero_real )
% 1.40/1.63 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 1.40/1.63 = zero_zero_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_complex_div_eq_0
% 1.40/1.63 thf(fact_2542_complex__mod__sqrt__Re__mult__cnj,axiom,
% 1.40/1.63 ( real_V1022390504157884413omplex
% 1.40/1.63 = ( ^ [Z5: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z5 @ ( cnj @ Z5 ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_mod_sqrt_Re_mult_cnj
% 1.40/1.63 thf(fact_2543_Re__complex__div__lt__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 1.40/1.63 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_complex_div_lt_0
% 1.40/1.63 thf(fact_2544_Re__complex__div__gt__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 1.40/1.63 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_complex_div_gt_0
% 1.40/1.63 thf(fact_2545_Re__complex__div__ge__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 1.40/1.63 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_complex_div_ge_0
% 1.40/1.63 thf(fact_2546_Re__complex__div__le__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 1.40/1.63 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % Re_complex_div_le_0
% 1.40/1.63 thf(fact_2547_Im__complex__div__lt__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 1.40/1.63 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_complex_div_lt_0
% 1.40/1.63 thf(fact_2548_Im__complex__div__gt__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 1.40/1.63 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_complex_div_gt_0
% 1.40/1.63 thf(fact_2549_Im__complex__div__ge__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 1.40/1.63 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_complex_div_ge_0
% 1.40/1.63 thf(fact_2550_Im__complex__div__le__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 1.40/1.63 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % Im_complex_div_le_0
% 1.40/1.63 thf(fact_2551_complex__mod__mult__cnj,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 1.40/1.63 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_mod_mult_cnj
% 1.40/1.63 thf(fact_2552_complex__div__gt__0,axiom,
% 1.40/1.63 ! [A: complex,B: complex] :
% 1.40/1.63 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 1.40/1.63 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 1.40/1.63 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 1.40/1.63 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_div_gt_0
% 1.40/1.63 thf(fact_2553_complex__norm__square,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 1.40/1.63 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_norm_square
% 1.40/1.63 thf(fact_2554_complex__add__cnj,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 1.40/1.63 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_add_cnj
% 1.40/1.63 thf(fact_2555_complex__diff__cnj,axiom,
% 1.40/1.63 ! [Z: complex] :
% 1.40/1.63 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 1.40/1.63 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_diff_cnj
% 1.40/1.63 thf(fact_2556_complex__div__cnj,axiom,
% 1.40/1.63 ( divide1717551699836669952omplex
% 1.40/1.63 = ( ^ [A4: complex,B4: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A4 @ ( cnj @ B4 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % complex_div_cnj
% 1.40/1.63 thf(fact_2557_cnj__add__mult__eq__Re,axiom,
% 1.40/1.63 ! [Z: complex,W: complex] :
% 1.40/1.63 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 1.40/1.63 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % cnj_add_mult_eq_Re
% 1.40/1.63 thf(fact_2558_integer__of__num_I3_J,axiom,
% 1.40/1.63 ! [N: num] :
% 1.40/1.63 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 1.40/1.63 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 1.40/1.63
% 1.40/1.63 % integer_of_num(3)
% 1.40/1.63 thf(fact_2559_bit__cut__integer__def,axiom,
% 1.40/1.63 ( code_bit_cut_integer
% 1.40/1.63 = ( ^ [K3: code_integer] :
% 1.40/1.63 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 1.40/1.63 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bit_cut_integer_def
% 1.40/1.63 thf(fact_2560_integer__of__num__def,axiom,
% 1.40/1.63 code_integer_of_num = numera6620942414471956472nteger ).
% 1.40/1.63
% 1.40/1.63 % integer_of_num_def
% 1.40/1.63 thf(fact_2561_integer__of__num__triv_I1_J,axiom,
% 1.40/1.63 ( ( code_integer_of_num @ one )
% 1.40/1.63 = one_one_Code_integer ) ).
% 1.40/1.63
% 1.40/1.63 % integer_of_num_triv(1)
% 1.40/1.63 thf(fact_2562_integer__of__num_I2_J,axiom,
% 1.40/1.63 ! [N: num] :
% 1.40/1.63 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 1.40/1.63 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % integer_of_num(2)
% 1.40/1.63 thf(fact_2563_integer__of__num__triv_I2_J,axiom,
% 1.40/1.63 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 1.40/1.63 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % integer_of_num_triv(2)
% 1.40/1.63 thf(fact_2564_bit__cut__integer__code,axiom,
% 1.40/1.63 ( code_bit_cut_integer
% 1.40/1.63 = ( ^ [K3: code_integer] :
% 1.40/1.63 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 1.40/1.63 @ ( produc9125791028180074456eger_o
% 1.40/1.63 @ ^ [R5: code_integer,S5: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S5 ) ) @ ( S5 = one_one_Code_integer ) )
% 1.40/1.63 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bit_cut_integer_code
% 1.40/1.63 thf(fact_2565_nat_Odisc__eq__case_I2_J,axiom,
% 1.40/1.63 ! [Nat: nat] :
% 1.40/1.63 ( ( Nat != zero_zero_nat )
% 1.40/1.63 = ( case_nat_o @ $false
% 1.40/1.63 @ ^ [Uu3: nat] : $true
% 1.40/1.63 @ Nat ) ) ).
% 1.40/1.63
% 1.40/1.63 % nat.disc_eq_case(2)
% 1.40/1.63 thf(fact_2566_nat_Odisc__eq__case_I1_J,axiom,
% 1.40/1.63 ! [Nat: nat] :
% 1.40/1.63 ( ( Nat = zero_zero_nat )
% 1.40/1.63 = ( case_nat_o @ $true
% 1.40/1.63 @ ^ [Uu3: nat] : $false
% 1.40/1.63 @ Nat ) ) ).
% 1.40/1.63
% 1.40/1.63 % nat.disc_eq_case(1)
% 1.40/1.63 thf(fact_2567_less__eq__nat_Osimps_I2_J,axiom,
% 1.40/1.63 ! [M: nat,N: nat] :
% 1.40/1.63 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 1.40/1.63 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % less_eq_nat.simps(2)
% 1.40/1.63 thf(fact_2568_max__Suc2,axiom,
% 1.40/1.63 ! [M: nat,N: nat] :
% 1.40/1.63 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 1.40/1.63 = ( case_nat_nat @ ( suc @ N )
% 1.40/1.63 @ ^ [M2: nat] : ( suc @ ( ord_max_nat @ M2 @ N ) )
% 1.40/1.63 @ M ) ) ).
% 1.40/1.63
% 1.40/1.63 % max_Suc2
% 1.40/1.63 thf(fact_2569_max__Suc1,axiom,
% 1.40/1.63 ! [N: nat,M: nat] :
% 1.40/1.63 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 1.40/1.63 = ( case_nat_nat @ ( suc @ N )
% 1.40/1.63 @ ^ [M2: nat] : ( suc @ ( ord_max_nat @ N @ M2 ) )
% 1.40/1.63 @ M ) ) ).
% 1.40/1.63
% 1.40/1.63 % max_Suc1
% 1.40/1.63 thf(fact_2570_diff__Suc,axiom,
% 1.40/1.63 ! [M: nat,N: nat] :
% 1.40/1.63 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 1.40/1.63 = ( case_nat_nat @ zero_zero_nat
% 1.40/1.63 @ ^ [K3: nat] : K3
% 1.40/1.63 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % diff_Suc
% 1.40/1.63 thf(fact_2571_divmod__integer__code,axiom,
% 1.40/1.63 ( code_divmod_integer
% 1.40/1.63 = ( ^ [K3: code_integer,L: code_integer] :
% 1.40/1.63 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 1.40/1.63 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 1.40/1.63 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L )
% 1.40/1.63 @ ( produc6916734918728496179nteger
% 1.40/1.63 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S5 ) ) )
% 1.40/1.63 @ ( code_divmod_abs @ K3 @ L ) ) )
% 1.40/1.63 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 1.40/1.63 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 1.40/1.63 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L )
% 1.40/1.63 @ ( produc6916734918728496179nteger
% 1.40/1.63 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S5 ) ) )
% 1.40/1.63 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % divmod_integer_code
% 1.40/1.63 thf(fact_2572_floor__real__def,axiom,
% 1.40/1.63 ( archim6058952711729229775r_real
% 1.40/1.63 = ( ^ [X4: real] :
% 1.40/1.63 ( the_int
% 1.40/1.63 @ ^ [Z5: int] :
% 1.40/1.63 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X4 )
% 1.40/1.63 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % floor_real_def
% 1.40/1.63 thf(fact_2573_floor__rat__def,axiom,
% 1.40/1.63 ( archim3151403230148437115or_rat
% 1.40/1.63 = ( ^ [X4: rat] :
% 1.40/1.63 ( the_int
% 1.40/1.63 @ ^ [Z5: int] :
% 1.40/1.63 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X4 )
% 1.40/1.63 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % floor_rat_def
% 1.40/1.63 thf(fact_2574_sgn__rat__def,axiom,
% 1.40/1.63 ( sgn_sgn_rat
% 1.40/1.63 = ( ^ [A4: rat] : ( if_rat @ ( A4 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A4 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % sgn_rat_def
% 1.40/1.63 thf(fact_2575_obtain__pos__sum,axiom,
% 1.40/1.63 ! [R2: rat] :
% 1.40/1.63 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 1.40/1.63 => ~ ! [S2: rat] :
% 1.40/1.63 ( ( ord_less_rat @ zero_zero_rat @ S2 )
% 1.40/1.63 => ! [T3: rat] :
% 1.40/1.63 ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 1.40/1.63 => ( R2
% 1.40/1.63 != ( plus_plus_rat @ S2 @ T3 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % obtain_pos_sum
% 1.40/1.63 thf(fact_2576_less__eq__rat__def,axiom,
% 1.40/1.63 ( ord_less_eq_rat
% 1.40/1.63 = ( ^ [X4: rat,Y4: rat] :
% 1.40/1.63 ( ( ord_less_rat @ X4 @ Y4 )
% 1.40/1.63 | ( X4 = Y4 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % less_eq_rat_def
% 1.40/1.63 thf(fact_2577_pred__def,axiom,
% 1.40/1.63 ( pred
% 1.40/1.63 = ( case_nat_nat @ zero_zero_nat
% 1.40/1.63 @ ^ [X25: nat] : X25 ) ) ).
% 1.40/1.63
% 1.40/1.63 % pred_def
% 1.40/1.63 thf(fact_2578_rat__inverse__code,axiom,
% 1.40/1.63 ! [P2: rat] :
% 1.40/1.63 ( ( quotient_of @ ( inverse_inverse_rat @ P2 ) )
% 1.40/1.63 = ( produc4245557441103728435nt_int
% 1.40/1.63 @ ^ [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 ) ) )
% 1.40/1.63 @ ( quotient_of @ P2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % rat_inverse_code
% 1.40/1.63 thf(fact_2579_bezw__0,axiom,
% 1.40/1.63 ! [X: nat] :
% 1.40/1.63 ( ( bezw @ X @ zero_zero_nat )
% 1.40/1.63 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % bezw_0
% 1.40/1.63 thf(fact_2580_quotient__of__number_I3_J,axiom,
% 1.40/1.63 ! [K: num] :
% 1.40/1.63 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 1.40/1.63 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % quotient_of_number(3)
% 1.40/1.63 thf(fact_2581_rat__one__code,axiom,
% 1.40/1.63 ( ( quotient_of @ one_one_rat )
% 1.40/1.63 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % rat_one_code
% 1.40/1.63 thf(fact_2582_rat__zero__code,axiom,
% 1.40/1.63 ( ( quotient_of @ zero_zero_rat )
% 1.40/1.63 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % rat_zero_code
% 1.40/1.63 thf(fact_2583_quotient__of__number_I5_J,axiom,
% 1.40/1.63 ! [K: num] :
% 1.40/1.63 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 1.40/1.63 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % quotient_of_number(5)
% 1.40/1.63 thf(fact_2584_quotient__of__number_I4_J,axiom,
% 1.40/1.63 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 1.40/1.63 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % quotient_of_number(4)
% 1.40/1.63 thf(fact_2585_diff__rat__def,axiom,
% 1.40/1.63 ( minus_minus_rat
% 1.40/1.63 = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % diff_rat_def
% 1.40/1.63 thf(fact_2586_divide__rat__def,axiom,
% 1.40/1.63 ( divide_divide_rat
% 1.40/1.63 = ( ^ [Q4: rat,R5: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % divide_rat_def
% 1.40/1.63 thf(fact_2587_rat__less__code,axiom,
% 1.40/1.63 ( ord_less_rat
% 1.40/1.63 = ( ^ [P6: rat,Q4: rat] :
% 1.40/1.63 ( produc4947309494688390418_int_o
% 1.40/1.63 @ ^ [A4: int,C3: int] :
% 1.40/1.63 ( produc4947309494688390418_int_o
% 1.40/1.63 @ ^ [B4: int,D2: int] : ( ord_less_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C3 @ B4 ) )
% 1.40/1.63 @ ( quotient_of @ Q4 ) )
% 1.40/1.63 @ ( quotient_of @ P6 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % rat_less_code
% 1.40/1.63 thf(fact_2588_rat__less__eq__code,axiom,
% 1.40/1.63 ( ord_less_eq_rat
% 1.40/1.63 = ( ^ [P6: rat,Q4: rat] :
% 1.40/1.63 ( produc4947309494688390418_int_o
% 1.40/1.63 @ ^ [A4: int,C3: int] :
% 1.40/1.63 ( produc4947309494688390418_int_o
% 1.40/1.63 @ ^ [B4: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C3 @ B4 ) )
% 1.40/1.63 @ ( quotient_of @ Q4 ) )
% 1.40/1.63 @ ( quotient_of @ P6 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % rat_less_eq_code
% 1.40/1.63 thf(fact_2589_quotient__of__int,axiom,
% 1.40/1.63 ! [A: int] :
% 1.40/1.63 ( ( quotient_of @ ( of_int @ A ) )
% 1.40/1.63 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % quotient_of_int
% 1.40/1.63 thf(fact_2590_rat__plus__code,axiom,
% 1.40/1.63 ! [P2: rat,Q2: rat] :
% 1.40/1.63 ( ( quotient_of @ ( plus_plus_rat @ P2 @ Q2 ) )
% 1.40/1.63 = ( produc4245557441103728435nt_int
% 1.40/1.63 @ ^ [A4: int,C3: int] :
% 1.40/1.63 ( produc4245557441103728435nt_int
% 1.40/1.63 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 1.40/1.63 @ ( quotient_of @ Q2 ) )
% 1.40/1.63 @ ( quotient_of @ P2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % rat_plus_code
% 1.40/1.63 thf(fact_2591_rat__minus__code,axiom,
% 1.40/1.63 ! [P2: rat,Q2: rat] :
% 1.40/1.63 ( ( quotient_of @ ( minus_minus_rat @ P2 @ Q2 ) )
% 1.40/1.63 = ( produc4245557441103728435nt_int
% 1.40/1.63 @ ^ [A4: int,C3: int] :
% 1.40/1.63 ( produc4245557441103728435nt_int
% 1.40/1.63 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 1.40/1.63 @ ( quotient_of @ Q2 ) )
% 1.40/1.63 @ ( quotient_of @ P2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % rat_minus_code
% 1.40/1.63 thf(fact_2592_normalize__denom__zero,axiom,
% 1.40/1.63 ! [P2: int] :
% 1.40/1.63 ( ( normalize @ ( product_Pair_int_int @ P2 @ zero_zero_int ) )
% 1.40/1.63 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % normalize_denom_zero
% 1.40/1.63 thf(fact_2593_normalize__crossproduct,axiom,
% 1.40/1.63 ! [Q2: int,S: int,P2: int,R2: int] :
% 1.40/1.63 ( ( Q2 != zero_zero_int )
% 1.40/1.63 => ( ( S != zero_zero_int )
% 1.40/1.63 => ( ( ( normalize @ ( product_Pair_int_int @ P2 @ Q2 ) )
% 1.40/1.63 = ( normalize @ ( product_Pair_int_int @ R2 @ S ) ) )
% 1.40/1.63 => ( ( times_times_int @ P2 @ S )
% 1.40/1.63 = ( times_times_int @ R2 @ Q2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % normalize_crossproduct
% 1.40/1.63 thf(fact_2594_rat__times__code,axiom,
% 1.40/1.63 ! [P2: rat,Q2: rat] :
% 1.40/1.63 ( ( quotient_of @ ( times_times_rat @ P2 @ Q2 ) )
% 1.40/1.63 = ( produc4245557441103728435nt_int
% 1.40/1.63 @ ^ [A4: int,C3: int] :
% 1.40/1.63 ( produc4245557441103728435nt_int
% 1.40/1.63 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ B4 ) @ ( times_times_int @ C3 @ D2 ) ) )
% 1.40/1.63 @ ( quotient_of @ Q2 ) )
% 1.40/1.63 @ ( quotient_of @ P2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % rat_times_code
% 1.40/1.63 thf(fact_2595_rat__divide__code,axiom,
% 1.40/1.63 ! [P2: rat,Q2: rat] :
% 1.40/1.63 ( ( quotient_of @ ( divide_divide_rat @ P2 @ Q2 ) )
% 1.40/1.63 = ( produc4245557441103728435nt_int
% 1.40/1.63 @ ^ [A4: int,C3: int] :
% 1.40/1.63 ( produc4245557441103728435nt_int
% 1.40/1.63 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ D2 ) @ ( times_times_int @ C3 @ B4 ) ) )
% 1.40/1.63 @ ( quotient_of @ Q2 ) )
% 1.40/1.63 @ ( quotient_of @ P2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % rat_divide_code
% 1.40/1.63 thf(fact_2596_Frct__code__post_I5_J,axiom,
% 1.40/1.63 ! [K: num] :
% 1.40/1.63 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 1.40/1.63 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Frct_code_post(5)
% 1.40/1.63 thf(fact_2597_Frct__code__post_I6_J,axiom,
% 1.40/1.63 ! [K: num,L2: num] :
% 1.40/1.63 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 1.40/1.63 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Frct_code_post(6)
% 1.40/1.63 thf(fact_2598_prod__decode__aux_Oelims,axiom,
% 1.40/1.63 ! [X: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 1.40/1.63 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 1.40/1.63 = Y2 )
% 1.40/1.63 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 1.40/1.63 => ( Y2
% 1.40/1.63 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 1.40/1.63 => ( Y2
% 1.40/1.63 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % prod_decode_aux.elims
% 1.40/1.63 thf(fact_2599_Frct__code__post_I3_J,axiom,
% 1.40/1.63 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 1.40/1.63 = one_one_rat ) ).
% 1.40/1.63
% 1.40/1.63 % Frct_code_post(3)
% 1.40/1.63 thf(fact_2600_Frct__code__post_I4_J,axiom,
% 1.40/1.63 ! [K: num] :
% 1.40/1.63 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 1.40/1.63 = ( numeral_numeral_rat @ K ) ) ).
% 1.40/1.63
% 1.40/1.63 % Frct_code_post(4)
% 1.40/1.63 thf(fact_2601_prod__decode__aux_Osimps,axiom,
% 1.40/1.63 ( nat_prod_decode_aux
% 1.40/1.63 = ( ^ [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 ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % prod_decode_aux.simps
% 1.40/1.63 thf(fact_2602_prod__decode__aux_Opelims,axiom,
% 1.40/1.63 ! [X: nat,Xa2: nat,Y2: product_prod_nat_nat] :
% 1.40/1.63 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 1.40/1.63 = Y2 )
% 1.40/1.63 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 1.40/1.63 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 1.40/1.63 => ( Y2
% 1.40/1.63 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 1.40/1.63 => ( Y2
% 1.40/1.63 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 1.40/1.63 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % prod_decode_aux.pelims
% 1.40/1.63 thf(fact_2603_Suc__0__div__numeral,axiom,
% 1.40/1.63 ! [K: num] :
% 1.40/1.63 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 1.40/1.63 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Suc_0_div_numeral
% 1.40/1.63 thf(fact_2604_drop__bit__numeral__minus__bit1,axiom,
% 1.40/1.63 ! [L2: num,K: num] :
% 1.40/1.63 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 1.40/1.63 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_numeral_minus_bit1
% 1.40/1.63 thf(fact_2605_drop__bit__nonnegative__int__iff,axiom,
% 1.40/1.63 ! [N: nat,K: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 1.40/1.63 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_nonnegative_int_iff
% 1.40/1.63 thf(fact_2606_drop__bit__negative__int__iff,axiom,
% 1.40/1.63 ! [N: nat,K: int] :
% 1.40/1.63 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 1.40/1.63 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_negative_int_iff
% 1.40/1.63 thf(fact_2607_drop__bit__minus__one,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 1.40/1.63 = ( uminus_uminus_int @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_minus_one
% 1.40/1.63 thf(fact_2608_fst__divmod__nat,axiom,
% 1.40/1.63 ! [M: nat,N: nat] :
% 1.40/1.63 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 1.40/1.63 = ( divide_divide_nat @ M @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % fst_divmod_nat
% 1.40/1.63 thf(fact_2609_drop__bit__Suc__minus__bit0,axiom,
% 1.40/1.63 ! [N: nat,K: num] :
% 1.40/1.63 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 1.40/1.63 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_Suc_minus_bit0
% 1.40/1.63 thf(fact_2610_drop__bit__numeral__minus__bit0,axiom,
% 1.40/1.63 ! [L2: num,K: num] :
% 1.40/1.63 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 1.40/1.63 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_numeral_minus_bit0
% 1.40/1.63 thf(fact_2611_drop__bit__Suc__minus__bit1,axiom,
% 1.40/1.63 ! [N: nat,K: num] :
% 1.40/1.63 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 1.40/1.63 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_Suc_minus_bit1
% 1.40/1.63 thf(fact_2612_drop__bit__push__bit__int,axiom,
% 1.40/1.63 ! [M: nat,N: nat,K: int] :
% 1.40/1.63 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 1.40/1.63 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_push_bit_int
% 1.40/1.63 thf(fact_2613_drop__bit__int__def,axiom,
% 1.40/1.63 ( bit_se8568078237143864401it_int
% 1.40/1.63 = ( ^ [N2: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_int_def
% 1.40/1.63 thf(fact_2614_Suc__0__mod__numeral,axiom,
% 1.40/1.63 ! [K: num] :
% 1.40/1.63 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 1.40/1.63 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Suc_0_mod_numeral
% 1.40/1.63 thf(fact_2615_finite__enumerate,axiom,
% 1.40/1.63 ! [S3: set_nat] :
% 1.40/1.63 ( ( finite_finite_nat @ S3 )
% 1.40/1.63 => ? [R3: nat > nat] :
% 1.40/1.63 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 1.40/1.63 & ! [N7: nat] :
% 1.40/1.63 ( ( ord_less_nat @ N7 @ ( finite_card_nat @ S3 ) )
% 1.40/1.63 => ( member_nat @ ( R3 @ N7 ) @ S3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_enumerate
% 1.40/1.63 thf(fact_2616_drop__bit__of__Suc__0,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 1.40/1.63 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_of_Suc_0
% 1.40/1.63 thf(fact_2617_drop__bit__nat__eq,axiom,
% 1.40/1.63 ! [N: nat,K: int] :
% 1.40/1.63 ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 1.40/1.63 = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_nat_eq
% 1.40/1.63 thf(fact_2618_drop__bit__nat__def,axiom,
% 1.40/1.63 ( bit_se8570568707652914677it_nat
% 1.40/1.63 = ( ^ [N2: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % drop_bit_nat_def
% 1.40/1.63 thf(fact_2619_rat__sgn__code,axiom,
% 1.40/1.63 ! [P2: rat] :
% 1.40/1.63 ( ( quotient_of @ ( sgn_sgn_rat @ P2 ) )
% 1.40/1.63 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P2 ) ) ) @ one_one_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % rat_sgn_code
% 1.40/1.63 thf(fact_2620_bezw__non__0,axiom,
% 1.40/1.63 ! [Y2: nat,X: nat] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ Y2 )
% 1.40/1.63 => ( ( bezw @ X @ Y2 )
% 1.40/1.63 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X @ Y2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y2 ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bezw_non_0
% 1.40/1.63 thf(fact_2621_bezw_Oelims,axiom,
% 1.40/1.63 ! [X: nat,Xa2: nat,Y2: product_prod_int_int] :
% 1.40/1.63 ( ( ( bezw @ X @ Xa2 )
% 1.40/1.63 = Y2 )
% 1.40/1.63 => ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.63 => ( Y2
% 1.40/1.63 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 1.40/1.63 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.63 => ( Y2
% 1.40/1.63 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bezw.elims
% 1.40/1.63 thf(fact_2622_bezw_Osimps,axiom,
% 1.40/1.63 ( bezw
% 1.40/1.63 = ( ^ [X4: nat,Y4: nat] : ( if_Pro3027730157355071871nt_int @ ( Y4 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Y4 ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bezw.simps
% 1.40/1.63 thf(fact_2623_bezw_Opelims,axiom,
% 1.40/1.63 ! [X: nat,Xa2: nat,Y2: product_prod_int_int] :
% 1.40/1.63 ( ( ( bezw @ X @ Xa2 )
% 1.40/1.63 = Y2 )
% 1.40/1.63 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 1.40/1.63 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 1.40/1.63 => ( Y2
% 1.40/1.63 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 1.40/1.63 & ( ( Xa2 != zero_zero_nat )
% 1.40/1.63 => ( Y2
% 1.40/1.63 = ( 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 ) ) ) ) ) ) ) )
% 1.40/1.63 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bezw.pelims
% 1.40/1.63 thf(fact_2624_one__mod__minus__numeral,axiom,
% 1.40/1.63 ! [N: num] :
% 1.40/1.63 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % one_mod_minus_numeral
% 1.40/1.63 thf(fact_2625_minus__numeral__mod__numeral,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % minus_numeral_mod_numeral
% 1.40/1.63 thf(fact_2626_numeral__mod__minus__numeral,axiom,
% 1.40/1.63 ! [M: num,N: num] :
% 1.40/1.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % numeral_mod_minus_numeral
% 1.40/1.63 thf(fact_2627_minus__one__mod__numeral,axiom,
% 1.40/1.63 ! [N: num] :
% 1.40/1.63 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.63 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % minus_one_mod_numeral
% 1.40/1.63 thf(fact_2628_normalize__def,axiom,
% 1.40/1.63 ( normalize
% 1.40/1.63 = ( ^ [P6: product_prod_int_int] :
% 1.40/1.63 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P6 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) )
% 1.40/1.63 @ ( if_Pro3027730157355071871nt_int
% 1.40/1.63 @ ( ( product_snd_int_int @ P6 )
% 1.40/1.63 = zero_zero_int )
% 1.40/1.63 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 1.40/1.63 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % normalize_def
% 1.40/1.63 thf(fact_2629_gcd__1__int,axiom,
% 1.40/1.63 ! [M: int] :
% 1.40/1.63 ( ( gcd_gcd_int @ M @ one_one_int )
% 1.40/1.63 = one_one_int ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_1_int
% 1.40/1.63 thf(fact_2630_gcd__neg__numeral__1__int,axiom,
% 1.40/1.63 ! [N: num,X: int] :
% 1.40/1.63 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 1.40/1.63 = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_neg_numeral_1_int
% 1.40/1.63 thf(fact_2631_gcd__neg__numeral__2__int,axiom,
% 1.40/1.63 ! [X: int,N: num] :
% 1.40/1.63 ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_neg_numeral_2_int
% 1.40/1.63 thf(fact_2632_gcd__ge__0__int,axiom,
% 1.40/1.63 ! [X: int,Y2: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y2 ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_ge_0_int
% 1.40/1.63 thf(fact_2633_bezout__int,axiom,
% 1.40/1.63 ! [X: int,Y2: int] :
% 1.40/1.63 ? [U2: int,V2: int] :
% 1.40/1.63 ( ( plus_plus_int @ ( times_times_int @ U2 @ X ) @ ( times_times_int @ V2 @ Y2 ) )
% 1.40/1.63 = ( gcd_gcd_int @ X @ Y2 ) ) ).
% 1.40/1.63
% 1.40/1.63 % bezout_int
% 1.40/1.63 thf(fact_2634_gcd__mult__distrib__int,axiom,
% 1.40/1.63 ! [K: int,M: int,N: int] :
% 1.40/1.63 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 1.40/1.63 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_mult_distrib_int
% 1.40/1.63 thf(fact_2635_gcd__le1__int,axiom,
% 1.40/1.63 ! [A: int,B: int] :
% 1.40/1.63 ( ( ord_less_int @ zero_zero_int @ A )
% 1.40/1.63 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_le1_int
% 1.40/1.63 thf(fact_2636_gcd__le2__int,axiom,
% 1.40/1.63 ! [B: int,A: int] :
% 1.40/1.63 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.63 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_le2_int
% 1.40/1.63 thf(fact_2637_gcd__cases__int,axiom,
% 1.40/1.63 ! [X: int,Y2: int,P: int > $o] :
% 1.40/1.63 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.63 => ( P @ ( gcd_gcd_int @ X @ Y2 ) ) ) )
% 1.40/1.63 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 1.40/1.63 => ( ( ord_less_eq_int @ Y2 @ zero_zero_int )
% 1.40/1.63 => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y2 ) ) ) ) )
% 1.40/1.63 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 1.40/1.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y2 )
% 1.40/1.63 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y2 ) ) ) )
% 1.40/1.63 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 1.40/1.63 => ( ( ord_less_eq_int @ Y2 @ zero_zero_int )
% 1.40/1.63 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y2 ) ) ) ) )
% 1.40/1.63 => ( P @ ( gcd_gcd_int @ X @ Y2 ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_cases_int
% 1.40/1.63 thf(fact_2638_gcd__unique__int,axiom,
% 1.40/1.63 ! [D: int,A: int,B: int] :
% 1.40/1.63 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 1.40/1.63 & ( dvd_dvd_int @ D @ A )
% 1.40/1.63 & ( dvd_dvd_int @ D @ B )
% 1.40/1.63 & ! [E3: int] :
% 1.40/1.63 ( ( ( dvd_dvd_int @ E3 @ A )
% 1.40/1.63 & ( dvd_dvd_int @ E3 @ B ) )
% 1.40/1.63 => ( dvd_dvd_int @ E3 @ D ) ) )
% 1.40/1.63 = ( D
% 1.40/1.63 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_unique_int
% 1.40/1.63 thf(fact_2639_gcd__1__nat,axiom,
% 1.40/1.63 ! [M: nat] :
% 1.40/1.63 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 1.40/1.63 = one_one_nat ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_1_nat
% 1.40/1.63 thf(fact_2640_gcd__Suc__0,axiom,
% 1.40/1.63 ! [M: nat] :
% 1.40/1.63 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 1.40/1.63 = ( suc @ zero_zero_nat ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_Suc_0
% 1.40/1.63 thf(fact_2641_gcd__pos__nat,axiom,
% 1.40/1.63 ! [M: nat,N: nat] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 1.40/1.63 = ( ( M != zero_zero_nat )
% 1.40/1.63 | ( N != zero_zero_nat ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_pos_nat
% 1.40/1.63 thf(fact_2642_gcd__mult__distrib__nat,axiom,
% 1.40/1.63 ! [K: nat,M: nat,N: nat] :
% 1.40/1.63 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 1.40/1.63 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_mult_distrib_nat
% 1.40/1.63 thf(fact_2643_gcd__le2__nat,axiom,
% 1.40/1.63 ! [B: nat,A: nat] :
% 1.40/1.63 ( ( B != zero_zero_nat )
% 1.40/1.63 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_le2_nat
% 1.40/1.63 thf(fact_2644_gcd__le1__nat,axiom,
% 1.40/1.63 ! [A: nat,B: nat] :
% 1.40/1.63 ( ( A != zero_zero_nat )
% 1.40/1.63 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_le1_nat
% 1.40/1.63 thf(fact_2645_gcd__diff2__nat,axiom,
% 1.40/1.63 ! [M: nat,N: nat] :
% 1.40/1.63 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.63 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 1.40/1.63 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_diff2_nat
% 1.40/1.63 thf(fact_2646_gcd__diff1__nat,axiom,
% 1.40/1.63 ! [N: nat,M: nat] :
% 1.40/1.63 ( ( ord_less_eq_nat @ N @ M )
% 1.40/1.63 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 1.40/1.63 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % gcd_diff1_nat
% 1.40/1.63 thf(fact_2647_bezout__nat,axiom,
% 1.40/1.63 ! [A: nat,B: nat] :
% 1.40/1.63 ( ( A != zero_zero_nat )
% 1.40/1.63 => ? [X5: nat,Y3: nat] :
% 1.40/1.63 ( ( times_times_nat @ A @ X5 )
% 1.40/1.63 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bezout_nat
% 1.40/1.63 thf(fact_2648_bezout__gcd__nat_H,axiom,
% 1.40/1.63 ! [B: nat,A: nat] :
% 1.40/1.63 ? [X5: nat,Y3: nat] :
% 1.40/1.63 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X5 ) )
% 1.40/1.63 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X5 ) @ ( times_times_nat @ B @ Y3 ) )
% 1.40/1.63 = ( gcd_gcd_nat @ A @ B ) ) )
% 1.40/1.63 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X5 ) )
% 1.40/1.63 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X5 ) @ ( times_times_nat @ A @ Y3 ) )
% 1.40/1.63 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bezout_gcd_nat'
% 1.40/1.63 thf(fact_2649_bezw__aux,axiom,
% 1.40/1.63 ! [X: nat,Y2: nat] :
% 1.40/1.63 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y2 ) )
% 1.40/1.63 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y2 ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y2 ) ) @ ( semiri1314217659103216013at_int @ Y2 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % bezw_aux
% 1.40/1.63 thf(fact_2650_nat__descend__induct,axiom,
% 1.40/1.63 ! [N: nat,P: nat > $o,M: nat] :
% 1.40/1.63 ( ! [K2: nat] :
% 1.40/1.63 ( ( ord_less_nat @ N @ K2 )
% 1.40/1.63 => ( P @ K2 ) )
% 1.40/1.63 => ( ! [K2: nat] :
% 1.40/1.63 ( ( ord_less_eq_nat @ K2 @ N )
% 1.40/1.63 => ( ! [I: nat] :
% 1.40/1.63 ( ( ord_less_nat @ K2 @ I )
% 1.40/1.63 => ( P @ I ) )
% 1.40/1.63 => ( P @ K2 ) ) )
% 1.40/1.63 => ( P @ M ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % nat_descend_induct
% 1.40/1.63 thf(fact_2651_card__greaterThanLessThan__int,axiom,
% 1.40/1.63 ! [L2: int,U: int] :
% 1.40/1.63 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 1.40/1.63 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_greaterThanLessThan_int
% 1.40/1.63 thf(fact_2652_xor__minus__numerals_I2_J,axiom,
% 1.40/1.63 ! [K: int,N: num] :
% 1.40/1.63 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.63 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % xor_minus_numerals(2)
% 1.40/1.63 thf(fact_2653_xor__minus__numerals_I1_J,axiom,
% 1.40/1.63 ! [N: num,K: int] :
% 1.40/1.63 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 1.40/1.63 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % xor_minus_numerals(1)
% 1.40/1.63 thf(fact_2654_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 1.40/1.63 ! [L2: int,U: int] :
% 1.40/1.63 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 1.40/1.63 = ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 1.40/1.63 thf(fact_2655_sub__BitM__One__eq,axiom,
% 1.40/1.63 ! [N: num] :
% 1.40/1.63 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 1.40/1.63 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % sub_BitM_One_eq
% 1.40/1.63 thf(fact_2656_greaterThanLessThan__upto,axiom,
% 1.40/1.63 ( set_or5832277885323065728an_int
% 1.40/1.63 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % greaterThanLessThan_upto
% 1.40/1.63 thf(fact_2657_card__greaterThanLessThan,axiom,
% 1.40/1.63 ! [L2: nat,U: nat] :
% 1.40/1.63 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 1.40/1.63 = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % card_greaterThanLessThan
% 1.40/1.63 thf(fact_2658_atLeastSucLessThan__greaterThanLessThan,axiom,
% 1.40/1.63 ! [L2: nat,U: nat] :
% 1.40/1.63 ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 1.40/1.63 = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeastSucLessThan_greaterThanLessThan
% 1.40/1.63 thf(fact_2659_tanh__real__bounds,axiom,
% 1.40/1.63 ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 1.40/1.63
% 1.40/1.63 % tanh_real_bounds
% 1.40/1.63 thf(fact_2660_nat__of__integer__non__positive,axiom,
% 1.40/1.63 ! [K: code_integer] :
% 1.40/1.63 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 1.40/1.63 => ( ( code_nat_of_integer @ K )
% 1.40/1.63 = zero_zero_nat ) ) ).
% 1.40/1.63
% 1.40/1.63 % nat_of_integer_non_positive
% 1.40/1.63 thf(fact_2661_Suc__funpow,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( compow_nat_nat @ N @ suc )
% 1.40/1.63 = ( plus_plus_nat @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % Suc_funpow
% 1.40/1.63 thf(fact_2662_nat__of__integer__code__post_I3_J,axiom,
% 1.40/1.63 ! [K: num] :
% 1.40/1.63 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 1.40/1.63 = ( numeral_numeral_nat @ K ) ) ).
% 1.40/1.63
% 1.40/1.63 % nat_of_integer_code_post(3)
% 1.40/1.63 thf(fact_2663_nat__of__integer__code__post_I2_J,axiom,
% 1.40/1.63 ( ( code_nat_of_integer @ one_one_Code_integer )
% 1.40/1.63 = one_one_nat ) ).
% 1.40/1.63
% 1.40/1.63 % nat_of_integer_code_post(2)
% 1.40/1.63 thf(fact_2664_nat__of__integer__code,axiom,
% 1.40/1.63 ( code_nat_of_integer
% 1.40/1.63 = ( ^ [K3: code_integer] :
% 1.40/1.63 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 1.40/1.63 @ ( produc1555791787009142072er_nat
% 1.40/1.63 @ ^ [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 ) )
% 1.40/1.63 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % nat_of_integer_code
% 1.40/1.63 thf(fact_2665_divmod__integer__eq__cases,axiom,
% 1.40/1.63 ( code_divmod_integer
% 1.40/1.63 = ( ^ [K3: code_integer,L: code_integer] :
% 1.40/1.63 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 1.40/1.63 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 1.40/1.63 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 1.40/1.63 @ ( if_Pro6119634080678213985nteger
% 1.40/1.63 @ ( ( sgn_sgn_Code_integer @ K3 )
% 1.40/1.63 = ( sgn_sgn_Code_integer @ L ) )
% 1.40/1.63 @ ( code_divmod_abs @ K3 @ L )
% 1.40/1.63 @ ( produc6916734918728496179nteger
% 1.40/1.63 @ ^ [R5: code_integer,S5: code_integer] : ( if_Pro6119634080678213985nteger @ ( S5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S5 ) ) )
% 1.40/1.63 @ ( code_divmod_abs @ K3 @ L ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % divmod_integer_eq_cases
% 1.40/1.63 thf(fact_2666_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 1.40/1.63 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 1.40/1.63 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 1.40/1.63 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 1.40/1.63
% 1.40/1.63 % max_nat.semilattice_neutr_order_axioms
% 1.40/1.63 thf(fact_2667_int__of__integer__code,axiom,
% 1.40/1.63 ( code_int_of_integer
% 1.40/1.63 = ( ^ [K3: code_integer] :
% 1.40/1.63 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 1.40/1.63 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 1.40/1.63 @ ( produc1553301316500091796er_int
% 1.40/1.63 @ ^ [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 ) )
% 1.40/1.63 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % int_of_integer_code
% 1.40/1.63 thf(fact_2668_int__of__integer__numeral,axiom,
% 1.40/1.63 ! [K: num] :
% 1.40/1.63 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 1.40/1.63 = ( numeral_numeral_int @ K ) ) ).
% 1.40/1.63
% 1.40/1.63 % int_of_integer_numeral
% 1.40/1.63 thf(fact_2669_plus__integer_Orep__eq,axiom,
% 1.40/1.63 ! [X: code_integer,Xa2: code_integer] :
% 1.40/1.63 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa2 ) )
% 1.40/1.63 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % plus_integer.rep_eq
% 1.40/1.63 thf(fact_2670_times__integer_Orep__eq,axiom,
% 1.40/1.63 ! [X: code_integer,Xa2: code_integer] :
% 1.40/1.63 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 1.40/1.63 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % times_integer.rep_eq
% 1.40/1.63 thf(fact_2671_one__integer_Orep__eq,axiom,
% 1.40/1.63 ( ( code_int_of_integer @ one_one_Code_integer )
% 1.40/1.63 = one_one_int ) ).
% 1.40/1.63
% 1.40/1.63 % one_integer.rep_eq
% 1.40/1.63 thf(fact_2672_card_Ocomp__fun__commute__on,axiom,
% 1.40/1.63 ( ( comp_nat_nat_nat @ suc @ suc )
% 1.40/1.63 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 1.40/1.63
% 1.40/1.63 % card.comp_fun_commute_on
% 1.40/1.63 thf(fact_2673_less__eq__integer_Orep__eq,axiom,
% 1.40/1.63 ( ord_le3102999989581377725nteger
% 1.40/1.63 = ( ^ [X4: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % less_eq_integer.rep_eq
% 1.40/1.63 thf(fact_2674_integer__less__eq__iff,axiom,
% 1.40/1.63 ( ord_le3102999989581377725nteger
% 1.40/1.63 = ( ^ [K3: code_integer,L: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % integer_less_eq_iff
% 1.40/1.63 thf(fact_2675_Code__Numeral_Onegative__def,axiom,
% 1.40/1.63 ( code_negative
% 1.40/1.63 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 1.40/1.63
% 1.40/1.63 % Code_Numeral.negative_def
% 1.40/1.63 thf(fact_2676_Code__Target__Int_Onegative__def,axiom,
% 1.40/1.63 ( code_Target_negative
% 1.40/1.63 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 1.40/1.63
% 1.40/1.63 % Code_Target_Int.negative_def
% 1.40/1.63 thf(fact_2677_times__int_Oabs__eq,axiom,
% 1.40/1.63 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 1.40/1.63 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 1.40/1.63 = ( abs_Integ
% 1.40/1.63 @ ( produc27273713700761075at_nat
% 1.40/1.63 @ ^ [X4: nat,Y4: nat] :
% 1.40/1.63 ( produc2626176000494625587at_nat
% 1.40/1.63 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U3 ) @ ( times_times_nat @ Y4 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V4 ) @ ( times_times_nat @ Y4 @ U3 ) ) ) )
% 1.40/1.63 @ Xa2
% 1.40/1.63 @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % times_int.abs_eq
% 1.40/1.63 thf(fact_2678_bij__betw__Suc,axiom,
% 1.40/1.63 ! [M7: set_nat,N3: set_nat] :
% 1.40/1.63 ( ( bij_betw_nat_nat @ suc @ M7 @ N3 )
% 1.40/1.63 = ( ( image_nat_nat @ suc @ M7 )
% 1.40/1.63 = N3 ) ) ).
% 1.40/1.63
% 1.40/1.63 % bij_betw_Suc
% 1.40/1.63 thf(fact_2679_image__Suc__atLeastAtMost,axiom,
% 1.40/1.63 ! [I2: nat,J: nat] :
% 1.40/1.63 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 1.40/1.63 = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % image_Suc_atLeastAtMost
% 1.40/1.63 thf(fact_2680_image__Suc__atLeastLessThan,axiom,
% 1.40/1.63 ! [I2: nat,J: nat] :
% 1.40/1.63 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 1.40/1.63 = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % image_Suc_atLeastLessThan
% 1.40/1.63 thf(fact_2681_zero__notin__Suc__image,axiom,
% 1.40/1.63 ! [A2: set_nat] :
% 1.40/1.63 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 1.40/1.63
% 1.40/1.63 % zero_notin_Suc_image
% 1.40/1.63 thf(fact_2682_image__Suc__lessThan,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.63 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 1.40/1.63
% 1.40/1.63 % image_Suc_lessThan
% 1.40/1.63 thf(fact_2683_image__Suc__atMost,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 1.40/1.63 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % image_Suc_atMost
% 1.40/1.63 thf(fact_2684_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 1.40/1.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeast0_atMost_Suc_eq_insert_0
% 1.40/1.63 thf(fact_2685_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 1.40/1.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % atLeast0_lessThan_Suc_eq_insert_0
% 1.40/1.63 thf(fact_2686_lessThan__Suc__eq__insert__0,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 1.40/1.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % lessThan_Suc_eq_insert_0
% 1.40/1.63 thf(fact_2687_atMost__Suc__eq__insert__0,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 1.40/1.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % atMost_Suc_eq_insert_0
% 1.40/1.63 thf(fact_2688_one__int__def,axiom,
% 1.40/1.63 ( one_one_int
% 1.40/1.63 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % one_int_def
% 1.40/1.63 thf(fact_2689_less__int_Oabs__eq,axiom,
% 1.40/1.63 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 1.40/1.63 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 1.40/1.63 = ( produc8739625826339149834_nat_o
% 1.40/1.63 @ ^ [X4: nat,Y4: nat] :
% 1.40/1.63 ( produc6081775807080527818_nat_o
% 1.40/1.63 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) )
% 1.40/1.63 @ Xa2
% 1.40/1.63 @ X ) ) ).
% 1.40/1.63
% 1.40/1.63 % less_int.abs_eq
% 1.40/1.63 thf(fact_2690_less__eq__int_Oabs__eq,axiom,
% 1.40/1.63 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 1.40/1.63 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 1.40/1.63 = ( produc8739625826339149834_nat_o
% 1.40/1.63 @ ^ [X4: nat,Y4: nat] :
% 1.40/1.63 ( produc6081775807080527818_nat_o
% 1.40/1.63 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ U3 @ Y4 ) ) )
% 1.40/1.63 @ Xa2
% 1.40/1.63 @ X ) ) ).
% 1.40/1.63
% 1.40/1.63 % less_eq_int.abs_eq
% 1.40/1.63 thf(fact_2691_plus__int_Oabs__eq,axiom,
% 1.40/1.63 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 1.40/1.63 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 1.40/1.63 = ( abs_Integ
% 1.40/1.63 @ ( produc27273713700761075at_nat
% 1.40/1.63 @ ^ [X4: nat,Y4: nat] :
% 1.40/1.63 ( produc2626176000494625587at_nat
% 1.40/1.63 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U3 ) @ ( plus_plus_nat @ Y4 @ V4 ) ) )
% 1.40/1.63 @ Xa2
% 1.40/1.63 @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % plus_int.abs_eq
% 1.40/1.63 thf(fact_2692_minus__int_Oabs__eq,axiom,
% 1.40/1.63 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 1.40/1.63 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 1.40/1.63 = ( abs_Integ
% 1.40/1.63 @ ( produc27273713700761075at_nat
% 1.40/1.63 @ ^ [X4: nat,Y4: nat] :
% 1.40/1.63 ( produc2626176000494625587at_nat
% 1.40/1.63 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V4 ) @ ( plus_plus_nat @ Y4 @ U3 ) ) )
% 1.40/1.63 @ Xa2
% 1.40/1.63 @ X ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % minus_int.abs_eq
% 1.40/1.63 thf(fact_2693_image__atLeastZeroLessThan__int,axiom,
% 1.40/1.63 ! [U: int] :
% 1.40/1.63 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 1.40/1.63 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 1.40/1.63 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % image_atLeastZeroLessThan_int
% 1.40/1.63 thf(fact_2694_image__minus__const__atLeastLessThan__nat,axiom,
% 1.40/1.63 ! [C: nat,Y2: nat,X: nat] :
% 1.40/1.63 ( ( ( ord_less_nat @ C @ Y2 )
% 1.40/1.63 => ( ( image_nat_nat
% 1.40/1.63 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 1.40/1.63 @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 1.40/1.63 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y2 @ C ) ) ) )
% 1.40/1.63 & ( ~ ( ord_less_nat @ C @ Y2 )
% 1.40/1.63 => ( ( ( ord_less_nat @ X @ Y2 )
% 1.40/1.63 => ( ( image_nat_nat
% 1.40/1.63 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 1.40/1.63 @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 1.40/1.63 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 1.40/1.63 & ( ~ ( ord_less_nat @ X @ Y2 )
% 1.40/1.63 => ( ( image_nat_nat
% 1.40/1.63 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 1.40/1.63 @ ( set_or4665077453230672383an_nat @ X @ Y2 ) )
% 1.40/1.63 = bot_bot_set_nat ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % image_minus_const_atLeastLessThan_nat
% 1.40/1.63 thf(fact_2695_suminf__eq__SUP__real,axiom,
% 1.40/1.63 ! [X8: nat > real] :
% 1.40/1.63 ( ( summable_real @ X8 )
% 1.40/1.63 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I3 ) )
% 1.40/1.63 => ( ( suminf_real @ X8 )
% 1.40/1.63 = ( comple1385675409528146559p_real
% 1.40/1.63 @ ( image_nat_real
% 1.40/1.63 @ ^ [I4: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I4 ) )
% 1.40/1.63 @ top_top_set_nat ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % suminf_eq_SUP_real
% 1.40/1.63 thf(fact_2696_Inf__real__def,axiom,
% 1.40/1.63 ( comple4887499456419720421f_real
% 1.40/1.63 = ( ^ [X2: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X2 ) ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % Inf_real_def
% 1.40/1.63 thf(fact_2697_finite__int__iff__bounded__le,axiom,
% 1.40/1.63 ( finite_finite_int
% 1.40/1.63 = ( ^ [S4: set_int] :
% 1.40/1.63 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S4 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_int_iff_bounded_le
% 1.40/1.63 thf(fact_2698_finite__int__iff__bounded,axiom,
% 1.40/1.63 ( finite_finite_int
% 1.40/1.63 = ( ^ [S4: set_int] :
% 1.40/1.63 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S4 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % finite_int_iff_bounded
% 1.40/1.63 thf(fact_2699_image__add__int__atLeastLessThan,axiom,
% 1.40/1.63 ! [L2: int,U: int] :
% 1.40/1.63 ( ( image_int_int
% 1.40/1.63 @ ^ [X4: int] : ( plus_plus_int @ X4 @ L2 )
% 1.40/1.63 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 1.40/1.63 = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 1.40/1.63
% 1.40/1.63 % image_add_int_atLeastLessThan
% 1.40/1.63 thf(fact_2700_range__mod,axiom,
% 1.40/1.63 ! [N: nat] :
% 1.40/1.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.63 => ( ( image_nat_nat
% 1.40/1.63 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N )
% 1.40/1.63 @ top_top_set_nat )
% 1.40/1.63 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 1.40/1.63
% 1.40/1.63 % range_mod
% 1.40/1.63 thf(fact_2701_UNIV__nat__eq,axiom,
% 1.40/1.63 ( top_top_set_nat
% 1.40/1.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % UNIV_nat_eq
% 1.40/1.64 thf(fact_2702_card__UNIV__unit,axiom,
% 1.40/1.64 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 1.40/1.64 = one_one_nat ) ).
% 1.40/1.64
% 1.40/1.64 % card_UNIV_unit
% 1.40/1.64 thf(fact_2703_card__UNIV__bool,axiom,
% 1.40/1.64 ( ( finite_card_o @ top_top_set_o )
% 1.40/1.64 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % card_UNIV_bool
% 1.40/1.64 thf(fact_2704_range__mult,axiom,
% 1.40/1.64 ! [A: real] :
% 1.40/1.64 ( ( ( A = zero_zero_real )
% 1.40/1.64 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 1.40/1.64 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 1.40/1.64 & ( ( A != zero_zero_real )
% 1.40/1.64 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 1.40/1.64 = top_top_set_real ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % range_mult
% 1.40/1.64 thf(fact_2705_root__def,axiom,
% 1.40/1.64 ( root
% 1.40/1.64 = ( ^ [N2: nat,X4: real] :
% 1.40/1.64 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 1.40/1.64 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 1.40/1.64 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N2 ) )
% 1.40/1.64 @ X4 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % root_def
% 1.40/1.64 thf(fact_2706_card__UNIV__char,axiom,
% 1.40/1.64 ( ( finite_card_char @ top_top_set_char )
% 1.40/1.64 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % card_UNIV_char
% 1.40/1.64 thf(fact_2707_UNIV__char__of__nat,axiom,
% 1.40/1.64 ( top_top_set_char
% 1.40/1.64 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % UNIV_char_of_nat
% 1.40/1.64 thf(fact_2708_sup__nat__def,axiom,
% 1.40/1.64 sup_sup_nat = ord_max_nat ).
% 1.40/1.64
% 1.40/1.64 % sup_nat_def
% 1.40/1.64 thf(fact_2709_sup__enat__def,axiom,
% 1.40/1.64 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 1.40/1.64
% 1.40/1.64 % sup_enat_def
% 1.40/1.64 thf(fact_2710_atLeastLessThan__add__Un,axiom,
% 1.40/1.64 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.64 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 1.40/1.64 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % atLeastLessThan_add_Un
% 1.40/1.64 thf(fact_2711_nat__of__char__less__256,axiom,
% 1.40/1.64 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % nat_of_char_less_256
% 1.40/1.64 thf(fact_2712_range__nat__of__char,axiom,
% 1.40/1.64 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 1.40/1.64 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % range_nat_of_char
% 1.40/1.64 thf(fact_2713_integer__of__char__code,axiom,
% 1.40/1.64 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B7: $o] :
% 1.40/1.64 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B7 ) )
% 1.40/1.64 = ( 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 @ B7 ) @ ( 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 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % integer_of_char_code
% 1.40/1.64 thf(fact_2714_String_Ochar__of__ascii__of,axiom,
% 1.40/1.64 ! [C: char] :
% 1.40/1.64 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 1.40/1.64 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % String.char_of_ascii_of
% 1.40/1.64 thf(fact_2715_DERIV__even__real__root,axiom,
% 1.40/1.64 ! [N: nat,X: real] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.64 => ( ( ord_less_real @ X @ zero_zero_real )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_even_real_root
% 1.40/1.64 thf(fact_2716_has__real__derivative__neg__dec__right,axiom,
% 1.40/1.64 ! [F: real > real,L2: real,X: real,S3: set_real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 1.40/1.64 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 1.40/1.64 => ? [D3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ D3 )
% 1.40/1.64 & ! [H3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ H3 )
% 1.40/1.64 => ( ( member_real @ ( plus_plus_real @ X @ H3 ) @ S3 )
% 1.40/1.64 => ( ( ord_less_real @ H3 @ D3 )
% 1.40/1.64 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H3 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % has_real_derivative_neg_dec_right
% 1.40/1.64 thf(fact_2717_has__real__derivative__pos__inc__right,axiom,
% 1.40/1.64 ! [F: real > real,L2: real,X: real,S3: set_real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 1.40/1.64 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 1.40/1.64 => ? [D3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ D3 )
% 1.40/1.64 & ! [H3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ H3 )
% 1.40/1.64 => ( ( member_real @ ( plus_plus_real @ X @ H3 ) @ S3 )
% 1.40/1.64 => ( ( ord_less_real @ H3 @ D3 )
% 1.40/1.64 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H3 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % has_real_derivative_pos_inc_right
% 1.40/1.64 thf(fact_2718_DERIV__neg__dec__right,axiom,
% 1.40/1.64 ! [F: real > real,L2: real,X: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 1.40/1.64 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 1.40/1.64 => ? [D3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ D3 )
% 1.40/1.64 & ! [H3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ H3 )
% 1.40/1.64 => ( ( ord_less_real @ H3 @ D3 )
% 1.40/1.64 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H3 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_neg_dec_right
% 1.40/1.64 thf(fact_2719_DERIV__pos__inc__right,axiom,
% 1.40/1.64 ! [F: real > real,L2: real,X: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 1.40/1.64 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 1.40/1.64 => ? [D3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ D3 )
% 1.40/1.64 & ! [H3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ H3 )
% 1.40/1.64 => ( ( ord_less_real @ H3 @ D3 )
% 1.40/1.64 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H3 ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_pos_inc_right
% 1.40/1.64 thf(fact_2720_deriv__nonneg__imp__mono,axiom,
% 1.40/1.64 ! [A: real,B: real,G: real > real,G2: real > real] :
% 1.40/1.64 ( ! [X5: real] :
% 1.40/1.64 ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 1.40/1.64 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X5 ) ) )
% 1.40/1.64 => ( ( ord_less_eq_real @ A @ B )
% 1.40/1.64 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % deriv_nonneg_imp_mono
% 1.40/1.64 thf(fact_2721_DERIV__nonneg__imp__nondecreasing,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ B )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ X5 )
% 1.40/1.64 => ( ( ord_less_eq_real @ X5 @ B )
% 1.40/1.64 => ? [Y: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ Y @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 1.40/1.64 & ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) )
% 1.40/1.64 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_nonneg_imp_nondecreasing
% 1.40/1.64 thf(fact_2722_DERIV__nonpos__imp__nonincreasing,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ B )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ X5 )
% 1.40/1.64 => ( ( ord_less_eq_real @ X5 @ B )
% 1.40/1.64 => ? [Y: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ Y @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 1.40/1.64 & ( ord_less_eq_real @ Y @ zero_zero_real ) ) ) )
% 1.40/1.64 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_nonpos_imp_nonincreasing
% 1.40/1.64 thf(fact_2723_DERIV__neg__imp__decreasing,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real] :
% 1.40/1.64 ( ( ord_less_real @ A @ B )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ X5 )
% 1.40/1.64 => ( ( ord_less_eq_real @ X5 @ B )
% 1.40/1.64 => ? [Y: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ Y @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 1.40/1.64 & ( ord_less_real @ Y @ zero_zero_real ) ) ) )
% 1.40/1.64 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_neg_imp_decreasing
% 1.40/1.64 thf(fact_2724_DERIV__pos__imp__increasing,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real] :
% 1.40/1.64 ( ( ord_less_real @ A @ B )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ X5 )
% 1.40/1.64 => ( ( ord_less_eq_real @ X5 @ B )
% 1.40/1.64 => ? [Y: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ Y @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 1.40/1.64 & ( ord_less_real @ zero_zero_real @ Y ) ) ) )
% 1.40/1.64 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_pos_imp_increasing
% 1.40/1.64 thf(fact_2725_DERIV__const__ratio__const,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real,K: real] :
% 1.40/1.64 ( ( A != B )
% 1.40/1.64 => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 1.40/1.64 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 1.40/1.64 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_const_ratio_const
% 1.40/1.64 thf(fact_2726_MVT2,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real,F2: real > real] :
% 1.40/1.64 ( ( ord_less_real @ A @ B )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ X5 )
% 1.40/1.64 => ( ( ord_less_eq_real @ X5 @ B )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ F @ ( F2 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 1.40/1.64 => ? [Z3: real] :
% 1.40/1.64 ( ( ord_less_real @ A @ Z3 )
% 1.40/1.64 & ( ord_less_real @ Z3 @ B )
% 1.40/1.64 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 1.40/1.64 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F2 @ Z3 ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % MVT2
% 1.40/1.64 thf(fact_2727_DERIV__const__average,axiom,
% 1.40/1.64 ! [A: real,B: real,V: real > real,K: real] :
% 1.40/1.64 ( ( A != B )
% 1.40/1.64 => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 1.40/1.64 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 1.40/1.64 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_const_average
% 1.40/1.64 thf(fact_2728_DERIV__local__min,axiom,
% 1.40/1.64 ! [F: real > real,L2: real,X: real,D: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 1.40/1.64 => ( ( ord_less_real @ zero_zero_real @ D )
% 1.40/1.64 => ( ! [Y3: real] :
% 1.40/1.64 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 1.40/1.64 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y3 ) ) )
% 1.40/1.64 => ( L2 = zero_zero_real ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_local_min
% 1.40/1.64 thf(fact_2729_DERIV__local__max,axiom,
% 1.40/1.64 ! [F: real > real,L2: real,X: real,D: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 1.40/1.64 => ( ( ord_less_real @ zero_zero_real @ D )
% 1.40/1.64 => ( ! [Y3: real] :
% 1.40/1.64 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 1.40/1.64 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X ) ) )
% 1.40/1.64 => ( L2 = zero_zero_real ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_local_max
% 1.40/1.64 thf(fact_2730_DERIV__ln__divide,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_ln_divide
% 1.40/1.64 thf(fact_2731_DERIV__pow,axiom,
% 1.40/1.64 ! [N: nat,X: real,S: set_real] :
% 1.40/1.64 ( has_fi5821293074295781190e_real
% 1.40/1.64 @ ^ [X4: real] : ( power_power_real @ X4 @ N )
% 1.40/1.64 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_pow
% 1.40/1.64 thf(fact_2732_DERIV__fun__pow,axiom,
% 1.40/1.64 ! [G: real > real,M: real,X: real,N: nat] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real
% 1.40/1.64 @ ^ [X4: real] : ( power_power_real @ ( G @ X4 ) @ N )
% 1.40/1.64 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_fun_pow
% 1.40/1.64 thf(fact_2733_has__real__derivative__powr,axiom,
% 1.40/1.64 ! [Z: real,R2: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ Z )
% 1.40/1.64 => ( has_fi5821293074295781190e_real
% 1.40/1.64 @ ^ [Z5: real] : ( powr_real @ Z5 @ R2 )
% 1.40/1.64 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % has_real_derivative_powr
% 1.40/1.64 thf(fact_2734_DERIV__log,axiom,
% 1.40/1.64 ! [X: real,B: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.64 => ( 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 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_log
% 1.40/1.64 thf(fact_2735_DERIV__fun__powr,axiom,
% 1.40/1.64 ! [G: real > real,M: real,X: real,R2: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 1.40/1.64 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real
% 1.40/1.64 @ ^ [X4: real] : ( powr_real @ ( G @ X4 ) @ R2 )
% 1.40/1.64 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_fun_powr
% 1.40/1.64 thf(fact_2736_DERIV__powr,axiom,
% 1.40/1.64 ! [G: real > real,M: real,X: real,F: real > real,R2: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 1.40/1.64 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 1.40/1.64 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real
% 1.40/1.64 @ ^ [X4: real] : ( powr_real @ ( G @ X4 ) @ ( F @ X4 ) )
% 1.40/1.64 @ ( 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 ) ) ) )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_powr
% 1.40/1.64 thf(fact_2737_DERIV__real__sqrt,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_real_sqrt
% 1.40/1.64 thf(fact_2738_DERIV__series_H,axiom,
% 1.40/1.64 ! [F: real > nat > real,F2: real > nat > real,X0: real,A: real,B: real,L4: nat > real] :
% 1.40/1.64 ( ! [N4: nat] :
% 1.40/1.64 ( has_fi5821293074295781190e_real
% 1.40/1.64 @ ^ [X4: real] : ( F @ X4 @ N4 )
% 1.40/1.64 @ ( F2 @ X0 @ N4 )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 1.40/1.64 => ( summable_real @ ( F @ X5 ) ) )
% 1.40/1.64 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 1.40/1.64 => ( ( summable_real @ ( F2 @ X0 ) )
% 1.40/1.64 => ( ( summable_real @ L4 )
% 1.40/1.64 => ( ! [N4: nat,X5: real,Y3: real] :
% 1.40/1.64 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 1.40/1.64 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 1.40/1.64 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X5 @ N4 ) @ ( F @ Y3 @ N4 ) ) ) @ ( times_times_real @ ( L4 @ N4 ) @ ( abs_abs_real @ ( minus_minus_real @ X5 @ Y3 ) ) ) ) ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real
% 1.40/1.64 @ ^ [X4: real] : ( suminf_real @ ( F @ X4 ) )
% 1.40/1.64 @ ( suminf_real @ ( F2 @ X0 ) )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_series'
% 1.40/1.64 thf(fact_2739_DERIV__arctan,axiom,
% 1.40/1.64 ! [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 ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_arctan
% 1.40/1.64 thf(fact_2740_arsinh__real__has__field__derivative,axiom,
% 1.40/1.64 ! [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 ) ) ).
% 1.40/1.64
% 1.40/1.64 % arsinh_real_has_field_derivative
% 1.40/1.64 thf(fact_2741_DERIV__real__sqrt__generic,axiom,
% 1.40/1.64 ! [X: real,D5: real] :
% 1.40/1.64 ( ( X != zero_zero_real )
% 1.40/1.64 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.64 => ( D5
% 1.40/1.64 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 1.40/1.64 => ( D5
% 1.40/1.64 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ sqrt @ D5 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_real_sqrt_generic
% 1.40/1.64 thf(fact_2742_arcosh__real__has__field__derivative,axiom,
% 1.40/1.64 ! [X: real,A2: set_real] :
% 1.40/1.64 ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.64 => ( 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 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % arcosh_real_has_field_derivative
% 1.40/1.64 thf(fact_2743_artanh__real__has__field__derivative,axiom,
% 1.40/1.64 ! [X: real,A2: set_real] :
% 1.40/1.64 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.64 => ( 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 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % artanh_real_has_field_derivative
% 1.40/1.64 thf(fact_2744_DERIV__power__series_H,axiom,
% 1.40/1.64 ! [R: real,F: nat > real,X0: real] :
% 1.40/1.64 ( ! [X5: real] :
% 1.40/1.64 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 1.40/1.64 => ( summable_real
% 1.40/1.64 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X5 @ N2 ) ) ) )
% 1.40/1.64 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 1.40/1.64 => ( ( ord_less_real @ zero_zero_real @ R )
% 1.40/1.64 => ( has_fi5821293074295781190e_real
% 1.40/1.64 @ ^ [X4: real] :
% 1.40/1.64 ( suminf_real
% 1.40/1.64 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) )
% 1.40/1.64 @ ( suminf_real
% 1.40/1.64 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_power_series'
% 1.40/1.64 thf(fact_2745_DERIV__real__root,axiom,
% 1.40/1.64 ! [N: nat,X: real] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_real_root
% 1.40/1.64 thf(fact_2746_DERIV__arccos,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.64 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.64 => ( 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 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_arccos
% 1.40/1.64 thf(fact_2747_DERIV__arcsin,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.64 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.64 => ( 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 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_arcsin
% 1.40/1.64 thf(fact_2748_Maclaurin__all__le,axiom,
% 1.40/1.64 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 1.40/1.64 ( ( ( Diff @ zero_zero_nat )
% 1.40/1.64 = F )
% 1.40/1.64 => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 1.40/1.64 => ? [T3: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 1.40/1.64 & ( ( F @ X )
% 1.40/1.64 = ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.64 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Maclaurin_all_le
% 1.40/1.64 thf(fact_2749_Maclaurin__all__le__objl,axiom,
% 1.40/1.64 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 1.40/1.64 ( ( ( ( Diff @ zero_zero_nat )
% 1.40/1.64 = F )
% 1.40/1.64 & ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 1.40/1.64 => ? [T3: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 1.40/1.64 & ( ( F @ X )
% 1.40/1.64 = ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.64 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Maclaurin_all_le_objl
% 1.40/1.64 thf(fact_2750_DERIV__odd__real__root,axiom,
% 1.40/1.64 ! [N: nat,X: real] :
% 1.40/1.64 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.64 => ( ( X != zero_zero_real )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_odd_real_root
% 1.40/1.64 thf(fact_2751_Maclaurin,axiom,
% 1.40/1.64 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ H2 )
% 1.40/1.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( ( Diff @ zero_zero_nat )
% 1.40/1.64 = F )
% 1.40/1.64 => ( ! [M5: nat,T3: real] :
% 1.40/1.64 ( ( ( ord_less_nat @ M5 @ N )
% 1.40/1.64 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 1.40/1.64 & ( ord_less_eq_real @ T3 @ H2 ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 1.40/1.64 => ? [T3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ T3 )
% 1.40/1.64 & ( ord_less_real @ T3 @ H2 )
% 1.40/1.64 & ( ( F @ H2 )
% 1.40/1.64 = ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.64 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Maclaurin
% 1.40/1.64 thf(fact_2752_Maclaurin2,axiom,
% 1.40/1.64 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ H2 )
% 1.40/1.64 => ( ( ( Diff @ zero_zero_nat )
% 1.40/1.64 = F )
% 1.40/1.64 => ( ! [M5: nat,T3: real] :
% 1.40/1.64 ( ( ( ord_less_nat @ M5 @ N )
% 1.40/1.64 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 1.40/1.64 & ( ord_less_eq_real @ T3 @ H2 ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 1.40/1.64 => ? [T3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ T3 )
% 1.40/1.64 & ( ord_less_eq_real @ T3 @ H2 )
% 1.40/1.64 & ( ( F @ H2 )
% 1.40/1.64 = ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.64 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Maclaurin2
% 1.40/1.64 thf(fact_2753_Maclaurin__minus,axiom,
% 1.40/1.64 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 1.40/1.64 ( ( ord_less_real @ H2 @ zero_zero_real )
% 1.40/1.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( ( Diff @ zero_zero_nat )
% 1.40/1.64 = F )
% 1.40/1.64 => ( ! [M5: nat,T3: real] :
% 1.40/1.64 ( ( ( ord_less_nat @ M5 @ N )
% 1.40/1.64 & ( ord_less_eq_real @ H2 @ T3 )
% 1.40/1.64 & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 1.40/1.64 => ? [T3: real] :
% 1.40/1.64 ( ( ord_less_real @ H2 @ T3 )
% 1.40/1.64 & ( ord_less_real @ T3 @ zero_zero_real )
% 1.40/1.64 & ( ( F @ H2 )
% 1.40/1.64 = ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.64 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Maclaurin_minus
% 1.40/1.64 thf(fact_2754_Maclaurin__all__lt,axiom,
% 1.40/1.64 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 1.40/1.64 ( ( ( Diff @ zero_zero_nat )
% 1.40/1.64 = F )
% 1.40/1.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( X != zero_zero_real )
% 1.40/1.64 => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 1.40/1.64 => ? [T3: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 1.40/1.64 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 1.40/1.64 & ( ( F @ X )
% 1.40/1.64 = ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.64 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Maclaurin_all_lt
% 1.40/1.64 thf(fact_2755_Maclaurin__bi__le,axiom,
% 1.40/1.64 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 1.40/1.64 ( ( ( Diff @ zero_zero_nat )
% 1.40/1.64 = F )
% 1.40/1.64 => ( ! [M5: nat,T3: real] :
% 1.40/1.64 ( ( ( ord_less_nat @ M5 @ N )
% 1.40/1.64 & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 1.40/1.64 => ? [T3: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 1.40/1.64 & ( ( F @ X )
% 1.40/1.64 = ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.64 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Maclaurin_bi_le
% 1.40/1.64 thf(fact_2756_Taylor,axiom,
% 1.40/1.64 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( ( Diff @ zero_zero_nat )
% 1.40/1.64 = F )
% 1.40/1.64 => ( ! [M5: nat,T3: real] :
% 1.40/1.64 ( ( ( ord_less_nat @ M5 @ N )
% 1.40/1.64 & ( ord_less_eq_real @ A @ T3 )
% 1.40/1.64 & ( ord_less_eq_real @ T3 @ B ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 1.40/1.64 => ( ( ord_less_eq_real @ A @ C )
% 1.40/1.64 => ( ( ord_less_eq_real @ C @ B )
% 1.40/1.64 => ( ( ord_less_eq_real @ A @ X )
% 1.40/1.64 => ( ( ord_less_eq_real @ X @ B )
% 1.40/1.64 => ( ( X != C )
% 1.40/1.64 => ? [T3: real] :
% 1.40/1.64 ( ( ( ord_less_real @ X @ C )
% 1.40/1.64 => ( ( ord_less_real @ X @ T3 )
% 1.40/1.64 & ( ord_less_real @ T3 @ C ) ) )
% 1.40/1.64 & ( ~ ( ord_less_real @ X @ C )
% 1.40/1.64 => ( ( ord_less_real @ C @ T3 )
% 1.40/1.64 & ( ord_less_real @ T3 @ X ) ) )
% 1.40/1.64 & ( ( F @ X )
% 1.40/1.64 = ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.64 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Taylor
% 1.40/1.64 thf(fact_2757_Taylor__up,axiom,
% 1.40/1.64 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( ( Diff @ zero_zero_nat )
% 1.40/1.64 = F )
% 1.40/1.64 => ( ! [M5: nat,T3: real] :
% 1.40/1.64 ( ( ( ord_less_nat @ M5 @ N )
% 1.40/1.64 & ( ord_less_eq_real @ A @ T3 )
% 1.40/1.64 & ( ord_less_eq_real @ T3 @ B ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 1.40/1.64 => ( ( ord_less_eq_real @ A @ C )
% 1.40/1.64 => ( ( ord_less_real @ C @ B )
% 1.40/1.64 => ? [T3: real] :
% 1.40/1.64 ( ( ord_less_real @ C @ T3 )
% 1.40/1.64 & ( ord_less_real @ T3 @ B )
% 1.40/1.64 & ( ( F @ B )
% 1.40/1.64 = ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.64 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Taylor_up
% 1.40/1.64 thf(fact_2758_Taylor__down,axiom,
% 1.40/1.64 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( ( Diff @ zero_zero_nat )
% 1.40/1.64 = F )
% 1.40/1.64 => ( ! [M5: nat,T3: real] :
% 1.40/1.64 ( ( ( ord_less_nat @ M5 @ N )
% 1.40/1.64 & ( ord_less_eq_real @ A @ T3 )
% 1.40/1.64 & ( ord_less_eq_real @ T3 @ B ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 1.40/1.64 => ( ( ord_less_real @ A @ C )
% 1.40/1.64 => ( ( ord_less_eq_real @ C @ B )
% 1.40/1.64 => ? [T3: real] :
% 1.40/1.64 ( ( ord_less_real @ A @ T3 )
% 1.40/1.64 & ( ord_less_real @ T3 @ C )
% 1.40/1.64 & ( ( F @ A )
% 1.40/1.64 = ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ N ) )
% 1.40/1.64 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Taylor_down
% 1.40/1.64 thf(fact_2759_Maclaurin__lemma2,axiom,
% 1.40/1.64 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B2: real] :
% 1.40/1.64 ( ! [M5: nat,T3: real] :
% 1.40/1.64 ( ( ( ord_less_nat @ M5 @ N )
% 1.40/1.64 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 1.40/1.64 & ( ord_less_eq_real @ T3 @ H2 ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 1.40/1.64 => ( ( N
% 1.40/1.64 = ( suc @ K ) )
% 1.40/1.64 => ! [M3: nat,T4: real] :
% 1.40/1.64 ( ( ( ord_less_nat @ M3 @ N )
% 1.40/1.64 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 1.40/1.64 & ( ord_less_eq_real @ T4 @ H2 ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real
% 1.40/1.64 @ ^ [U3: real] :
% 1.40/1.64 ( minus_minus_real @ ( Diff @ M3 @ U3 )
% 1.40/1.64 @ ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M3 @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ U3 @ P6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M3 ) ) )
% 1.40/1.64 @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ U3 @ ( minus_minus_nat @ N @ M3 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M3 ) ) ) ) ) )
% 1.40/1.64 @ ( minus_minus_real @ ( Diff @ ( suc @ M3 ) @ T4 )
% 1.40/1.64 @ ( plus_plus_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M3 ) @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ T4 @ P6 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) )
% 1.40/1.64 @ ( times_times_real @ B2 @ ( divide_divide_real @ ( power_power_real @ T4 @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) ) ) ) )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Maclaurin_lemma2
% 1.40/1.64 thf(fact_2760_DERIV__arctan__series,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.64 => ( has_fi5821293074295781190e_real
% 1.40/1.64 @ ^ [X9: real] :
% 1.40/1.64 ( suminf_real
% 1.40/1.64 @ ^ [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 ) ) ) ) )
% 1.40/1.64 @ ( suminf_real
% 1.40/1.64 @ ^ [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 ) ) ) ) ) )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_arctan_series
% 1.40/1.64 thf(fact_2761_DERIV__real__root__generic,axiom,
% 1.40/1.64 ! [N: nat,X: real,D5: real] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( X != zero_zero_real )
% 1.40/1.64 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.64 => ( ( ord_less_real @ zero_zero_real @ X )
% 1.40/1.64 => ( D5
% 1.40/1.64 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 1.40/1.64 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.64 => ( ( ord_less_real @ X @ zero_zero_real )
% 1.40/1.64 => ( D5
% 1.40/1.64 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 1.40/1.64 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.64 => ( D5
% 1.40/1.64 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D5 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_real_root_generic
% 1.40/1.64 thf(fact_2762_isCont__Lb__Ub,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ B )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ( ord_less_eq_real @ A @ X5 )
% 1.40/1.64 & ( ord_less_eq_real @ X5 @ B ) )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 1.40/1.64 => ? [L5: real,M9: real] :
% 1.40/1.64 ( ! [X3: real] :
% 1.40/1.64 ( ( ( ord_less_eq_real @ A @ X3 )
% 1.40/1.64 & ( ord_less_eq_real @ X3 @ B ) )
% 1.40/1.64 => ( ( ord_less_eq_real @ L5 @ ( F @ X3 ) )
% 1.40/1.64 & ( ord_less_eq_real @ ( F @ X3 ) @ M9 ) ) )
% 1.40/1.64 & ! [Y: real] :
% 1.40/1.64 ( ( ( ord_less_eq_real @ L5 @ Y )
% 1.40/1.64 & ( ord_less_eq_real @ Y @ M9 ) )
% 1.40/1.64 => ? [X5: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ X5 )
% 1.40/1.64 & ( ord_less_eq_real @ X5 @ B )
% 1.40/1.64 & ( ( F @ X5 )
% 1.40/1.64 = Y ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % isCont_Lb_Ub
% 1.40/1.64 thf(fact_2763_isCont__real__sqrt,axiom,
% 1.40/1.64 ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 1.40/1.64
% 1.40/1.64 % isCont_real_sqrt
% 1.40/1.64 thf(fact_2764_isCont__real__root,axiom,
% 1.40/1.64 ! [X: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N ) ) ).
% 1.40/1.64
% 1.40/1.64 % isCont_real_root
% 1.40/1.64 thf(fact_2765_isCont__inverse__function2,axiom,
% 1.40/1.64 ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 1.40/1.64 ( ( ord_less_real @ A @ X )
% 1.40/1.64 => ( ( ord_less_real @ X @ B )
% 1.40/1.64 => ( ! [Z3: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ Z3 )
% 1.40/1.64 => ( ( ord_less_eq_real @ Z3 @ B )
% 1.40/1.64 => ( ( G @ ( F @ Z3 ) )
% 1.40/1.64 = Z3 ) ) )
% 1.40/1.64 => ( ! [Z3: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ Z3 )
% 1.40/1.64 => ( ( ord_less_eq_real @ Z3 @ B )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % isCont_inverse_function2
% 1.40/1.64 thf(fact_2766_isCont__arcosh,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 1.40/1.64
% 1.40/1.64 % isCont_arcosh
% 1.40/1.64 thf(fact_2767_LIM__cos__div__sin,axiom,
% 1.40/1.64 ( filterlim_real_real
% 1.40/1.64 @ ^ [X4: real] : ( divide_divide_real @ ( cos_real @ X4 ) @ ( sin_real @ X4 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 1.40/1.64
% 1.40/1.64 % LIM_cos_div_sin
% 1.40/1.64 thf(fact_2768_isCont__arccos,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.64 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % isCont_arccos
% 1.40/1.64 thf(fact_2769_isCont__arcsin,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.64 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % isCont_arcsin
% 1.40/1.64 thf(fact_2770_LIM__less__bound,axiom,
% 1.40/1.64 ! [B: real,X: real,F: real > real] :
% 1.40/1.64 ( ( ord_less_real @ B @ X )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 1.40/1.64 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 1.40/1.64 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 1.40/1.64 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % LIM_less_bound
% 1.40/1.64 thf(fact_2771_isCont__artanh,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 1.40/1.64 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % isCont_artanh
% 1.40/1.64 thf(fact_2772_isCont__inverse__function,axiom,
% 1.40/1.64 ! [D: real,X: real,G: real > real,F: real > real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ D )
% 1.40/1.64 => ( ! [Z3: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D )
% 1.40/1.64 => ( ( G @ ( F @ Z3 ) )
% 1.40/1.64 = Z3 ) )
% 1.40/1.64 => ( ! [Z3: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % isCont_inverse_function
% 1.40/1.64 thf(fact_2773_GMVT_H,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F2: real > real] :
% 1.40/1.64 ( ( ord_less_real @ A @ B )
% 1.40/1.64 => ( ! [Z3: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ Z3 )
% 1.40/1.64 => ( ( ord_less_eq_real @ Z3 @ B )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 1.40/1.64 => ( ! [Z3: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ Z3 )
% 1.40/1.64 => ( ( ord_less_eq_real @ Z3 @ B )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 1.40/1.64 => ( ! [Z3: real] :
% 1.40/1.64 ( ( ord_less_real @ A @ Z3 )
% 1.40/1.64 => ( ( ord_less_real @ Z3 @ B )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 1.40/1.64 => ( ! [Z3: real] :
% 1.40/1.64 ( ( ord_less_real @ A @ Z3 )
% 1.40/1.64 => ( ( ord_less_real @ Z3 @ B )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ F @ ( F2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 1.40/1.64 => ? [C2: real] :
% 1.40/1.64 ( ( ord_less_real @ A @ C2 )
% 1.40/1.64 & ( ord_less_real @ C2 @ B )
% 1.40/1.64 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 1.40/1.64 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F2 @ C2 ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % GMVT'
% 1.40/1.64 thf(fact_2774_summable__Leibniz_I2_J,axiom,
% 1.40/1.64 ! [A: nat > real] :
% 1.40/1.64 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ( ( topolo6980174941875973593q_real @ A )
% 1.40/1.64 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 1.40/1.64 => ! [N7: nat] :
% 1.40/1.64 ( member_real
% 1.40/1.64 @ ( suminf_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 1.40/1.64 @ ( set_or1222579329274155063t_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable_Leibniz(2)
% 1.40/1.64 thf(fact_2775_summable__Leibniz_I3_J,axiom,
% 1.40/1.64 ! [A: nat > real] :
% 1.40/1.64 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ( ( topolo6980174941875973593q_real @ A )
% 1.40/1.64 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 1.40/1.64 => ! [N7: nat] :
% 1.40/1.64 ( member_real
% 1.40/1.64 @ ( suminf_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 1.40/1.64 @ ( set_or1222579329274155063t_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) )
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable_Leibniz(3)
% 1.40/1.64 thf(fact_2776_filterlim__Suc,axiom,
% 1.40/1.64 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 1.40/1.64
% 1.40/1.64 % filterlim_Suc
% 1.40/1.64 thf(fact_2777_mult__nat__left__at__top,axiom,
% 1.40/1.64 ! [C: nat] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ C )
% 1.40/1.64 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % mult_nat_left_at_top
% 1.40/1.64 thf(fact_2778_mult__nat__right__at__top,axiom,
% 1.40/1.64 ! [C: nat] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ C )
% 1.40/1.64 => ( filterlim_nat_nat
% 1.40/1.64 @ ^ [X4: nat] : ( times_times_nat @ X4 @ C )
% 1.40/1.64 @ at_top_nat
% 1.40/1.64 @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % mult_nat_right_at_top
% 1.40/1.64 thf(fact_2779_monoseq__convergent,axiom,
% 1.40/1.64 ! [X8: nat > real,B2: real] :
% 1.40/1.64 ( ( topolo6980174941875973593q_real @ X8 )
% 1.40/1.64 => ( ! [I3: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I3 ) ) @ B2 )
% 1.40/1.64 => ~ ! [L5: real] :
% 1.40/1.64 ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L5 ) @ at_top_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % monoseq_convergent
% 1.40/1.64 thf(fact_2780_LIMSEQ__root,axiom,
% 1.40/1.64 ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ one_one_real )
% 1.40/1.64 @ at_top_nat ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_root
% 1.40/1.64 thf(fact_2781_nested__sequence__unique,axiom,
% 1.40/1.64 ! [F: nat > real,G: nat > real] :
% 1.40/1.64 ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N4 ) ) @ ( G @ N4 ) )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 1.40/1.64 => ( ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 1.40/1.64 @ at_top_nat )
% 1.40/1.64 => ? [L3: real] :
% 1.40/1.64 ( ! [N7: nat] : ( ord_less_eq_real @ ( F @ N7 ) @ L3 )
% 1.40/1.64 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L3 ) @ at_top_nat )
% 1.40/1.64 & ! [N7: nat] : ( ord_less_eq_real @ L3 @ ( G @ N7 ) )
% 1.40/1.64 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L3 ) @ at_top_nat ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % nested_sequence_unique
% 1.40/1.64 thf(fact_2782_LIMSEQ__inverse__zero,axiom,
% 1.40/1.64 ! [X8: nat > real] :
% 1.40/1.64 ( ! [R3: real] :
% 1.40/1.64 ? [N5: nat] :
% 1.40/1.64 ! [N4: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ N5 @ N4 )
% 1.40/1.64 => ( ord_less_real @ R3 @ ( X8 @ N4 ) ) )
% 1.40/1.64 => ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( inverse_inverse_real @ ( X8 @ N2 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 1.40/1.64 @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_inverse_zero
% 1.40/1.64 thf(fact_2783_lim__inverse__n_H,axiom,
% 1.40/1.64 ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 1.40/1.64 @ at_top_nat ) ).
% 1.40/1.64
% 1.40/1.64 % lim_inverse_n'
% 1.40/1.64 thf(fact_2784_LIMSEQ__root__const,axiom,
% 1.40/1.64 ! [C: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ C )
% 1.40/1.64 => ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( root @ N2 @ C )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ one_one_real )
% 1.40/1.64 @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_root_const
% 1.40/1.64 thf(fact_2785_LIMSEQ__inverse__real__of__nat,axiom,
% 1.40/1.64 ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 1.40/1.64 @ at_top_nat ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_inverse_real_of_nat
% 1.40/1.64 thf(fact_2786_LIMSEQ__inverse__real__of__nat__add,axiom,
% 1.40/1.64 ! [R2: real] :
% 1.40/1.64 ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ R2 )
% 1.40/1.64 @ at_top_nat ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_inverse_real_of_nat_add
% 1.40/1.64 thf(fact_2787_increasing__LIMSEQ,axiom,
% 1.40/1.64 ! [F: nat > real,L2: real] :
% 1.40/1.64 ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ ( F @ N4 ) @ L2 )
% 1.40/1.64 => ( ! [E2: real] :
% 1.40/1.64 ( ( ord_less_real @ zero_zero_real @ E2 )
% 1.40/1.64 => ? [N7: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N7 ) @ E2 ) ) )
% 1.40/1.64 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % increasing_LIMSEQ
% 1.40/1.64 thf(fact_2788_LIMSEQ__realpow__zero,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.64 => ( ( ord_less_real @ X @ one_one_real )
% 1.40/1.64 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_realpow_zero
% 1.40/1.64 thf(fact_2789_LIMSEQ__divide__realpow__zero,axiom,
% 1.40/1.64 ! [X: real,A: real] :
% 1.40/1.64 ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.64 => ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N2 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 1.40/1.64 @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_divide_realpow_zero
% 1.40/1.64 thf(fact_2790_LIMSEQ__abs__realpow__zero2,axiom,
% 1.40/1.64 ! [C: real] :
% 1.40/1.64 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 1.40/1.64 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_abs_realpow_zero2
% 1.40/1.64 thf(fact_2791_LIMSEQ__abs__realpow__zero,axiom,
% 1.40/1.64 ! [C: real] :
% 1.40/1.64 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 1.40/1.64 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_abs_realpow_zero
% 1.40/1.64 thf(fact_2792_LIMSEQ__inverse__realpow__zero,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_real @ one_one_real @ X )
% 1.40/1.64 => ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N2 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 1.40/1.64 @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_inverse_realpow_zero
% 1.40/1.64 thf(fact_2793_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 1.40/1.64 ! [R2: real] :
% 1.40/1.64 ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ R2 )
% 1.40/1.64 @ at_top_nat ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_inverse_real_of_nat_add_minus
% 1.40/1.64 thf(fact_2794_tendsto__exp__limit__sequentially,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 1.40/1.64 @ at_top_nat ) ).
% 1.40/1.64
% 1.40/1.64 % tendsto_exp_limit_sequentially
% 1.40/1.64 thf(fact_2795_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 1.40/1.64 ! [R2: real] :
% 1.40/1.64 ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ R2 )
% 1.40/1.64 @ at_top_nat ) ).
% 1.40/1.64
% 1.40/1.64 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 1.40/1.64 thf(fact_2796_summable__Leibniz_I1_J,axiom,
% 1.40/1.64 ! [A: nat > real] :
% 1.40/1.64 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ( ( topolo6980174941875973593q_real @ A )
% 1.40/1.64 => ( summable_real
% 1.40/1.64 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable_Leibniz(1)
% 1.40/1.64 thf(fact_2797_summable,axiom,
% 1.40/1.64 ! [A: nat > real] :
% 1.40/1.64 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 1.40/1.64 => ( summable_real
% 1.40/1.64 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable
% 1.40/1.64 thf(fact_2798_cos__diff__limit__1,axiom,
% 1.40/1.64 ! [Theta: nat > real,Theta2: real] :
% 1.40/1.64 ( ( filterlim_nat_real
% 1.40/1.64 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ one_one_real )
% 1.40/1.64 @ at_top_nat )
% 1.40/1.64 => ~ ! [K2: nat > int] :
% 1.40/1.64 ~ ( filterlim_nat_real
% 1.40/1.64 @ ^ [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 ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ Theta2 )
% 1.40/1.64 @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % cos_diff_limit_1
% 1.40/1.64 thf(fact_2799_cos__limit__1,axiom,
% 1.40/1.64 ! [Theta: nat > real] :
% 1.40/1.64 ( ( filterlim_nat_real
% 1.40/1.64 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ one_one_real )
% 1.40/1.64 @ at_top_nat )
% 1.40/1.64 => ? [K2: nat > int] :
% 1.40/1.64 ( filterlim_nat_real
% 1.40/1.64 @ ^ [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 ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 1.40/1.64 @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % cos_limit_1
% 1.40/1.64 thf(fact_2800_summable__Leibniz_I4_J,axiom,
% 1.40/1.64 ! [A: nat > real] :
% 1.40/1.64 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ( ( topolo6980174941875973593q_real @ A )
% 1.40/1.64 => ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] :
% 1.40/1.64 ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real
% 1.40/1.64 @ ( suminf_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 1.40/1.64 @ at_top_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable_Leibniz(4)
% 1.40/1.64 thf(fact_2801_zeroseq__arctan__series,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 1.40/1.64 => ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 1.40/1.64 @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % zeroseq_arctan_series
% 1.40/1.64 thf(fact_2802_summable__Leibniz_H_I3_J,axiom,
% 1.40/1.64 ! [A: nat > real] :
% 1.40/1.64 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 1.40/1.64 => ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] :
% 1.40/1.64 ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real
% 1.40/1.64 @ ( suminf_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 1.40/1.64 @ at_top_nat ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable_Leibniz'(3)
% 1.40/1.64 thf(fact_2803_summable__Leibniz_H_I2_J,axiom,
% 1.40/1.64 ! [A: nat > real,N: nat] :
% 1.40/1.64 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 1.40/1.64 => ( ord_less_eq_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 1.40/1.64 @ ( suminf_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable_Leibniz'(2)
% 1.40/1.64 thf(fact_2804_sums__alternating__upper__lower,axiom,
% 1.40/1.64 ! [A: nat > real] :
% 1.40/1.64 ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 1.40/1.64 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ? [L3: real] :
% 1.40/1.64 ( ! [N7: nat] :
% 1.40/1.64 ( ord_less_eq_real
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 1.40/1.64 @ L3 )
% 1.40/1.64 & ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] :
% 1.40/1.64 ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ L3 )
% 1.40/1.64 @ at_top_nat )
% 1.40/1.64 & ! [N7: nat] :
% 1.40/1.64 ( ord_less_eq_real @ L3
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) )
% 1.40/1.64 & ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] :
% 1.40/1.64 ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ L3 )
% 1.40/1.64 @ at_top_nat ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % sums_alternating_upper_lower
% 1.40/1.64 thf(fact_2805_summable__Leibniz_I5_J,axiom,
% 1.40/1.64 ! [A: nat > real] :
% 1.40/1.64 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ( ( topolo6980174941875973593q_real @ A )
% 1.40/1.64 => ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] :
% 1.40/1.64 ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real
% 1.40/1.64 @ ( suminf_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 1.40/1.64 @ at_top_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable_Leibniz(5)
% 1.40/1.64 thf(fact_2806_summable__Leibniz_H_I5_J,axiom,
% 1.40/1.64 ! [A: nat > real] :
% 1.40/1.64 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 1.40/1.64 => ( filterlim_nat_real
% 1.40/1.64 @ ^ [N2: nat] :
% 1.40/1.64 ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real
% 1.40/1.64 @ ( suminf_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 1.40/1.64 @ at_top_nat ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable_Leibniz'(5)
% 1.40/1.64 thf(fact_2807_summable__Leibniz_H_I4_J,axiom,
% 1.40/1.64 ! [A: nat > real,N: nat] :
% 1.40/1.64 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N4 ) )
% 1.40/1.64 => ( ! [N4: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N4 ) ) @ ( A @ N4 ) )
% 1.40/1.64 => ( ord_less_eq_real
% 1.40/1.64 @ ( suminf_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 1.40/1.64 @ ( groups6591440286371151544t_real
% 1.40/1.64 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 1.40/1.64 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable_Leibniz'(4)
% 1.40/1.64 thf(fact_2808_real__bounded__linear,axiom,
% 1.40/1.64 ( real_V5970128139526366754l_real
% 1.40/1.64 = ( ^ [F3: real > real] :
% 1.40/1.64 ? [C3: real] :
% 1.40/1.64 ( F3
% 1.40/1.64 = ( ^ [X4: real] : ( times_times_real @ X4 @ C3 ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % real_bounded_linear
% 1.40/1.64 thf(fact_2809_tendsto__exp__limit__at__right,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( filterlim_real_real
% 1.40/1.64 @ ^ [Y4: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y4 ) ) @ ( divide_divide_real @ one_one_real @ Y4 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % tendsto_exp_limit_at_right
% 1.40/1.64 thf(fact_2810_tendsto__arcosh__at__left__1,axiom,
% 1.40/1.64 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 1.40/1.64
% 1.40/1.64 % tendsto_arcosh_at_left_1
% 1.40/1.64 thf(fact_2811_filterlim__tan__at__right,axiom,
% 1.40/1.64 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 ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % filterlim_tan_at_right
% 1.40/1.64 thf(fact_2812_tendsto__arctan__at__bot,axiom,
% 1.40/1.64 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 1.40/1.64
% 1.40/1.64 % tendsto_arctan_at_bot
% 1.40/1.64 thf(fact_2813_greaterThan__0,axiom,
% 1.40/1.64 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 1.40/1.64 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % greaterThan_0
% 1.40/1.64 thf(fact_2814_greaterThan__Suc,axiom,
% 1.40/1.64 ! [K: nat] :
% 1.40/1.64 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 1.40/1.64 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % greaterThan_Suc
% 1.40/1.64 thf(fact_2815_tanh__real__at__bot,axiom,
% 1.40/1.64 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 1.40/1.64
% 1.40/1.64 % tanh_real_at_bot
% 1.40/1.64 thf(fact_2816_artanh__real__at__right__1,axiom,
% 1.40/1.64 filterlim_real_real @ artanh_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ one_one_real ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % artanh_real_at_right_1
% 1.40/1.64 thf(fact_2817_DERIV__pos__imp__increasing__at__bot,axiom,
% 1.40/1.64 ! [B: real,F: real > real,Flim: real] :
% 1.40/1.64 ( ! [X5: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ X5 @ B )
% 1.40/1.64 => ? [Y: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ Y @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 1.40/1.64 & ( ord_less_real @ zero_zero_real @ Y ) ) )
% 1.40/1.64 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 1.40/1.64 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_pos_imp_increasing_at_bot
% 1.40/1.64 thf(fact_2818_filterlim__pow__at__bot__odd,axiom,
% 1.40/1.64 ! [N: nat,F: real > real,F4: filter_real] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( filterlim_real_real @ F @ at_bot_real @ F4 )
% 1.40/1.64 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.64 => ( filterlim_real_real
% 1.40/1.64 @ ^ [X4: real] : ( power_power_real @ ( F @ X4 ) @ N )
% 1.40/1.64 @ at_bot_real
% 1.40/1.64 @ F4 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % filterlim_pow_at_bot_odd
% 1.40/1.64 thf(fact_2819_filterlim__pow__at__bot__even,axiom,
% 1.40/1.64 ! [N: nat,F: real > real,F4: filter_real] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( filterlim_real_real @ F @ at_bot_real @ F4 )
% 1.40/1.64 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 1.40/1.64 => ( filterlim_real_real
% 1.40/1.64 @ ^ [X4: real] : ( power_power_real @ ( F @ X4 ) @ N )
% 1.40/1.64 @ at_top_real
% 1.40/1.64 @ F4 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % filterlim_pow_at_bot_even
% 1.40/1.64 thf(fact_2820_at__bot__le__at__infinity,axiom,
% 1.40/1.64 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 1.40/1.64
% 1.40/1.64 % at_bot_le_at_infinity
% 1.40/1.64 thf(fact_2821_at__top__le__at__infinity,axiom,
% 1.40/1.64 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 1.40/1.64
% 1.40/1.64 % at_top_le_at_infinity
% 1.40/1.64 thf(fact_2822_sqrt__at__top,axiom,
% 1.40/1.64 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 1.40/1.64
% 1.40/1.64 % sqrt_at_top
% 1.40/1.64 thf(fact_2823_tanh__real__at__top,axiom,
% 1.40/1.64 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 1.40/1.64
% 1.40/1.64 % tanh_real_at_top
% 1.40/1.64 thf(fact_2824_artanh__real__at__left__1,axiom,
% 1.40/1.64 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 1.40/1.64
% 1.40/1.64 % artanh_real_at_left_1
% 1.40/1.64 thf(fact_2825_tendsto__power__div__exp__0,axiom,
% 1.40/1.64 ! [K: nat] :
% 1.40/1.64 ( filterlim_real_real
% 1.40/1.64 @ ^ [X4: real] : ( divide_divide_real @ ( power_power_real @ X4 @ K ) @ ( exp_real @ X4 ) )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 1.40/1.64 @ at_top_real ) ).
% 1.40/1.64
% 1.40/1.64 % tendsto_power_div_exp_0
% 1.40/1.64 thf(fact_2826_tendsto__exp__limit__at__top,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( filterlim_real_real
% 1.40/1.64 @ ^ [Y4: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y4 ) ) @ Y4 )
% 1.40/1.64 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 1.40/1.64 @ at_top_real ) ).
% 1.40/1.64
% 1.40/1.64 % tendsto_exp_limit_at_top
% 1.40/1.64 thf(fact_2827_filterlim__tan__at__left,axiom,
% 1.40/1.64 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 ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % filterlim_tan_at_left
% 1.40/1.64 thf(fact_2828_DERIV__neg__imp__decreasing__at__top,axiom,
% 1.40/1.64 ! [B: real,F: real > real,Flim: real] :
% 1.40/1.64 ( ! [X5: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ B @ X5 )
% 1.40/1.64 => ? [Y: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ F @ Y @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 1.40/1.64 & ( ord_less_real @ Y @ zero_zero_real ) ) )
% 1.40/1.64 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 1.40/1.64 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_neg_imp_decreasing_at_top
% 1.40/1.64 thf(fact_2829_tendsto__arctan__at__top,axiom,
% 1.40/1.64 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 1.40/1.64
% 1.40/1.64 % tendsto_arctan_at_top
% 1.40/1.64 thf(fact_2830_GMVT,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real,G: real > real] :
% 1.40/1.64 ( ( ord_less_real @ A @ B )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ( ord_less_eq_real @ A @ X5 )
% 1.40/1.64 & ( ord_less_eq_real @ X5 @ B ) )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ( ord_less_real @ A @ X5 )
% 1.40/1.64 & ( ord_less_real @ X5 @ B ) )
% 1.40/1.64 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ( ord_less_eq_real @ A @ X5 )
% 1.40/1.64 & ( ord_less_eq_real @ X5 @ B ) )
% 1.40/1.64 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ G ) )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ( ord_less_real @ A @ X5 )
% 1.40/1.64 & ( ord_less_real @ X5 @ B ) )
% 1.40/1.64 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 1.40/1.64 => ? [G_c: real,F_c: real,C2: real] :
% 1.40/1.64 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 1.40/1.64 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 1.40/1.64 & ( ord_less_real @ A @ C2 )
% 1.40/1.64 & ( ord_less_real @ C2 @ B )
% 1.40/1.64 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 1.40/1.64 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % GMVT
% 1.40/1.64 thf(fact_2831_eventually__sequentially__Suc,axiom,
% 1.40/1.64 ! [P: nat > $o] :
% 1.40/1.64 ( ( eventually_nat
% 1.40/1.64 @ ^ [I4: nat] : ( P @ ( suc @ I4 ) )
% 1.40/1.64 @ at_top_nat )
% 1.40/1.64 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % eventually_sequentially_Suc
% 1.40/1.64 thf(fact_2832_eventually__sequentially__seg,axiom,
% 1.40/1.64 ! [P: nat > $o,K: nat] :
% 1.40/1.64 ( ( eventually_nat
% 1.40/1.64 @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 1.40/1.64 @ at_top_nat )
% 1.40/1.64 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % eventually_sequentially_seg
% 1.40/1.64 thf(fact_2833_sequentially__offset,axiom,
% 1.40/1.64 ! [P: nat > $o,K: nat] :
% 1.40/1.64 ( ( eventually_nat @ P @ at_top_nat )
% 1.40/1.64 => ( eventually_nat
% 1.40/1.64 @ ^ [I4: nat] : ( P @ ( plus_plus_nat @ I4 @ K ) )
% 1.40/1.64 @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % sequentially_offset
% 1.40/1.64 thf(fact_2834_le__sequentially,axiom,
% 1.40/1.64 ! [F4: filter_nat] :
% 1.40/1.64 ( ( ord_le2510731241096832064er_nat @ F4 @ at_top_nat )
% 1.40/1.64 = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F4 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % le_sequentially
% 1.40/1.64 thf(fact_2835_eventually__sequentially,axiom,
% 1.40/1.64 ! [P: nat > $o] :
% 1.40/1.64 ( ( eventually_nat @ P @ at_top_nat )
% 1.40/1.64 = ( ? [N6: nat] :
% 1.40/1.64 ! [N2: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ N6 @ N2 )
% 1.40/1.64 => ( P @ N2 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % eventually_sequentially
% 1.40/1.64 thf(fact_2836_eventually__sequentiallyI,axiom,
% 1.40/1.64 ! [C: nat,P: nat > $o] :
% 1.40/1.64 ( ! [X5: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ C @ X5 )
% 1.40/1.64 => ( P @ X5 ) )
% 1.40/1.64 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % eventually_sequentiallyI
% 1.40/1.64 thf(fact_2837_eventually__at__right__to__0,axiom,
% 1.40/1.64 ! [P: real > $o,A: real] :
% 1.40/1.64 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 1.40/1.64 = ( eventually_real
% 1.40/1.64 @ ^ [X4: real] : ( P @ ( plus_plus_real @ X4 @ A ) )
% 1.40/1.64 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % eventually_at_right_to_0
% 1.40/1.64 thf(fact_2838_Bseq__eq__bounded,axiom,
% 1.40/1.64 ! [F: nat > real,A: real,B: real] :
% 1.40/1.64 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 1.40/1.64 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 1.40/1.64
% 1.40/1.64 % Bseq_eq_bounded
% 1.40/1.64 thf(fact_2839_Bseq__realpow,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.64 => ( ( ord_less_eq_real @ X @ one_one_real )
% 1.40/1.64 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Bseq_realpow
% 1.40/1.64 thf(fact_2840_GreatestI__ex__nat,axiom,
% 1.40/1.64 ! [P: nat > $o,B: nat] :
% 1.40/1.64 ( ? [X_1: nat] : ( P @ X_1 )
% 1.40/1.64 => ( ! [Y3: nat] :
% 1.40/1.64 ( ( P @ Y3 )
% 1.40/1.64 => ( ord_less_eq_nat @ Y3 @ B ) )
% 1.40/1.64 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % GreatestI_ex_nat
% 1.40/1.64 thf(fact_2841_Greatest__le__nat,axiom,
% 1.40/1.64 ! [P: nat > $o,K: nat,B: nat] :
% 1.40/1.64 ( ( P @ K )
% 1.40/1.64 => ( ! [Y3: nat] :
% 1.40/1.64 ( ( P @ Y3 )
% 1.40/1.64 => ( ord_less_eq_nat @ Y3 @ B ) )
% 1.40/1.64 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Greatest_le_nat
% 1.40/1.64 thf(fact_2842_GreatestI__nat,axiom,
% 1.40/1.64 ! [P: nat > $o,K: nat,B: nat] :
% 1.40/1.64 ( ( P @ K )
% 1.40/1.64 => ( ! [Y3: nat] :
% 1.40/1.64 ( ( P @ Y3 )
% 1.40/1.64 => ( ord_less_eq_nat @ Y3 @ B ) )
% 1.40/1.64 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % GreatestI_nat
% 1.40/1.64 thf(fact_2843_atLeastSucAtMost__greaterThanAtMost,axiom,
% 1.40/1.64 ! [L2: nat,U: nat] :
% 1.40/1.64 ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 1.40/1.64 = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 1.40/1.64
% 1.40/1.64 % atLeastSucAtMost_greaterThanAtMost
% 1.40/1.64 thf(fact_2844_atLeast__Suc__greaterThan,axiom,
% 1.40/1.64 ! [K: nat] :
% 1.40/1.64 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 1.40/1.64 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 1.40/1.64
% 1.40/1.64 % atLeast_Suc_greaterThan
% 1.40/1.64 thf(fact_2845_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 1.40/1.64 ! [L2: int,U: int] :
% 1.40/1.64 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 1.40/1.64 = ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 1.40/1.64
% 1.40/1.64 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 1.40/1.64 thf(fact_2846_decseq__bounded,axiom,
% 1.40/1.64 ! [X8: nat > real,B2: real] :
% 1.40/1.64 ( ( order_9091379641038594480t_real @ X8 )
% 1.40/1.64 => ( ! [I3: nat] : ( ord_less_eq_real @ B2 @ ( X8 @ I3 ) )
% 1.40/1.64 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % decseq_bounded
% 1.40/1.64 thf(fact_2847_greaterThanAtMost__upto,axiom,
% 1.40/1.64 ( set_or6656581121297822940st_int
% 1.40/1.64 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % greaterThanAtMost_upto
% 1.40/1.64 thf(fact_2848_decseq__convergent,axiom,
% 1.40/1.64 ! [X8: nat > real,B2: real] :
% 1.40/1.64 ( ( order_9091379641038594480t_real @ X8 )
% 1.40/1.64 => ( ! [I3: nat] : ( ord_less_eq_real @ B2 @ ( X8 @ I3 ) )
% 1.40/1.64 => ~ ! [L5: real] :
% 1.40/1.64 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L5 ) @ at_top_nat )
% 1.40/1.64 => ~ ! [I: nat] : ( ord_less_eq_real @ L5 @ ( X8 @ I ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % decseq_convergent
% 1.40/1.64 thf(fact_2849_atLeast__Suc,axiom,
% 1.40/1.64 ! [K: nat] :
% 1.40/1.64 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 1.40/1.64 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % atLeast_Suc
% 1.40/1.64 thf(fact_2850_MVT,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real] :
% 1.40/1.64 ( ( ord_less_real @ A @ B )
% 1.40/1.64 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ord_less_real @ A @ X5 )
% 1.40/1.64 => ( ( ord_less_real @ X5 @ B )
% 1.40/1.64 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 1.40/1.64 => ? [L3: real,Z3: real] :
% 1.40/1.64 ( ( ord_less_real @ A @ Z3 )
% 1.40/1.64 & ( ord_less_real @ Z3 @ B )
% 1.40/1.64 & ( has_fi5821293074295781190e_real @ F @ L3 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 1.40/1.64 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 1.40/1.64 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L3 ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % MVT
% 1.40/1.64 thf(fact_2851_continuous__on__arcosh_H,axiom,
% 1.40/1.64 ! [A2: set_real,F: real > real] :
% 1.40/1.64 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( member_real @ X5 @ A2 )
% 1.40/1.64 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 1.40/1.64 => ( topolo5044208981011980120l_real @ A2
% 1.40/1.64 @ ^ [X4: real] : ( arcosh_real @ ( F @ X4 ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % continuous_on_arcosh'
% 1.40/1.64 thf(fact_2852_continuous__image__closed__interval,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real] :
% 1.40/1.64 ( ( ord_less_eq_real @ A @ B )
% 1.40/1.64 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 1.40/1.64 => ? [C2: real,D3: real] :
% 1.40/1.64 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 1.40/1.64 = ( set_or1222579329274155063t_real @ C2 @ D3 ) )
% 1.40/1.64 & ( ord_less_eq_real @ C2 @ D3 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % continuous_image_closed_interval
% 1.40/1.64 thf(fact_2853_continuous__on__arcosh,axiom,
% 1.40/1.64 ! [A2: set_real] :
% 1.40/1.64 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 1.40/1.64 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 1.40/1.64
% 1.40/1.64 % continuous_on_arcosh
% 1.40/1.64 thf(fact_2854_continuous__on__arccos_H,axiom,
% 1.40/1.64 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 1.40/1.64
% 1.40/1.64 % continuous_on_arccos'
% 1.40/1.64 thf(fact_2855_continuous__on__arcsin_H,axiom,
% 1.40/1.64 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 1.40/1.64
% 1.40/1.64 % continuous_on_arcsin'
% 1.40/1.64 thf(fact_2856_continuous__on__artanh_H,axiom,
% 1.40/1.64 ! [A2: set_real,F: real > real] :
% 1.40/1.64 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( member_real @ X5 @ A2 )
% 1.40/1.64 => ( member_real @ ( F @ X5 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 1.40/1.64 => ( topolo5044208981011980120l_real @ A2
% 1.40/1.64 @ ^ [X4: real] : ( artanh_real @ ( F @ X4 ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % continuous_on_artanh'
% 1.40/1.64 thf(fact_2857_continuous__on__artanh,axiom,
% 1.40/1.64 ! [A2: set_real] :
% 1.40/1.64 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 1.40/1.64 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 1.40/1.64
% 1.40/1.64 % continuous_on_artanh
% 1.40/1.64 thf(fact_2858_DERIV__isconst2,axiom,
% 1.40/1.64 ! [A: real,B: real,F: real > real,X: real] :
% 1.40/1.64 ( ( ord_less_real @ A @ B )
% 1.40/1.64 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 1.40/1.64 => ( ! [X5: real] :
% 1.40/1.64 ( ( ord_less_real @ A @ X5 )
% 1.40/1.64 => ( ( ord_less_real @ X5 @ B )
% 1.40/1.64 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 1.40/1.64 => ( ( ord_less_eq_real @ A @ X )
% 1.40/1.64 => ( ( ord_less_eq_real @ X @ B )
% 1.40/1.64 => ( ( F @ X )
% 1.40/1.64 = ( F @ A ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % DERIV_isconst2
% 1.40/1.64 thf(fact_2859_less__eq__int_Orep__eq,axiom,
% 1.40/1.64 ( ord_less_eq_int
% 1.40/1.64 = ( ^ [X4: int,Xa4: int] :
% 1.40/1.64 ( produc8739625826339149834_nat_o
% 1.40/1.64 @ ^ [Y4: nat,Z5: nat] :
% 1.40/1.64 ( produc6081775807080527818_nat_o
% 1.40/1.64 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y4 @ V4 ) @ ( plus_plus_nat @ U3 @ Z5 ) ) )
% 1.40/1.64 @ ( rep_Integ @ X4 )
% 1.40/1.64 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % less_eq_int.rep_eq
% 1.40/1.64 thf(fact_2860_less__int_Orep__eq,axiom,
% 1.40/1.64 ( ord_less_int
% 1.40/1.64 = ( ^ [X4: int,Xa4: int] :
% 1.40/1.64 ( produc8739625826339149834_nat_o
% 1.40/1.64 @ ^ [Y4: nat,Z5: nat] :
% 1.40/1.64 ( produc6081775807080527818_nat_o
% 1.40/1.64 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y4 @ V4 ) @ ( plus_plus_nat @ U3 @ Z5 ) ) )
% 1.40/1.64 @ ( rep_Integ @ X4 )
% 1.40/1.64 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % less_int.rep_eq
% 1.40/1.64 thf(fact_2861_mono__times__nat,axiom,
% 1.40/1.64 ! [N: nat] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % mono_times_nat
% 1.40/1.64 thf(fact_2862_mono__Suc,axiom,
% 1.40/1.64 order_mono_nat_nat @ suc ).
% 1.40/1.64
% 1.40/1.64 % mono_Suc
% 1.40/1.64 thf(fact_2863_incseq__bounded,axiom,
% 1.40/1.64 ! [X8: nat > real,B2: real] :
% 1.40/1.64 ( ( order_mono_nat_real @ X8 )
% 1.40/1.64 => ( ! [I3: nat] : ( ord_less_eq_real @ ( X8 @ I3 ) @ B2 )
% 1.40/1.64 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % incseq_bounded
% 1.40/1.64 thf(fact_2864_incseq__convergent,axiom,
% 1.40/1.64 ! [X8: nat > real,B2: real] :
% 1.40/1.64 ( ( order_mono_nat_real @ X8 )
% 1.40/1.64 => ( ! [I3: nat] : ( ord_less_eq_real @ ( X8 @ I3 ) @ B2 )
% 1.40/1.64 => ~ ! [L5: real] :
% 1.40/1.64 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L5 ) @ at_top_nat )
% 1.40/1.64 => ~ ! [I: nat] : ( ord_less_eq_real @ ( X8 @ I ) @ L5 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % incseq_convergent
% 1.40/1.64 thf(fact_2865_mono__ge2__power__minus__self,axiom,
% 1.40/1.64 ! [K: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 1.40/1.64 => ( order_mono_nat_nat
% 1.40/1.64 @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % mono_ge2_power_minus_self
% 1.40/1.64 thf(fact_2866_inj__sgn__power,axiom,
% 1.40/1.64 ! [N: nat] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( inj_on_real_real
% 1.40/1.64 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 1.40/1.64 @ top_top_set_real ) ) ).
% 1.40/1.64
% 1.40/1.64 % inj_sgn_power
% 1.40/1.64 thf(fact_2867_log__inj,axiom,
% 1.40/1.64 ! [B: real] :
% 1.40/1.64 ( ( ord_less_real @ one_one_real @ B )
% 1.40/1.64 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % log_inj
% 1.40/1.64 thf(fact_2868_inj__on__diff__nat,axiom,
% 1.40/1.64 ! [N3: set_nat,K: nat] :
% 1.40/1.64 ( ! [N4: nat] :
% 1.40/1.64 ( ( member_nat @ N4 @ N3 )
% 1.40/1.64 => ( ord_less_eq_nat @ K @ N4 ) )
% 1.40/1.64 => ( inj_on_nat_nat
% 1.40/1.64 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 1.40/1.64 @ N3 ) ) ).
% 1.40/1.64
% 1.40/1.64 % inj_on_diff_nat
% 1.40/1.64 thf(fact_2869_inj__Suc,axiom,
% 1.40/1.64 ! [N3: set_nat] : ( inj_on_nat_nat @ suc @ N3 ) ).
% 1.40/1.64
% 1.40/1.64 % inj_Suc
% 1.40/1.64 thf(fact_2870_summable__reindex,axiom,
% 1.40/1.64 ! [F: nat > real,G: nat > nat] :
% 1.40/1.64 ( ( summable_real @ F )
% 1.40/1.64 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 1.40/1.64 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 1.40/1.64 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % summable_reindex
% 1.40/1.64 thf(fact_2871_suminf__reindex__mono,axiom,
% 1.40/1.64 ! [F: nat > real,G: nat > nat] :
% 1.40/1.64 ( ( summable_real @ F )
% 1.40/1.64 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 1.40/1.64 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 1.40/1.64 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % suminf_reindex_mono
% 1.40/1.64 thf(fact_2872_inj__on__char__of__nat,axiom,
% 1.40/1.64 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % inj_on_char_of_nat
% 1.40/1.64 thf(fact_2873_suminf__reindex,axiom,
% 1.40/1.64 ! [F: nat > real,G: nat > nat] :
% 1.40/1.64 ( ( summable_real @ F )
% 1.40/1.64 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 1.40/1.64 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 1.40/1.64 => ( ! [X5: nat] :
% 1.40/1.64 ( ~ ( member_nat @ X5 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 1.40/1.64 => ( ( F @ X5 )
% 1.40/1.64 = zero_zero_real ) )
% 1.40/1.64 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 1.40/1.64 = ( suminf_real @ F ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % suminf_reindex
% 1.40/1.64 thf(fact_2874_nonneg__incseq__Bseq__subseq__iff,axiom,
% 1.40/1.64 ! [F: nat > real,G: nat > nat] :
% 1.40/1.64 ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 1.40/1.64 => ( ( order_mono_nat_real @ F )
% 1.40/1.64 => ( ( order_5726023648592871131at_nat @ G )
% 1.40/1.64 => ( ( bfun_nat_real
% 1.40/1.64 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 1.40/1.64 @ at_top_nat )
% 1.40/1.64 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % nonneg_incseq_Bseq_subseq_iff
% 1.40/1.64 thf(fact_2875_strict__mono__imp__increasing,axiom,
% 1.40/1.64 ! [F: nat > nat,N: nat] :
% 1.40/1.64 ( ( order_5726023648592871131at_nat @ F )
% 1.40/1.64 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % strict_mono_imp_increasing
% 1.40/1.64 thf(fact_2876_powr__real__of__int_H,axiom,
% 1.40/1.64 ! [X: real,N: int] :
% 1.40/1.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 1.40/1.64 => ( ( ( X != zero_zero_real )
% 1.40/1.64 | ( ord_less_int @ zero_zero_int @ N ) )
% 1.40/1.64 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 1.40/1.64 = ( power_int_real @ X @ N ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % powr_real_of_int'
% 1.40/1.64 thf(fact_2877_num__of__nat_Osimps_I2_J,axiom,
% 1.40/1.64 ! [N: nat] :
% 1.40/1.64 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( num_of_nat @ ( suc @ N ) )
% 1.40/1.64 = ( inc @ ( num_of_nat @ N ) ) ) )
% 1.40/1.64 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( num_of_nat @ ( suc @ N ) )
% 1.40/1.64 = one ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % num_of_nat.simps(2)
% 1.40/1.64 thf(fact_2878_num__of__nat__numeral__eq,axiom,
% 1.40/1.64 ! [Q2: num] :
% 1.40/1.64 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 1.40/1.64 = Q2 ) ).
% 1.40/1.64
% 1.40/1.64 % num_of_nat_numeral_eq
% 1.40/1.64 thf(fact_2879_num__of__nat_Osimps_I1_J,axiom,
% 1.40/1.64 ( ( num_of_nat @ zero_zero_nat )
% 1.40/1.64 = one ) ).
% 1.40/1.64
% 1.40/1.64 % num_of_nat.simps(1)
% 1.40/1.64 thf(fact_2880_numeral__num__of__nat,axiom,
% 1.40/1.64 ! [N: nat] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 1.40/1.64 = N ) ) ).
% 1.40/1.64
% 1.40/1.64 % numeral_num_of_nat
% 1.40/1.64 thf(fact_2881_num__of__nat__One,axiom,
% 1.40/1.64 ! [N: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 1.40/1.64 => ( ( num_of_nat @ N )
% 1.40/1.64 = one ) ) ).
% 1.40/1.64
% 1.40/1.64 % num_of_nat_One
% 1.40/1.64 thf(fact_2882_num__of__nat__double,axiom,
% 1.40/1.64 ! [N: nat] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 1.40/1.64 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % num_of_nat_double
% 1.40/1.64 thf(fact_2883_num__of__nat__plus__distrib,axiom,
% 1.40/1.64 ! [M: nat,N: nat] :
% 1.40/1.64 ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.40/1.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.64 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 1.40/1.64 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % num_of_nat_plus_distrib
% 1.40/1.64 thf(fact_2884_pred__nat__def,axiom,
% 1.40/1.64 ( pred_nat
% 1.40/1.64 = ( collec3392354462482085612at_nat
% 1.40/1.64 @ ( produc6081775807080527818_nat_o
% 1.40/1.64 @ ^ [M6: nat,N2: nat] :
% 1.40/1.64 ( N2
% 1.40/1.64 = ( suc @ M6 ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % pred_nat_def
% 1.40/1.64 thf(fact_2885_pow_Osimps_I3_J,axiom,
% 1.40/1.64 ! [X: num,Y2: num] :
% 1.40/1.64 ( ( pow @ X @ ( bit1 @ Y2 ) )
% 1.40/1.64 = ( times_times_num @ ( sqr @ ( pow @ X @ Y2 ) ) @ X ) ) ).
% 1.40/1.64
% 1.40/1.64 % pow.simps(3)
% 1.40/1.64 thf(fact_2886_sorted__list__of__set__lessThan__Suc,axiom,
% 1.40/1.64 ! [K: nat] :
% 1.40/1.64 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 1.40/1.64 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % sorted_list_of_set_lessThan_Suc
% 1.40/1.64 thf(fact_2887_sorted__list__of__set__atMost__Suc,axiom,
% 1.40/1.64 ! [K: nat] :
% 1.40/1.64 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 1.40/1.64 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % sorted_list_of_set_atMost_Suc
% 1.40/1.64 thf(fact_2888_sqr_Osimps_I2_J,axiom,
% 1.40/1.64 ! [N: num] :
% 1.40/1.64 ( ( sqr @ ( bit0 @ N ) )
% 1.40/1.64 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % sqr.simps(2)
% 1.40/1.64 thf(fact_2889_sqr_Osimps_I1_J,axiom,
% 1.40/1.64 ( ( sqr @ one )
% 1.40/1.64 = one ) ).
% 1.40/1.64
% 1.40/1.64 % sqr.simps(1)
% 1.40/1.64 thf(fact_2890_sqr__conv__mult,axiom,
% 1.40/1.64 ( sqr
% 1.40/1.64 = ( ^ [X4: num] : ( times_times_num @ X4 @ X4 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % sqr_conv_mult
% 1.40/1.64 thf(fact_2891_sorted__list__of__set__greaterThanAtMost,axiom,
% 1.40/1.64 ! [I2: nat,J: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 1.40/1.64 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 1.40/1.64 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % sorted_list_of_set_greaterThanAtMost
% 1.40/1.64 thf(fact_2892_sorted__list__of__set__greaterThanLessThan,axiom,
% 1.40/1.64 ! [I2: nat,J: nat] :
% 1.40/1.64 ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 1.40/1.64 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 1.40/1.64 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % sorted_list_of_set_greaterThanLessThan
% 1.40/1.64 thf(fact_2893_pow_Osimps_I2_J,axiom,
% 1.40/1.64 ! [X: num,Y2: num] :
% 1.40/1.64 ( ( pow @ X @ ( bit0 @ Y2 ) )
% 1.40/1.64 = ( sqr @ ( pow @ X @ Y2 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % pow.simps(2)
% 1.40/1.64 thf(fact_2894_sqr_Osimps_I3_J,axiom,
% 1.40/1.64 ! [N: num] :
% 1.40/1.64 ( ( sqr @ ( bit1 @ N ) )
% 1.40/1.64 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % sqr.simps(3)
% 1.40/1.64 thf(fact_2895_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 1.40/1.64 ! [N: nat,J: nat,I2: nat] :
% 1.40/1.64 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I2 ) )
% 1.40/1.64 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N )
% 1.40/1.64 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % nth_sorted_list_of_set_greaterThanAtMost
% 1.40/1.64 thf(fact_2896_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 1.40/1.64 ! [N: nat,J: nat,I2: nat] :
% 1.40/1.64 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 1.40/1.64 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N )
% 1.40/1.64 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % nth_sorted_list_of_set_greaterThanLessThan
% 1.40/1.64 thf(fact_2897_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 1.40/1.64 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 1.40/1.64 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 1.40/1.64 = Y2 )
% 1.40/1.64 => ( ( ? [Uu: $o,Uv: $o] :
% 1.40/1.64 ( X
% 1.40/1.64 = ( vEBT_Leaf @ Uu @ Uv ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 = ( Xa2 != one_one_nat ) ) )
% 1.40/1.64 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 = ( ~ ( ( Deg2 = Xa2 )
% 1.40/1.64 & ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 1.40/1.64 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 & ( case_o184042715313410164at_nat
% 1.40/1.64 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 1.40/1.64 & ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 @ ( produc6081775807080527818_nat_o
% 1.40/1.64 @ ^ [Mi3: nat,Ma3: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 1.40/1.64 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 & ! [I4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X2 ) )
% 1.40/1.64 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 1.40/1.64 & ( ( Mi3 = Ma3 )
% 1.40/1.64 => ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 & ( ( Mi3 != Ma3 )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 1.40/1.64 & ! [X4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 1.40/1.64 => ( ( ord_less_nat @ Mi3 @ X4 )
% 1.40/1.64 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 1.40/1.64 @ Mima ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % VEBT_internal.valid'.elims(1)
% 1.40/1.64 thf(fact_2898_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 1.40/1.64 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.64 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 1.40/1.64 => ( ( ? [Uu: $o,Uv: $o] :
% 1.40/1.64 ( X
% 1.40/1.64 = ( vEBT_Leaf @ Uu @ Uv ) )
% 1.40/1.64 => ( Xa2 != one_one_nat ) )
% 1.40/1.64 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 1.40/1.64 => ~ ( ( Deg2 = Xa2 )
% 1.40/1.64 & ! [X3: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 1.40/1.64 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 & ( case_o184042715313410164at_nat
% 1.40/1.64 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 1.40/1.64 & ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 @ ( produc6081775807080527818_nat_o
% 1.40/1.64 @ ^ [Mi3: nat,Ma3: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 1.40/1.64 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 & ! [I4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X2 ) )
% 1.40/1.64 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 1.40/1.64 & ( ( Mi3 = Ma3 )
% 1.40/1.64 => ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 & ( ( Mi3 != Ma3 )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 1.40/1.64 & ! [X4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 1.40/1.64 => ( ( ord_less_nat @ Mi3 @ X4 )
% 1.40/1.64 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 1.40/1.64 @ Mima ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % VEBT_internal.valid'.elims(2)
% 1.40/1.64 thf(fact_2899_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 1.40/1.64 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 1.40/1.64 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg4 )
% 1.40/1.64 = ( ( Deg = Deg4 )
% 1.40/1.64 & ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.64 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 1.40/1.64 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 & ( case_o184042715313410164at_nat
% 1.40/1.64 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X2 )
% 1.40/1.64 & ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 @ ( produc6081775807080527818_nat_o
% 1.40/1.64 @ ^ [Mi3: nat,Ma3: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 1.40/1.64 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 1.40/1.64 & ! [I4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X2 ) )
% 1.40/1.64 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 1.40/1.64 & ( ( Mi3 = Ma3 )
% 1.40/1.64 => ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 & ( ( Mi3 != Ma3 )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 1.40/1.64 & ! [X4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 1.40/1.64 => ( ( ord_less_nat @ Mi3 @ X4 )
% 1.40/1.64 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 1.40/1.64 @ Mima2 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % VEBT_internal.valid'.simps(2)
% 1.40/1.64 thf(fact_2900_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 1.40/1.64 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.64 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 1.40/1.64 => ( ( ? [Uu: $o,Uv: $o] :
% 1.40/1.64 ( X
% 1.40/1.64 = ( vEBT_Leaf @ Uu @ Uv ) )
% 1.40/1.64 => ( Xa2 = one_one_nat ) )
% 1.40/1.64 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 1.40/1.64 => ( ( Deg2 = Xa2 )
% 1.40/1.64 & ! [X5: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 1.40/1.64 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 & ( case_o184042715313410164at_nat
% 1.40/1.64 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 1.40/1.64 & ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 @ ( produc6081775807080527818_nat_o
% 1.40/1.64 @ ^ [Mi3: nat,Ma3: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 1.40/1.64 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 & ! [I4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X2 ) )
% 1.40/1.64 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 1.40/1.64 & ( ( Mi3 = Ma3 )
% 1.40/1.64 => ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 & ( ( Mi3 != Ma3 )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 1.40/1.64 & ! [X4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 1.40/1.64 => ( ( ord_less_nat @ Mi3 @ X4 )
% 1.40/1.64 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 1.40/1.64 @ Mima ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % VEBT_internal.valid'.elims(3)
% 1.40/1.64 thf(fact_2901_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 1.40/1.64 ! [X: vEBT_VEBT,Xa2: nat,Y2: $o] :
% 1.40/1.64 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 1.40/1.64 = Y2 )
% 1.40/1.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.64 => ( ! [Uu: $o,Uv: $o] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( vEBT_Leaf @ Uu @ Uv ) )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( Xa2 = one_one_nat ) )
% 1.40/1.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) ) )
% 1.40/1.64 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( ( Deg2 = Xa2 )
% 1.40/1.64 & ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 1.40/1.64 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 & ( case_o184042715313410164at_nat
% 1.40/1.64 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 1.40/1.64 & ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 @ ( produc6081775807080527818_nat_o
% 1.40/1.64 @ ^ [Mi3: nat,Ma3: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 1.40/1.64 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 & ! [I4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X2 ) )
% 1.40/1.64 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 1.40/1.64 & ( ( Mi3 = Ma3 )
% 1.40/1.64 => ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 & ( ( Mi3 != Ma3 )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 1.40/1.64 & ! [X4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 1.40/1.64 => ( ( ord_less_nat @ Mi3 @ X4 )
% 1.40/1.64 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 1.40/1.64 @ Mima ) ) )
% 1.40/1.64 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % VEBT_internal.valid'.pelims(1)
% 1.40/1.64 thf(fact_2902_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 1.40/1.64 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.64 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 1.40/1.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.64 => ( ! [Uu: $o,Uv: $o] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( vEBT_Leaf @ Uu @ Uv ) )
% 1.40/1.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) )
% 1.40/1.64 => ( Xa2 != one_one_nat ) ) )
% 1.40/1.64 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 1.40/1.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 1.40/1.64 => ~ ( ( Deg2 = Xa2 )
% 1.40/1.64 & ! [X3: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 1.40/1.64 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 & ( case_o184042715313410164at_nat
% 1.40/1.64 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 1.40/1.64 & ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 @ ( produc6081775807080527818_nat_o
% 1.40/1.64 @ ^ [Mi3: nat,Ma3: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 1.40/1.64 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 & ! [I4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X2 ) )
% 1.40/1.64 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 1.40/1.64 & ( ( Mi3 = Ma3 )
% 1.40/1.64 => ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 & ( ( Mi3 != Ma3 )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 1.40/1.64 & ! [X4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 1.40/1.64 => ( ( ord_less_nat @ Mi3 @ X4 )
% 1.40/1.64 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 1.40/1.64 @ Mima ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % VEBT_internal.valid'.pelims(2)
% 1.40/1.64 thf(fact_2903_Sup__int__def,axiom,
% 1.40/1.64 ( complete_Sup_Sup_int
% 1.40/1.64 = ( ^ [X2: set_int] :
% 1.40/1.64 ( the_int
% 1.40/1.64 @ ^ [X4: int] :
% 1.40/1.64 ( ( member_int @ X4 @ X2 )
% 1.40/1.64 & ! [Y4: int] :
% 1.40/1.64 ( ( member_int @ Y4 @ X2 )
% 1.40/1.64 => ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Sup_int_def
% 1.40/1.64 thf(fact_2904_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 1.40/1.64 ! [X: vEBT_VEBT,Xa2: nat] :
% 1.40/1.64 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 1.40/1.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 1.40/1.64 => ( ! [Uu: $o,Uv: $o] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( vEBT_Leaf @ Uu @ Uv ) )
% 1.40/1.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) )
% 1.40/1.64 => ( Xa2 = one_one_nat ) ) )
% 1.40/1.64 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 1.40/1.64 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 1.40/1.64 => ( ( Deg2 = Xa2 )
% 1.40/1.64 & ! [X5: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 1.40/1.64 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 1.40/1.64 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 & ( case_o184042715313410164at_nat
% 1.40/1.64 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 1.40/1.64 & ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 @ ( produc6081775807080527818_nat_o
% 1.40/1.64 @ ^ [Mi3: nat,Ma3: nat] :
% 1.40/1.64 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 1.40/1.64 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 & ! [I4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 1.40/1.64 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X2 ) )
% 1.40/1.64 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 1.40/1.64 & ( ( Mi3 = Ma3 )
% 1.40/1.64 => ! [X4: vEBT_VEBT] :
% 1.40/1.64 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 1.40/1.64 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X2 ) ) )
% 1.40/1.64 & ( ( Mi3 != Ma3 )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 1.40/1.64 & ! [X4: nat] :
% 1.40/1.64 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 1.40/1.64 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X4 )
% 1.40/1.64 => ( ( ord_less_nat @ Mi3 @ X4 )
% 1.40/1.64 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 1.40/1.64 @ Mima ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % VEBT_internal.valid'.pelims(3)
% 1.40/1.64 thf(fact_2905_less__eq,axiom,
% 1.40/1.64 ! [M: nat,N: nat] :
% 1.40/1.64 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 1.40/1.64 = ( ord_less_nat @ M @ N ) ) ).
% 1.40/1.64
% 1.40/1.64 % less_eq
% 1.40/1.64 thf(fact_2906_pred__nat__trancl__eq__le,axiom,
% 1.40/1.64 ! [M: nat,N: nat] :
% 1.40/1.64 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 1.40/1.64 = ( ord_less_eq_nat @ M @ N ) ) ).
% 1.40/1.64
% 1.40/1.64 % pred_nat_trancl_eq_le
% 1.40/1.64 thf(fact_2907_min__Suc__Suc,axiom,
% 1.40/1.64 ! [M: nat,N: nat] :
% 1.40/1.64 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 1.40/1.64 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % min_Suc_Suc
% 1.40/1.64 thf(fact_2908_min__0R,axiom,
% 1.40/1.64 ! [N: nat] :
% 1.40/1.64 ( ( ord_min_nat @ N @ zero_zero_nat )
% 1.40/1.64 = zero_zero_nat ) ).
% 1.40/1.64
% 1.40/1.64 % min_0R
% 1.40/1.64 thf(fact_2909_min__0L,axiom,
% 1.40/1.64 ! [N: nat] :
% 1.40/1.64 ( ( ord_min_nat @ zero_zero_nat @ N )
% 1.40/1.64 = zero_zero_nat ) ).
% 1.40/1.64
% 1.40/1.64 % min_0L
% 1.40/1.64 thf(fact_2910_min__numeral__Suc,axiom,
% 1.40/1.64 ! [K: num,N: nat] :
% 1.40/1.64 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 1.40/1.64 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % min_numeral_Suc
% 1.40/1.64 thf(fact_2911_min__Suc__numeral,axiom,
% 1.40/1.64 ! [N: nat,K: num] :
% 1.40/1.64 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 1.40/1.64 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % min_Suc_numeral
% 1.40/1.64 thf(fact_2912_inf__nat__def,axiom,
% 1.40/1.64 inf_inf_nat = ord_min_nat ).
% 1.40/1.64
% 1.40/1.64 % inf_nat_def
% 1.40/1.64 thf(fact_2913_concat__bit__assoc__sym,axiom,
% 1.40/1.64 ! [M: nat,N: nat,K: int,L2: int,R2: int] :
% 1.40/1.64 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L2 ) @ R2 )
% 1.40/1.64 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L2 @ R2 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % concat_bit_assoc_sym
% 1.40/1.64 thf(fact_2914_min__diff,axiom,
% 1.40/1.64 ! [M: nat,I2: nat,N: nat] :
% 1.40/1.64 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N @ I2 ) )
% 1.40/1.64 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I2 ) ) ).
% 1.40/1.64
% 1.40/1.64 % min_diff
% 1.40/1.64 thf(fact_2915_nat__mult__min__left,axiom,
% 1.40/1.64 ! [M: nat,N: nat,Q2: nat] :
% 1.40/1.64 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 1.40/1.64 = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % nat_mult_min_left
% 1.40/1.64 thf(fact_2916_nat__mult__min__right,axiom,
% 1.40/1.64 ! [M: nat,N: nat,Q2: nat] :
% 1.40/1.64 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 1.40/1.64 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % nat_mult_min_right
% 1.40/1.64 thf(fact_2917_take__bit__concat__bit__eq,axiom,
% 1.40/1.64 ! [M: nat,N: nat,K: int,L2: int] :
% 1.40/1.64 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L2 ) )
% 1.40/1.64 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L2 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % take_bit_concat_bit_eq
% 1.40/1.64 thf(fact_2918_min__Suc2,axiom,
% 1.40/1.64 ! [M: nat,N: nat] :
% 1.40/1.64 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 1.40/1.64 = ( case_nat_nat @ zero_zero_nat
% 1.40/1.64 @ ^ [M2: nat] : ( suc @ ( ord_min_nat @ M2 @ N ) )
% 1.40/1.64 @ M ) ) ).
% 1.40/1.64
% 1.40/1.64 % min_Suc2
% 1.40/1.64 thf(fact_2919_min__Suc1,axiom,
% 1.40/1.64 ! [N: nat,M: nat] :
% 1.40/1.64 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 1.40/1.64 = ( case_nat_nat @ zero_zero_nat
% 1.40/1.64 @ ^ [M2: nat] : ( suc @ ( ord_min_nat @ N @ M2 ) )
% 1.40/1.64 @ M ) ) ).
% 1.40/1.64
% 1.40/1.64 % min_Suc1
% 1.40/1.64 thf(fact_2920_Rats__eq__int__div__nat,axiom,
% 1.40/1.64 ( field_5140801741446780682s_real
% 1.40/1.64 = ( collect_real
% 1.40/1.64 @ ^ [Uu3: real] :
% 1.40/1.64 ? [I4: int,N2: nat] :
% 1.40/1.64 ( ( Uu3
% 1.40/1.64 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 1.40/1.64 & ( N2 != zero_zero_nat ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Rats_eq_int_div_nat
% 1.40/1.64 thf(fact_2921_min__enat__simps_I2_J,axiom,
% 1.40/1.64 ! [Q2: extended_enat] :
% 1.40/1.64 ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 1.40/1.64 = zero_z5237406670263579293d_enat ) ).
% 1.40/1.64
% 1.40/1.64 % min_enat_simps(2)
% 1.40/1.64 thf(fact_2922_min__enat__simps_I3_J,axiom,
% 1.40/1.64 ! [Q2: extended_enat] :
% 1.40/1.64 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 1.40/1.64 = zero_z5237406670263579293d_enat ) ).
% 1.40/1.64
% 1.40/1.64 % min_enat_simps(3)
% 1.40/1.64 thf(fact_2923_Rats__abs__iff,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ( ( member_real @ ( abs_abs_real @ X ) @ field_5140801741446780682s_real )
% 1.40/1.64 = ( member_real @ X @ field_5140801741446780682s_real ) ) ).
% 1.40/1.64
% 1.40/1.64 % Rats_abs_iff
% 1.40/1.64 thf(fact_2924_Rats__dense__in__real,axiom,
% 1.40/1.64 ! [X: real,Y2: real] :
% 1.40/1.64 ( ( ord_less_real @ X @ Y2 )
% 1.40/1.64 => ? [X5: real] :
% 1.40/1.64 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 1.40/1.64 & ( ord_less_real @ X @ X5 )
% 1.40/1.64 & ( ord_less_real @ X5 @ Y2 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Rats_dense_in_real
% 1.40/1.64 thf(fact_2925_Rats__no__bot__less,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ? [X5: real] :
% 1.40/1.64 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 1.40/1.64 & ( ord_less_real @ X5 @ X ) ) ).
% 1.40/1.64
% 1.40/1.64 % Rats_no_bot_less
% 1.40/1.64 thf(fact_2926_Rats__no__top__le,axiom,
% 1.40/1.64 ! [X: real] :
% 1.40/1.64 ? [X5: real] :
% 1.40/1.64 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 1.40/1.64 & ( ord_less_eq_real @ X @ X5 ) ) ).
% 1.40/1.64
% 1.40/1.64 % Rats_no_top_le
% 1.40/1.64 thf(fact_2927_Rats__eq__int__div__int,axiom,
% 1.40/1.64 ( field_5140801741446780682s_real
% 1.40/1.64 = ( collect_real
% 1.40/1.64 @ ^ [Uu3: real] :
% 1.40/1.64 ? [I4: int,J3: int] :
% 1.40/1.64 ( ( Uu3
% 1.40/1.64 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 1.40/1.64 & ( J3 != zero_zero_int ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Rats_eq_int_div_int
% 1.40/1.64 thf(fact_2928_inf__enat__def,axiom,
% 1.40/1.64 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 1.40/1.64
% 1.40/1.64 % inf_enat_def
% 1.40/1.64 thf(fact_2929_rat__floor__lemma,axiom,
% 1.40/1.64 ! [A: int,B: int] :
% 1.40/1.64 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 1.40/1.64 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % rat_floor_lemma
% 1.40/1.64 thf(fact_2930_mult__rat,axiom,
% 1.40/1.64 ! [A: int,B: int,C: int,D: int] :
% 1.40/1.64 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 1.40/1.64 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % mult_rat
% 1.40/1.64 thf(fact_2931_divide__rat,axiom,
% 1.40/1.64 ! [A: int,B: int,C: int,D: int] :
% 1.40/1.64 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 1.40/1.64 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % divide_rat
% 1.40/1.64 thf(fact_2932_less__rat,axiom,
% 1.40/1.64 ! [B: int,D: int,A: int,C: int] :
% 1.40/1.64 ( ( B != zero_zero_int )
% 1.40/1.64 => ( ( D != zero_zero_int )
% 1.40/1.64 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 1.40/1.64 = ( 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 ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % less_rat
% 1.40/1.64 thf(fact_2933_add__rat,axiom,
% 1.40/1.64 ! [B: int,D: int,A: int,C: int] :
% 1.40/1.64 ( ( B != zero_zero_int )
% 1.40/1.64 => ( ( D != zero_zero_int )
% 1.40/1.64 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 1.40/1.64 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % add_rat
% 1.40/1.64 thf(fact_2934_le__rat,axiom,
% 1.40/1.64 ! [B: int,D: int,A: int,C: int] :
% 1.40/1.64 ( ( B != zero_zero_int )
% 1.40/1.64 => ( ( D != zero_zero_int )
% 1.40/1.64 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 1.40/1.64 = ( 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 ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % le_rat
% 1.40/1.64 thf(fact_2935_diff__rat,axiom,
% 1.40/1.64 ! [B: int,D: int,A: int,C: int] :
% 1.40/1.64 ( ( B != zero_zero_int )
% 1.40/1.64 => ( ( D != zero_zero_int )
% 1.40/1.64 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 1.40/1.64 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % diff_rat
% 1.40/1.64 thf(fact_2936_sgn__rat,axiom,
% 1.40/1.64 ! [A: int,B: int] :
% 1.40/1.64 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 1.40/1.64 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % sgn_rat
% 1.40/1.64 thf(fact_2937_Fract__of__int__eq,axiom,
% 1.40/1.64 ! [K: int] :
% 1.40/1.64 ( ( fract @ K @ one_one_int )
% 1.40/1.64 = ( ring_1_of_int_rat @ K ) ) ).
% 1.40/1.64
% 1.40/1.64 % Fract_of_int_eq
% 1.40/1.64 thf(fact_2938_One__rat__def,axiom,
% 1.40/1.64 ( one_one_rat
% 1.40/1.64 = ( fract @ one_one_int @ one_one_int ) ) ).
% 1.40/1.64
% 1.40/1.64 % One_rat_def
% 1.40/1.64 thf(fact_2939_eq__rat_I1_J,axiom,
% 1.40/1.64 ! [B: int,D: int,A: int,C: int] :
% 1.40/1.64 ( ( B != zero_zero_int )
% 1.40/1.64 => ( ( D != zero_zero_int )
% 1.40/1.64 => ( ( ( fract @ A @ B )
% 1.40/1.64 = ( fract @ C @ D ) )
% 1.40/1.64 = ( ( times_times_int @ A @ D )
% 1.40/1.64 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % eq_rat(1)
% 1.40/1.64 thf(fact_2940_mult__rat__cancel,axiom,
% 1.40/1.64 ! [C: int,A: int,B: int] :
% 1.40/1.64 ( ( C != zero_zero_int )
% 1.40/1.64 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 1.40/1.64 = ( fract @ A @ B ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % mult_rat_cancel
% 1.40/1.64 thf(fact_2941_eq__rat_I2_J,axiom,
% 1.40/1.64 ! [A: int] :
% 1.40/1.64 ( ( fract @ A @ zero_zero_int )
% 1.40/1.64 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 1.40/1.64
% 1.40/1.64 % eq_rat(2)
% 1.40/1.64 thf(fact_2942_Fract__of__nat__eq,axiom,
% 1.40/1.64 ! [K: nat] :
% 1.40/1.64 ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 1.40/1.64 = ( semiri681578069525770553at_rat @ K ) ) ).
% 1.40/1.64
% 1.40/1.64 % Fract_of_nat_eq
% 1.40/1.64 thf(fact_2943_Zero__rat__def,axiom,
% 1.40/1.64 ( zero_zero_rat
% 1.40/1.64 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 1.40/1.64
% 1.40/1.64 % Zero_rat_def
% 1.40/1.64 thf(fact_2944_rat__number__collapse_I3_J,axiom,
% 1.40/1.64 ! [W: num] :
% 1.40/1.64 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 1.40/1.64 = ( numeral_numeral_rat @ W ) ) ).
% 1.40/1.64
% 1.40/1.64 % rat_number_collapse(3)
% 1.40/1.64 thf(fact_2945_rat__number__expand_I3_J,axiom,
% 1.40/1.64 ( numeral_numeral_rat
% 1.40/1.64 = ( ^ [K3: num] : ( fract @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % rat_number_expand(3)
% 1.40/1.64 thf(fact_2946_one__less__Fract__iff,axiom,
% 1.40/1.64 ! [B: int,A: int] :
% 1.40/1.64 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.64 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 1.40/1.64 = ( ord_less_int @ B @ A ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % one_less_Fract_iff
% 1.40/1.64 thf(fact_2947_Fract__less__one__iff,axiom,
% 1.40/1.64 ! [B: int,A: int] :
% 1.40/1.64 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.64 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 1.40/1.64 = ( ord_less_int @ A @ B ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Fract_less_one_iff
% 1.40/1.64 thf(fact_2948_rat__number__collapse_I5_J,axiom,
% 1.40/1.64 ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 1.40/1.64 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 1.40/1.64
% 1.40/1.64 % rat_number_collapse(5)
% 1.40/1.64 thf(fact_2949_Fract__add__one,axiom,
% 1.40/1.64 ! [N: int,M: int] :
% 1.40/1.64 ( ( N != zero_zero_int )
% 1.40/1.64 => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 1.40/1.64 = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Fract_add_one
% 1.40/1.64 thf(fact_2950_zero__le__Fract__iff,axiom,
% 1.40/1.64 ! [B: int,A: int] :
% 1.40/1.64 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 1.40/1.64 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % zero_le_Fract_iff
% 1.40/1.64 thf(fact_2951_Fract__le__zero__iff,axiom,
% 1.40/1.64 ! [B: int,A: int] :
% 1.40/1.64 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.64 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 1.40/1.64 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Fract_le_zero_iff
% 1.40/1.64 thf(fact_2952_one__le__Fract__iff,axiom,
% 1.40/1.64 ! [B: int,A: int] :
% 1.40/1.64 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.64 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 1.40/1.64 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % one_le_Fract_iff
% 1.40/1.64 thf(fact_2953_Fract__le__one__iff,axiom,
% 1.40/1.64 ! [B: int,A: int] :
% 1.40/1.64 ( ( ord_less_int @ zero_zero_int @ B )
% 1.40/1.64 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 1.40/1.64 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Fract_le_one_iff
% 1.40/1.64 thf(fact_2954_rat__number__collapse_I4_J,axiom,
% 1.40/1.64 ! [W: num] :
% 1.40/1.64 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 1.40/1.64 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % rat_number_collapse(4)
% 1.40/1.64 thf(fact_2955_rat__number__expand_I5_J,axiom,
% 1.40/1.64 ! [K: num] :
% 1.40/1.64 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 1.40/1.64 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 1.40/1.64
% 1.40/1.64 % rat_number_expand(5)
% 1.40/1.64 thf(fact_2956_take__bit__numeral__minus__numeral__int,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.64 = ( case_option_int_num @ zero_zero_int
% 1.40/1.64 @ ^ [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 ) ) )
% 1.40/1.64 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % take_bit_numeral_minus_numeral_int
% 1.40/1.64 thf(fact_2957_take__bit__num__simps_I1_J,axiom,
% 1.40/1.64 ! [M: num] :
% 1.40/1.64 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 1.40/1.64 = none_num ) ).
% 1.40/1.64
% 1.40/1.64 % take_bit_num_simps(1)
% 1.40/1.64 thf(fact_2958_take__bit__num__simps_I2_J,axiom,
% 1.40/1.64 ! [N: nat] :
% 1.40/1.64 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 1.40/1.64 = ( some_num @ one ) ) ).
% 1.40/1.64
% 1.40/1.64 % take_bit_num_simps(2)
% 1.40/1.64 thf(fact_2959_take__bit__num__simps_I5_J,axiom,
% 1.40/1.64 ! [R2: num] :
% 1.40/1.64 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 1.40/1.64 = ( some_num @ one ) ) ).
% 1.40/1.64
% 1.40/1.64 % take_bit_num_simps(5)
% 1.40/1.64 thf(fact_2960_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 1.40/1.64 ! [N: nat] :
% 1.40/1.64 ( ( bit_take_bit_num @ N @ one )
% 1.40/1.64 = ( case_nat_option_num @ none_num
% 1.40/1.64 @ ^ [N2: nat] : ( some_num @ one )
% 1.40/1.64 @ N ) ) ).
% 1.40/1.64
% 1.40/1.64 % Code_Abstract_Nat.take_bit_num_code(1)
% 1.40/1.64 thf(fact_2961_take__bit__num__def,axiom,
% 1.40/1.64 ( bit_take_bit_num
% 1.40/1.64 = ( ^ [N2: nat,M6: num] :
% 1.40/1.64 ( if_option_num
% 1.40/1.64 @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) )
% 1.40/1.64 = zero_zero_nat )
% 1.40/1.64 @ none_num
% 1.40/1.64 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % take_bit_num_def
% 1.40/1.64 thf(fact_2962_and__minus__numerals_I3_J,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 1.40/1.64 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_minus_numerals(3)
% 1.40/1.64 thf(fact_2963_and__minus__numerals_I7_J,axiom,
% 1.40/1.64 ! [N: num,M: num] :
% 1.40/1.64 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 1.40/1.64 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_minus_numerals(7)
% 1.40/1.64 thf(fact_2964_take__bit__num__simps_I4_J,axiom,
% 1.40/1.64 ! [N: nat,M: num] :
% 1.40/1.64 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 1.40/1.64 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % take_bit_num_simps(4)
% 1.40/1.64 thf(fact_2965_take__bit__num__simps_I3_J,axiom,
% 1.40/1.64 ! [N: nat,M: num] :
% 1.40/1.64 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 1.40/1.64 = ( case_o6005452278849405969um_num @ none_num
% 1.40/1.64 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 1.40/1.64 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % take_bit_num_simps(3)
% 1.40/1.64 thf(fact_2966_take__bit__num__simps_I7_J,axiom,
% 1.40/1.64 ! [R2: num,M: num] :
% 1.40/1.64 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 1.40/1.64 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % take_bit_num_simps(7)
% 1.40/1.64 thf(fact_2967_take__bit__num__simps_I6_J,axiom,
% 1.40/1.64 ! [R2: num,M: num] :
% 1.40/1.64 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 1.40/1.64 = ( case_o6005452278849405969um_num @ none_num
% 1.40/1.64 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 1.40/1.64 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % take_bit_num_simps(6)
% 1.40/1.64 thf(fact_2968_and__minus__numerals_I8_J,axiom,
% 1.40/1.64 ! [N: num,M: num] :
% 1.40/1.64 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 1.40/1.64 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_minus_numerals(8)
% 1.40/1.64 thf(fact_2969_and__minus__numerals_I4_J,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 1.40/1.64 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_minus_numerals(4)
% 1.40/1.64 thf(fact_2970_and__not__num_Osimps_I8_J,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 1.40/1.64 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 1.40/1.64 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 1.40/1.64 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.simps(8)
% 1.40/1.64 thf(fact_2971_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 1.40/1.64 ! [N: nat,M: num] :
% 1.40/1.64 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 1.40/1.64 = ( case_nat_option_num @ none_num
% 1.40/1.64 @ ^ [N2: nat] :
% 1.40/1.64 ( case_o6005452278849405969um_num @ none_num
% 1.40/1.64 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 1.40/1.64 @ ( bit_take_bit_num @ N2 @ M ) )
% 1.40/1.64 @ N ) ) ).
% 1.40/1.64
% 1.40/1.64 % Code_Abstract_Nat.take_bit_num_code(2)
% 1.40/1.64 thf(fact_2972_and__not__num_Osimps_I4_J,axiom,
% 1.40/1.64 ! [M: num] :
% 1.40/1.64 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 1.40/1.64 = ( some_num @ ( bit0 @ M ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.simps(4)
% 1.40/1.64 thf(fact_2973_and__not__num_Osimps_I2_J,axiom,
% 1.40/1.64 ! [N: num] :
% 1.40/1.64 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 1.40/1.64 = ( some_num @ one ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.simps(2)
% 1.40/1.64 thf(fact_2974_and__not__num_Osimps_I1_J,axiom,
% 1.40/1.64 ( ( bit_and_not_num @ one @ one )
% 1.40/1.64 = none_num ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.simps(1)
% 1.40/1.64 thf(fact_2975_and__not__num_Osimps_I3_J,axiom,
% 1.40/1.64 ! [N: num] :
% 1.40/1.64 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 1.40/1.64 = none_num ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.simps(3)
% 1.40/1.64 thf(fact_2976_and__not__num_Osimps_I7_J,axiom,
% 1.40/1.64 ! [M: num] :
% 1.40/1.64 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 1.40/1.64 = ( some_num @ ( bit0 @ M ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.simps(7)
% 1.40/1.64 thf(fact_2977_and__not__num__eq__Some__iff,axiom,
% 1.40/1.64 ! [M: num,N: num,Q2: num] :
% 1.40/1.64 ( ( ( bit_and_not_num @ M @ N )
% 1.40/1.64 = ( some_num @ Q2 ) )
% 1.40/1.64 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.64 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num_eq_Some_iff
% 1.40/1.64 thf(fact_2978_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 1.40/1.64 ! [N: nat,M: num] :
% 1.40/1.64 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 1.40/1.64 = ( case_nat_option_num @ none_num
% 1.40/1.64 @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 1.40/1.64 @ N ) ) ).
% 1.40/1.64
% 1.40/1.64 % Code_Abstract_Nat.take_bit_num_code(3)
% 1.40/1.64 thf(fact_2979_and__not__num__eq__None__iff,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( ( bit_and_not_num @ M @ N )
% 1.40/1.64 = none_num )
% 1.40/1.64 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.64 = zero_zero_int ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num_eq_None_iff
% 1.40/1.64 thf(fact_2980_int__numeral__and__not__num,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 1.40/1.64 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % int_numeral_and_not_num
% 1.40/1.64 thf(fact_2981_int__numeral__not__and__num,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 1.40/1.64 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % int_numeral_not_and_num
% 1.40/1.64 thf(fact_2982_positive__rat,axiom,
% 1.40/1.64 ! [A: int,B: int] :
% 1.40/1.64 ( ( positive @ ( fract @ A @ B ) )
% 1.40/1.64 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % positive_rat
% 1.40/1.64 thf(fact_2983_Rat_Opositive__add,axiom,
% 1.40/1.64 ! [X: rat,Y2: rat] :
% 1.40/1.64 ( ( positive @ X )
% 1.40/1.64 => ( ( positive @ Y2 )
% 1.40/1.64 => ( positive @ ( plus_plus_rat @ X @ Y2 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Rat.positive_add
% 1.40/1.64 thf(fact_2984_Rat_Opositive__mult,axiom,
% 1.40/1.64 ! [X: rat,Y2: rat] :
% 1.40/1.64 ( ( positive @ X )
% 1.40/1.64 => ( ( positive @ Y2 )
% 1.40/1.64 => ( positive @ ( times_times_rat @ X @ Y2 ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Rat.positive_mult
% 1.40/1.64 thf(fact_2985_Rat_Opositive_Orep__eq,axiom,
% 1.40/1.64 ( positive
% 1.40/1.64 = ( ^ [X4: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X4 ) ) @ ( product_snd_int_int @ ( rep_Rat @ X4 ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % Rat.positive.rep_eq
% 1.40/1.64 thf(fact_2986_and__not__num_Oelims,axiom,
% 1.40/1.64 ! [X: num,Xa2: num,Y2: option_num] :
% 1.40/1.64 ( ( ( bit_and_not_num @ X @ Xa2 )
% 1.40/1.64 = Y2 )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( Y2 != none_num ) ) )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ( ? [N4: num] :
% 1.40/1.64 ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( some_num @ one ) ) ) )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ( ? [N4: num] :
% 1.40/1.64 ( Xa2
% 1.40/1.64 = ( bit1 @ N4 ) )
% 1.40/1.64 => ( Y2 != none_num ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N4 ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit1 @ N4 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N4 ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit1 @ M5 ) )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit1 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 1.40/1.64 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 1.40/1.64 @ ( bit_and_not_num @ M5 @ N4 ) ) ) ) )
% 1.40/1.64 => ~ ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit1 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit1 @ N4 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.elims
% 1.40/1.64 thf(fact_2987_and__not__num_Osimps_I5_J,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 1.40/1.64 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.simps(5)
% 1.40/1.64 thf(fact_2988_and__not__num_Osimps_I6_J,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 1.40/1.64 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.simps(6)
% 1.40/1.64 thf(fact_2989_and__not__num_Osimps_I9_J,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 1.40/1.64 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.simps(9)
% 1.40/1.64 thf(fact_2990_and__not__num_Opelims,axiom,
% 1.40/1.64 ! [X: num,Xa2: num,Y2: option_num] :
% 1.40/1.64 ( ( ( bit_and_not_num @ X @ Xa2 )
% 1.40/1.64 = Y2 )
% 1.40/1.64 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( ( Y2 = none_num )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( some_num @ one ) )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N4 ) ) ) ) ) )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit1 @ N4 ) )
% 1.40/1.64 => ( ( Y2 = none_num )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N4 ) ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( some_num @ ( bit0 @ M5 ) ) )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N4 ) ) )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit1 @ N4 ) )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N4 ) ) )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N4 ) ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit1 @ M5 ) )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( some_num @ ( bit0 @ M5 ) ) )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit1 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 1.40/1.64 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 1.40/1.64 @ ( bit_and_not_num @ M5 @ N4 ) ) )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 1.40/1.64 => ~ ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit1 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit1 @ N4 ) )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N4 ) ) )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_not_num.pelims
% 1.40/1.64 thf(fact_2991_and__num_Oelims,axiom,
% 1.40/1.64 ! [X: num,Xa2: num,Y2: option_num] :
% 1.40/1.64 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 1.40/1.64 = Y2 )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( some_num @ one ) ) ) )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ( ? [N4: num] :
% 1.40/1.64 ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.64 => ( Y2 != none_num ) ) )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ( ? [N4: num] :
% 1.40/1.64 ( Xa2
% 1.40/1.64 = ( bit1 @ N4 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( some_num @ one ) ) ) )
% 1.40/1.64 => ( ( ? [M5: num] :
% 1.40/1.64 ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( Y2 != none_num ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit1 @ N4 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) ) ) )
% 1.40/1.64 => ( ( ? [M5: num] :
% 1.40/1.64 ( X
% 1.40/1.64 = ( bit1 @ M5 ) )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( some_num @ one ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit1 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) ) ) )
% 1.40/1.64 => ~ ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit1 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit1 @ N4 ) )
% 1.40/1.64 => ( Y2
% 1.40/1.64 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 1.40/1.64 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 1.40/1.64 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_num.elims
% 1.40/1.64 thf(fact_2992_and__num_Osimps_I5_J,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 1.40/1.64 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_num.simps(5)
% 1.40/1.64 thf(fact_2993_and__num_Osimps_I1_J,axiom,
% 1.40/1.64 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 1.40/1.64 = ( some_num @ one ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_num.simps(1)
% 1.40/1.64 thf(fact_2994_and__num_Osimps_I3_J,axiom,
% 1.40/1.64 ! [N: num] :
% 1.40/1.64 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 1.40/1.64 = ( some_num @ one ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_num.simps(3)
% 1.40/1.64 thf(fact_2995_and__num_Osimps_I7_J,axiom,
% 1.40/1.64 ! [M: num] :
% 1.40/1.64 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 1.40/1.64 = ( some_num @ one ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_num.simps(7)
% 1.40/1.64 thf(fact_2996_and__num_Osimps_I2_J,axiom,
% 1.40/1.64 ! [N: num] :
% 1.40/1.64 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 1.40/1.64 = none_num ) ).
% 1.40/1.64
% 1.40/1.64 % and_num.simps(2)
% 1.40/1.64 thf(fact_2997_and__num_Osimps_I4_J,axiom,
% 1.40/1.64 ! [M: num] :
% 1.40/1.64 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 1.40/1.64 = none_num ) ).
% 1.40/1.64
% 1.40/1.64 % and_num.simps(4)
% 1.40/1.64 thf(fact_2998_and__num_Osimps_I6_J,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 1.40/1.64 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_num.simps(6)
% 1.40/1.64 thf(fact_2999_and__num_Osimps_I8_J,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 1.40/1.64 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_num.simps(8)
% 1.40/1.64 thf(fact_3000_and__num_Osimps_I9_J,axiom,
% 1.40/1.64 ! [M: num,N: num] :
% 1.40/1.64 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 1.40/1.64 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 1.40/1.64 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 1.40/1.64 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 1.40/1.64
% 1.40/1.64 % and_num.simps(9)
% 1.40/1.64 thf(fact_3001_and__num_Opelims,axiom,
% 1.40/1.64 ! [X: num,Xa2: num,Y2: option_num] :
% 1.40/1.64 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa2 )
% 1.40/1.64 = Y2 )
% 1.40/1.64 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( some_num @ one ) )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.64 => ( ( Y2 = none_num )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N4 ) ) ) ) ) )
% 1.40/1.64 => ( ( ( X = one )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit1 @ N4 ) )
% 1.40/1.64 => ( ( Y2
% 1.40/1.64 = ( some_num @ one ) )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N4 ) ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ( ( Xa2 = one )
% 1.40/1.64 => ( ( Y2 = none_num )
% 1.40/1.64 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 1.40/1.64 => ( ! [M5: num] :
% 1.40/1.64 ( ( X
% 1.40/1.64 = ( bit0 @ M5 ) )
% 1.40/1.64 => ! [N4: num] :
% 1.40/1.64 ( ( Xa2
% 1.40/1.64 = ( bit0 @ N4 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit0 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit1 @ N4 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N4 ) ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit1 @ M5 ) )
% 1.40/1.65 => ( ( Xa2 = one )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( some_num @ one ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit1 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit0 @ N4 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 1.40/1.65 => ~ ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit1 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit1 @ N4 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 1.40/1.65 @ ^ [N8: num] : ( some_num @ ( bit1 @ N8 ) )
% 1.40/1.65 @ ( bit_un7362597486090784418nd_num @ M5 @ N4 ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % and_num.pelims
% 1.40/1.65 thf(fact_3002_xor__num_Oelims,axiom,
% 1.40/1.65 ! [X: num,Xa2: num,Y2: option_num] :
% 1.40/1.65 ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 1.40/1.65 = Y2 )
% 1.40/1.65 => ( ( ( X = one )
% 1.40/1.65 => ( ( Xa2 = one )
% 1.40/1.65 => ( Y2 != none_num ) ) )
% 1.40/1.65 => ( ( ( X = one )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit0 @ N4 ) )
% 1.40/1.65 => ( Y2
% 1.40/1.65 != ( some_num @ ( bit1 @ N4 ) ) ) ) )
% 1.40/1.65 => ( ( ( X = one )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit1 @ N4 ) )
% 1.40/1.65 => ( Y2
% 1.40/1.65 != ( some_num @ ( bit0 @ N4 ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit0 @ M5 ) )
% 1.40/1.65 => ( ( Xa2 = one )
% 1.40/1.65 => ( Y2
% 1.40/1.65 != ( some_num @ ( bit1 @ M5 ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit0 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit0 @ N4 ) )
% 1.40/1.65 => ( Y2
% 1.40/1.65 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit0 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit1 @ N4 ) )
% 1.40/1.65 => ( Y2
% 1.40/1.65 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit1 @ M5 ) )
% 1.40/1.65 => ( ( Xa2 = one )
% 1.40/1.65 => ( Y2
% 1.40/1.65 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit1 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit0 @ N4 ) )
% 1.40/1.65 => ( Y2
% 1.40/1.65 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) ) ) ) )
% 1.40/1.65 => ~ ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit1 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit1 @ N4 ) )
% 1.40/1.65 => ( Y2
% 1.40/1.65 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.elims
% 1.40/1.65 thf(fact_3003_xor__num_Osimps_I1_J,axiom,
% 1.40/1.65 ( ( bit_un2480387367778600638or_num @ one @ one )
% 1.40/1.65 = none_num ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.simps(1)
% 1.40/1.65 thf(fact_3004_xor__num_Osimps_I5_J,axiom,
% 1.40/1.65 ! [M: num,N: num] :
% 1.40/1.65 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 1.40/1.65 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.simps(5)
% 1.40/1.65 thf(fact_3005_xor__num_Osimps_I9_J,axiom,
% 1.40/1.65 ! [M: num,N: num] :
% 1.40/1.65 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 1.40/1.65 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.simps(9)
% 1.40/1.65 thf(fact_3006_xor__num_Osimps_I7_J,axiom,
% 1.40/1.65 ! [M: num] :
% 1.40/1.65 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 1.40/1.65 = ( some_num @ ( bit0 @ M ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.simps(7)
% 1.40/1.65 thf(fact_3007_xor__num_Osimps_I4_J,axiom,
% 1.40/1.65 ! [M: num] :
% 1.40/1.65 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 1.40/1.65 = ( some_num @ ( bit1 @ M ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.simps(4)
% 1.40/1.65 thf(fact_3008_xor__num_Osimps_I3_J,axiom,
% 1.40/1.65 ! [N: num] :
% 1.40/1.65 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 1.40/1.65 = ( some_num @ ( bit0 @ N ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.simps(3)
% 1.40/1.65 thf(fact_3009_xor__num_Osimps_I2_J,axiom,
% 1.40/1.65 ! [N: num] :
% 1.40/1.65 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 1.40/1.65 = ( some_num @ ( bit1 @ N ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.simps(2)
% 1.40/1.65 thf(fact_3010_xor__num_Osimps_I6_J,axiom,
% 1.40/1.65 ! [M: num,N: num] :
% 1.40/1.65 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 1.40/1.65 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.simps(6)
% 1.40/1.65 thf(fact_3011_xor__num_Osimps_I8_J,axiom,
% 1.40/1.65 ! [M: num,N: num] :
% 1.40/1.65 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 1.40/1.65 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.simps(8)
% 1.40/1.65 thf(fact_3012_xor__num_Opelims,axiom,
% 1.40/1.65 ! [X: num,Xa2: num,Y2: option_num] :
% 1.40/1.65 ( ( ( bit_un2480387367778600638or_num @ X @ Xa2 )
% 1.40/1.65 = Y2 )
% 1.40/1.65 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 1.40/1.65 => ( ( ( X = one )
% 1.40/1.65 => ( ( Xa2 = one )
% 1.40/1.65 => ( ( Y2 = none_num )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 1.40/1.65 => ( ( ( X = one )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit0 @ N4 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( some_num @ ( bit1 @ N4 ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N4 ) ) ) ) ) )
% 1.40/1.65 => ( ( ( X = one )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit1 @ N4 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( some_num @ ( bit0 @ N4 ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N4 ) ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit0 @ M5 ) )
% 1.40/1.65 => ( ( Xa2 = one )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( some_num @ ( bit1 @ M5 ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit0 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit0 @ N4 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit0 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit1 @ N4 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N4 ) ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit1 @ M5 ) )
% 1.40/1.65 => ( ( Xa2 = one )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( some_num @ ( bit0 @ M5 ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 1.40/1.65 => ( ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit1 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit0 @ N4 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N4 ) ) ) ) ) )
% 1.40/1.65 => ~ ! [M5: num] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( bit1 @ M5 ) )
% 1.40/1.65 => ! [N4: num] :
% 1.40/1.65 ( ( Xa2
% 1.40/1.65 = ( bit1 @ N4 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N4 ) ) )
% 1.40/1.65 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % xor_num.pelims
% 1.40/1.65 thf(fact_3013_and__num__rel__dict,axiom,
% 1.40/1.65 bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 1.40/1.65
% 1.40/1.65 % and_num_rel_dict
% 1.40/1.65 thf(fact_3014_xor__num__rel__dict,axiom,
% 1.40/1.65 bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 1.40/1.65
% 1.40/1.65 % xor_num_rel_dict
% 1.40/1.65 thf(fact_3015_and__num__dict,axiom,
% 1.40/1.65 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 1.40/1.65
% 1.40/1.65 % and_num_dict
% 1.40/1.65 thf(fact_3016_xor__num__dict,axiom,
% 1.40/1.65 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 1.40/1.65
% 1.40/1.65 % xor_num_dict
% 1.40/1.65 thf(fact_3017_Bit__Operations_Otake__bit__num__code,axiom,
% 1.40/1.65 ( bit_take_bit_num
% 1.40/1.65 = ( ^ [N2: nat,M6: num] :
% 1.40/1.65 ( produc478579273971653890on_num
% 1.40/1.65 @ ^ [A4: nat,X4: num] :
% 1.40/1.65 ( case_nat_option_num @ none_num
% 1.40/1.65 @ ^ [O: nat] :
% 1.40/1.65 ( case_num_option_num @ ( some_num @ one )
% 1.40/1.65 @ ^ [P6: num] :
% 1.40/1.65 ( case_o6005452278849405969um_num @ none_num
% 1.40/1.65 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 1.40/1.65 @ ( bit_take_bit_num @ O @ P6 ) )
% 1.40/1.65 @ ^ [P6: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P6 ) ) )
% 1.40/1.65 @ X4 )
% 1.40/1.65 @ A4 )
% 1.40/1.65 @ ( product_Pair_nat_num @ N2 @ M6 ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % Bit_Operations.take_bit_num_code
% 1.40/1.65 thf(fact_3018_num__of__integer__code,axiom,
% 1.40/1.65 ( code_num_of_integer
% 1.40/1.65 = ( ^ [K3: code_integer] :
% 1.40/1.65 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 1.40/1.65 @ ( produc7336495610019696514er_num
% 1.40/1.65 @ ^ [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 ) )
% 1.40/1.65 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % num_of_integer_code
% 1.40/1.65 thf(fact_3019_upt__rec__numeral,axiom,
% 1.40/1.65 ! [M: num,N: num] :
% 1.40/1.65 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 1.40/1.65 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 1.40/1.65 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 1.40/1.65 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 1.40/1.65 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 1.40/1.65 = nil_nat ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % upt_rec_numeral
% 1.40/1.65 thf(fact_3020_remdups__upt,axiom,
% 1.40/1.65 ! [M: nat,N: nat] :
% 1.40/1.65 ( ( remdups_nat @ ( upt @ M @ N ) )
% 1.40/1.65 = ( upt @ M @ N ) ) ).
% 1.40/1.65
% 1.40/1.65 % remdups_upt
% 1.40/1.65 thf(fact_3021_hd__upt,axiom,
% 1.40/1.65 ! [I2: nat,J: nat] :
% 1.40/1.65 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.65 => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 1.40/1.65 = I2 ) ) ).
% 1.40/1.65
% 1.40/1.65 % hd_upt
% 1.40/1.65 thf(fact_3022_drop__upt,axiom,
% 1.40/1.65 ! [M: nat,I2: nat,J: nat] :
% 1.40/1.65 ( ( drop_nat @ M @ ( upt @ I2 @ J ) )
% 1.40/1.65 = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J ) ) ).
% 1.40/1.65
% 1.40/1.65 % drop_upt
% 1.40/1.65 thf(fact_3023_length__upt,axiom,
% 1.40/1.65 ! [I2: nat,J: nat] :
% 1.40/1.65 ( ( size_size_list_nat @ ( upt @ I2 @ J ) )
% 1.40/1.65 = ( minus_minus_nat @ J @ I2 ) ) ).
% 1.40/1.65
% 1.40/1.65 % length_upt
% 1.40/1.65 thf(fact_3024_take__upt,axiom,
% 1.40/1.65 ! [I2: nat,M: nat,N: nat] :
% 1.40/1.65 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N )
% 1.40/1.65 => ( ( take_nat @ M @ ( upt @ I2 @ N ) )
% 1.40/1.65 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % take_upt
% 1.40/1.65 thf(fact_3025_upt__conv__Nil,axiom,
% 1.40/1.65 ! [J: nat,I2: nat] :
% 1.40/1.65 ( ( ord_less_eq_nat @ J @ I2 )
% 1.40/1.65 => ( ( upt @ I2 @ J )
% 1.40/1.65 = nil_nat ) ) ).
% 1.40/1.65
% 1.40/1.65 % upt_conv_Nil
% 1.40/1.65 thf(fact_3026_sorted__list__of__set__range,axiom,
% 1.40/1.65 ! [M: nat,N: nat] :
% 1.40/1.65 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 1.40/1.65 = ( upt @ M @ N ) ) ).
% 1.40/1.65
% 1.40/1.65 % sorted_list_of_set_range
% 1.40/1.65 thf(fact_3027_upt__eq__Nil__conv,axiom,
% 1.40/1.65 ! [I2: nat,J: nat] :
% 1.40/1.65 ( ( ( upt @ I2 @ J )
% 1.40/1.65 = nil_nat )
% 1.40/1.65 = ( ( J = zero_zero_nat )
% 1.40/1.65 | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % upt_eq_Nil_conv
% 1.40/1.65 thf(fact_3028_nth__upt,axiom,
% 1.40/1.65 ! [I2: nat,K: nat,J: nat] :
% 1.40/1.65 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 1.40/1.65 => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 1.40/1.65 = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % nth_upt
% 1.40/1.65 thf(fact_3029_atMost__upto,axiom,
% 1.40/1.65 ( set_ord_atMost_nat
% 1.40/1.65 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % atMost_upto
% 1.40/1.65 thf(fact_3030_atLeastLessThan__upt,axiom,
% 1.40/1.65 ( set_or4665077453230672383an_nat
% 1.40/1.65 = ( ^ [I4: nat,J3: nat] : ( set_nat2 @ ( upt @ I4 @ J3 ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % atLeastLessThan_upt
% 1.40/1.65 thf(fact_3031_atLeastAtMost__upt,axiom,
% 1.40/1.65 ( set_or1269000886237332187st_nat
% 1.40/1.65 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M6 ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % atLeastAtMost_upt
% 1.40/1.65 thf(fact_3032_greaterThanLessThan__upt,axiom,
% 1.40/1.65 ( set_or5834768355832116004an_nat
% 1.40/1.65 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M6 ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % greaterThanLessThan_upt
% 1.40/1.65 thf(fact_3033_atLeast__upt,axiom,
% 1.40/1.65 ( set_ord_lessThan_nat
% 1.40/1.65 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N2 ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % atLeast_upt
% 1.40/1.65 thf(fact_3034_greaterThanAtMost__upt,axiom,
% 1.40/1.65 ( set_or6659071591806873216st_nat
% 1.40/1.65 = ( ^ [N2: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M6 ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % greaterThanAtMost_upt
% 1.40/1.65 thf(fact_3035_upt__conv__Cons__Cons,axiom,
% 1.40/1.65 ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 1.40/1.65 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 1.40/1.65 = ( upt @ M @ Q2 ) )
% 1.40/1.65 = ( ( cons_nat @ N @ Ns )
% 1.40/1.65 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % upt_conv_Cons_Cons
% 1.40/1.65 thf(fact_3036_upt__0,axiom,
% 1.40/1.65 ! [I2: nat] :
% 1.40/1.65 ( ( upt @ I2 @ zero_zero_nat )
% 1.40/1.65 = nil_nat ) ).
% 1.40/1.65
% 1.40/1.65 % upt_0
% 1.40/1.65 thf(fact_3037_distinct__upt,axiom,
% 1.40/1.65 ! [I2: nat,J: nat] : ( distinct_nat @ ( upt @ I2 @ J ) ) ).
% 1.40/1.65
% 1.40/1.65 % distinct_upt
% 1.40/1.65 thf(fact_3038_upt__conv__Cons,axiom,
% 1.40/1.65 ! [I2: nat,J: nat] :
% 1.40/1.65 ( ( ord_less_nat @ I2 @ J )
% 1.40/1.65 => ( ( upt @ I2 @ J )
% 1.40/1.65 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % upt_conv_Cons
% 1.40/1.65 thf(fact_3039_upt__add__eq__append,axiom,
% 1.40/1.65 ! [I2: nat,J: nat,K: nat] :
% 1.40/1.65 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.65 => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 1.40/1.65 = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % upt_add_eq_append
% 1.40/1.65 thf(fact_3040_upt__eq__Cons__conv,axiom,
% 1.40/1.65 ! [I2: nat,J: nat,X: nat,Xs: list_nat] :
% 1.40/1.65 ( ( ( upt @ I2 @ J )
% 1.40/1.65 = ( cons_nat @ X @ Xs ) )
% 1.40/1.65 = ( ( ord_less_nat @ I2 @ J )
% 1.40/1.65 & ( I2 = X )
% 1.40/1.65 & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 1.40/1.65 = Xs ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % upt_eq_Cons_conv
% 1.40/1.65 thf(fact_3041_upt__rec,axiom,
% 1.40/1.65 ( upt
% 1.40/1.65 = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % upt_rec
% 1.40/1.65 thf(fact_3042_upt__Suc__append,axiom,
% 1.40/1.65 ! [I2: nat,J: nat] :
% 1.40/1.65 ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.65 => ( ( upt @ I2 @ ( suc @ J ) )
% 1.40/1.65 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % upt_Suc_append
% 1.40/1.65 thf(fact_3043_upt__Suc,axiom,
% 1.40/1.65 ! [I2: nat,J: nat] :
% 1.40/1.65 ( ( ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.65 => ( ( upt @ I2 @ ( suc @ J ) )
% 1.40/1.65 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 1.40/1.65 & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 1.40/1.65 => ( ( upt @ I2 @ ( suc @ J ) )
% 1.40/1.65 = nil_nat ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % upt_Suc
% 1.40/1.65 thf(fact_3044_sum__list__upt,axiom,
% 1.40/1.65 ! [M: nat,N: nat] :
% 1.40/1.65 ( ( ord_less_eq_nat @ M @ N )
% 1.40/1.65 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 1.40/1.65 = ( groups3542108847815614940at_nat
% 1.40/1.65 @ ^ [X4: nat] : X4
% 1.40/1.65 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % sum_list_upt
% 1.40/1.65 thf(fact_3045_map__Suc__upt,axiom,
% 1.40/1.65 ! [M: nat,N: nat] :
% 1.40/1.65 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 1.40/1.65 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % map_Suc_upt
% 1.40/1.65 thf(fact_3046_map__add__upt,axiom,
% 1.40/1.65 ! [N: nat,M: nat] :
% 1.40/1.65 ( ( map_nat_nat
% 1.40/1.65 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 1.40/1.65 @ ( upt @ zero_zero_nat @ M ) )
% 1.40/1.65 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % map_add_upt
% 1.40/1.65 thf(fact_3047_map__decr__upt,axiom,
% 1.40/1.65 ! [M: nat,N: nat] :
% 1.40/1.65 ( ( map_nat_nat
% 1.40/1.65 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 1.40/1.65 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 1.40/1.65 = ( upt @ M @ N ) ) ).
% 1.40/1.65
% 1.40/1.65 % map_decr_upt
% 1.40/1.65 thf(fact_3048_Divides_Oadjust__div__def,axiom,
% 1.40/1.65 ( adjust_div
% 1.40/1.65 = ( produc8211389475949308722nt_int
% 1.40/1.65 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % Divides.adjust_div_def
% 1.40/1.65 thf(fact_3049_card__length__sum__list__rec,axiom,
% 1.40/1.65 ! [M: nat,N3: nat] :
% 1.40/1.65 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 1.40/1.65 => ( ( finite_card_list_nat
% 1.40/1.65 @ ( collect_list_nat
% 1.40/1.65 @ ^ [L: list_nat] :
% 1.40/1.65 ( ( ( size_size_list_nat @ L )
% 1.40/1.65 = M )
% 1.40/1.65 & ( ( groups4561878855575611511st_nat @ L )
% 1.40/1.65 = N3 ) ) ) )
% 1.40/1.65 = ( plus_plus_nat
% 1.40/1.65 @ ( finite_card_list_nat
% 1.40/1.65 @ ( collect_list_nat
% 1.40/1.65 @ ^ [L: list_nat] :
% 1.40/1.65 ( ( ( size_size_list_nat @ L )
% 1.40/1.65 = ( minus_minus_nat @ M @ one_one_nat ) )
% 1.40/1.65 & ( ( groups4561878855575611511st_nat @ L )
% 1.40/1.65 = N3 ) ) ) )
% 1.40/1.65 @ ( finite_card_list_nat
% 1.40/1.65 @ ( collect_list_nat
% 1.40/1.65 @ ^ [L: list_nat] :
% 1.40/1.65 ( ( ( size_size_list_nat @ L )
% 1.40/1.65 = M )
% 1.40/1.65 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L ) @ one_one_nat )
% 1.40/1.65 = N3 ) ) ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % card_length_sum_list_rec
% 1.40/1.65 thf(fact_3050_card__length__sum__list,axiom,
% 1.40/1.65 ! [M: nat,N3: nat] :
% 1.40/1.65 ( ( finite_card_list_nat
% 1.40/1.65 @ ( collect_list_nat
% 1.40/1.65 @ ^ [L: list_nat] :
% 1.40/1.65 ( ( ( size_size_list_nat @ L )
% 1.40/1.65 = M )
% 1.40/1.65 & ( ( groups4561878855575611511st_nat @ L )
% 1.40/1.65 = N3 ) ) ) )
% 1.40/1.65 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N3 @ M ) @ one_one_nat ) @ N3 ) ) ).
% 1.40/1.65
% 1.40/1.65 % card_length_sum_list
% 1.40/1.65 thf(fact_3051_sorted__wrt__upt,axiom,
% 1.40/1.65 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 1.40/1.65
% 1.40/1.65 % sorted_wrt_upt
% 1.40/1.65 thf(fact_3052_sorted__upt,axiom,
% 1.40/1.65 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 1.40/1.65
% 1.40/1.65 % sorted_upt
% 1.40/1.65 thf(fact_3053_sorted__wrt__less__idx,axiom,
% 1.40/1.65 ! [Ns: list_nat,I2: nat] :
% 1.40/1.65 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 1.40/1.65 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 1.40/1.65 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % sorted_wrt_less_idx
% 1.40/1.65 thf(fact_3054_sorted__upto,axiom,
% 1.40/1.65 ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 1.40/1.65
% 1.40/1.65 % sorted_upto
% 1.40/1.65 thf(fact_3055_sorted__wrt__upto,axiom,
% 1.40/1.65 ! [I2: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I2 @ J ) ) ).
% 1.40/1.65
% 1.40/1.65 % sorted_wrt_upto
% 1.40/1.65 thf(fact_3056_tl__upt,axiom,
% 1.40/1.65 ! [M: nat,N: nat] :
% 1.40/1.65 ( ( tl_nat @ ( upt @ M @ N ) )
% 1.40/1.65 = ( upt @ ( suc @ M ) @ N ) ) ).
% 1.40/1.65
% 1.40/1.65 % tl_upt
% 1.40/1.65 thf(fact_3057_VEBT_Osize_I3_J,axiom,
% 1.40/1.65 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 1.40/1.65 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 1.40/1.65 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % VEBT.size(3)
% 1.40/1.65 thf(fact_3058_VEBT_Osize__gen_I1_J,axiom,
% 1.40/1.65 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 1.40/1.65 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 1.40/1.65 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % VEBT.size_gen(1)
% 1.40/1.65 thf(fact_3059_pairs__le__eq__Sigma,axiom,
% 1.40/1.65 ! [M: nat] :
% 1.40/1.65 ( ( collec3392354462482085612at_nat
% 1.40/1.65 @ ( produc6081775807080527818_nat_o
% 1.40/1.65 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ M ) ) )
% 1.40/1.65 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 1.40/1.65 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % pairs_le_eq_Sigma
% 1.40/1.65 thf(fact_3060_card__le__Suc__Max,axiom,
% 1.40/1.65 ! [S3: set_nat] :
% 1.40/1.65 ( ( finite_finite_nat @ S3 )
% 1.40/1.65 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % card_le_Suc_Max
% 1.40/1.65 thf(fact_3061_divide__nat__def,axiom,
% 1.40/1.65 ( divide_divide_nat
% 1.40/1.65 = ( ^ [M6: nat,N2: nat] :
% 1.40/1.65 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 1.40/1.65 @ ( lattic8265883725875713057ax_nat
% 1.40/1.65 @ ( collect_nat
% 1.40/1.65 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N2 ) @ M6 ) ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % divide_nat_def
% 1.40/1.65 thf(fact_3062_gcd__is__Max__divisors__nat,axiom,
% 1.40/1.65 ! [N: nat,M: nat] :
% 1.40/1.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.40/1.65 => ( ( gcd_gcd_nat @ M @ N )
% 1.40/1.65 = ( lattic8265883725875713057ax_nat
% 1.40/1.65 @ ( collect_nat
% 1.40/1.65 @ ^ [D2: nat] :
% 1.40/1.65 ( ( dvd_dvd_nat @ D2 @ M )
% 1.40/1.65 & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % gcd_is_Max_divisors_nat
% 1.40/1.65 thf(fact_3063_prod__encode__prod__decode__aux,axiom,
% 1.40/1.65 ! [K: nat,M: nat] :
% 1.40/1.65 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 1.40/1.65 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 1.40/1.65
% 1.40/1.65 % prod_encode_prod_decode_aux
% 1.40/1.65 thf(fact_3064_le__prod__encode__2,axiom,
% 1.40/1.65 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % le_prod_encode_2
% 1.40/1.65 thf(fact_3065_le__prod__encode__1,axiom,
% 1.40/1.65 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % le_prod_encode_1
% 1.40/1.65 thf(fact_3066_prod__encode__def,axiom,
% 1.40/1.65 ( nat_prod_encode
% 1.40/1.65 = ( produc6842872674320459806at_nat
% 1.40/1.65 @ ^ [M6: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N2 ) ) @ M6 ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % prod_encode_def
% 1.40/1.65 thf(fact_3067_list__encode_Oelims,axiom,
% 1.40/1.65 ! [X: list_nat,Y2: nat] :
% 1.40/1.65 ( ( ( nat_list_encode @ X )
% 1.40/1.65 = Y2 )
% 1.40/1.65 => ( ( ( X = nil_nat )
% 1.40/1.65 => ( Y2 != zero_zero_nat ) )
% 1.40/1.65 => ~ ! [X5: nat,Xs2: list_nat] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( cons_nat @ X5 @ Xs2 ) )
% 1.40/1.65 => ( Y2
% 1.40/1.65 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % list_encode.elims
% 1.40/1.65 thf(fact_3068_list__encode_Osimps_I2_J,axiom,
% 1.40/1.65 ! [X: nat,Xs: list_nat] :
% 1.40/1.65 ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 1.40/1.65 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % list_encode.simps(2)
% 1.40/1.65 thf(fact_3069_list__encode_Opelims,axiom,
% 1.40/1.65 ! [X: list_nat,Y2: nat] :
% 1.40/1.65 ( ( ( nat_list_encode @ X )
% 1.40/1.65 = Y2 )
% 1.40/1.65 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 1.40/1.65 => ( ( ( X = nil_nat )
% 1.40/1.65 => ( ( Y2 = zero_zero_nat )
% 1.40/1.65 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 1.40/1.65 => ~ ! [X5: nat,Xs2: list_nat] :
% 1.40/1.65 ( ( X
% 1.40/1.65 = ( cons_nat @ X5 @ Xs2 ) )
% 1.40/1.65 => ( ( Y2
% 1.40/1.65 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 1.40/1.65 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X5 @ Xs2 ) ) ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % list_encode.pelims
% 1.40/1.65 thf(fact_3070_Gcd__nat__eq__one,axiom,
% 1.40/1.65 ! [N3: set_nat] :
% 1.40/1.65 ( ( member_nat @ one_one_nat @ N3 )
% 1.40/1.65 => ( ( gcd_Gcd_nat @ N3 )
% 1.40/1.65 = one_one_nat ) ) ).
% 1.40/1.65
% 1.40/1.65 % Gcd_nat_eq_one
% 1.40/1.65 thf(fact_3071_Gcd__int__greater__eq__0,axiom,
% 1.40/1.65 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 1.40/1.65
% 1.40/1.65 % Gcd_int_greater_eq_0
% 1.40/1.65 thf(fact_3072_of__nat__eq__id,axiom,
% 1.40/1.65 semiri1316708129612266289at_nat = id_nat ).
% 1.40/1.65
% 1.40/1.65 % of_nat_eq_id
% 1.40/1.65 thf(fact_3073_Rat_Opositive__def,axiom,
% 1.40/1.65 ( positive
% 1.40/1.65 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 1.40/1.65 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ).
% 1.40/1.65
% 1.40/1.65 % Rat.positive_def
% 1.40/1.65 thf(fact_3074_sort__upt,axiom,
% 1.40/1.65 ! [M: nat,N: nat] :
% 1.40/1.65 ( ( linord738340561235409698at_nat
% 1.40/1.65 @ ^ [X4: nat] : X4
% 1.40/1.65 @ ( upt @ M @ N ) )
% 1.40/1.65 = ( upt @ M @ N ) ) ).
% 1.40/1.65
% 1.40/1.65 % sort_upt
% 1.40/1.65 thf(fact_3075_sort__upto,axiom,
% 1.40/1.65 ! [I2: int,J: int] :
% 1.40/1.65 ( ( linord1735203802627413978nt_int
% 1.40/1.65 @ ^ [X4: int] : X4
% 1.40/1.65 @ ( upto @ I2 @ J ) )
% 1.40/1.65 = ( upto @ I2 @ J ) ) ).
% 1.40/1.65
% 1.40/1.65 % sort_upto
% 1.40/1.65
% 1.40/1.65 % Helper facts (32)
% 1.40/1.65 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 1.40/1.65 ! [X: int,Y2: int] :
% 1.40/1.65 ( ( if_int @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 1.40/1.65 ! [X: int,Y2: int] :
% 1.40/1.65 ( ( if_int @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 1.40/1.65 ! [X: nat,Y2: nat] :
% 1.40/1.65 ( ( if_nat @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 1.40/1.65 ! [X: nat,Y2: nat] :
% 1.40/1.65 ( ( if_nat @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 1.40/1.65 ! [X: num,Y2: num] :
% 1.40/1.65 ( ( if_num @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 1.40/1.65 ! [X: num,Y2: num] :
% 1.40/1.65 ( ( if_num @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 1.40/1.65 ! [X: rat,Y2: rat] :
% 1.40/1.65 ( ( if_rat @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 1.40/1.65 ! [X: rat,Y2: rat] :
% 1.40/1.65 ( ( if_rat @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 1.40/1.65 ! [X: real,Y2: real] :
% 1.40/1.65 ( ( if_real @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 1.40/1.65 ! [X: real,Y2: real] :
% 1.40/1.65 ( ( if_real @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 1.40/1.65 ! [P: real > $o] :
% 1.40/1.65 ( ( P @ ( fChoice_real @ P ) )
% 1.40/1.65 = ( ? [X2: real] : ( P @ X2 ) ) ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 1.40/1.65 ! [X: code_integer,Y2: code_integer] :
% 1.40/1.65 ( ( if_Code_integer @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 1.40/1.65 ! [X: code_integer,Y2: code_integer] :
% 1.40/1.65 ( ( if_Code_integer @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 1.40/1.65 ! [X: set_int,Y2: set_int] :
% 1.40/1.65 ( ( if_set_int @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 1.40/1.65 ! [X: set_int,Y2: set_int] :
% 1.40/1.65 ( ( if_set_int @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 1.40/1.65 ! [X: vEBT_VEBT,Y2: vEBT_VEBT] :
% 1.40/1.65 ( ( if_VEBT_VEBT @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 1.40/1.65 ! [X: vEBT_VEBT,Y2: vEBT_VEBT] :
% 1.40/1.65 ( ( if_VEBT_VEBT @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 1.40/1.65 ! [X: list_int,Y2: list_int] :
% 1.40/1.65 ( ( if_list_int @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 1.40/1.65 ! [X: list_int,Y2: list_int] :
% 1.40/1.65 ( ( if_list_int @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 1.40/1.65 ! [X: list_nat,Y2: list_nat] :
% 1.40/1.65 ( ( if_list_nat @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 1.40/1.65 ! [X: list_nat,Y2: list_nat] :
% 1.40/1.65 ( ( if_list_nat @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 1.40/1.65 ! [X: option_num,Y2: option_num] :
% 1.40/1.65 ( ( if_option_num @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 1.40/1.65 ! [X: option_num,Y2: option_num] :
% 1.40/1.65 ( ( if_option_num @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 1.40/1.65 ! [X: product_prod_int_int,Y2: product_prod_int_int] :
% 1.40/1.65 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 1.40/1.65 ! [X: product_prod_int_int,Y2: product_prod_int_int] :
% 1.40/1.65 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 1.40/1.65 ! [X: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 1.40/1.65 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 1.40/1.65 ! [X: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 1.40/1.65 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 1.40/1.65 ! [X: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 1.40/1.65 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 1.40/1.65 ! [X: produc6271795597528267376eger_o,Y2: produc6271795597528267376eger_o] :
% 1.40/1.65 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 1.40/1.65 ! [P: $o] :
% 1.40/1.65 ( ( P = $true )
% 1.40/1.65 | ( P = $false ) ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 1.40/1.65 ! [X: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 1.40/1.65 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y2 )
% 1.40/1.65 = Y2 ) ).
% 1.40/1.65
% 1.40/1.65 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 1.40/1.65 ! [X: produc8923325533196201883nteger,Y2: produc8923325533196201883nteger] :
% 1.40/1.65 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y2 )
% 1.40/1.65 = X ) ).
% 1.40/1.65
% 1.40/1.65 % Conjectures (1)
% 1.40/1.65 thf(conj_0,conjecture,
% 1.40/1.65 ! [I3: nat] :
% 1.40/1.65 ( ~ ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 1.40/1.65 | ( ( ( ( vEBT_VEBT_high @ ( ord_max_nat @ ma @ xa ) @ na )
% 1.40/1.65 != I3 )
% 1.40/1.65 | ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( append_VEBT_VEBT @ ( take_VEBT_VEBT @ ( vEBT_VEBT_high @ xa @ na ) @ treeList ) @ ( append_VEBT_VEBT @ ( cons_VEBT_VEBT @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ nil_VEBT_VEBT ) @ ( drop_VEBT_VEBT @ ( plus_plus_nat @ ( vEBT_VEBT_high @ xa @ na ) @ one_one_nat ) @ treeList ) ) ) @ I3 ) @ ( vEBT_VEBT_low @ ( ord_max_nat @ ma @ xa ) @ na ) ) )
% 1.40/1.65 & ! [Y3: nat] :
% 1.40/1.65 ( ( ( vEBT_VEBT_high @ Y3 @ na )
% 1.40/1.65 != I3 )
% 1.40/1.65 | ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( append_VEBT_VEBT @ ( take_VEBT_VEBT @ ( vEBT_VEBT_high @ xa @ na ) @ treeList ) @ ( append_VEBT_VEBT @ ( cons_VEBT_VEBT @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ nil_VEBT_VEBT ) @ ( drop_VEBT_VEBT @ ( plus_plus_nat @ ( vEBT_VEBT_high @ xa @ na ) @ one_one_nat ) @ treeList ) ) ) @ I3 ) @ ( vEBT_VEBT_low @ Y3 @ na ) )
% 1.40/2.18 | ( ( ord_less_nat @ mi @ Y3 )
% 1.40/2.18 & ( ord_less_eq_nat @ Y3 @ ( ord_max_nat @ ma @ xa ) ) ) ) ) ) ).
% 1.40/2.18
% 1.40/2.18 %------------------------------------------------------------------------------
% 1.40/2.18 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.R6sJoc8Nls/cvc5---1.0.5_17726.p...
% 1.40/2.18 (declare-sort $$unsorted 0)
% 1.40/2.18 (declare-sort tptp.produc8923325533196201883nteger 0)
% 1.40/2.18 (declare-sort tptp.option4927543243414619207at_nat 0)
% 1.40/2.18 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 1.40/2.18 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 1.40/2.18 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 1.40/2.18 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 1.40/2.18 (declare-sort tptp.list_list_VEBT_VEBT 0)
% 1.40/2.18 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 1.40/2.18 (declare-sort tptp.product_prod_num_num 0)
% 1.40/2.18 (declare-sort tptp.product_prod_nat_num 0)
% 1.40/2.18 (declare-sort tptp.product_prod_nat_nat 0)
% 1.40/2.18 (declare-sort tptp.product_prod_int_int 0)
% 1.40/2.18 (declare-sort tptp.list_list_nat 0)
% 1.40/2.18 (declare-sort tptp.list_list_int 0)
% 1.40/2.18 (declare-sort tptp.list_VEBT_VEBT 0)
% 1.40/2.18 (declare-sort tptp.set_list_nat 0)
% 1.40/2.18 (declare-sort tptp.set_VEBT_VEBT 0)
% 1.40/2.18 (declare-sort tptp.set_Product_unit 0)
% 1.40/2.18 (declare-sort tptp.list_complex 0)
% 1.40/2.18 (declare-sort tptp.set_complex 0)
% 1.40/2.18 (declare-sort tptp.filter_real 0)
% 1.40/2.18 (declare-sort tptp.option_num 0)
% 1.40/2.18 (declare-sort tptp.filter_nat 0)
% 1.40/2.18 (declare-sort tptp.set_char 0)
% 1.40/2.18 (declare-sort tptp.list_real 0)
% 1.40/2.18 (declare-sort tptp.set_real 0)
% 1.40/2.18 (declare-sort tptp.list_nat 0)
% 1.40/2.18 (declare-sort tptp.list_int 0)
% 1.40/2.18 (declare-sort tptp.vEBT_VEBT 0)
% 1.40/2.18 (declare-sort tptp.set_nat 0)
% 1.40/2.18 (declare-sort tptp.set_int 0)
% 1.40/2.18 (declare-sort tptp.code_integer 0)
% 1.40/2.18 (declare-sort tptp.extended_enat 0)
% 1.40/2.18 (declare-sort tptp.list_o 0)
% 1.40/2.18 (declare-sort tptp.complex 0)
% 1.40/2.18 (declare-sort tptp.set_o 0)
% 1.40/2.18 (declare-sort tptp.char 0)
% 1.40/2.18 (declare-sort tptp.real 0)
% 1.40/2.18 (declare-sort tptp.rat 0)
% 1.40/2.18 (declare-sort tptp.num 0)
% 1.40/2.18 (declare-sort tptp.nat 0)
% 1.40/2.18 (declare-sort tptp.int 0)
% 1.40/2.18 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 1.40/2.18 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 1.40/2.18 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 1.40/2.18 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 1.40/2.18 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 1.40/2.18 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 1.40/2.18 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 1.40/2.18 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.bit_un5425074673868309765um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 1.40/2.18 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.bit_un3595099601533988841um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 1.40/2.18 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 1.40/2.18 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 1.40/2.18 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 1.40/2.18 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 1.40/2.18 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 1.40/2.18 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 1.40/2.18 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 1.40/2.18 (declare-fun tptp.code_negative (tptp.num) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 1.40/2.18 (declare-fun tptp.code_positive (tptp.num) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 1.40/2.18 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 1.40/2.18 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 1.40/2.18 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 1.40/2.18 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 1.40/2.18 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 1.40/2.18 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 1.40/2.18 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 1.40/2.18 (declare-fun tptp.im (tptp.complex) tptp.real)
% 1.40/2.18 (declare-fun tptp.re (tptp.complex) tptp.real)
% 1.40/2.18 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.imaginary_unit () tptp.complex)
% 1.40/2.18 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 1.40/2.18 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 1.40/2.18 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 1.40/2.18 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 1.40/2.18 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 1.40/2.18 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 1.40/2.18 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 1.40/2.18 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 1.40/2.18 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 1.40/2.18 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 1.40/2.18 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 1.40/2.18 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 1.40/2.18 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 1.40/2.18 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 1.40/2.18 (declare-fun tptp.at_top_real () tptp.filter_real)
% 1.40/2.18 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 1.40/2.18 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 1.40/2.18 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 1.40/2.18 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 1.40/2.18 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 1.40/2.18 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 1.40/2.18 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 1.40/2.18 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 1.40/2.18 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 1.40/2.18 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 1.40/2.18 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 1.40/2.18 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 1.40/2.18 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 1.40/2.18 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 1.40/2.18 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 1.40/2.18 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 1.40/2.18 (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)
% 1.40/2.18 (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)
% 1.40/2.18 (declare-fun tptp.comp_C3531382070062128313er_num ((-> tptp.code_integer tptp.code_integer) (-> tptp.num tptp.code_integer) tptp.num) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 1.40/2.18 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 1.40/2.18 (declare-fun tptp.id_o (Bool) Bool)
% 1.40/2.18 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 1.40/2.18 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 1.40/2.18 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 1.40/2.18 (declare-fun tptp.map_fu898904425404107465nt_o_o ((-> tptp.rat tptp.product_prod_int_int) (-> Bool Bool) (-> tptp.product_prod_int_int Bool) tptp.rat) Bool)
% 1.40/2.18 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 1.40/2.18 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 1.40/2.18 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 1.40/2.18 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 1.40/2.18 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.one_one_complex () tptp.complex)
% 1.40/2.18 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.one_one_int () tptp.int)
% 1.40/2.18 (declare-fun tptp.one_one_nat () tptp.nat)
% 1.40/2.18 (declare-fun tptp.one_one_rat () tptp.rat)
% 1.40/2.18 (declare-fun tptp.one_one_real () tptp.real)
% 1.40/2.18 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 1.40/2.18 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 1.40/2.18 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 1.40/2.18 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.zero_zero_int () tptp.int)
% 1.40/2.18 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 1.40/2.18 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 1.40/2.18 (declare-fun tptp.zero_zero_real () tptp.real)
% 1.40/2.18 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 1.40/2.18 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 1.40/2.18 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 1.40/2.18 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 1.40/2.18 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 1.40/2.18 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 1.40/2.18 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 1.40/2.18 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 1.40/2.18 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 1.40/2.18 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 1.40/2.18 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 1.40/2.18 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 1.40/2.18 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 1.40/2.18 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 1.40/2.18 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 1.40/2.18 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 1.40/2.18 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 1.40/2.18 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 1.40/2.18 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 1.40/2.18 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 1.40/2.18 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 1.40/2.18 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 1.40/2.18 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 1.40/2.18 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 1.40/2.18 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 1.40/2.18 (declare-fun tptp.append_o (tptp.list_o tptp.list_o) tptp.list_o)
% 1.40/2.18 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 1.40/2.18 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.append_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 1.40/2.18 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 1.40/2.18 (declare-fun tptp.drop_o (tptp.nat tptp.list_o) tptp.list_o)
% 1.40/2.18 (declare-fun tptp.drop_complex (tptp.nat tptp.list_complex) tptp.list_complex)
% 1.40/2.18 (declare-fun tptp.drop_int (tptp.nat tptp.list_int) tptp.list_int)
% 1.40/2.18 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.drop_P8868858903918902087at_nat (tptp.nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 1.40/2.18 (declare-fun tptp.drop_real (tptp.nat tptp.list_real) tptp.list_real)
% 1.40/2.18 (declare-fun tptp.drop_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.linord1735203802627413978nt_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 1.40/2.18 (declare-fun tptp.linord738340561235409698at_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.cons_o (Bool tptp.list_o) tptp.list_o)
% 1.40/2.18 (declare-fun tptp.cons_complex (tptp.complex tptp.list_complex) tptp.list_complex)
% 1.40/2.18 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 1.40/2.18 (declare-fun tptp.cons_list_int (tptp.list_int tptp.list_list_int) tptp.list_list_int)
% 1.40/2.18 (declare-fun tptp.cons_list_nat (tptp.list_nat tptp.list_list_nat) tptp.list_list_nat)
% 1.40/2.18 (declare-fun tptp.cons_list_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.list_list_VEBT_VEBT) tptp.list_list_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.cons_P6512896166579812791at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 1.40/2.18 (declare-fun tptp.cons_real (tptp.real tptp.list_real) tptp.list_real)
% 1.40/2.18 (declare-fun tptp.cons_VEBT_VEBT (tptp.vEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.nil_o () tptp.list_o)
% 1.40/2.18 (declare-fun tptp.nil_int () tptp.list_int)
% 1.40/2.18 (declare-fun tptp.nil_list_int () tptp.list_list_int)
% 1.40/2.18 (declare-fun tptp.nil_list_nat () tptp.list_list_nat)
% 1.40/2.18 (declare-fun tptp.nil_list_VEBT_VEBT () tptp.list_list_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.nil_nat () tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.nil_VEBT_VEBT () tptp.list_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 1.40/2.18 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 1.40/2.18 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 1.40/2.18 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 1.40/2.18 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 1.40/2.18 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 1.40/2.18 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 1.40/2.18 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 1.40/2.18 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 1.40/2.18 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 1.40/2.18 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 1.40/2.18 (declare-fun tptp.take_o (tptp.nat tptp.list_o) tptp.list_o)
% 1.40/2.18 (declare-fun tptp.take_complex (tptp.nat tptp.list_complex) tptp.list_complex)
% 1.40/2.18 (declare-fun tptp.take_int (tptp.nat tptp.list_int) tptp.list_int)
% 1.40/2.18 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.take_P2173866234530122223at_nat (tptp.nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 1.40/2.18 (declare-fun tptp.take_real (tptp.nat tptp.list_real) tptp.list_real)
% 1.40/2.18 (declare-fun tptp.take_VEBT_VEBT (tptp.nat tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 1.40/2.18 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 1.40/2.18 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 1.40/2.18 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 1.40/2.18 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 1.40/2.18 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 1.40/2.18 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 1.40/2.18 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 1.40/2.18 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 1.40/2.18 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 1.40/2.18 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 1.40/2.18 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 1.40/2.18 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 1.40/2.18 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 1.40/2.18 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 1.40/2.18 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 1.40/2.18 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 1.40/2.18 (declare-fun tptp.inc (tptp.num) tptp.num)
% 1.40/2.18 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 1.40/2.18 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 1.40/2.18 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 1.40/2.18 (declare-fun tptp.one () tptp.num)
% 1.40/2.18 (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)
% 1.40/2.18 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 1.40/2.18 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 1.40/2.18 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 1.40/2.18 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 1.40/2.18 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 1.40/2.18 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 1.40/2.18 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 1.40/2.18 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 1.40/2.18 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 1.40/2.18 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 1.40/2.18 (declare-fun tptp.none_num () tptp.option_num)
% 1.40/2.18 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 1.40/2.18 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 1.40/2.18 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 1.40/2.18 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 1.40/2.18 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 1.40/2.18 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 1.40/2.18 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 1.40/2.18 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 1.40/2.18 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 1.40/2.18 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 1.40/2.18 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 1.40/2.18 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 1.40/2.18 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 1.40/2.18 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 1.40/2.18 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 1.40/2.18 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 1.40/2.18 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 1.40/2.18 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 1.40/2.18 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 1.40/2.18 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 1.40/2.18 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 1.40/2.18 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 1.40/2.18 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 1.40/2.18 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 1.40/2.18 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 1.40/2.18 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 1.40/2.18 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 1.40/2.18 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 1.40/2.18 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 1.40/2.18 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 1.40/2.18 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 1.40/2.18 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 1.40/2.18 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 1.40/2.18 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 1.40/2.18 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 1.40/2.18 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 1.40/2.18 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 1.40/2.18 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 1.40/2.18 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 1.40/2.18 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 1.40/2.18 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 1.40/2.18 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 1.40/2.18 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 1.40/2.18 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 1.40/2.18 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 1.40/2.18 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 1.40/2.18 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 1.40/2.18 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 1.40/2.18 (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)
% 1.40/2.18 (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)
% 1.40/2.18 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 1.40/2.18 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 1.40/2.18 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 1.40/2.18 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 1.40/2.18 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 1.40/2.18 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 1.40/2.18 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 1.40/2.18 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 1.40/2.18 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 1.40/2.18 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 1.40/2.18 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 1.40/2.18 (declare-fun tptp.positive (tptp.rat) Bool)
% 1.40/2.18 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 1.40/2.18 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 1.40/2.18 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 1.40/2.18 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 1.40/2.18 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 1.40/2.18 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 1.40/2.18 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 1.40/2.18 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 1.40/2.18 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 1.40/2.18 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 1.40/2.18 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 1.40/2.18 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 1.40/2.18 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 1.40/2.18 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 1.40/2.18 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 1.40/2.18 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 1.40/2.18 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 1.40/2.18 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 1.40/2.18 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 1.40/2.18 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 1.40/2.18 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 1.40/2.18 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 1.40/2.18 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 1.40/2.18 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 1.40/2.18 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 1.40/2.18 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 1.40/2.18 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 1.40/2.18 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 1.40/2.18 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 1.40/2.18 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 1.40/2.18 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 1.40/2.18 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 1.40/2.18 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 1.40/2.18 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 1.40/2.18 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 1.40/2.18 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 1.40/2.18 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 1.40/2.18 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 1.40/2.18 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 1.40/2.18 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 1.40/2.18 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 1.40/2.18 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 1.40/2.18 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.pi () tptp.real)
% 1.40/2.18 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 1.40/2.18 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 1.40/2.18 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 1.40/2.18 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 1.40/2.18 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 1.40/2.18 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 1.40/2.18 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 1.40/2.18 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 1.40/2.18 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 1.40/2.18 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 1.40/2.18 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 1.40/2.18 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 1.40/2.18 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 1.40/2.18 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 1.40/2.18 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 1.40/2.18 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 1.40/2.18 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 1.40/2.18 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 1.40/2.18 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 1.40/2.18 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 1.40/2.18 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 1.40/2.18 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 1.40/2.18 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 1.40/2.18 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 1.40/2.18 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 1.40/2.18 (declare-fun tptp.deg () tptp.nat)
% 1.40/2.18 (declare-fun tptp.m () tptp.nat)
% 1.40/2.18 (declare-fun tptp.ma () tptp.nat)
% 1.40/2.18 (declare-fun tptp.mi () tptp.nat)
% 1.40/2.18 (declare-fun tptp.na () tptp.nat)
% 1.40/2.18 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 1.40/2.18 (declare-fun tptp.xa () tptp.nat)
% 1.40/2.18 (assert (@ (@ tptp.ord_less_nat tptp.mi) tptp.xa))
% 1.40/2.18 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 1.40/2.18 (assert (not (or (= tptp.xa tptp.mi) (= tptp.xa tptp.ma))))
% 1.40/2.18 (assert (not (= tptp.mi (@ (@ tptp.ord_max_nat tptp.ma) tptp.xa))))
% 1.40/2.18 (assert (= tptp.na tptp.m))
% 1.40/2.18 (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)))
% 1.40/2.18 (assert (and (not (= tptp.xa tptp.mi)) (not (= tptp.xa tptp.ma))))
% 1.40/2.18 (assert (forall ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M))))))
% 1.40/2.18 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 1.40/2.18 (assert (@ (@ tptp.ord_less_nat tptp.xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 1.40/2.18 (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 ((Y tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low Y) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y) (@ (@ tptp.ord_less_eq_nat Y) tptp.ma)))))))))
% 1.40/2.18 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 1.40/2.18 (assert (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na)) (@ _let_1 tptp.m)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)) (@ _let_1 tptp.na)))))
% 1.40/2.18 (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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I)))))
% 1.40/2.18 (assert (=> (= tptp.mi tptp.ma) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))))
% 1.40/2.18 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 1.40/2.18 (assert (let ((_let_1 (@ (@ tptp.ord_max_nat tptp.ma) tptp.xa))) (and (@ (@ tptp.ord_less_eq_nat tptp.mi) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))))
% 1.40/2.18 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X4) N2))) (@ (@ tptp.vEBT_VEBT_low X4) N2)))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (=> (= tptp.mi (@ (@ tptp.ord_max_nat tptp.ma) tptp.xa)) (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.append_VEBT_VEBT (@ (@ tptp.take_VEBT_VEBT _let_1) tptp.treeList)) (@ (@ tptp.append_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT (@ (@ tptp.vEBT_vebt_insert (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na))) tptp.nil_VEBT_VEBT)) (@ (@ tptp.drop_VEBT_VEBT (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) tptp.treeList))))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))))))
% 1.40/2.18 (assert (forall ((B tptp.real) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X) Y2))))))
% 1.40/2.18 (assert (forall ((B tptp.rat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X) Y2))))))
% 1.40/2.18 (assert (forall ((B tptp.nat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X) Y2))))))
% 1.40/2.18 (assert (forall ((B tptp.int) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_nat X) Y2))))))
% 1.40/2.18 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 1.40/2.18 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 1.40/2.18 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 1.40/2.18 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 1.40/2.18 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 1.40/2.18 (assert (forall ((B tptp.real) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X) Y2))))))
% 1.40/2.18 (assert (forall ((B tptp.rat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X) Y2))))))
% 1.40/2.18 (assert (forall ((B tptp.nat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X) Y2))))))
% 1.40/2.18 (assert (forall ((B tptp.int) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_nat X) Y2))))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 1.40/2.18 (assert (forall ((I tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.append_VEBT_VEBT (@ (@ tptp.take_VEBT_VEBT _let_1) tptp.treeList)) (@ (@ tptp.append_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT (@ (@ tptp.vEBT_vebt_insert (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na))) tptp.nil_VEBT_VEBT)) (@ (@ tptp.drop_VEBT_VEBT (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) tptp.treeList)))) I)) X2))) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1))) (@ (@ tptp.vEBT_vebt_insert tptp.summary) _let_1)) tptp.summary)) I))))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_12)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ tptp.set_complex2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) N))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.append_VEBT_VEBT Xs) (@ (@ tptp.append_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) tptp.nil_VEBT_VEBT)) Ys))) (@ tptp.size_s6755466524823107622T_VEBT Xs)) X)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (X Bool) (Ys tptp.list_o)) (= (@ (@ tptp.nth_o (@ (@ tptp.append_o Xs) (@ (@ tptp.append_o (@ (@ tptp.cons_o X) tptp.nil_o)) Ys))) (@ tptp.size_size_list_o Xs)) X)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (X tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.append_nat Xs) (@ (@ tptp.append_nat (@ (@ tptp.cons_nat X) tptp.nil_nat)) Ys))) (@ tptp.size_size_list_nat Xs)) X)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (X tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.nth_int (@ (@ tptp.append_int Xs) (@ (@ tptp.append_int (@ (@ tptp.cons_int X) tptp.nil_int)) Ys))) (@ tptp.size_size_list_int Xs)) X)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 1.40/2.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 1.40/2.18 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 1.40/2.18 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 1.40/2.18 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (Xs tptp.list_VEBT_VEBT) (N tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat M) _let_1) (=> (@ (@ tptp.ord_less_nat N) _let_1) (=> (not (= M N)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.append_VEBT_VEBT (@ (@ tptp.take_VEBT_VEBT N) Xs)) (@ (@ tptp.append_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X) tptp.nil_VEBT_VEBT)) (@ (@ tptp.drop_VEBT_VEBT (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) Xs)))) M) (@ (@ tptp.nth_VEBT_VEBT Xs) M))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (Xs tptp.list_o) (N tptp.nat) (X Bool)) (let ((_let_1 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.ord_less_nat M) _let_1) (=> (@ (@ tptp.ord_less_nat N) _let_1) (=> (not (= M N)) (= (@ (@ tptp.nth_o (@ (@ tptp.append_o (@ (@ tptp.take_o N) Xs)) (@ (@ tptp.append_o (@ (@ tptp.cons_o X) tptp.nil_o)) (@ (@ tptp.drop_o (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) Xs)))) M) (@ (@ tptp.nth_o Xs) M))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (Xs tptp.list_nat) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat M) _let_1) (=> (@ (@ tptp.ord_less_nat N) _let_1) (=> (not (= M N)) (= (@ (@ tptp.nth_nat (@ (@ tptp.append_nat (@ (@ tptp.take_nat N) Xs)) (@ (@ tptp.append_nat (@ (@ tptp.cons_nat X) tptp.nil_nat)) (@ (@ tptp.drop_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) Xs)))) M) (@ (@ tptp.nth_nat Xs) M))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (Xs tptp.list_int) (N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat M) _let_1) (=> (@ (@ tptp.ord_less_nat N) _let_1) (=> (not (= M N)) (= (@ (@ tptp.nth_int (@ (@ tptp.append_int (@ (@ tptp.take_int N) Xs)) (@ (@ tptp.append_int (@ (@ tptp.cons_int X) tptp.nil_int)) (@ (@ tptp.drop_int (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) Xs)))) M) (@ (@ tptp.nth_int Xs) M))))))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 1.40/2.18 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 1.40/2.18 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 1.40/2.18 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 1.40/2.18 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 1.40/2.18 (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)))))))))
% 1.40/2.18 (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)))))))))
% 1.40/2.18 (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)))))))))
% 1.40/2.18 (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)))))))))
% 1.40/2.18 (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)))))))))
% 1.40/2.18 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 1.40/2.18 (assert (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member8440522571783428010at_nat A) (@ tptp.collec3392354462482085612at_nat P)) (@ P A))))
% 1.40/2.18 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 1.40/2.18 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 1.40/2.18 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 1.40/2.18 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 1.40/2.18 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 1.40/2.18 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) A2))) A2)))
% 1.40/2.18 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X4 tptp.complex)) (@ (@ tptp.member_complex X4) A2))) A2)))
% 1.40/2.18 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X4 tptp.real)) (@ (@ tptp.member_real X4) A2))) A2)))
% 1.40/2.18 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A2))) A2)))
% 1.40/2.18 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A2))) A2)))
% 1.40/2.18 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A2))) A2)))
% 1.40/2.18 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X5 tptp.complex)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_complex P) (@ tptp.collect_complex Q)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X5 tptp.list_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M) N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M) N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M) N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M) N))))
% 1.40/2.18 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 1.40/2.18 (assert (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X3) tptp.na) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.ord_less_nat Xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_insert X3) Xa)) tptp.na)))))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 1.40/2.18 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 1.40/2.18 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 1.40/2.18 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 1.40/2.18 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 1.40/2.18 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 1.40/2.18 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 1.40/2.18 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 1.40/2.18 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 1.40/2.18 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 1.40/2.18 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 1.40/2.18 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 1.40/2.18 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 1.40/2.18 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 1.40/2.18 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 1.40/2.18 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 1.40/2.18 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 1.40/2.18 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 1.40/2.18 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 1.40/2.18 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N3)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N3)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N3)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N3)))))))
% 1.40/2.18 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 1.40/2.18 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 1.40/2.18 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 1.40/2.18 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N3)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N3)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N3)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N3)))))))
% 1.40/2.18 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 1.40/2.18 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 1.40/2.18 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 1.40/2.18 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 1.40/2.18 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 1.40/2.18 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 1.40/2.18 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 1.40/2.18 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 1.40/2.18 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 1.40/2.18 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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 ((N4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N4)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat)))))))))))
% 1.40/2.18 (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 ((N4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))))))))
% 1.40/2.18 (assert (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.append_VEBT_VEBT (@ (@ tptp.take_VEBT_VEBT _let_1) tptp.treeList)) (@ (@ tptp.append_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT (@ (@ tptp.vEBT_vebt_insert (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na))) tptp.nil_VEBT_VEBT)) (@ (@ tptp.drop_VEBT_VEBT (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) tptp.treeList))))) (@ (@ tptp.vEBT_invar_vebt X3) tptp.na)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.drop_VEBT_VEBT N) Xs)) I2) (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.plus_plus_nat N) I2))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ tptp.drop_o N) Xs)) I2) (@ (@ tptp.nth_o Xs) (@ (@ tptp.plus_plus_nat N) I2))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ tptp.drop_nat N) Xs)) I2) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.plus_plus_nat N) I2))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ tptp.drop_int N) Xs)) I2) (@ (@ tptp.nth_int Xs) (@ (@ tptp.plus_plus_nat N) I2))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (= (= tptp.nil_VEBT_VEBT (@ (@ tptp.drop_VEBT_VEBT N) Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (= (= tptp.nil_o (@ (@ tptp.drop_o N) Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (= tptp.nil_nat (@ (@ tptp.drop_nat N) Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (= (= tptp.nil_int (@ (@ tptp.drop_int N) Xs)) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.drop_VEBT_VEBT N) Xs) tptp.nil_VEBT_VEBT) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (= (= (@ (@ tptp.drop_o N) Xs) tptp.nil_o) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.drop_nat N) Xs) tptp.nil_nat) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (= (= (@ (@ tptp.drop_int N) Xs) tptp.nil_int) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N) (= (@ (@ tptp.drop_VEBT_VEBT N) Xs) tptp.nil_VEBT_VEBT))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N) (= (@ (@ tptp.drop_o N) Xs) tptp.nil_o))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N) (= (@ (@ tptp.drop_nat N) Xs) tptp.nil_nat))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N) (= (@ (@ tptp.drop_int N) Xs) tptp.nil_int))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (N tptp.nat)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.append_VEBT_VEBT Xs) Ys)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N)) (@ (@ tptp.nth_VEBT_VEBT Ys) N))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o) (N tptp.nat)) (= (@ (@ tptp.nth_o (@ (@ tptp.append_o Xs) Ys)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_o Xs)) N)) (@ (@ tptp.nth_o Ys) N))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (N tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.append_nat Xs) Ys)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat Xs)) N)) (@ (@ tptp.nth_nat Ys) N))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (N tptp.nat)) (= (@ (@ tptp.nth_int (@ (@ tptp.append_int Xs) Ys)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_int Xs)) N)) (@ (@ tptp.nth_int Ys) N))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.append_VEBT_VEBT Xs) (@ (@ tptp.cons_VEBT_VEBT X) Ys))) (@ tptp.size_s6755466524823107622T_VEBT Xs)) X)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (X Bool) (Ys tptp.list_o)) (= (@ (@ tptp.nth_o (@ (@ tptp.append_o Xs) (@ (@ tptp.cons_o X) Ys))) (@ tptp.size_size_list_o Xs)) X)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (X tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.append_nat Xs) (@ (@ tptp.cons_nat X) Ys))) (@ tptp.size_size_list_nat Xs)) X)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (X tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.nth_int (@ (@ tptp.append_int Xs) (@ (@ tptp.cons_int X) Ys))) (@ tptp.size_size_list_int Xs)) X)))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.append_VEBT_VEBT (@ (@ tptp.take_VEBT_VEBT N) Xs)) (@ (@ tptp.drop_VEBT_VEBT N) Xs)) Xs)))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (= (@ (@ tptp.append_int (@ (@ tptp.take_int N) Xs)) (@ (@ tptp.drop_int N) Xs)) Xs)))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.append_nat (@ (@ tptp.take_nat N) Xs)) (@ (@ tptp.drop_nat N) Xs)) Xs)))
% 1.40/2.18 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 1.40/2.18 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 1.40/2.18 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1))) (@ (@ tptp.vEBT_vebt_insert tptp.summary) _let_1)) tptp.summary)) tptp.na)))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (N tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_int (@ (@ tptp.take_int N) Xs)) I2) (@ (@ tptp.nth_int Xs) I2)))))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.take_VEBT_VEBT N) Xs)) I2) (@ (@ tptp.nth_VEBT_VEBT Xs) I2)))))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.take_nat N) Xs)) I2) (@ (@ tptp.nth_nat Xs) I2)))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 1.40/2.18 (assert (forall ((X21 tptp.vEBT_VEBT) (X22 tptp.list_VEBT_VEBT) (Y21 tptp.vEBT_VEBT) (Y22 tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.cons_VEBT_VEBT X21) X22) (@ (@ tptp.cons_VEBT_VEBT Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 1.40/2.18 (assert (forall ((X21 tptp.int) (X22 tptp.list_int) (Y21 tptp.int) (Y22 tptp.list_int)) (= (= (@ (@ tptp.cons_int X21) X22) (@ (@ tptp.cons_int Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 1.40/2.18 (assert (forall ((X21 tptp.nat) (X22 tptp.list_nat) (Y21 tptp.nat) (Y22 tptp.list_nat)) (= (= (@ (@ tptp.cons_nat X21) X22) (@ (@ tptp.cons_nat Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 1.40/2.18 (assert (forall ((A tptp.list_VEBT_VEBT) (B tptp.list_VEBT_VEBT) (C tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.append_VEBT_VEBT A))) (= (@ (@ tptp.append_VEBT_VEBT (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_VEBT_VEBT B) C))))))
% 1.40/2.18 (assert (forall ((A tptp.list_int) (B tptp.list_int) (C tptp.list_int)) (let ((_let_1 (@ tptp.append_int A))) (= (@ (@ tptp.append_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_int B) C))))))
% 1.40/2.18 (assert (forall ((A tptp.list_nat) (B tptp.list_nat) (C tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat A))) (= (@ (@ tptp.append_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_nat B) C))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Zs tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.append_VEBT_VEBT Xs))) (= (@ (@ tptp.append_VEBT_VEBT (@ _let_1 Ys)) Zs) (@ _let_1 (@ (@ tptp.append_VEBT_VEBT Ys) Zs))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Zs tptp.list_int)) (let ((_let_1 (@ tptp.append_int Xs))) (= (@ (@ tptp.append_int (@ _let_1 Ys)) Zs) (@ _let_1 (@ (@ tptp.append_int Ys) Zs))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Xs))) (= (@ (@ tptp.append_nat (@ _let_1 Ys)) Zs) (@ _let_1 (@ (@ tptp.append_nat Ys) Zs))))))
% 1.40/2.18 (assert (forall ((Ys tptp.list_VEBT_VEBT) (Xs tptp.list_VEBT_VEBT) (Zs tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.append_VEBT_VEBT Ys) Xs) (@ (@ tptp.append_VEBT_VEBT Zs) Xs)) (= Ys Zs))))
% 1.40/2.18 (assert (forall ((Ys tptp.list_int) (Xs tptp.list_int) (Zs tptp.list_int)) (= (= (@ (@ tptp.append_int Ys) Xs) (@ (@ tptp.append_int Zs) Xs)) (= Ys Zs))))
% 1.40/2.18 (assert (forall ((Ys tptp.list_nat) (Xs tptp.list_nat) (Zs tptp.list_nat)) (= (= (@ (@ tptp.append_nat Ys) Xs) (@ (@ tptp.append_nat Zs) Xs)) (= Ys Zs))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Zs tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.append_VEBT_VEBT Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs)) (= Ys Zs)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Zs tptp.list_int)) (let ((_let_1 (@ tptp.append_int Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs)) (= Ys Zs)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs)) (= Ys Zs)))))
% 1.40/2.18 (assert (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt X3) tptp.na))))
% 1.40/2.18 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y2) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y2)) X))))))))
% 1.40/2.18 (assert (forall ((A tptp.list_VEBT_VEBT)) (= (@ (@ tptp.append_VEBT_VEBT A) tptp.nil_VEBT_VEBT) A)))
% 1.40/2.18 (assert (forall ((A tptp.list_int)) (= (@ (@ tptp.append_int A) tptp.nil_int) A)))
% 1.40/2.18 (assert (forall ((A tptp.list_nat)) (= (@ (@ tptp.append_nat A) tptp.nil_nat) A)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.append_VEBT_VEBT Xs) tptp.nil_VEBT_VEBT) Xs)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.append_int Xs) tptp.nil_int) Xs)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.append_nat Xs) tptp.nil_nat) Xs)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.append_VEBT_VEBT Xs) Ys) Xs) (= Ys tptp.nil_VEBT_VEBT))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= (@ (@ tptp.append_int Xs) Ys) Xs) (= Ys tptp.nil_int))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs) Ys) Xs) (= Ys tptp.nil_nat))))
% 1.40/2.18 (assert (forall ((Y2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (= Y2 (@ (@ tptp.append_VEBT_VEBT Y2) Ys)) (= Ys tptp.nil_VEBT_VEBT))))
% 1.40/2.18 (assert (forall ((Y2 tptp.list_int) (Ys tptp.list_int)) (= (= Y2 (@ (@ tptp.append_int Y2) Ys)) (= Ys tptp.nil_int))))
% 1.40/2.18 (assert (forall ((Y2 tptp.list_nat) (Ys tptp.list_nat)) (= (= Y2 (@ (@ tptp.append_nat Y2) Ys)) (= Ys tptp.nil_nat))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.append_VEBT_VEBT Xs) Ys) Ys) (= Xs tptp.nil_VEBT_VEBT))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= (@ (@ tptp.append_int Xs) Ys) Ys) (= Xs tptp.nil_int))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs) Ys) Ys) (= Xs tptp.nil_nat))))
% 1.40/2.18 (assert (forall ((Y2 tptp.list_VEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (= Y2 (@ (@ tptp.append_VEBT_VEBT Xs) Y2)) (= Xs tptp.nil_VEBT_VEBT))))
% 1.40/2.18 (assert (forall ((Y2 tptp.list_int) (Xs tptp.list_int)) (= (= Y2 (@ (@ tptp.append_int Xs) Y2)) (= Xs tptp.nil_int))))
% 1.40/2.18 (assert (forall ((Y2 tptp.list_nat) (Xs tptp.list_nat)) (= (= Y2 (@ (@ tptp.append_nat Xs) Y2)) (= Xs tptp.nil_nat))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (= tptp.nil_VEBT_VEBT (@ (@ tptp.append_VEBT_VEBT Xs) Ys)) (and (= Xs tptp.nil_VEBT_VEBT) (= Ys tptp.nil_VEBT_VEBT)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= tptp.nil_int (@ (@ tptp.append_int Xs) Ys)) (and (= Xs tptp.nil_int) (= Ys tptp.nil_int)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= tptp.nil_nat (@ (@ tptp.append_nat Xs) Ys)) (and (= Xs tptp.nil_nat) (= Ys tptp.nil_nat)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.append_VEBT_VEBT Xs) Ys) tptp.nil_VEBT_VEBT) (and (= Xs tptp.nil_VEBT_VEBT) (= Ys tptp.nil_VEBT_VEBT)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= (@ (@ tptp.append_int Xs) Ys) tptp.nil_int) (and (= Xs tptp.nil_int) (= Ys tptp.nil_int)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs) Ys) tptp.nil_nat) (and (= Xs tptp.nil_nat) (= Ys tptp.nil_nat)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Us tptp.list_VEBT_VEBT) (Vs tptp.list_VEBT_VEBT)) (=> (or (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Us) (@ tptp.size_s6755466524823107622T_VEBT Vs))) (= (= (@ (@ tptp.append_VEBT_VEBT Xs) Us) (@ (@ tptp.append_VEBT_VEBT Ys) Vs)) (and (= Xs Ys) (= Us Vs))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o) (Us tptp.list_o) (Vs tptp.list_o)) (=> (or (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys)) (= (@ tptp.size_size_list_o Us) (@ tptp.size_size_list_o Vs))) (= (= (@ (@ tptp.append_o Xs) Us) (@ (@ tptp.append_o Ys) Vs)) (and (= Xs Ys) (= Us Vs))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Us tptp.list_nat) (Vs tptp.list_nat)) (=> (or (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (= (@ tptp.size_size_list_nat Us) (@ tptp.size_size_list_nat Vs))) (= (= (@ (@ tptp.append_nat Xs) Us) (@ (@ tptp.append_nat Ys) Vs)) (and (= Xs Ys) (= Us Vs))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Us tptp.list_int) (Vs tptp.list_int)) (=> (or (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)) (= (@ tptp.size_size_list_int Us) (@ tptp.size_size_list_int Vs))) (= (= (@ (@ tptp.append_int Xs) Us) (@ (@ tptp.append_int Ys) Vs)) (and (= Xs Ys) (= Us Vs))))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.drop_VEBT_VEBT N) (@ (@ tptp.drop_VEBT_VEBT M) Xs)) (@ (@ tptp.drop_VEBT_VEBT (@ (@ tptp.plus_plus_nat N) M)) Xs))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.drop_nat N) (@ (@ tptp.drop_nat M) Xs)) (@ (@ tptp.drop_nat (@ (@ tptp.plus_plus_nat N) M)) Xs))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 1.40/2.18 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 1.40/2.18 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 1.40/2.18 (assert (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_insert tptp.summary) X)) tptp.m))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (=> (@ (@ tptp.vEBT_invar_vebt X) tptp.na) (=> (@ (@ tptp.ord_less_nat Xa2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_insert X) Xa2)) tptp.na))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Y2 tptp.vEBT_VEBT)) (= (= (@ (@ tptp.append_VEBT_VEBT Xs) (@ (@ tptp.cons_VEBT_VEBT X) tptp.nil_VEBT_VEBT)) (@ (@ tptp.append_VEBT_VEBT Ys) (@ (@ tptp.cons_VEBT_VEBT Y2) tptp.nil_VEBT_VEBT))) (and (= Xs Ys) (= X Y2)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (X tptp.int) (Ys tptp.list_int) (Y2 tptp.int)) (= (= (@ (@ tptp.append_int Xs) (@ (@ tptp.cons_int X) tptp.nil_int)) (@ (@ tptp.append_int Ys) (@ (@ tptp.cons_int Y2) tptp.nil_int))) (and (= Xs Ys) (= X Y2)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (X tptp.nat) (Ys tptp.list_nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.append_nat Xs) (@ (@ tptp.cons_nat X) tptp.nil_nat)) (@ (@ tptp.append_nat Ys) (@ (@ tptp.cons_nat Y2) tptp.nil_nat))) (and (= Xs Ys) (= X Y2)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.append_VEBT_VEBT Xs) Ys)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_size_list_o (@ (@ tptp.append_o Xs) Ys)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.append_nat Xs) Ys)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_nat Ys)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.append_int Xs) Ys)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_int Ys)))))
% 1.40/2.18 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N) (= (@ (@ tptp.take_VEBT_VEBT N) Xs) Xs))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N) (= (@ (@ tptp.take_o N) Xs) Xs))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N) (= (@ (@ tptp.take_nat N) Xs) Xs))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N) (= (@ (@ tptp.take_int N) Xs) Xs))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.take_VEBT_VEBT N) Xs) Xs) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (= (= (@ (@ tptp.take_o N) Xs) Xs) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.take_nat N) Xs) Xs) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (= (= (@ (@ tptp.take_int N) Xs) Xs) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (not (= (@ (@ tptp.cons_VEBT_VEBT X) Xs) Xs))))
% 1.40/2.18 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (not (= (@ (@ tptp.cons_int X) Xs) Xs))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (not (= (@ (@ tptp.cons_nat X) Xs) Xs))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) B2) (forall ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X4))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ _let_1 B2)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_complex) (B2 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) B2) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X4))) (=> (@ _let_1 (@ tptp.set_complex2 Xs)) (@ _let_1 B2)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_real) (B2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B2) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B2)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (B2 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B2) (forall ((X4 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X4))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B2)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B2) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B2)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (B2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B2) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B2)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs Ys)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys))) (not (= Xs Ys)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys))) (not (= Xs Ys)))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o Xs2) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Xs1 tptp.list_VEBT_VEBT) (Zs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Us tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.append_VEBT_VEBT Xs))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys (@ (@ tptp.append_VEBT_VEBT Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_VEBT_VEBT Zs) Us)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Xs1 tptp.list_int) (Zs tptp.list_int) (Ys tptp.list_int) (Us tptp.list_int)) (let ((_let_1 (@ tptp.append_int Xs))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys (@ (@ tptp.append_int Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_int Zs) Us)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Xs1 tptp.list_nat) (Zs tptp.list_nat) (Ys tptp.list_nat) (Us tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Xs))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys (@ (@ tptp.append_nat Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_nat Zs) Us)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Zs tptp.list_VEBT_VEBT) (Ts tptp.list_VEBT_VEBT)) (= (= (@ (@ tptp.append_VEBT_VEBT Xs) Ys) (@ (@ tptp.append_VEBT_VEBT Zs) Ts)) (exists ((Us2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.append_VEBT_VEBT Us2))) (or (and (= Xs (@ (@ tptp.append_VEBT_VEBT Zs) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_VEBT_VEBT Xs) Us2) Zs) (= Ys (@ _let_1 Ts)))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Zs tptp.list_int) (Ts tptp.list_int)) (= (= (@ (@ tptp.append_int Xs) Ys) (@ (@ tptp.append_int Zs) Ts)) (exists ((Us2 tptp.list_int)) (let ((_let_1 (@ tptp.append_int Us2))) (or (and (= Xs (@ (@ tptp.append_int Zs) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_int Xs) Us2) Zs) (= Ys (@ _let_1 Ts)))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_nat) (Ts tptp.list_nat)) (= (= (@ (@ tptp.append_nat Xs) Ys) (@ (@ tptp.append_nat Zs) Ts)) (exists ((Us2 tptp.list_nat)) (let ((_let_1 (@ tptp.append_nat Us2))) (or (and (= Xs (@ (@ tptp.append_nat Zs) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_nat Xs) Us2) Zs) (= Ys (@ _let_1 Ts)))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ tptp.take_VEBT_VEBT I3))) (= (@ _let_1 Xs) (@ _let_1 Ys)))) (= Xs Ys))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ tptp.take_nat I3))) (= (@ _let_1 Xs) (@ _let_1 Ys)))) (= Xs Ys))))
% 1.40/2.18 (assert (forall ((X21 tptp.vEBT_VEBT) (X22 tptp.list_VEBT_VEBT)) (not (= tptp.nil_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X21) X22)))))
% 1.40/2.18 (assert (forall ((X21 tptp.int) (X22 tptp.list_int)) (not (= tptp.nil_int (@ (@ tptp.cons_int X21) X22)))))
% 1.40/2.18 (assert (forall ((X21 tptp.nat) (X22 tptp.list_nat)) (not (= tptp.nil_nat (@ (@ tptp.cons_nat X21) X22)))))
% 1.40/2.18 (assert (forall ((List tptp.list_VEBT_VEBT) (X21 tptp.vEBT_VEBT) (X22 tptp.list_VEBT_VEBT)) (=> (= List (@ (@ tptp.cons_VEBT_VEBT X21) X22)) (not (= List tptp.nil_VEBT_VEBT)))))
% 1.40/2.18 (assert (forall ((List tptp.list_int) (X21 tptp.int) (X22 tptp.list_int)) (=> (= List (@ (@ tptp.cons_int X21) X22)) (not (= List tptp.nil_int)))))
% 1.40/2.18 (assert (forall ((List tptp.list_nat) (X21 tptp.nat) (X22 tptp.list_nat)) (=> (= List (@ (@ tptp.cons_nat X21) X22)) (not (= List tptp.nil_nat)))))
% 1.40/2.18 (assert (forall ((Y2 tptp.list_VEBT_VEBT)) (=> (not (= Y2 tptp.nil_VEBT_VEBT)) (not (forall ((X212 tptp.vEBT_VEBT) (X222 tptp.list_VEBT_VEBT)) (not (= Y2 (@ (@ tptp.cons_VEBT_VEBT X212) X222))))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.list_int)) (=> (not (= Y2 tptp.nil_int)) (not (forall ((X212 tptp.int) (X222 tptp.list_int)) (not (= Y2 (@ (@ tptp.cons_int X212) X222))))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.list_nat)) (=> (not (= Y2 tptp.nil_nat)) (not (forall ((X212 tptp.nat) (X222 tptp.list_nat)) (not (= Y2 (@ (@ tptp.cons_nat X212) X222))))))))
% 1.40/2.18 (assert (forall ((X tptp.list_int)) (=> (forall ((X5 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.cons_int X5) Xs2)))) (= X tptp.nil_int))))
% 1.40/2.18 (assert (forall ((X tptp.list_nat)) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X5) Xs2)))) (= X tptp.nil_nat))))
% 1.40/2.18 (assert (forall ((X tptp.list_list_VEBT_VEBT)) (=> (not (= X tptp.nil_list_VEBT_VEBT)) (=> (forall ((Xss tptp.list_list_VEBT_VEBT)) (not (= X (@ (@ tptp.cons_list_VEBT_VEBT tptp.nil_VEBT_VEBT) Xss)))) (not (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Xss tptp.list_list_VEBT_VEBT)) (not (= X (@ (@ tptp.cons_list_VEBT_VEBT (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) Xss)))))))))
% 1.40/2.18 (assert (forall ((X tptp.list_list_int)) (=> (not (= X tptp.nil_list_int)) (=> (forall ((Xss tptp.list_list_int)) (not (= X (@ (@ tptp.cons_list_int tptp.nil_int) Xss)))) (not (forall ((X5 tptp.int) (Xs2 tptp.list_int) (Xss tptp.list_list_int)) (not (= X (@ (@ tptp.cons_list_int (@ (@ tptp.cons_int X5) Xs2)) Xss)))))))))
% 1.40/2.18 (assert (forall ((X tptp.list_list_nat)) (=> (not (= X tptp.nil_list_nat)) (=> (forall ((Xss tptp.list_list_nat)) (not (= X (@ (@ tptp.cons_list_nat tptp.nil_nat) Xss)))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Xss tptp.list_list_nat)) (not (= X (@ (@ tptp.cons_list_nat (@ (@ tptp.cons_nat X5) Xs2)) Xss)))))))))
% 1.40/2.18 (assert (forall ((X tptp.list_VEBT_VEBT)) (=> (not (= X tptp.nil_VEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (not (= X (@ (@ tptp.cons_VEBT_VEBT X5) tptp.nil_VEBT_VEBT)))) (not (forall ((X5 tptp.vEBT_VEBT) (Y3 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (not (= X (@ (@ tptp.cons_VEBT_VEBT X5) (@ (@ tptp.cons_VEBT_VEBT Y3) Xs2))))))))))
% 1.40/2.18 (assert (forall ((X tptp.list_int)) (=> (not (= X tptp.nil_int)) (=> (forall ((X5 tptp.int)) (not (= X (@ (@ tptp.cons_int X5) tptp.nil_int)))) (not (forall ((X5 tptp.int) (Y3 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.cons_int X5) (@ (@ tptp.cons_int Y3) Xs2))))))))))
% 1.40/2.18 (assert (forall ((X tptp.list_nat)) (=> (not (= X tptp.nil_nat)) (=> (forall ((X5 tptp.nat)) (not (= X (@ (@ tptp.cons_nat X5) tptp.nil_nat)))) (not (forall ((X5 tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X5) (@ (@ tptp.cons_nat Y3) Xs2))))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (= (not (= Xs tptp.nil_VEBT_VEBT)) (exists ((Y4 tptp.vEBT_VEBT) (Ys2 tptp.list_VEBT_VEBT)) (= Xs (@ (@ tptp.cons_VEBT_VEBT Y4) Ys2))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int)) (= (not (= Xs tptp.nil_int)) (exists ((Y4 tptp.int) (Ys2 tptp.list_int)) (= Xs (@ (@ tptp.cons_int Y4) Ys2))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat)) (= (not (= Xs tptp.nil_nat)) (exists ((Y4 tptp.nat) (Ys2 tptp.list_nat)) (= Xs (@ (@ tptp.cons_nat Y4) Ys2))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) tptp.nil_VEBT_VEBT)) (=> (forall ((Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (@ (@ P tptp.nil_VEBT_VEBT) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3))) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3)))) (@ (@ P Xs) Ys)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_VEBT_VEBT tptp.list_int Bool)) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (=> (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_int) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) tptp.nil_int)) (=> (forall ((Y3 tptp.int) (Ys3 tptp.list_int)) (@ (@ P tptp.nil_VEBT_VEBT) (@ (@ tptp.cons_int Y3) Ys3))) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.int) (Ys3 tptp.list_int)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)))) (@ (@ P Xs) Ys)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_VEBT_VEBT tptp.list_nat Bool)) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (=> (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_nat) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) tptp.nil_nat)) (=> (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (@ (@ P tptp.nil_VEBT_VEBT) (@ (@ tptp.cons_nat Y3) Ys3))) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (@ (@ P Xs) Ys)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_int tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_int) (Ys tptp.list_VEBT_VEBT)) (=> (@ (@ P tptp.nil_int) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.int) (Xs2 tptp.list_int)) (@ (@ P (@ (@ tptp.cons_int X5) Xs2)) tptp.nil_VEBT_VEBT)) (=> (forall ((Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (@ (@ P tptp.nil_int) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3))) (=> (forall ((X5 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_int X5) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3)))) (@ (@ P Xs) Ys)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_int tptp.list_int Bool)) (Xs tptp.list_int) (Ys tptp.list_int)) (=> (@ (@ P tptp.nil_int) tptp.nil_int) (=> (forall ((X5 tptp.int) (Xs2 tptp.list_int)) (@ (@ P (@ (@ tptp.cons_int X5) Xs2)) tptp.nil_int)) (=> (forall ((Y3 tptp.int) (Ys3 tptp.list_int)) (@ (@ P tptp.nil_int) (@ (@ tptp.cons_int Y3) Ys3))) (=> (forall ((X5 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.int) (Ys3 tptp.list_int)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_int X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)))) (@ (@ P Xs) Ys)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_int tptp.list_nat Bool)) (Xs tptp.list_int) (Ys tptp.list_nat)) (=> (@ (@ P tptp.nil_int) tptp.nil_nat) (=> (forall ((X5 tptp.int) (Xs2 tptp.list_int)) (@ (@ P (@ (@ tptp.cons_int X5) Xs2)) tptp.nil_nat)) (=> (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (@ (@ P tptp.nil_int) (@ (@ tptp.cons_nat Y3) Ys3))) (=> (forall ((X5 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_int X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (@ (@ P Xs) Ys)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_nat tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (=> (@ (@ P tptp.nil_nat) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) tptp.nil_VEBT_VEBT)) (=> (forall ((Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3))) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3)))) (@ (@ P Xs) Ys)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_nat tptp.list_int Bool)) (Xs tptp.list_nat) (Ys tptp.list_int)) (=> (@ (@ P tptp.nil_nat) tptp.nil_int) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) tptp.nil_int)) (=> (forall ((Y3 tptp.int) (Ys3 tptp.list_int)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_int Y3) Ys3))) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)))) (@ (@ P Xs) Ys)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_nat tptp.list_nat Bool)) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ P tptp.nil_nat) tptp.nil_nat) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) tptp.nil_nat)) (=> (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (@ (@ P tptp.nil_nat) (@ (@ tptp.cons_nat Y3) Ys3))) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (@ (@ P Xs) Ys)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.list_VEBT_VEBT Bool))) (=> (not (= Xs tptp.nil_VEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (@ P (@ (@ tptp.cons_VEBT_VEBT X5) tptp.nil_VEBT_VEBT))) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (not (= Xs2 tptp.nil_VEBT_VEBT)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2))))) (@ P Xs))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (P (-> tptp.list_int Bool))) (=> (not (= Xs tptp.nil_int)) (=> (forall ((X5 tptp.int)) (@ P (@ (@ tptp.cons_int X5) tptp.nil_int))) (=> (forall ((X5 tptp.int) (Xs2 tptp.list_int)) (=> (not (= Xs2 tptp.nil_int)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_int X5) Xs2))))) (@ P Xs))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.list_nat Bool))) (=> (not (= Xs tptp.nil_nat)) (=> (forall ((X5 tptp.nat)) (@ P (@ (@ tptp.cons_nat X5) tptp.nil_nat))) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (=> (not (= Xs2 tptp.nil_nat)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_nat X5) Xs2))))) (@ P Xs))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.product_prod_nat_nat) (X22 tptp.list_P6011104703257516679at_nat) (X21 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat Y2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat X22)) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X21) X22)))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.complex) (X22 tptp.list_complex) (X21 tptp.complex)) (let ((_let_1 (@ tptp.member_complex Y2))) (=> (@ _let_1 (@ tptp.set_complex2 X22)) (@ _let_1 (@ tptp.set_complex2 (@ (@ tptp.cons_complex X21) X22)))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.real) (X22 tptp.list_real) (X21 tptp.real)) (let ((_let_1 (@ tptp.member_real Y2))) (=> (@ _let_1 (@ tptp.set_real2 X22)) (@ _let_1 (@ tptp.set_real2 (@ (@ tptp.cons_real X21) X22)))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.vEBT_VEBT) (X22 tptp.list_VEBT_VEBT) (X21 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT Y2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 X22)) (@ _let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.cons_VEBT_VEBT X21) X22)))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.int) (X22 tptp.list_int) (X21 tptp.int)) (let ((_let_1 (@ tptp.member_int Y2))) (=> (@ _let_1 (@ tptp.set_int2 X22)) (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.cons_int X21) X22)))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.nat) (X22 tptp.list_nat) (X21 tptp.nat)) (let ((_let_1 (@ tptp.member_nat Y2))) (=> (@ _let_1 (@ tptp.set_nat2 X22)) (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.cons_nat X21) X22)))))))
% 1.40/2.18 (assert (forall ((X21 tptp.product_prod_nat_nat) (X22 tptp.list_P6011104703257516679at_nat)) (@ (@ tptp.member8440522571783428010at_nat X21) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X21) X22)))))
% 1.40/2.18 (assert (forall ((X21 tptp.complex) (X22 tptp.list_complex)) (@ (@ tptp.member_complex X21) (@ tptp.set_complex2 (@ (@ tptp.cons_complex X21) X22)))))
% 1.40/2.18 (assert (forall ((X21 tptp.real) (X22 tptp.list_real)) (@ (@ tptp.member_real X21) (@ tptp.set_real2 (@ (@ tptp.cons_real X21) X22)))))
% 1.40/2.18 (assert (forall ((X21 tptp.vEBT_VEBT) (X22 tptp.list_VEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X21) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.cons_VEBT_VEBT X21) X22)))))
% 1.40/2.18 (assert (forall ((X21 tptp.int) (X22 tptp.list_int)) (@ (@ tptp.member_int X21) (@ tptp.set_int2 (@ (@ tptp.cons_int X21) X22)))))
% 1.40/2.18 (assert (forall ((X21 tptp.nat) (X22 tptp.list_nat)) (@ (@ tptp.member_nat X21) (@ tptp.set_nat2 (@ (@ tptp.cons_nat X21) X22)))))
% 1.40/2.18 (assert (forall ((E tptp.product_prod_nat_nat) (A tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat E) (@ tptp.set_Pr5648618587558075414at_nat A)) (=> (forall ((Z2 tptp.list_P6011104703257516679at_nat)) (not (= A (@ (@ tptp.cons_P6512896166579812791at_nat E) Z2)))) (not (forall ((Z1 tptp.product_prod_nat_nat) (Z2 tptp.list_P6011104703257516679at_nat)) (=> (= A (@ (@ tptp.cons_P6512896166579812791at_nat Z1) Z2)) (not (@ (@ tptp.member8440522571783428010at_nat E) (@ tptp.set_Pr5648618587558075414at_nat Z2))))))))))
% 1.40/2.18 (assert (forall ((E tptp.complex) (A tptp.list_complex)) (=> (@ (@ tptp.member_complex E) (@ tptp.set_complex2 A)) (=> (forall ((Z2 tptp.list_complex)) (not (= A (@ (@ tptp.cons_complex E) Z2)))) (not (forall ((Z1 tptp.complex) (Z2 tptp.list_complex)) (=> (= A (@ (@ tptp.cons_complex Z1) Z2)) (not (@ (@ tptp.member_complex E) (@ tptp.set_complex2 Z2))))))))))
% 1.40/2.18 (assert (forall ((E tptp.real) (A tptp.list_real)) (=> (@ (@ tptp.member_real E) (@ tptp.set_real2 A)) (=> (forall ((Z2 tptp.list_real)) (not (= A (@ (@ tptp.cons_real E) Z2)))) (not (forall ((Z1 tptp.real) (Z2 tptp.list_real)) (=> (= A (@ (@ tptp.cons_real Z1) Z2)) (not (@ (@ tptp.member_real E) (@ tptp.set_real2 Z2))))))))))
% 1.40/2.18 (assert (forall ((E tptp.vEBT_VEBT) (A tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT E) (@ tptp.set_VEBT_VEBT2 A)) (=> (forall ((Z2 tptp.list_VEBT_VEBT)) (not (= A (@ (@ tptp.cons_VEBT_VEBT E) Z2)))) (not (forall ((Z1 tptp.vEBT_VEBT) (Z2 tptp.list_VEBT_VEBT)) (=> (= A (@ (@ tptp.cons_VEBT_VEBT Z1) Z2)) (not (@ (@ tptp.member_VEBT_VEBT E) (@ tptp.set_VEBT_VEBT2 Z2))))))))))
% 1.40/2.18 (assert (forall ((E tptp.int) (A tptp.list_int)) (=> (@ (@ tptp.member_int E) (@ tptp.set_int2 A)) (=> (forall ((Z2 tptp.list_int)) (not (= A (@ (@ tptp.cons_int E) Z2)))) (not (forall ((Z1 tptp.int) (Z2 tptp.list_int)) (=> (= A (@ (@ tptp.cons_int Z1) Z2)) (not (@ (@ tptp.member_int E) (@ tptp.set_int2 Z2))))))))))
% 1.40/2.18 (assert (forall ((E tptp.nat) (A tptp.list_nat)) (=> (@ (@ tptp.member_nat E) (@ tptp.set_nat2 A)) (=> (forall ((Z2 tptp.list_nat)) (not (= A (@ (@ tptp.cons_nat E) Z2)))) (not (forall ((Z1 tptp.nat) (Z2 tptp.list_nat)) (=> (= A (@ (@ tptp.cons_nat Z1) Z2)) (not (@ (@ tptp.member_nat E) (@ tptp.set_nat2 Z2))))))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat Y2))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.cons_P6512896166579812791at_nat X) Xs))) (or (= Y2 X) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.complex) (X tptp.complex) (Xs tptp.list_complex)) (let ((_let_1 (@ tptp.member_complex Y2))) (=> (@ _let_1 (@ tptp.set_complex2 (@ (@ tptp.cons_complex X) Xs))) (or (= Y2 X) (@ _let_1 (@ tptp.set_complex2 Xs)))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.real) (X tptp.real) (Xs tptp.list_real)) (let ((_let_1 (@ tptp.member_real Y2))) (=> (@ _let_1 (@ tptp.set_real2 (@ (@ tptp.cons_real X) Xs))) (or (= Y2 X) (@ _let_1 (@ tptp.set_real2 Xs)))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.vEBT_VEBT) (X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT Y2))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.cons_VEBT_VEBT X) Xs))) (or (= Y2 X) (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.int) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.member_int Y2))) (=> (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.cons_int X) Xs))) (or (= Y2 X) (@ _let_1 (@ tptp.set_int2 Xs)))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.member_nat Y2))) (=> (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.cons_nat X) Xs))) (or (= Y2 X) (@ _let_1 (@ tptp.set_nat2 Xs)))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.cons_VEBT_VEBT X) Xs)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) (@ tptp.set_nat2 (@ (@ tptp.cons_nat X) Xs)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) (@ tptp.set_int2 (@ (@ tptp.cons_int X) Xs)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Ys4 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys4)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs2 tptp.list_o)) (=> (forall ((Ys4 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys4)) (@ tptp.size_size_list_o Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys4 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys4)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))))
% 1.40/2.18 (assert (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys4 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys4)) (@ tptp.size_size_list_int Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.cons_VEBT_VEBT X))) (= (@ (@ tptp.append_VEBT_VEBT (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.append_VEBT_VEBT Xs) Ys))))))
% 1.40/2.18 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.cons_int X))) (= (@ (@ tptp.append_int (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.append_int Xs) Ys))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X))) (= (@ (@ tptp.append_nat (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.append_nat Xs) Ys))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xs1 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Xs tptp.list_VEBT_VEBT) (Zs tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.cons_VEBT_VEBT X))) (=> (= (@ _let_1 Xs1) Ys) (=> (= Xs (@ (@ tptp.append_VEBT_VEBT Xs1) Zs)) (= (@ _let_1 Xs) (@ (@ tptp.append_VEBT_VEBT Ys) Zs)))))))
% 1.40/2.18 (assert (forall ((X tptp.int) (Xs1 tptp.list_int) (Ys tptp.list_int) (Xs tptp.list_int) (Zs tptp.list_int)) (let ((_let_1 (@ tptp.cons_int X))) (=> (= (@ _let_1 Xs1) Ys) (=> (= Xs (@ (@ tptp.append_int Xs1) Zs)) (= (@ _let_1 Xs) (@ (@ tptp.append_int Ys) Zs)))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (Xs1 tptp.list_nat) (Ys tptp.list_nat) (Xs tptp.list_nat) (Zs tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X))) (=> (= (@ _let_1 Xs1) Ys) (=> (= Xs (@ (@ tptp.append_nat Xs1) Zs)) (= (@ _let_1 Xs) (@ (@ tptp.append_nat Ys) Zs)))))))
% 1.40/2.18 (assert (forall ((Ys tptp.list_VEBT_VEBT)) (= (@ (@ tptp.append_VEBT_VEBT tptp.nil_VEBT_VEBT) Ys) Ys)))
% 1.40/2.18 (assert (forall ((Ys tptp.list_int)) (= (@ (@ tptp.append_int tptp.nil_int) Ys) Ys)))
% 1.40/2.18 (assert (forall ((Ys tptp.list_nat)) (= (@ (@ tptp.append_nat tptp.nil_nat) Ys) Ys)))
% 1.40/2.18 (assert (forall ((A tptp.list_VEBT_VEBT)) (= (@ (@ tptp.append_VEBT_VEBT tptp.nil_VEBT_VEBT) A) A)))
% 1.40/2.18 (assert (forall ((A tptp.list_int)) (= (@ (@ tptp.append_int tptp.nil_int) A) A)))
% 1.40/2.18 (assert (forall ((A tptp.list_nat)) (= (@ (@ tptp.append_nat tptp.nil_nat) A) A)))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= Xs Ys) (= Xs (@ (@ tptp.append_VEBT_VEBT tptp.nil_VEBT_VEBT) Ys)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= Xs Ys) (= Xs (@ (@ tptp.append_int tptp.nil_int) Ys)))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= Xs Ys) (= Xs (@ (@ tptp.append_nat tptp.nil_nat) Ys)))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.take_VEBT_VEBT N) tptp.nil_VEBT_VEBT) tptp.nil_VEBT_VEBT)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.take_int N) tptp.nil_int) tptp.nil_int)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.take_nat N) tptp.nil_nat) tptp.nil_nat)))
% 1.40/2.18 (assert (forall ((X tptp.product_prod_nat_nat) (N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.take_P2173866234530122223at_nat N) Xs))) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs))))))
% 1.40/2.18 (assert (forall ((X tptp.complex) (N tptp.nat) (Xs tptp.list_complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _let_1 (@ tptp.set_complex2 (@ (@ tptp.take_complex N) Xs))) (@ _let_1 (@ tptp.set_complex2 Xs))))))
% 1.40/2.18 (assert (forall ((X tptp.real) (N tptp.nat) (Xs tptp.list_real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 (@ tptp.set_real2 (@ (@ tptp.take_real N) Xs))) (@ _let_1 (@ tptp.set_real2 Xs))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.take_VEBT_VEBT N) Xs))) (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs))))))
% 1.40/2.18 (assert (forall ((X tptp.int) (N tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.take_int N) Xs))) (@ _let_1 (@ tptp.set_int2 Xs))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.take_nat N) Xs))) (@ _let_1 (@ tptp.set_nat2 Xs))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.take_VEBT_VEBT N) Xs))) (@ tptp.set_VEBT_VEBT2 Xs))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ tptp.take_nat N) Xs))) (@ tptp.set_nat2 Xs))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ tptp.take_int N) Xs))) (@ tptp.set_int2 Xs))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.drop_VEBT_VEBT N) tptp.nil_VEBT_VEBT) tptp.nil_VEBT_VEBT)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.drop_int N) tptp.nil_int) tptp.nil_int)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.drop_nat N) tptp.nil_nat) tptp.nil_nat)))
% 1.40/2.18 (assert (forall ((X tptp.product_prod_nat_nat) (N tptp.nat) (Xs tptp.list_P6011104703257516679at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.drop_P8868858903918902087at_nat N) Xs))) (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs))))))
% 1.40/2.18 (assert (forall ((X tptp.complex) (N tptp.nat) (Xs tptp.list_complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _let_1 (@ tptp.set_complex2 (@ (@ tptp.drop_complex N) Xs))) (@ _let_1 (@ tptp.set_complex2 Xs))))))
% 1.40/2.18 (assert (forall ((X tptp.real) (N tptp.nat) (Xs tptp.list_real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 (@ tptp.set_real2 (@ (@ tptp.drop_real N) Xs))) (@ _let_1 (@ tptp.set_real2 Xs))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.drop_VEBT_VEBT N) Xs))) (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs))))))
% 1.40/2.18 (assert (forall ((X tptp.int) (N tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 (@ (@ tptp.drop_int N) Xs))) (@ _let_1 (@ tptp.set_int2 Xs))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 (@ (@ tptp.drop_nat N) Xs))) (@ _let_1 (@ tptp.set_nat2 Xs))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.drop_VEBT_VEBT N) Xs))) (@ tptp.set_VEBT_VEBT2 Xs))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ tptp.drop_nat N) Xs))) (@ tptp.set_nat2 Xs))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ tptp.drop_int N) Xs))) (@ tptp.set_int2 Xs))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (P (-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT Bool))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3))))) (@ (@ P Xs) Ys))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o) (P (-> tptp.list_VEBT_VEBT tptp.list_o Bool))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_o Ys)) (=> (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_o) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 Bool) (Ys3 tptp.list_o)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_o Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_o Y3) Ys3))))) (@ (@ P Xs) Ys))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat) (P (-> tptp.list_VEBT_VEBT tptp.list_nat Bool))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_nat) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_nat Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3))))) (@ (@ P Xs) Ys))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int) (P (-> tptp.list_VEBT_VEBT tptp.list_int Bool))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_int Ys)) (=> (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_int) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.int) (Ys3 tptp.list_int)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_int Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3))))) (@ (@ P Xs) Ys))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT) (P (-> tptp.list_o tptp.list_VEBT_VEBT Bool))) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ P tptp.nil_o) tptp.nil_VEBT_VEBT) (=> (forall ((X5 Bool) (Xs2 tptp.list_o) (Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_o X5) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3))))) (@ (@ P Xs) Ys))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o) (P (-> tptp.list_o tptp.list_o Bool))) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys)) (=> (@ (@ P tptp.nil_o) tptp.nil_o) (=> (forall ((X5 Bool) (Xs2 tptp.list_o) (Y3 Bool) (Ys3 tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_o X5) Xs2)) (@ (@ tptp.cons_o Y3) Ys3))))) (@ (@ P Xs) Ys))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_nat) (P (-> tptp.list_o tptp.list_nat Bool))) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_nat Ys)) (=> (@ (@ P tptp.nil_o) tptp.nil_nat) (=> (forall ((X5 Bool) (Xs2 tptp.list_o) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_nat Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_o X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3))))) (@ (@ P Xs) Ys))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_int) (P (-> tptp.list_o tptp.list_int Bool))) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_int Ys)) (=> (@ (@ P tptp.nil_o) tptp.nil_int) (=> (forall ((X5 Bool) (Xs2 tptp.list_o) (Y3 tptp.int) (Ys3 tptp.list_int)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_int Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_o X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3))))) (@ (@ P Xs) Ys))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT) (P (-> tptp.list_nat tptp.list_VEBT_VEBT Bool))) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (@ (@ P tptp.nil_nat) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3))))) (@ (@ P Xs) Ys))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_o) (P (-> tptp.list_nat tptp.list_o Bool))) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_o Ys)) (=> (@ (@ P tptp.nil_nat) tptp.nil_o) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 Bool) (Ys3 tptp.list_o)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_o Ys3)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_o Y3) Ys3))))) (@ (@ P Xs) Ys))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Zs tptp.list_VEBT_VEBT) (P (-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT Bool))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs)) (=> (@ (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_VEBT_VEBT) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT) (Z3 tptp.vEBT_VEBT) (Zs2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys3))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs2)) (=> (@ (@ (@ P Xs2) Ys3) Zs2) (@ (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3)) (@ (@ tptp.cons_VEBT_VEBT Z3) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Zs tptp.list_o) (P (-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT tptp.list_o Bool))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Zs)) (=> (@ (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_VEBT_VEBT) tptp.nil_o) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT) (Z3 Bool) (Zs2 tptp.list_o)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys3))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Zs2)) (=> (@ (@ (@ P Xs2) Ys3) Zs2) (@ (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3)) (@ (@ tptp.cons_o Z3) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Zs tptp.list_nat) (P (-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs)) (=> (@ (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_VEBT_VEBT) tptp.nil_nat) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT) (Z3 tptp.nat) (Zs2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys3))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs2)) (=> (@ (@ (@ P Xs2) Ys3) Zs2) (@ (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3)) (@ (@ tptp.cons_nat Z3) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (Zs tptp.list_int) (P (-> tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs)) (=> (@ (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_VEBT_VEBT) tptp.nil_int) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.vEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT) (Z3 tptp.int) (Zs2 tptp.list_int)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys3))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs2)) (=> (@ (@ (@ P Xs2) Ys3) Zs2) (@ (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_VEBT_VEBT Y3) Ys3)) (@ (@ tptp.cons_int Z3) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o) (Zs tptp.list_VEBT_VEBT) (P (-> tptp.list_VEBT_VEBT tptp.list_o tptp.list_VEBT_VEBT Bool))) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs)) (=> (@ (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_o) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 Bool) (Ys3 tptp.list_o) (Z3 tptp.vEBT_VEBT) (Zs2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_size_list_o Ys3))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs2)) (=> (@ (@ (@ P Xs2) Ys3) Zs2) (@ (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_o Y3) Ys3)) (@ (@ tptp.cons_VEBT_VEBT Z3) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o) (Zs tptp.list_o) (P (-> tptp.list_VEBT_VEBT tptp.list_o tptp.list_o Bool))) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Zs)) (=> (@ (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_o) tptp.nil_o) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 Bool) (Ys3 tptp.list_o) (Z3 Bool) (Zs2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys3))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Zs2)) (=> (@ (@ (@ P Xs2) Ys3) Zs2) (@ (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_o Y3) Ys3)) (@ (@ tptp.cons_o Z3) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o) (Zs tptp.list_nat) (P (-> tptp.list_VEBT_VEBT tptp.list_o tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs)) (=> (@ (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_o) tptp.nil_nat) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 Bool) (Ys3 tptp.list_o) (Z3 tptp.nat) (Zs2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_o Ys3))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Zs2)) (=> (@ (@ (@ P Xs2) Ys3) Zs2) (@ (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_o Y3) Ys3)) (@ (@ tptp.cons_nat Z3) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o) (Zs tptp.list_int) (P (-> tptp.list_VEBT_VEBT tptp.list_o tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs)) (=> (@ (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_o) tptp.nil_int) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 Bool) (Ys3 tptp.list_o) (Z3 tptp.int) (Zs2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_o Ys3))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Zs2)) (=> (@ (@ (@ P Xs2) Ys3) Zs2) (@ (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_o Y3) Ys3)) (@ (@ tptp.cons_int Z3) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat) (Zs tptp.list_VEBT_VEBT) (P (-> tptp.list_VEBT_VEBT tptp.list_nat tptp.list_VEBT_VEBT Bool))) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs)) (=> (@ (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_nat) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.nat) (Ys3 tptp.list_nat) (Z3 tptp.vEBT_VEBT) (Zs2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_size_list_nat Ys3))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs2)) (=> (@ (@ (@ P Xs2) Ys3) Zs2) (@ (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)) (@ (@ tptp.cons_VEBT_VEBT Z3) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat) (Zs tptp.list_o) (P (-> tptp.list_VEBT_VEBT tptp.list_nat tptp.list_o Bool))) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Zs)) (=> (@ (@ (@ P tptp.nil_VEBT_VEBT) tptp.nil_nat) tptp.nil_o) (=> (forall ((X5 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT) (Y3 tptp.nat) (Ys3 tptp.list_nat) (Z3 Bool) (Zs2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_nat Ys3))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Zs2)) (=> (@ (@ (@ P Xs2) Ys3) Zs2) (@ (@ (@ P (@ (@ tptp.cons_VEBT_VEBT X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)) (@ (@ tptp.cons_o Z3) Zs2))))))) (@ (@ (@ P Xs) Ys) Zs))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_VEBT_VEBT) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_VEBT_VEBT Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat) (Z3 tptp.int) (Zs2 tptp.list_int) (W2 tptp.vEBT_VEBT) (Ws2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)) (@ (@ tptp.cons_int Z3) Zs2)) (@ (@ tptp.cons_VEBT_VEBT W2) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_o) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_o Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_o) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat) (Z3 tptp.int) (Zs2 tptp.list_int) (W2 Bool) (Ws2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)) (@ (@ tptp.cons_int Z3) Zs2)) (@ (@ tptp.cons_o W2) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_nat) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_nat) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat) (Z3 tptp.int) (Zs2 tptp.list_int) (W2 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)) (@ (@ tptp.cons_int Z3) Zs2)) (@ (@ tptp.cons_nat W2) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_int) (P (-> tptp.list_nat tptp.list_nat tptp.list_int tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_nat) tptp.nil_int) tptp.nil_int) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat) (Z3 tptp.int) (Zs2 tptp.list_int) (W2 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Zs2))) (let ((_let_2 (@ tptp.size_size_list_nat Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)) (@ (@ tptp.cons_int Z3) Zs2)) (@ (@ tptp.cons_int W2) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_VEBT_VEBT) (Ws tptp.list_VEBT_VEBT) (P (-> tptp.list_nat tptp.list_int tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT Bool))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_VEBT_VEBT) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int) (Z3 tptp.vEBT_VEBT) (Zs2 tptp.list_VEBT_VEBT) (W2 tptp.vEBT_VEBT) (Ws2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_VEBT_VEBT Z3) Zs2)) (@ (@ tptp.cons_VEBT_VEBT W2) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_VEBT_VEBT) (Ws tptp.list_o) (P (-> tptp.list_nat tptp.list_int tptp.list_VEBT_VEBT tptp.list_o Bool))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_VEBT_VEBT) tptp.nil_o) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int) (Z3 tptp.vEBT_VEBT) (Zs2 tptp.list_VEBT_VEBT) (W2 Bool) (Ws2 tptp.list_o)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_VEBT_VEBT Z3) Zs2)) (@ (@ tptp.cons_o W2) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_VEBT_VEBT) (Ws tptp.list_nat) (P (-> tptp.list_nat tptp.list_int tptp.list_VEBT_VEBT tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_VEBT_VEBT) tptp.nil_nat) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int) (Z3 tptp.vEBT_VEBT) (Zs2 tptp.list_VEBT_VEBT) (W2 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_VEBT_VEBT Z3) Zs2)) (@ (@ tptp.cons_nat W2) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_VEBT_VEBT) (Ws tptp.list_int) (P (-> tptp.list_nat tptp.list_int tptp.list_VEBT_VEBT tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_VEBT_VEBT) tptp.nil_int) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int) (Z3 tptp.vEBT_VEBT) (Zs2 tptp.list_VEBT_VEBT) (W2 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_VEBT_VEBT Z3) Zs2)) (@ (@ tptp.cons_int W2) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_o) (Ws tptp.list_VEBT_VEBT) (P (-> tptp.list_nat tptp.list_int tptp.list_o tptp.list_VEBT_VEBT Bool))) (let ((_let_1 (@ tptp.size_size_list_o Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_o) tptp.nil_VEBT_VEBT) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int) (Z3 Bool) (Zs2 tptp.list_o) (W2 tptp.vEBT_VEBT) (Ws2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_size_list_o Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_s6755466524823107622T_VEBT Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_o Z3) Zs2)) (@ (@ tptp.cons_VEBT_VEBT W2) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 1.40/2.18 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_o) (Ws tptp.list_o) (P (-> tptp.list_nat tptp.list_int tptp.list_o tptp.list_o Bool))) (let ((_let_1 (@ tptp.size_size_list_o Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Ws)) (=> (@ (@ (@ (@ P tptp.nil_nat) tptp.nil_int) tptp.nil_o) tptp.nil_o) (=> (forall ((X5 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int) (Z3 Bool) (Zs2 tptp.list_o) (W2 Bool) (Ws2 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Zs2))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_o Ws2)) (=> (@ (@ (@ (@ P Xs2) Ys3) Zs2) Ws2) (@ (@ (@ (@ P (@ (@ tptp.cons_nat X5) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_o Z3) Zs2)) (@ (@ tptp.cons_o W2) Ws2))))))))) (@ (@ (@ (@ P Xs) Ys) Zs) Ws))))))))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y2) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y2) (or (@ (@ tptp.vEBT_vebt_member T) Y2) (= X Y2)))))))))
% 1.40/2.18 (assert (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y2) _let_1)) X)) N) X)))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y2) _let_1)) X)) N) Y2)))))
% 1.40/2.18 (assert (= (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 1.40/2.18 (assert (forall ((X tptp.nat)) (=> (forall ((N4 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N4) N4)))) (not (forall ((N4 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N4) (@ tptp.suc N4)))))))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 1.40/2.18 (assert (forall ((X23 tptp.nat) (Y23 tptp.nat)) (= (= (@ tptp.suc X23) (@ tptp.suc Y23)) (= X23 Y23))))
% 1.40/2.18 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (= tptp.vEBT_VEBT_high (lambda ((X4 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.divide_divide_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 1.40/2.18 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y2)) (= X Y2))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M) N)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M2 tptp.nat)) (and (= M (@ tptp.suc M2)) (@ (@ tptp.ord_less_nat N) M2))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P N) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 1.40/2.18 (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)))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 1.40/2.18 (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))))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X5 tptp.nat)) (@ (@ R X5) X5)) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((N4 tptp.nat)) (@ (@ R N4) (@ tptp.suc N4))) (@ (@ R M) N)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N4) (=> (@ P N4) (@ P (@ tptp.suc N4))))) (@ P N))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M3)) N4) (@ P M3))) (@ P N4))) (@ P N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 1.40/2.18 (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)))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 1.40/2.18 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P J) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N4) (=> (@ (@ tptp.ord_less_nat N4) J) (=> (@ P (@ tptp.suc N4)) (@ P N4))))) (@ P I2))))))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P I2) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N4) (=> (@ (@ tptp.ord_less_nat N4) J) (=> (@ P N4) (@ P (@ tptp.suc N4)))))) (@ P J))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K2 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 1.40/2.18 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))))
% 1.40/2.18 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 1.40/2.18 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 1.40/2.18 (assert (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (=> (not (= X Y2)) (=> (not (@ (@ tptp.ord_less_nat X) Y2)) (@ (@ tptp.ord_less_nat Y2) X)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (not (@ P N4)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N4) (not (@ P M3)))))) (@ P N))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N4) (@ P M3))) (@ P N4))) (@ P N))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 1.40/2.18 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y tptp.nat)) (=> (@ P Y) (@ (@ tptp.ord_less_eq_nat Y) X5)))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 1.40/2.18 (assert (forall ((V tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.18 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N2) (= M6 N2)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.18 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (not (= M6 N2))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (L2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L2) (=> (= (@ (@ tptp.plus_plus_nat M) L2) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I2)) I2))))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) I2))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (exists ((K3 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M6) K3))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (exists ((N4 tptp.nat)) (= L2 (@ (@ tptp.plus_plus_nat K) N4))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N) Q2)))))
% 1.40/2.18 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N4) (@ (@ tptp.ord_less_nat (@ F M5)) (@ F N4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M) N) Q2))))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N)))))))
% 1.40/2.18 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary)) N) (= Deg N))))
% 1.40/2.18 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList3) S2))))))
% 1.40/2.18 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N))))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 1.40/2.18 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 1.40/2.18 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 1.40/2.18 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N4 tptp.extended_enat)) (=> (forall ((M3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M3) N4) (@ P M3))) (@ P N4))) (@ P N))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N) K)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q2)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I2) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) I2))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N)) M)))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N))) M)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (= tptp.ord_less_eq_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y4) (= X4 Y4)))))
% 1.40/2.18 (assert (forall ((S3 tptp.set_real)) (=> (exists ((X3 tptp.real)) (@ (@ tptp.member_real X3) S3)) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Z4)))) (exists ((Y3 tptp.real)) (and (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real X3) Y3))) (forall ((Z4 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Z4))) (@ (@ tptp.ord_less_eq_real Y3) Z4)))))))))
% 1.40/2.18 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.power_power_real X) N4))))))
% 1.40/2.18 (assert (= tptp.vEBT_VEBT_low (lambda ((X4 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 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 TreeList2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) _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) TreeList2) Summary)) X))))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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 TreeList2)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))))
% 1.40/2.18 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (let ((_let_2 (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1))) (let ((_let_3 (@ tptp.product_Pair_nat_nat tptp.mi))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 (@ (@ tptp.ord_max_nat tptp.xa) tptp.ma)))) tptp.deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_insert _let_2) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_2)) (@ (@ tptp.vEBT_vebt_insert tptp.summary) _let_1)) tptp.summary)))))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 1.40/2.18 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 1.40/2.18 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 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) TreeList2) 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))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N)) (and (= M _let_1) (= N _let_1))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N)))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 1.40/2.18 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N)) N) M))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M)) N) M))))
% 1.40/2.18 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 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) TreeList2) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N) K)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 1.40/2.18 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList2 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 TreeList2) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ 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) TreeList2) 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 TreeList2) _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)))))))))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 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 TreeList2) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ 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) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _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))))))))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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)))
% 1.40/2.18 (assert (forall ((K tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 1.40/2.18 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va))))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N) A)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (= (@ (@ tptp.power_power_real X5) N) A) (forall ((Y tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.power_power_real Y) N) A)) (= Y X5)))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 1.40/2.18 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N4 tptp.nat)) (=> (@ P (@ tptp.suc N4)) (@ P N4))) (@ P tptp.zero_zero_nat)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (@ (@ P X5) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X5) Y3) (@ (@ P (@ tptp.suc X5)) (@ tptp.suc Y3)))) (@ (@ P M) N))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ tptp.suc N4)))) (@ P N)))))
% 1.40/2.18 (assert (forall ((Y2 tptp.nat)) (=> (not (= Y2 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y2 (@ tptp.suc Nat3))))))))
% 1.40/2.18 (assert (forall ((Nat tptp.nat) (X23 tptp.nat)) (=> (= Nat (@ tptp.suc X23)) (not (= Nat tptp.zero_zero_nat)))))
% 1.40/2.18 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 1.40/2.18 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((X23 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X23)))))
% 1.40/2.18 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (not (@ P N4)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N4) (not (@ P M3))))))) (@ P N)))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 1.40/2.18 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y2) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y2) (@ _let_1 Q22))))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P J3))))))))))
% 1.40/2.18 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 1.40/2.18 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N))) M) tptp.one_one_nat))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P2 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P2) (=> (@ (@ tptp.ord_less_nat M) P2) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N4) P2) (=> (@ P N4) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N4)) P2))))) (@ P M)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (forall ((S2 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q2) S2))))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (forall ((S2 tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S2))))))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (N tptp.nat) (Y2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y2) N)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X) (exists ((Q3 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y2) (@ (@ tptp.times_times_nat N) Q3))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M6 tptp.nat)) (= N (@ tptp.suc M6))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N)) A))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))))
% 1.40/2.18 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N) (= N tptp.zero_zero_nat)))))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N 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 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N4)) Y2))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 1.40/2.18 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N)) Q2))) (@ _let_1 N)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M7 tptp.nat)) (=> (@ P X) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M7))) (not (forall ((M5 tptp.nat)) (=> (@ P M5) (not (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M5)))))))))))
% 1.40/2.18 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 1.40/2.18 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X23)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M) N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (@ P N4) (@ P (@ tptp.suc N4))))) (@ P N))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N) K)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N)) (and (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (N 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) N))))))
% 1.40/2.18 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N) Q2))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M) N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) M)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N) M) (= N tptp.one_one_nat)))))
% 1.40/2.18 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 1.40/2.18 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 1.40/2.18 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P I4))))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ (@ tptp.plus_plus_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N)) (@ _let_1 M)))))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N)) (@ _let_1 N)))))))))
% 1.40/2.18 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ 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) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X5) N))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (=> (forall ((N4 tptp.nat)) (=> (@ P N4) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ P N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 1.40/2.18 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ 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) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) (@ (@ tptp.vEBT_VEBT_low X5) N))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 1.40/2.18 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B2) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B2) N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N)) N)) (@ (@ tptp.modulo_modulo_nat A2) N)))))
% 1.40/2.18 (assert (forall ((X23 tptp.num) (Y23 tptp.num)) (= (= (@ tptp.bit0 X23) (@ tptp.bit0 Y23)) (= X23 Y23))))
% 1.40/2.18 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 1.40/2.18 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N) K)) (@ _let_1 K)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N) K)) (@ _let_1 K)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N) K)) (@ _let_1 K)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L2) tptp.zero_zero_int)))
% 1.40/2.18 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))))))
% 1.40/2.18 (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)))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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))))))))
% 1.40/2.18 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 1.40/2.18 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B3 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) 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) B3) (=> (@ (@ tptp.ord_less_eq_int B3) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B2) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B2) N))))))
% 1.40/2.18 (assert (forall ((X tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K)) X)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B3 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 B3) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B3) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_eq_int B3) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 1.40/2.18 (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)))))))
% 1.40/2.18 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 1.40/2.18 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 1.40/2.18 (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)))))))
% 1.40/2.18 (assert (forall ((A2 tptp.int) (N tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N)) N)) (@ (@ tptp.modulo_modulo_int A2) N)))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))))
% 1.40/2.18 (assert (forall ((A tptp.int) (B3 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) B3) (=> (@ (@ tptp.ord_less_eq_int B3) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B3)) (@ _let_1 B))))))))
% 1.40/2.18 (assert (forall ((A tptp.int) (A3 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A3) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A3) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))))
% 1.40/2.18 (assert (forall ((B3 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 B3) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ _let_1 Q5)))))))
% 1.40/2.18 (assert (forall ((A tptp.int) (B3 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) B3) (=> (@ (@ tptp.ord_less_eq_int B3) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B3))))))))
% 1.40/2.18 (assert (forall ((A tptp.int) (A3 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A3) B))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3))))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4))))))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 1.40/2.18 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 1.40/2.18 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 1.40/2.18 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 1.40/2.18 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L2) L2)))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((W tptp.int) (Z12 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z12) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z12)) (@ _let_1 Z22))))))
% 1.40/2.18 (assert (forall ((Z12 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z12) Z22)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z12) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 1.40/2.18 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 1.40/2.18 (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)))))))))
% 1.40/2.18 (assert (forall ((X23 tptp.num)) (not (= tptp.one (@ tptp.bit0 X23)))))
% 1.40/2.18 (assert (forall ((A2 tptp.nat) (B2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B2) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B2) N))))))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va2) Vb) Vc)))))
% 1.40/2.18 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) (@ (@ tptp.times_times_int K) D))))))))))
% 1.40/2.18 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X))))
% 1.40/2.18 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 1.40/2.18 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))
% 1.40/2.18 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5))))))
% 1.40/2.18 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5)))))))
% 1.40/2.18 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool) (D3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) D3)))) (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))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv)))) (=> (forall ((Uu Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu) true)))) (=> (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) 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)))))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2)))))))))
% 1.40/2.18 (assert (forall ((Y2 tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y2 (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X222 Bool)) (not (= Y2 (@ (@ tptp.vEBT_Leaf X212) X222))))))))
% 1.40/2.18 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X22 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X22)))))
% 1.40/2.18 (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))))))))
% 1.40/2.18 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 1.40/2.18 (assert (forall ((Uv2 Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv2)))))
% 1.40/2.18 (assert (forall ((Uu2 Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu2) true)))))
% 1.40/2.18 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2)) X5)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 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 Va))) TreeList3) Summary2)) X5)))))))))))
% 1.40/2.18 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2)) X5)))))))))
% 1.40/2.18 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw)))) (=> (forall ((Ux 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) Ux) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 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)) X5)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 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)) X5)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd)) X5)))))))))))
% 1.40/2.18 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 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 Va))) TreeList3) Summary2)) X5)))))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Y2 Bool)) (let ((_let_1 (not Y2))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y2) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv))) Y2) (=> (=> (exists ((Uu Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu) true))) Y2) (=> (=> (exists ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) 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))) Y2))))))))))
% 1.40/2.18 (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))))))))))))
% 1.40/2.18 (assert (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X))))
% 1.40/2.18 (assert (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy))))
% 1.40/2.18 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 1.40/2.18 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 1.40/2.18 (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))))))))
% 1.40/2.18 (assert (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv)))) (=> (forall ((Uu Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu) 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))))))))))
% 1.40/2.18 (assert (forall ((V tptp.nat) (TreeList2 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) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList2) Summary)))))
% 1.40/2.18 (assert (forall ((X tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P3)) (= (=> (@ _let_1 X) P) (=> _let_2 P3))))))))
% 1.40/2.18 (assert (forall ((X tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P3)) (= (and (@ _let_1 X) P) (and _let_2 P3))))))))
% 1.40/2.18 (assert (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A1) A22) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= A22 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 N4) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (=> (= M5 (@ tptp.suc N4)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 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))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 N4) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ 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))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M5 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))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A22 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M5) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M5)) (=> (= M5 (@ tptp.suc N4)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N4) M5)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M5)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ 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))) M5)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2)))))))))))))))))))))))))))))))
% 1.40/2.18 (assert (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A4 Bool) (B4 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A4) B4))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= A23 (@ (@ tptp.plus_plus_nat N2) N2)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X2))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N2))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A23 (@ (@ tptp.plus_plus_nat N2) _let_1)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X2))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2)))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 N2)) (= A23 (@ (@ tptp.plus_plus_nat N2) N2)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X4) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N2))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList) Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 _let_3)) (= A23 (@ (@ tptp.plus_plus_nat N2) _let_3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) (@ (@ tptp.vEBT_VEBT_low X4) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))))))
% 1.40/2.18 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 1.40/2.18 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))))
% 1.40/2.18 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X4 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X4) (@ (@ tptp.vEBT_VEBT_membermima T2) X4)))))
% 1.40/2.18 (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)))))))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (@ (@ P N4) (@ (@ tptp.modulo_modulo_nat M5) N4)) (@ (@ P M5) N4)))) (@ (@ P M) N)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N) (@ (@ tptp.divide_divide_int K) _let_1)) L2)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X))))
% 1.40/2.18 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L2) L2)))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ _let_1 L2)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L2) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L2)) R2)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((Ux2 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) Ux2) Uy)) Uz))))
% 1.40/2.18 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 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) Va2) Vb)) X) (or (= X Mi) (= X Ma)))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ P A5) B5) (@ (@ P B5) A5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) tptp.zero_zero_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.plus_plus_nat A5) B5))))) (@ (@ P A) B))))))
% 1.40/2.18 (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)))))))))))
% 1.40/2.18 (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)))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y2 (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y2 (@ _let_1 true))) (=> (not _let_3) (= Y2 _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X _let_1) (not (= Y2 _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X _let_1) (not (= Y2 _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 (= Y2 (@ (@ (@ (@ 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 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 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 (= Y2 (@ (@ (@ 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))))))))))))))))))))
% 1.40/2.18 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 1.40/2.18 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N)) (not (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N))) (@ _let_1 N)))))
% 1.40/2.18 (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))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N) _let_1)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ (@ tptp.divide_divide_nat N) _let_1))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 1.40/2.18 (assert (forall ((W tptp.int) (Z12 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z12) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z12)) (@ _let_1 Z22))))))
% 1.40/2.18 (assert (forall ((Z12 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z12) Z22)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z12) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 1.40/2.18 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M) N) (@ _let_1 M))))))
% 1.40/2.18 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_int M) N) (=> (@ (@ tptp.dvd_dvd_int N) M) (= M N))))))))
% 1.40/2.18 (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)))))))
% 1.40/2.18 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M) N))))))
% 1.40/2.18 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D3)) (= (@ _let_2 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D3))))))))))
% 1.40/2.18 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y2)) D)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y2)) D))) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((K tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N) (@ (@ tptp.times_times_int K) M))) (@ _let_1 N)))))
% 1.40/2.18 (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))))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N))))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K) N)))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 1.40/2.18 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D3))))))))
% 1.40/2.18 (assert (forall ((Z tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z) N)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N)) (not (@ (@ tptp.dvd_dvd_nat N) M)))))
% 1.40/2.18 (assert (forall ((D tptp.int) (P3 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P3 X5) (@ P3 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (exists ((X_1 tptp.int)) (@ P3 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 1.40/2.18 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P1 X5) (@ P1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P1 X5))))) (=> (exists ((X_1 tptp.int)) (@ P1 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N)) M) (= N tptp.one_one_nat)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M)) M) (= N tptp.one_one_nat)))))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 1.40/2.18 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 1.40/2.18 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S 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 TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 1.40/2.18 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 1.40/2.18 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 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 TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (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 X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (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) TreeList2) 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 TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))))
% 1.40/2.18 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 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 TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)))) (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 ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (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 ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y2 (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) Y2) (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 ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S2))) (= Y2 (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 1.40/2.18 (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 ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ 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 Va))) 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))))))))))))))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu) Uv)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) 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 ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y2) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu) Uv))) Y2) (=> (=> (exists ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) Y2) (=> (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))) (= Y2 (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))) (= Y2 (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 ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (= Y2 (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 1.40/2.18 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) 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 TreeList2) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (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 TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)))) (=> (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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ 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 Va))) 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))))))))))))))))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y2 (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) Y2) (=> (=> (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))) Y2) (=> (=> (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))) Y2) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ 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 Va))) TreeList3) Summary2))) (= Y2 (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y2 (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y2 (@ _let_1 true))) (=> (not _let_3) (= Y2 _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S2))) (=> (= X _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (=> (= X _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (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) (=> (= Y2 (@ (@ (@ (@ 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 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 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) (=> (= Y2 (@ (@ (@ 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))))))))))))))))))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X) _let_1) (@ (@ tptp.divide_divide_nat Y2) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y2)) (= X Y2)))))))
% 1.40/2.18 (assert (forall ((X tptp.nat) (Y2 tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y2 (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y2) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (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.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 1.40/2.18 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y2 (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 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 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) (=> (= Y2 (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT 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))))))))))))))))))))))
% 1.40/2.18 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= 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) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (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 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))))))))))))))))))))))))))
% 1.40/2.18 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (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 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))))))))))))))))))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 1.40/2.18 (assert (forall ((I2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I2) N) (= (@ _let_1 (@ _let_1 I2)) I2)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 1.40/2.18 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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)))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (or (@ (@ tptp.ord_less_nat M) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))))
% 1.40/2.18 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I2 tptp.nat)) (=> (@ P K) (=> (forall ((N4 tptp.nat)) (=> (@ P (@ tptp.suc N4)) (@ P N4))) (@ P (@ (@ tptp.minus_minus_nat K) I2))))))
% 1.40/2.18 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 1.40/2.18 (assert (forall ((J tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (or (@ (@ tptp.ord_less_nat N) M) (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 1.40/2.18 (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))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N) L2)))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 M)))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X5)) (@ _let_2 Y3)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X5)) (@ _let_1 Y3)) D3)))))))))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))))
% 1.40/2.18 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 1.40/2.18 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 1.40/2.18 (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))))
% 1.40/2.18 (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))))))
% 1.40/2.18 (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)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 1.40/2.19 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N2)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M)) M) (@ (@ tptp.ord_max_nat N) M))))
% 1.40/2.19 (assert (forall ((Z tptp.extended_enat) (Y2 tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y2) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y2) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y2)) Z))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I2))) N))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N 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)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N))))))
% 1.40/2.19 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N 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)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N)))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N 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)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N))))))
% 1.40/2.19 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N 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)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N)))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N 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)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N))))))
% 1.40/2.19 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N 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)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M) N)))))
% 1.40/2.19 (assert (forall ((Q2 tptp.nat) (N 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 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))))
% 1.40/2.19 (assert (forall ((R2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N) (=> (@ (@ tptp.ord_less_eq_nat R2) M) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M) R2)) (= (@ (@ tptp.modulo_modulo_nat M) N) R2))))))
% 1.40/2.19 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N2)) N2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 1.40/2.19 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N2)) N2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 1.40/2.19 (assert (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N2))))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N 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)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N))))))
% 1.40/2.19 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N 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)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N)))))
% 1.40/2.19 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N2))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 1.40/2.19 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N4 tptp.nat)) (not (= X (@ tptp.suc N4))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (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.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))))))))))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y2 (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S2))) (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) (=> (= Y2 (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))))))))))))))))))
% 1.40/2.19 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S2 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) S2))) (=> (= 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))))))))))))))))
% 1.40/2.19 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) (=> (= 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) (S2 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) S2))) (=> (= 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))))))))))))))))
% 1.40/2.19 (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 ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) 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) (Vd 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) Vd))) (=> (= 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))))))))))))))))))
% 1.40/2.19 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy2))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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) (=> (= Y2 (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (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) (=> (= Y2 (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) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (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) (=> (= Y2 (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))))))))))))))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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) (Vd 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) Vd))) (=> (= 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)))))))))))))))))
% 1.40/2.19 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A5 tptp.real) (B5 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (=> (@ (@ P B5) C2) (=> (@ (@ tptp.ord_less_eq_real A5) B5) (=> (@ (@ tptp.ord_less_eq_real B5) C2) (@ _let_1 C2))))))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((D4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D4) (forall ((A5 tptp.real) (B5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A5) X5) (@ (@ tptp.ord_less_eq_real X5) B5) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B5) A5)) D4)) (@ (@ P A5) B5)))))))) (@ (@ P A) B))))))
% 1.40/2.19 (assert (= tptp.nat_triangle (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (assert (forall ((X tptp.nat) (Y2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y2 (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y2) (=> (@ _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 ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (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 (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y2 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N)) _let_1)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X4))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ P M6))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X4))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N tptp.one_one_int)) (and (= M _let_1) (= N _let_1)))))))
% 1.40/2.19 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 1.40/2.19 (assert (= tptp.minus_minus_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (@ (@ tptp.plus_plus_real X4) (@ tptp.uminus_uminus_real Y4)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y2))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y2) (@ tptp.uminus_uminus_real X)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.uminus_uminus_real X)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y2))))
% 1.40/2.19 (assert (forall ((A2 tptp.int) (B2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B2) N)) (@ (@ tptp.divide_divide_int A2) N))))))
% 1.40/2.19 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) _let_1))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) K))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 1.40/2.19 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N) (@ tptp.zero_n2687167440665602831ol_nat (not (= N _let_1)))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N)) (@ tptp.bit0 (@ _let_1 N))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 1.40/2.19 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) tptp.one)))))
% 1.40/2.19 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 1.40/2.19 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N)))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 1.40/2.19 (assert (forall ((X23 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X23) (@ tptp.bit1 X32)))))
% 1.40/2.19 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 1.40/2.19 (assert (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N4))))) (=> (forall ((N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N4))))) (=> (forall ((M5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit0 N4))))) (=> (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit1 N4))))) (=> (forall ((M5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit0 N4))))) (not (forall ((M5 tptp.num) (N4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit1 N4))))))))))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.num)) (=> (not (= Y2 tptp.one)) (=> (forall ((X24 tptp.num)) (not (= Y2 (@ tptp.bit0 X24)))) (not (forall ((X33 tptp.num)) (not (= Y2 (@ tptp.bit1 X33)))))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (B2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B2) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B2) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) D5))))) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X3) D5))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (B2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B2) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B2) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) D5))))) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X3) D5))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.plus_plus_int X5) D5))))) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X3) D5))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.plus_plus_int X5) D5))))) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X3) D5))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.19 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))
% 1.40/2.19 (assert (forall ((D tptp.int) (D5 tptp.int) (B2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D5) (forall ((X3 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) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X3) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X3) D5)) T)))))))))
% 1.40/2.19 (assert (forall ((D tptp.int) (D5 tptp.int) (B2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D5) (forall ((X3 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) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X3) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X3) D5)) T))))))))))
% 1.40/2.19 (assert (forall ((D tptp.int) (D5 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D5) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X3))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D5)) T))))))))))
% 1.40/2.19 (assert (forall ((D tptp.int) (D5 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D5) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X3))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D5)) T)))))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X2 tptp.int)) (@ P X2)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X4))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (T tptp.int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B2) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (= X3 T) (= (@ (@ tptp.minus_minus_int X3) D5) T))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (T tptp.int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (=> (@ (@ tptp.member_int T) B2) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (= X3 T)) (not (= (@ (@ tptp.minus_minus_int X3) D5) T)))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (B2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X3) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X3) D5)) T)))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (T tptp.int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (=> (@ (@ tptp.member_int T) B2) (forall ((X3 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) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.minus_minus_int X3) D5))))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (= X3 T) (= (@ (@ tptp.plus_plus_int X3) D5) T))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (=> (@ (@ tptp.member_int T) A2) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (= X3 T)) (not (= (@ (@ tptp.plus_plus_int X3) D5) T)))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (=> (@ (@ tptp.member_int T) A2) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X3) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X3) D5)) T))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (forall ((X3 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) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.plus_plus_int X3) D5)))))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (forall ((X3 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) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.plus_plus_int X3) D5)))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X3) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X3) D5)) T))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (T tptp.int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B2) (forall ((X3 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) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.minus_minus_int X3) D5))))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (B2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B2) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X3) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X3) D5)) T)))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P3 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B2) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D5))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P3 X5) (@ P3 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D5))))) (= (exists ((X2 tptp.int)) (@ P X2)) (or (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (@ P3 X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B2) (@ P (@ (@ tptp.plus_plus_int Y4) X4))))))))))))))
% 1.40/2.19 (assert (forall ((D5 tptp.int) (P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D5) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P3 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D5))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P3 X5) (@ P3 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D5))))) (= (exists ((X2 tptp.int)) (@ P X2)) (or (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (@ P3 X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D5)) (exists ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) A2) (@ P (@ (@ tptp.minus_minus_int Y4) X4))))))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 1.40/2.19 (assert (= tptp.nat_set_decode (lambda ((X4 tptp.nat)) (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X4) (@ (@ tptp.power_power_nat _let_1) N2))))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 1.40/2.19 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 1.40/2.19 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K)))))
% 1.40/2.19 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 1.40/2.19 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.pred_numeral K)))))
% 1.40/2.19 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K)))))
% 1.40/2.19 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 1.40/2.19 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 1.40/2.19 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (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)))))))
% 1.40/2.19 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real) (Z tptp.real)) (= (= X (@ (@ tptp.minus_minus_real Y2) Z)) (= Y2 (@ (@ tptp.plus_plus_real X) Z)))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int M) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N) (@ (@ tptp.plus_plus_int N) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 1.40/2.19 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 1.40/2.19 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 1.40/2.19 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X)))))
% 1.40/2.19 (assert (forall ((D tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 1.40/2.19 (assert (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))))
% 1.40/2.19 (assert (= tptp.ord_less_int (lambda ((N2 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N2)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N 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 N)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))))))
% 1.40/2.19 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X)))) tptp.one_one_real)))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N2))) (@ (@ 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) N2)) N2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat N) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 1.40/2.19 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 1.40/2.19 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (exists ((N4 tptp.nat)) (and (not (@ P N4)) (@ P (@ tptp.suc N4))))))))
% 1.40/2.19 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))))
% 1.40/2.19 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N2)) (@ (@ tptp.modulo_modulo_nat M6) N2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I4) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (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))))))))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) (@ tptp.semiri1314217659103216013at_int M))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) (@ tptp.semiri1314217659103216013at_int M))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W)))))
% 1.40/2.19 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N))))
% 1.40/2.19 (assert (forall ((N tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y2)))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 1.40/2.19 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 1.40/2.19 (assert (forall ((Z tptp.int)) (=> (forall ((N4 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N4)))) (not (forall ((N4 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))))
% 1.40/2.19 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N4 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N4))) (=> (forall ((N4 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))) (@ P Z)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.19 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N4 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N4))))))
% 1.40/2.19 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N4 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N4))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N))) Z))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 1.40/2.19 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N2 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y tptp.real)) (exists ((N4 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) X)))))))
% 1.40/2.19 (assert (forall ((M tptp.int)) (=> (forall ((N4 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N4)))) (not (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 1.40/2.19 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 1.40/2.19 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N2 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 1.40/2.19 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N4 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4)))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 1.40/2.19 (assert (forall ((D tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D))))))
% 1.40/2.19 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N4)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4))))))))
% 1.40/2.19 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (= K (@ tptp.semiri1314217659103216013at_int N4)))))))
% 1.40/2.19 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N4 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N4)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4)))) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4)))))))))
% 1.40/2.19 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))))
% 1.40/2.19 (assert (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))))))
% 1.40/2.19 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N4 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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 ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M5)) X)) C))) (= X tptp.zero_zero_real)))))))
% 1.40/2.19 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N4 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N4))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4))))))))
% 1.40/2.19 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y2 tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y2))) (and (=> (@ (@ tptp.ord_less_eq_nat Y2) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y2)))) (=> (@ (@ tptp.ord_less_nat X) Y2) (@ P tptp.zero_zero_int))))))
% 1.40/2.19 (assert (forall ((N 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 N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X)))) tptp.one_one_real)))
% 1.40/2.19 (assert (forall ((X tptp.real) (N 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 N)) X)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) N)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 1.40/2.19 (assert (forall ((X tptp.int) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y2) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y2)) _let_1)))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (forall ((N 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))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((Y2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))))
% 1.40/2.19 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 1.40/2.19 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 1.40/2.19 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 1.40/2.19 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 1.40/2.19 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 1.40/2.19 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 1.40/2.19 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 1.40/2.19 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 1.40/2.19 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y2 tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y2) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y2 (@ tptp.bit1 M5)))))) (=> (=> _let_3 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (not (= Y2 _let_1)))))) (=> (=> (exists ((N4 tptp.num)) (= X (@ tptp.bit0 N4))) (=> _let_1 (not (= Y2 (@ tptp.bit0 tptp.one))))) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit0 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit0 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y2 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))) (=> (=> (exists ((N4 tptp.num)) (= X (@ tptp.bit1 N4))) _let_2) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit1 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M5)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))) (not (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit1 N4)) (forall ((M5 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M5)) (not (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5)))))))))))))))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 1.40/2.19 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 1.40/2.19 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (= (@ tptp.ln_ln_real X) tptp.zero_zero_real) (= X tptp.one_one_real)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (= (@ _let_1 (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X)) (=> (@ _let_1 X) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y2))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) Y2)) Y2)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ (@ tptp.sums_real G) X) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) X))))
% 1.40/2.19 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y2 tptp.real)) (=> (@ (@ tptp.sums_real G) X) (=> (@ (@ tptp.sums_real F) Y2) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ F (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X) Y2))))))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ F I4)) (@ G I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) tptp.one_one_nat)))) _let_1))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N2)))) tptp.one_one_real))
% 1.40/2.19 (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 ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 1.40/2.19 (assert (forall ((N 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 N))) tptp.one_one_real)))
% 1.40/2.19 (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 ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N2))))))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.one_one_real)))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) U)) Y2))) V)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y) (@ (@ tptp.ord_less_eq_real Y) B))))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (forall ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 1.40/2.19 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y2)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 1.40/2.19 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))))
% 1.40/2.19 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y2))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arctan Y2))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N5 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N4) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N4))) (@ G N4))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))))))))))))))
% 1.40/2.19 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 1.40/2.19 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 1.40/2.19 (assert (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N)) M) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))))
% 1.40/2.19 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 1.40/2.19 (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)))
% 1.40/2.19 (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)))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ (@ tptp.power_power_real Z) I4))))))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N 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) N)) (@ (@ 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) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K)))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 1.40/2.19 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 1.40/2.19 (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))
% 1.40/2.19 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ 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 N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K))))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ 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 N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) X4)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))) tptp.zero_zero_complex))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X4 tptp.complex)) X4)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y2)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y2)))))))))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D3))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ F (@ _let_2 _let_1))) (@ F (@ _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real F))))))
% 1.40/2.19 (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)))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 1.40/2.19 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 1.40/2.19 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 1.40/2.19 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 1.40/2.19 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 1.40/2.19 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.zero_zero_real)))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.one_one_real)))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 1.40/2.19 (assert (forall ((N tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.one_one_real)))
% 1.40/2.19 (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))
% 1.40/2.19 (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)))
% 1.40/2.19 (assert (forall ((N tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (exists ((R3 tptp.real) (A5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X (@ _let_1 (@ tptp.cos_real A5))) (= Y2 (@ _let_1 (@ tptp.sin_real A5))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) (@ tptp.abs_abs_real X))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y2))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2))))) tptp.one_one_real)))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y2))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_2 Y2) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2)) (@ _let_1 X))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.pi) (=> (= (@ tptp.cos_real X) (@ tptp.cos_real Y2)) (= X Y2)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 1.40/2.19 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 1.40/2.19 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y2)) (@ (@ tptp.ord_less_real Y2) X)))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y2)) (@ tptp.cos_real X)))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) tptp.pi))))))
% 1.40/2.19 (assert (forall ((Y2 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) Y2) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.pi) (= X (@ tptp.cos_real T3)) (= Y2 (@ tptp.sin_real T3)))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 1.40/2.19 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 1.40/2.19 (assert (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X5) tptp.zero_zero_real) (forall ((Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y) tptp.zero_zero_real)) (= Y X5))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y2)) (@ tptp.cos_real X)))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) tptp.pi) (= (@ tptp.cos_real X5) Y2) (forall ((Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ tptp.cos_real Y) Y2)) (= Y X5)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y2) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X (@ tptp.cos_real T3)) (= Y2 (@ tptp.sin_real T3)))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X (@ tptp.cos_real T3)) (= Y2 (@ tptp.sin_real T3))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X (@ tptp.cos_real T3)) (not (= Y2 (@ tptp.sin_real T3))))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y2)) (= X Y2))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y2)) (@ _let_1 Y2)))))))))))
% 1.40/2.19 (assert (forall ((Y2 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)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y2)) (@ tptp.sin_real X))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (exists ((X4 tptp.int)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y2)) (@ (@ tptp.ord_less_real X) Y2))))))))))
% 1.40/2.19 (assert (forall ((Y2 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)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y2)) (@ tptp.sin_real X))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (exists ((X5 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)) X5) (@ (@ tptp.ord_less_eq_real X5) _let_1) (= (@ tptp.sin_real X5) Y2) (forall ((Y 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)) Y) (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ tptp.sin_real Y) Y2)) (= Y X5)))))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (or (exists ((X4 tptp.nat)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X4 tptp.nat)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (or (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X) T3) (@ (@ tptp.ord_less_real T3) 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.tan_real X))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 1.40/2.19 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y2) (@ tptp.tan_real X5)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (exists ((X5 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)) X5) (@ (@ tptp.ord_less_real X5) _let_1) (= (@ tptp.tan_real X5) Y2))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) (@ tptp.tan_real Y2)) (@ _let_1 Y2)))))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 Y2) (=> (@ _let_1 _let_2) (=> (@ _let_3 X) (=> (@ (@ tptp.ord_less_real X) _let_2) (= (@ _let_1 X) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y2)) (@ tptp.tan_real X))))))))))))
% 1.40/2.19 (assert (forall ((Y2 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)) Y2) (=> (@ (@ tptp.ord_less_real Y2) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y2)) (@ tptp.tan_real X))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (exists ((X5 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)) X5) (@ (@ tptp.ord_less_real X5) _let_1) (= (@ tptp.tan_real X5) Y2) (forall ((Y 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)) Y) (@ (@ tptp.ord_less_real Y) _let_1) (= (@ tptp.tan_real Y) Y2)) (= Y X5)))))))))
% 1.40/2.19 (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)))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y2)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y2)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X5) Y2))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (@ _let_2 Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (=> (@ (@ tptp.ord_less_real Y2) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y2))))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (= (@ tptp.tan_real X) Y2) (= (@ tptp.arctan Y2) X)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arctan Y2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_real _let_1) _let_2) (= (@ tptp.tan_real _let_1) Y2))))))
% 1.40/2.19 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B6 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 N))) (@ (@ tptp.times_times_real B6) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z3) (@ (@ tptp.ord_less_real Z3) _let_1) (= (@ tptp.tan_real Z3) X)))))))
% 1.40/2.19 (assert (= tptp.cos_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ tptp.semiri2265585572941072030t_real N2))) tptp.zero_zero_real)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.cos_real X))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))
% 1.40/2.19 (assert (= tptp.sin_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N2)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N)))))))))
% 1.40/2.19 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R2)))) (@ (@ tptp.power_power_nat N) R2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 1.40/2.19 (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)))))))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T3)) (@ tptp.sin_real T3)))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))
% 1.40/2.19 (assert (= tptp.binomial (lambda ((N2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K3))) (let ((_let_2 (@ tptp.ord_less_nat N2))) (@ (@ (@ 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 N2) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N2) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (= (@ tptp.sqrt X) (@ tptp.sqrt Y2)) (= X Y2))))
% 1.40/2.19 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_real X) Y2))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 1.40/2.19 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ tptp.exp_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y2)) (@ _let_1 Y2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))))
% 1.40/2.19 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))))
% 1.40/2.19 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)) (@ (@ tptp.ord_less_eq_nat K) N))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X)) K))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y2)) (@ (@ tptp.times_times_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R2)) (@ (@ tptp.power_power_nat N) R2)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X) Y2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.binomial N) K)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K))) _let_1))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X) Y2))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X)) (@ tptp.sqrt Y2))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y2) Y2))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))))
% 1.40/2.19 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 1.40/2.19 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) K))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y2) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) (@ (@ tptp.minus_minus_real Y2) tptp.one_one_real)) (= (@ tptp.exp_real X5) Y2))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y2)) X)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y2)) Y2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N)))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (K4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K4) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K4)) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K4)))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (K4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K4) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K4) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K4)) (@ _let_1 K))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2) (@ (@ tptp.ord_less_real X) (@ tptp.sqrt Y2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt Y2)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 1.40/2.19 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (K4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K4) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K4) N) (@ (@ tptp.ord_less_nat (@ _let_1 K4)) (@ _let_1 K))))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (K4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K4) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K4)) N) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K4)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (@ tptp.binomial N))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real) (X tptp.real)) (=> (= (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (= (@ tptp.sqrt X) Y2)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y2)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) Y2) (= X tptp.zero_zero_real)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) X) (= Y2 tptp.zero_zero_real)))))
% 1.40/2.19 (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)))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2) _let_1)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y2))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))) (@ (@ tptp.plus_plus_real X) Y2))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N) (= (@ tptp.sqrt (@ _let_3 N)) (@ _let_3 (@ (@ tptp.divide_divide_nat N) _let_2)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 1.40/2.19 (assert (forall ((Y2 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 Y2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y2))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) N) (@ (@ tptp.power_power_real X) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y2) _let_1)))))) tptp.one_one_real))))
% 1.40/2.19 (assert (forall ((X tptp.real) (U tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y2)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))) U))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N)) (@ tptp.exp_real X)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (U tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X) _let_4) (=> (@ (@ tptp.ord_less_real Y2) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y2) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y2) _let_2)))) U)))))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (assert (= tptp.arctan (lambda ((X4 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 X4) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 1.40/2.19 (assert (= tptp.tanh_real (lambda ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) N)))))))
% 1.40/2.19 (assert (= tptp.arsinh_real (lambda ((X4 tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 1.40/2.19 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 1.40/2.19 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y2)) Y2)))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y2)) Y2)))))
% 1.40/2.19 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 1.40/2.19 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y2)) (@ tptp.arccos X)))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y2)) (@ (@ tptp.ord_less_eq_real Y2) X))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y2)) (= X Y2)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y2)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y2)) (= X Y2))))))
% 1.40/2.19 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K3)) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N))) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y2))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y2)) (@ tptp.arccos X)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y2)) (@ (@ tptp.ord_less_real Y2) X))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y2)) tptp.pi)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y2)) (@ (@ tptp.ord_less_real X) Y2))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y2)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y2)) Y2))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N)) M)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R2) K3))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N)) R2))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arccos Y2))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arccos Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))))
% 1.40/2.19 (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) (not (= (@ tptp.sin_real (@ tptp.arccos X)) tptp.zero_zero_real))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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) (not (= (@ tptp.cos_real (@ tptp.arcsin X)) tptp.zero_zero_real))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N)) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 1.40/2.19 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arccos Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.cos_real _let_1) Y2)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N 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 N) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ (@ tptp.power_power_nat X) I4)))) (@ 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 N))) (@ (@ 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) N))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arcsin Y2))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_eq_real _let_2) _let_1))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (= (@ tptp.sin_real _let_1) Y2))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.sin_real _let_1) Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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)) Y2) (=> (@ (@ tptp.ord_less_eq_real Y2) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y2) (@ _let_1 (@ tptp.sin_real Y2)))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y2))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) 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)) Y2) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y2)) X))))))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) N2)))
% 1.40/2.19 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N 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 N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X)) N)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 1.40/2.19 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 1.40/2.19 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X)) (@ tptp.uminus1482373934393186551omplex X)))))
% 1.40/2.19 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))))
% 1.40/2.19 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) A) tptp.one_one_real)))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y2) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_real X) Y2)))))))))
% 1.40/2.19 (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_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) A))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_real A) X)))))))
% 1.40/2.19 (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_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X) (= (@ _let_2 (@ (@ tptp.log A) X)) (@ _let_1 X))))))))
% 1.40/2.19 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 1.40/2.19 (assert (forall ((Z tptp.complex) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ (@ tptp.divide1717551699836669952omplex Z) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z))) _let_1)))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_real X) Y2)))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))))
% 1.40/2.19 (assert (not (= tptp.imaginary_unit tptp.one_one_complex)))
% 1.40/2.19 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.numera6690914467698888265omplex W)))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X 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_1 (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))))))
% 1.40/2.19 (assert (= tptp.divide_divide_real (lambda ((X4 tptp.real) (Y4 tptp.real)) (@ (@ tptp.times_times_real X4) (@ tptp.inverse_inverse_real Y4)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))))))
% 1.40/2.19 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (= (@ (@ tptp.complex2 X) Y2) tptp.imaginary_unit) (and (= X tptp.zero_zero_real) (= Y2 tptp.one_one_real)))))
% 1.40/2.19 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 B))))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B) _let_1)))))))
% 1.40/2.19 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N4 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 1.40/2.19 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2)))) (and (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 1.40/2.19 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N4 tptp.nat)) (=> (not (= N4 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N4))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y2) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y2)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y2)))))))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y2) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ tptp.minus_minus_real (@ _let_1 X)) (@ _let_1 Y2)))))))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) (@ tptp.semiri5074537144036343181t_real N))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X)))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 1.40/2.19 (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)))))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 1.40/2.19 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (= tptp.divide1717551699836669952omplex (lambda ((X4 tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.times_times_complex X4) (@ tptp.invers8013647133539491842omplex Y4)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 1.40/2.19 (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)))
% 1.40/2.19 (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)))))))))))
% 1.40/2.19 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 1.40/2.19 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 1.40/2.19 (assert (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X) tptp.one_one_real) (= X tptp.zero_zero_real)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N))))))
% 1.40/2.19 (assert (= (@ tptp.cis tptp.pi) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 1.40/2.19 (assert (forall ((A tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y2)) Y2)))))
% 1.40/2.19 (assert (forall ((A 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 X) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X)) X)))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N))))))
% 1.40/2.19 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y2))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real) (Y2 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) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y2) A))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real A) B))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y2))) (=> (@ (@ 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 Y2)) (@ _let_1 X)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_eq_real X) Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real) (Y2 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) Y2) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y2) A)))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real) (Y2 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) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y2) A)) (@ (@ tptp.powr_real X) A)))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X) (@ _let_1 Y2)) (= X Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (@ _let_1 (@ (@ tptp.powr_real X) Y2)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y2) B))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X) Y2)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y2) A))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y2)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y2) A))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y2)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y2) A))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X) Y2)) (@ (@ tptp.times_times_real Y2) (@ tptp.ln_ln_real X))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (B tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y2)) (@ (@ tptp.times_times_real Y2) (@ _let_1 X)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_real Y2) X))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y2)) (@ (@ tptp.ord_less_real X) Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y2) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y2))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.arcosh_real (@ tptp.cosh_real X)) X))))
% 1.40/2.19 (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)))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X) N)))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y2)) X))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y2) (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y2)))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y2)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y2))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y2)) X) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.log B) X)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ 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) N))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 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 Y2)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y2)))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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) Y2)) X) (@ (@ tptp.ord_less_eq_real Y2) (@ (@ tptp.log B) X)))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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) Y2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y2))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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)) Y2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y2)))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 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 Y2) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y2)) X))))))
% 1.40/2.19 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ 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) N))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real Y2) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y2)) X))))))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real (@ _let_1 X)) Y2) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) Y2)))))))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real Y2) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y2)) X))))))))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real (@ _let_1 X)) Y2) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y2))))))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) _let_2))))) tptp.one_one_int))))))))
% 1.40/2.19 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ 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 N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))))))
% 1.40/2.19 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 1.40/2.19 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 1.40/2.19 (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))
% 1.40/2.19 (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))
% 1.40/2.19 (assert (forall ((Z tptp.complex)) (exists ((A5 tptp.complex) (R3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ tptp.exp_complex A5))))))
% 1.40/2.19 (assert (forall ((R2 tptp.real) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y2)) (@ (@ tptp.complex2 (@ _let_1 X)) (@ _let_1 Y2))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X) Y2)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X) R2)) (@ (@ tptp.times_times_real Y2) R2)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X) Y2)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X) R2)) Y2))))
% 1.40/2.19 (assert (forall ((R2 tptp.real) (X tptp.real) (Y2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R2) X)) Y2))))
% 1.40/2.19 (assert (= tptp.cis (lambda ((B4 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B4))))))
% 1.40/2.19 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 1.40/2.19 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A5 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A5))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A5)))))))))
% 1.40/2.19 (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)))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (= tptp.arctan (lambda ((Y4 tptp.real)) (@ tptp.the_real (lambda ((X4 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)) X4) (@ (@ tptp.ord_less_real X4) _let_1) (= (@ tptp.tan_real X4) Y4))))))))
% 1.40/2.19 (assert (= tptp.arcsin (lambda ((Y4 tptp.real)) (@ tptp.the_real (lambda ((X4 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)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.sin_real X4) Y4))))))))
% 1.40/2.19 (assert (forall ((L2 tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))) _let_1)))))))))))))))))
% 1.40/2.19 (assert (= (@ tptp.csqrt tptp.one_one_complex) tptp.one_one_complex))
% 1.40/2.19 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 1.40/2.19 (assert (forall ((K tptp.int)) (not (forall ((N4 tptp.nat) (L3 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L3)) (@ tptp.semiri1314217659103216013at_int N4))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X) (@ tptp.the_real (lambda ((X4 tptp.real)) false))))))
% 1.40/2.19 (assert (= tptp.sgn_sgn_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (= tptp.arccos (lambda ((Y4 tptp.real)) (@ tptp.the_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (= (@ tptp.cos_real X4) Y4)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A1) A22) A32) (=> (=> (= A22 tptp.zero_zero_int) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q3 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A22 tptp.zero_zero_int)) (not (= A1 (@ (@ tptp.times_times_int Q3) A22)))))) (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 A22)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A22)) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) A22)) R3)))))))))))))
% 1.40/2.19 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A12 K3) (= A23 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 (= A12 K3) (= A23 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 (= A12 K3) (= A23 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))))))))
% 1.40/2.19 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X4) tptp.zero_zero_real))))))
% 1.40/2.19 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X4) tptp.zero_zero_real)))))))
% 1.40/2.19 (assert (forall ((L2 tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))))))))))))))))
% 1.40/2.19 (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)))))))))))
% 1.40/2.19 (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))))))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))))))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 1.40/2.19 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 1.40/2.19 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 1.40/2.19 (assert (forall ((I2 tptp.int)) (= (= (@ tptp.nat2 I2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((X tptp.num) (N tptp.nat) (Y2 tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) (@ tptp.nat2 Y2)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y2))))
% 1.40/2.19 (assert (forall ((Y2 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (= Y2 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 1.40/2.19 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 1.40/2.19 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 1.40/2.19 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 1.40/2.19 (assert (= tptp.numeral_numeral_nat (lambda ((I4 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I4)))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y2) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y2)))))
% 1.40/2.19 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z6) (= (= (@ tptp.nat2 Z) (@ tptp.nat2 Z6)) (= Z Z6)))))))
% 1.40/2.19 (assert (= (lambda ((P4 (-> tptp.nat Bool))) (forall ((X7 tptp.nat)) (@ P4 X7))) (lambda ((P5 (-> tptp.nat Bool))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ P5 (@ tptp.nat2 X4)))))))
% 1.40/2.19 (assert (= (lambda ((P4 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P4 X7))) (lambda ((P5 (-> tptp.nat Bool))) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ P5 (@ tptp.nat2 X4)))))))
% 1.40/2.19 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 1.40/2.19 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N)))))
% 1.40/2.19 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 1.40/2.19 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z6) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z6)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))))
% 1.40/2.19 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))
% 1.40/2.19 (assert (= tptp.suc (lambda ((A4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) tptp.one_one_int)))))
% 1.40/2.19 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z6) (=> (@ (@ tptp.ord_less_eq_int Z6) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z6)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6)))))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X) Y2)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y2))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y2))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y2))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((Z tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N)))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y2)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y2))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 1.40/2.19 (assert (forall ((A tptp.real) (N 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)) N)) X) (=> (= X (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z6)))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 1.40/2.19 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X23)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 1.40/2.19 (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))))))))))))
% 1.40/2.19 (assert (= tptp.arg (lambda ((Z5 tptp.complex)) (@ (@ (@ tptp.if_real (= Z5 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z5) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int)))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int) tptp.one_one_int)))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) tptp.zero_zero_int)))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.zero_zero_int)))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) B)) (@ _let_1 B)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int) (R2 tptp.int) (S tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ tptp.bit_concat_bit N))) (= (= (@ (@ _let_2 K) L2) (@ (@ _let_2 R2) S)) (and (= (@ _let_1 K) (@ _let_1 R2)) (= L2 S)))))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y2))))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y2)) X))))
% 1.40/2.19 (assert (forall ((Y2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y2)) Y2))))
% 1.40/2.19 (assert (forall ((Y2 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y2) Ya)) Z)))))
% 1.40/2.19 (assert (forall ((Y2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_eq_int Y2) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y2)) Z)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ _let_1 tptp.zero_zero_int)))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y2)) (@ (@ tptp.bit_se1409905431419307370or_int X) Y2)) (@ (@ tptp.plus_plus_int X) Y2))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((Y2 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y2) Ya)) Z)))))
% 1.40/2.19 (assert (forall ((Y2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y2) (=> (@ (@ tptp.ord_less_int Y2) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y2)) Z)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 1.40/2.19 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 1.40/2.19 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 1.40/2.19 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 1.40/2.19 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))))
% 1.40/2.19 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 1.40/2.19 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) tptp.zero_zero_nat)))
% 1.40/2.19 (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)))
% 1.40/2.19 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) tptp.one_one_nat)))
% 1.40/2.19 (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)))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 1.40/2.19 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 1.40/2.19 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X5 tptp.num)) (=> (@ P X5) (@ P (@ tptp.inc X5)))) (@ P X)))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y2)) (@ tptp.inc (@ _let_1 Y2))))))
% 1.40/2.19 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 1.40/2.19 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 1.40/2.19 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 1.40/2.19 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 1.40/2.19 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y2)) (@ (@ tptp.plus_plus_num (@ _let_1 Y2)) X)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.zero_zero_real))))
% 1.40/2.19 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_real))))
% 1.40/2.19 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 1.40/2.19 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 1.40/2.19 (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))))))))))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 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) Y2) (and (=> _let_5 (= Y2 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y2 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 1.40/2.19 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ 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) N2))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N))))
% 1.40/2.19 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N))))
% 1.40/2.19 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N)))))
% 1.40/2.19 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N)))))
% 1.40/2.19 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 1.40/2.19 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L2)) N) (or (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) (@ (@ tptp.minus_minus_nat N) M)))))))
% 1.40/2.19 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N))))))))
% 1.40/2.19 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))))))
% 1.40/2.19 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N2) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))))))
% 1.40/2.19 (assert (forall ((K tptp.int)) (not (forall ((N4 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 N4) M3) (= (@ _let_1 M3) (@ _let_1 N4))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (not (@ _let_1 N4)))))))))))
% 1.40/2.19 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N2))))))))
% 1.40/2.19 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 1.40/2.19 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int 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) Y2) (=> _let_1 (not (=> (and (=> _let_6 (= Y2 (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y2 (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 1.40/2.19 (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))))))))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 1.40/2.19 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N)))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 1.40/2.19 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N2))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat N) _let_1))))))
% 1.40/2.19 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K2 tptp.int) (L3 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) L3)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L3) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))) (@ (@ P K2) L3)))))) (@ (@ P A0) A1)))))
% 1.40/2.19 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (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) A1)))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 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) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bit1 M5)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y2 _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit0 N4)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N4)) _let_1))))))))) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit0 N4)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N4) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N4)) _let_1))))))))) (=> (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit1 N4)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N4)) _let_1))))))))) (not (forall ((N4 tptp.num)) (=> (= X (@ tptp.bit1 N4)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N4) M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N4)) _let_1))))))))))))))))))))))))
% 1.40/2.19 (assert (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z5) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 1.40/2.19 (assert (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z7) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 1.40/2.19 (assert (forall ((X tptp.vEBT_VEBT) (Y2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y2) (=> (@ _let_2 X) (=> (=> (= X _let_1) (=> Y2 (not (@ _let_2 _let_1)))) (=> (forall ((Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) true))) (=> (= X _let_1) (=> (not Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2))) (=> (= X _let_1) (=> Y2 (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 Y2) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 1.40/2.19 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X) (=> (forall ((Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) 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))))))))))))
% 1.40/2.19 (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 ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 1.40/2.19 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2)))))
% 1.40/2.19 (assert (forall ((Y2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y2)))))
% 1.40/2.19 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 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 N2) _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 N2) _let_1))))))))))
% 1.40/2.19 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M6)) (not (@ _let_2 N2)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y2 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) Y2) (=> _let_1 (not (=> (and (=> _let_2 (= Y2 (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y2 tptp.nil_int))) (not _let_1)))))))))
% 1.40/2.19 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ _let_1 K)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L2) (@ (@ tptp.bit_se545348938243370406it_int N) L2))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I2) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I2))))
% 1.40/2.19 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I2) J)) (@ (@ tptp.ord_less_int J) I2))))
% 1.40/2.19 (assert (forall ((J tptp.int) (I2 tptp.int)) (=> (@ (@ tptp.ord_less_int J) I2) (= (@ (@ tptp.upto I2) J) tptp.nil_int))))
% 1.40/2.19 (assert (forall ((I2 tptp.int)) (= (@ (@ tptp.upto I2) I2) (@ (@ tptp.cons_int I2) tptp.nil_int))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N))))))
% 1.40/2.19 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 1.40/2.19 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) J3)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))))
% 1.40/2.19 (assert (= tptp.upto (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I4) J3) tptp.nil_int))))
% 1.40/2.19 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I4) J3)) __flatten_var_0))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y2) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X) Y2)))))))
% 1.40/2.19 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 1.40/2.19 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M))))))
% 1.40/2.19 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N) M))))))
% 1.40/2.19 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 1.40/2.19 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (= tptp.upto (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I4) J3)) (@ (@ tptp.cons_int I4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))) tptp.nil_int))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y2 tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y2) (and (=> _let_1 (= Y2 (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y2 tptp.nil_int)))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 1.40/2.19 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 1.40/2.19 (assert (forall ((X tptp.int) (N tptp.nat) (Y2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y2) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y2)) _let_1)))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (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)))))))))))))
% 1.40/2.19 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A2)))))))
% 1.40/2.19 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 1.40/2.19 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 1.40/2.19 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 1.40/2.19 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N6) (@ (@ tptp.ord_less_nat X4) M6)))))))
% 1.40/2.19 (assert (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N3) (@ (@ tptp.ord_less_nat X5) N))) (@ tptp.finite_finite_nat N3))))
% 1.40/2.19 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N6) (@ (@ tptp.ord_less_eq_nat X4) M6)))))))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N4) (@ F N4))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) U)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((Uu2 Bool) (Uv2 Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D) (= D tptp.one_one_nat))))
% 1.40/2.19 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 1.40/2.19 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 1.40/2.19 (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)))
% 1.40/2.19 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N3))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int)))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N) M))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.zero_zero_int)))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) K))))))
% 1.40/2.19 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K))))))
% 1.40/2.19 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 1.40/2.19 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 1.40/2.19 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))))))
% 1.40/2.19 (assert (= tptp.finite_finite_nat (lambda ((S4 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S4) (@ tptp.set_ord_atMost_nat K3))))))
% 1.40/2.19 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X) (@ _let_1 Y2)) (= X Y2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_real X) Y2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y2)) (@ (@ tptp.ord_less_eq_real X) Y2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) tptp.one_one_real) tptp.one_one_real))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.one_one_real) (= X tptp.one_one_real)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y2)) (@ _let_1 Y2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y2)) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 Y2))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N))) (= (@ _let_1 (@ _let_2 X)) (@ _let_2 (@ _let_1 X)))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X) (@ (@ tptp.root M) (@ (@ tptp.root N) X)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y2)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ _let_1 Y2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ _let_1 X))))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) Y2) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y2)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real) (Y2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X) Y2) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y2)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X)) (@ tptp.sgn_sgn_real X)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N3) X)) (@ (@ tptp.root N) X)))))))
% 1.40/2.19 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y2) N))) (@ tptp.abs_abs_real Y2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N3) X))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N3) X)) (@ (@ tptp.root N) X)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Y2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (=> (= (@ (@ tptp.power_power_real Y2) N) X) (= (@ (@ tptp.root N) X) Y2))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X) N)) X)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Y2 tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y2) N) X) (= (@ (@ tptp.root N) X) Y2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X) N)) X))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (=> (@ (@ 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 N) X)) (@ (@ tptp.root N3) X))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N))) Y2))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (B tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N) B)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X)))))))
% 1.40/2.19 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N) X)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y4 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N)) X) (@ P Y4))))))))
% 1.40/2.19 (assert (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M6 tptp.int)) (exists ((N2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M6) (@ tptp.abs_abs_int N2)) (@ (@ tptp.member_int N2) S3)))))))
% 1.40/2.19 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (@ (@ tptp.member_nat N2) S3)))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M5) (exists ((N7 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N7) (@ (@ tptp.member_nat N7) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 1.40/2.19 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ (@ tptp.member_nat N2) S3)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 1.40/2.19 (assert (= tptp.finite_finite_nat (lambda ((S4 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S4) (@ tptp.set_ord_lessThan_nat K3))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 1.40/2.19 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X2 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X2 M6)) (@ X2 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X4))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (@ P M6))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X4))))))
% 1.40/2.19 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L2) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat N) (@ _let_1 N))))))
% 1.40/2.19 (assert (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N3))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ 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) N) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I3))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ B I4)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 1.40/2.19 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)))
% 1.40/2.19 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I4) N)))) (@ tptp.suc N))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 1.40/2.19 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 1.40/2.19 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 1.40/2.19 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L2) tptp.zero_z3403309356797280102nteger)))
% 1.40/2.19 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L2) L2)))
% 1.40/2.19 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 1.40/2.19 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 1.40/2.19 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X)) (@ tptp.real_V1022390504157884413omplex X))))
% 1.40/2.19 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 1.40/2.19 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y2)))))
% 1.40/2.19 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.re X)))))
% 1.40/2.19 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.real_V1022390504157884413omplex X))))
% 1.40/2.19 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= tptp.one_one_int tptp.one_one_int))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 1.40/2.19 (assert (forall ((N3 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N3)) N))))
% 1.40/2.19 (assert (forall ((S3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) S3))))
% 1.40/2.19 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) N))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 1.40/2.19 (assert (= tptp.csqrt (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z5))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z5))) (let ((_let_4 (@ tptp.im Z5))) (@ (@ 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)))))))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.power_power_complex X) N)) tptp.zero_zero_real))))
% 1.40/2.19 (assert (forall ((V tptp.num)) (= (@ tptp.im (@ tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)))
% 1.40/2.19 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.re Z))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_real (@ tptp.re X)) N)))))
% 1.40/2.19 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))))))))
% 1.40/2.19 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 1.40/2.19 (assert (= (@ tptp.im tptp.one_one_complex) tptp.zero_zero_real))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X) Y2)) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y2)))))
% 1.40/2.19 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.im X)))))
% 1.40/2.19 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.real_V1022390504157884413omplex X))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X) Y2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.im Y2))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.re Y2))))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (=> (= (@ tptp.re X) (@ tptp.re Y2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.abs_abs_real (@ tptp.im Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (=> (= (@ tptp.im X) (@ tptp.im Y2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.abs_abs_real (@ tptp.re Y2)))))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X) Y2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.re Y2))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.im Y2))))))
% 1.40/2.19 (assert (= tptp.plus_plus_complex (lambda ((X4 tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X4)) (@ tptp.re Y4))) (@ (@ tptp.plus_plus_real (@ tptp.im X4)) (@ tptp.im Y4))))))
% 1.40/2.19 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X4))) (@ _let_1 (@ tptp.im X4)))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (= tptp.times_times_complex (lambda ((X4 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.re Y4))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X4)))) (let ((_let_3 (@ tptp.im Y4))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X4)))) (@ (@ 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))))))))))
% 1.40/2.19 (assert (= tptp.exp_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z5)))) (@ tptp.cis (@ tptp.im Z5))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z5 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 Z5)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z5)) _let_1)))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y2))) (let ((_let_3 (@ tptp.re Y2))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X) Y2)) (@ (@ 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)))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y2))) (let ((_let_3 (@ tptp.re Y2))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X) Y2)) (@ (@ 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)))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (= tptp.invers8013647133539491842omplex (lambda ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X4))) (let ((_let_3 (@ tptp.re X4))) (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)))))))))
% 1.40/2.19 (assert (= tptp.divide1717551699836669952omplex (lambda ((X4 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y4))) (let ((_let_3 (@ tptp.re Y4))) (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 X4)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X4)))) (@ (@ 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)))))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y2) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= X (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y2)) (and (= X tptp.zero_zero_complex) (= Y2 tptp.zero_zero_complex)))))))
% 1.40/2.19 (assert (forall ((Y2 tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y2) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y2) X) (and (= X tptp.zero_zero_complex) (= Y2 tptp.zero_zero_complex)))))))
% 1.40/2.19 (assert (forall ((I2 tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I2) J))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (= tptp.code_positive tptp.numera6620942414471956472nteger))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X) Y2)) (@ (@ tptp.times_times_complex (@ tptp.cnj X)) (@ tptp.cnj Y2)))))
% 1.40/2.19 (assert (= (@ tptp.cnj tptp.one_one_complex) tptp.one_one_complex))
% 1.40/2.19 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.cnj Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (N tptp.nat)) (= (@ tptp.cnj (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex (@ tptp.cnj X)) N))))
% 1.40/2.19 (assert (forall ((X tptp.complex) (Y2 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.plus_plus_complex X) Y2)) (@ (@ tptp.plus_plus_complex (@ tptp.cnj X)) (@ tptp.cnj Y2)))))
% 1.40/2.19 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.cnj _let_1) _let_1))))
% 1.40/2.19 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.cnj _let_1) _let_1))))
% 1.40/2.19 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z5 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z5) (@ tptp.cnj Z5)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (= tptp.code_integer_of_num tptp.numera6620942414471956472nteger))
% 1.40/2.19 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 1.40/2.19 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 1.40/2.19 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 1.40/2.19 (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) (S5 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S5))) (= S5 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 1.40/2.19 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 1.40/2.19 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M2 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M2) N)))) M)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M2 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M2)))) M)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N))))))
% 1.40/2.19 (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) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 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) S5)))))) _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) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 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)) S5)))))) _let_1))))))))))))
% 1.40/2.19 (assert (= tptp.archim6058952711729229775r_real (lambda ((X4 tptp.real)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z5)) X4) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))
% 1.40/2.19 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X4 tptp.rat)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z5)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))
% 1.40/2.19 (assert (= tptp.sgn_sgn_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (= A4 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A4)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 1.40/2.19 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (not (forall ((S2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S2) (forall ((T3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T3) (not (= R2 (@ (@ tptp.plus_plus_rat S2) T3)))))))))))
% 1.40/2.19 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_rat X4) Y4) (= X4 Y4)))))
% 1.40/2.19 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X25 tptp.nat)) X25))))
% 1.40/2.19 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P2)) (@ (@ 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 P2)))))
% 1.40/2.19 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.bezw X) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 1.40/2.19 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int)))
% 1.40/2.19 (assert (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R5)))))
% 1.40/2.19 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))
% 1.40/2.19 (assert (= tptp.ord_less_rat (lambda ((P6 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C3 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 C3) B4)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P6)))))
% 1.40/2.19 (assert (= tptp.ord_less_eq_rat (lambda ((P6 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C3 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 C3) B4)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P6)))))
% 1.40/2.19 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 1.40/2.19 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C3 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) C3))) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 1.40/2.19 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C3 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) C3))) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 1.40/2.19 (assert (forall ((P2 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 1.40/2.19 (assert (forall ((Q2 tptp.int) (S tptp.int) (P2 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S))) (= (@ (@ tptp.times_times_int P2) S) (@ (@ tptp.times_times_int R2) Q2)))))))
% 1.40/2.19 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C3 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 C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 1.40/2.19 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C3 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 C3) B4))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y2 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) Y2) (and (=> _let_2 (= Y2 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y2 (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 1.40/2.19 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat 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) Y2) (=> _let_1 (not (=> (and (=> _let_3 (= Y2 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y2 (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N) K)) (@ _let_1 K)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N) _let_1) _let_1))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N) M)) K)))))
% 1.40/2.19 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N2 tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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 ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N7) (@ tptp.finite_card_nat S3)) (@ (@ tptp.member_nat (@ R3 N7)) S3))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))))
% 1.40/2.19 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 1.40/2.19 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P2)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P2)))) tptp.one_one_int))))
% 1.40/2.19 (assert (forall ((Y2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y2) (@ (@ tptp.modulo_modulo_nat X) Y2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y2) (= (@ (@ tptp.bezw X) Y2) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y2)))))))))))
% 1.40/2.19 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y2 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) Y2) (and (=> _let_3 (= Y2 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y2 (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2))))))))))))))
% 1.40/2.19 (assert (= tptp.bezw (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y4) (@ (@ tptp.modulo_modulo_nat X4) Y4)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y4 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 X4) Y4)))))))))))
% 1.40/2.19 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y2 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat 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) Y2) (=> _let_1 (not (=> (and (=> _let_4 (= Y2 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y2 (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N)))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N))))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))))
% 1.40/2.19 (assert (= tptp.normalize (lambda ((P6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P6))) (let ((_let_2 (@ tptp.product_fst_int_int P6))) (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)))))))))))))
% 1.40/2.19 (assert (forall ((M tptp.int)) (= (@ (@ tptp.gcd_gcd_int M) tptp.one_one_int) tptp.one_one_int)))
% 1.40/2.19 (assert (forall ((N tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X) (@ (@ tptp.gcd_gcd_int _let_1) X)))))
% 1.40/2.19 (assert (forall ((X tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.gcd_gcd_int X))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X) Y2))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int)) (exists ((U2 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U2) X)) (@ (@ tptp.times_times_int V2) Y2)) (@ (@ tptp.gcd_gcd_int X) Y2)))))
% 1.40/2.19 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int K)) (@ (@ tptp.gcd_gcd_int M) N)) (@ (@ tptp.gcd_gcd_int (@ _let_1 M)) (@ _let_1 N))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.int) (Y2 tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X))) (let ((_let_2 (@ P (@ _let_1 Y2)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y2))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y2) 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 Y2))) (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 Y2)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 1.40/2.19 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N)) (or (not (= M tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 1.40/2.19 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M) N)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 1.40/2.19 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 1.40/2.19 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X5))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X5))) (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)))))))))))))
% 1.40/2.19 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X) Y2))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X) Y2)) (@ (@ 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 Y2)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I) (@ P I))) (@ P K2)))) (@ P M)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((K tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))))
% 1.40/2.19 (assert (forall ((N tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N) tptp.one)) K)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))
% 1.40/2.19 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 1.40/2.19 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 1.40/2.19 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 1.40/2.19 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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) (S5 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S5 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)) S5)))))) _let_1))))))))))
% 1.40/2.19 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y4) X4))) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.ord_less_nat Y4) X4))))
% 1.40/2.19 (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)))))))))
% 1.40/2.19 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= (@ tptp.code_int_of_integer tptp.one_one_Code_integer) tptp.one_one_int))
% 1.40/2.19 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 1.40/2.19 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X4 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa4)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (= tptp.code_negative (@ (@ tptp.comp_C3531382070062128313er_num tptp.uminus1351360451143612070nteger) tptp.numera6620942414471956472nteger)))
% 1.40/2.19 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 1.40/2.19 (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 ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y4))) (let ((_let_2 (@ tptp.times_times_nat X4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0))) Xa2) X)))))
% 1.40/2.19 (assert (forall ((M7 tptp.set_nat) (N3 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N3) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N3))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N))))))
% 1.40/2.19 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 1.40/2.19 (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 ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V4)) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0))) Xa2) X))))
% 1.40/2.19 (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 ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V4)) (@ (@ tptp.plus_plus_nat U3) Y4)))) __flatten_var_0))) Xa2) X))))
% 1.40/2.19 (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 ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U3)) (@ (@ tptp.plus_plus_nat Y4) V4)))) __flatten_var_0))) Xa2) X)))))
% 1.40/2.19 (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 ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V4)) (@ (@ tptp.plus_plus_nat Y4) U3)))) __flatten_var_0))) Xa2) X)))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (forall ((C tptp.nat) (Y2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y2))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y2))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y2))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y2) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 1.40/2.19 (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 ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X8) (@ tptp.set_ord_lessThan_nat I4)))) tptp.top_top_set_nat)))))))
% 1.40/2.19 (assert (= tptp.comple4887499456419720421f_real (lambda ((X2 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X2))))))
% 1.40/2.19 (assert (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_atMost_int K3))))))
% 1.40/2.19 (assert (= tptp.finite_finite_int (lambda ((S4 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S4)) (@ tptp.set_ord_lessThan_int K3))))))
% 1.40/2.19 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int X4) L2))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L2))) (@ (@ tptp.set_or4662586982721622107an_int L2) U))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 1.40/2.19 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 1.40/2.19 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 1.40/2.19 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (assert (= tptp.root (lambda ((N2 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y4 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N2)))) X4)))))
% 1.40/2.19 (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)))))))))))
% 1.40/2.19 (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)))))))))))))
% 1.40/2.19 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 1.40/2.19 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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))))))))))))
% 1.40/2.19 (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))))))))))))
% 1.40/2.19 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B7 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.integer_of_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B7)) (@ (@ 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 B7)) _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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real 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 N))) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))))
% 1.40/2.19 (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 ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H3) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 1.40/2.19 (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 ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H3) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 1.40/2.19 (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 ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.ord_less_real H3) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X) H3))) (@ F X)))))))))))
% 1.40/2.19 (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 ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.ord_less_real H3) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.plus_plus_real X) H3))))))))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X5)))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ G A)) (@ G B)))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F2 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F2 Z3)))))))))
% 1.40/2.19 (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 ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X5) 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)))))))
% 1.40/2.19 (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 ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X)) (@ F Y3)))) (= L2 tptp.zero_zero_real))))))
% 1.40/2.19 (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 ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X)))) (= L2 tptp.zero_zero_real))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real X4) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S))))
% 1.40/2.19 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (N 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 ((X4 tptp.real)) (@ (@ tptp.power_power_real (@ G X4)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 1.40/2.19 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z5 tptp.real)) (@ (@ tptp.powr_real Z5) 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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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 ((X4 tptp.real)) (@ (@ tptp.powr_real (@ G X4)) 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)))))))
% 1.40/2.19 (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 ((X4 tptp.real)) (@ (@ tptp.powr_real (@ G X4)) (@ F X4)))) (@ (@ 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)))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F2 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L4 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F2 X0))) (=> (forall ((N4 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ (@ F X4) N4))) (@ (@ F2 X0) N4)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X5)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L4) (=> (forall ((N4 tptp.nat) (X5 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X5) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X5) N4)) (@ (@ F Y3) N4)))) (@ (@ tptp.times_times_real (@ L4 N4)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X5) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X4 tptp.real)) (@ tptp.suminf_real (@ F X4)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X tptp.real) (D5 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) (= D5 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D5 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D5) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X5) N2)))))) (=> (@ (@ 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 ((X4 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X4) (@ tptp.suc N2))))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X0) N2))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 1.40/2.19 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M5 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 1.40/2.19 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 1.40/2.19 (assert (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 1.40/2.19 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real H2) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T3) (@ (@ tptp.ord_less_real T3) 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 1.40/2.19 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M5 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))))
% 1.40/2.19 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) 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 ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T3) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T3) (@ _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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N))))))))))))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real C) T3) (@ (@ tptp.ord_less_real T3) 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real A) T3) (@ (@ tptp.ord_less_real T3) 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 N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B2 tptp.real)) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M3 tptp.nat) (T4 tptp.real)) (let ((_let_1 (@ tptp.suc M3))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U3 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M3))) (@ (@ tptp.minus_minus_real (@ (@ Diff M3) U3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M3) P6)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real U3) P6)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U3) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M3)) P6)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real T4) P6)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T4) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real))))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (X tptp.real) (D5 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D5 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= 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) (= D5 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D5) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) F))) (exists ((L5 tptp.real) (M9 tptp.real)) (and (forall ((X3 tptp.real)) (let ((_let_1 (@ F X3))) (=> (and (@ (@ tptp.ord_less_eq_real A) X3) (@ (@ tptp.ord_less_eq_real X3) B)) (and (@ (@ tptp.ord_less_eq_real L5) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M9))))) (forall ((Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L5) Y) (@ (@ tptp.ord_less_eq_real Y) M9)) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B) (= (@ F X5) Y)))))))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.sqrt)))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (@ tptp.root N))))
% 1.40/2.19 (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 ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (= (@ G (@ F Z3)) Z3)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G)))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcosh_real))))
% 1.40/2.19 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X4 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X4)) (@ tptp.sin_real X4)))) (@ 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)))
% 1.40/2.19 (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.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arccos)))))
% 1.40/2.19 (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.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcsin)))))
% 1.40/2.19 (assert (forall ((B tptp.real) (X tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real B) X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X)))))))
% 1.40/2.19 (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.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.artanh_real)))))
% 1.40/2.19 (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 ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X))) D) (= (@ G (@ F Z3)) Z3))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) G)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F2 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (exists ((C2 tptp.real)) (and (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F2 C2))))))))))))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 1.40/2.19 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_nat X4) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 1.40/2.19 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X8 I3))) B2)) (not (forall ((L5 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L5)) tptp.at_top_nat))))))))
% 1.40/2.19 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N4))) (@ G N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ G N4))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L3 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L3))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N7)) L3)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L3) (@ G N7))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 1.40/2.19 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N5 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N4) (@ (@ tptp.ord_less_real R3) (@ X8 N4)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 1.40/2.19 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 1.40/2.19 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 1.40/2.19 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 1.40/2.19 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ F (@ tptp.suc N4)))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N4)) L2)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.plus_plus_real (@ F N7)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L2)) tptp.at_top_nat))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 1.40/2.19 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N2)))) N2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_nat)))
% 1.40/2.19 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 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 N2)))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2))))))))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2)))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))))))))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L3 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L3))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)))) L3)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 1.40/2.19 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N4))) (=> (forall ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N4))) (@ A N4))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 1.40/2.19 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C3 tptp.real)) (= F3 (lambda ((X4 tptp.real)) (@ (@ tptp.times_times_real X4) C3)))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y4 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y4))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y4)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 1.40/2.19 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5849166863359141190n_real tptp.one_one_real))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))
% 1.40/2.19 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 1.40/2.19 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 1.40/2.19 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X5) B) (exists ((Y tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F4) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real (@ F X4)) N))) tptp.at_bot_real) F4))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F4) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X4 tptp.real)) (@ (@ tptp.power_power_real (@ F X4)) N))) tptp.at_top_real) F4))))))
% 1.40/2.19 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 1.40/2.19 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 1.40/2.19 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 1.40/2.19 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 1.40/2.19 (assert (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5984915006950818249n_real tptp.one_one_real))))
% 1.40/2.19 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X4 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X4) K)) (@ tptp.exp_real X4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y4 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) Y4))) Y4))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_real)))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X5) (exists ((Y tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 1.40/2.19 (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))
% 1.40/2.19 (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 ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) F))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X5) (@ (@ tptp.ord_less_real X5) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) G))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X5) (@ (@ tptp.ord_less_real X5) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C2) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 1.40/2.19 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ tptp.suc I4)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 1.40/2.19 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N2) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 1.40/2.19 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I4) K)))) tptp.at_top_nat))))
% 1.40/2.19 (assert (forall ((F4 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F4) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N6)) F4)))))
% 1.40/2.19 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N6 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N2) (@ P N2)))))))
% 1.40/2.19 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X5) (@ P X5))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 1.40/2.19 (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 ((X4 tptp.real)) (@ P (@ (@ tptp.plus_plus_real X4) A)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 1.40/2.19 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 1.40/2.19 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 1.40/2.19 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 1.40/2.19 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real B2) (@ X8 I3))) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 1.40/2.19 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3)))))
% 1.40/2.19 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real B2) (@ X8 I3))) (not (forall ((L5 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L5)) tptp.at_top_nat) (not (forall ((I tptp.nat)) (@ (@ tptp.ord_less_eq_real L5) (@ X8 I)))))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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 ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((L3 tptp.real) (Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L3) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L3)))))))))
% 1.40/2.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ _let_1 (lambda ((X4 tptp.real)) (@ tptp.arcosh_real (@ F X4)))))))))
% 1.40/2.19 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (exists ((C2 tptp.real) (D3 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C2) D3)) (@ (@ tptp.ord_less_eq_real C2) D3)))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 1.40/2.19 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 1.40/2.19 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A2) (@ (@ tptp.member_real (@ F X5)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)))) (@ _let_1 (lambda ((X4 tptp.real)) (@ tptp.artanh_real (@ F X4)))))))))
% 1.40/2.19 (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))))
% 1.40/2.19 (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 ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X) (=> (@ (@ tptp.ord_less_eq_real X) B) (= (@ F X) (@ F A)))))))))
% 1.40/2.19 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y4 tptp.nat) (Z5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y4) V4)) (@ (@ tptp.plus_plus_nat U3) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa4)))))
% 1.40/2.19 (assert (= tptp.ord_less_int (lambda ((X4 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y4 tptp.nat) (Z5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y4) V4)) (@ (@ tptp.plus_plus_nat U3) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa4)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 1.40/2.19 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 1.40/2.19 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I3)) B2)) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 1.40/2.19 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B2 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I3)) B2)) (not (forall ((L5 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L5)) tptp.at_top_nat) (not (forall ((I tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I)) L5))))))))))
% 1.40/2.19 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M6)) M6))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y4 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N)))) tptp.top_top_set_real))))
% 1.40/2.19 (assert (forall ((B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.inj_on_real_real (@ tptp.log B)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 1.40/2.19 (assert (forall ((N3 tptp.set_nat) (K tptp.nat)) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.member_nat N4) N3) (@ (@ tptp.ord_less_eq_nat K) N4))) (@ (@ tptp.inj_on_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) K))) N3))))
% 1.40/2.19 (assert (forall ((N3 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N3)))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (@ tptp.summable_real (@ (@ tptp.comp_nat_real_nat F) G)))))))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G))) (@ tptp.suminf_real F)))))))
% 1.40/2.19 (assert (@ (@ tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (=> (forall ((X5 tptp.nat)) (=> (not (@ (@ tptp.member_nat X5) (@ (@ tptp.image_nat_nat G) tptp.top_top_set_nat))) (= (@ F X5) tptp.zero_zero_real))) (= (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G)) (@ tptp.suminf_real F))))))))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5))) (=> (@ tptp.order_mono_nat_real F) (=> (@ tptp.order_5726023648592871131at_nat G) (= (@ (@ tptp.bfun_nat_real (lambda ((X4 tptp.nat)) (@ F (@ G X4)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))))
% 1.40/2.19 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 1.40/2.19 (assert (forall ((X tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (or (not (= X tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X) N))))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 1.40/2.19 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 1.40/2.19 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N))))))))
% 1.40/2.19 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M6)))))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y2)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y2))) X)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 1.40/2.19 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 1.40/2.19 (assert (= tptp.sqr (lambda ((X4 tptp.num)) (@ (@ tptp.times_times_num X4) X4))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Y2 tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y2)) (@ tptp.sqr (@ _let_1 Y2))))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))))
% 1.40/2.19 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y2) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu) Uv))) (= Y2 (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)) (= Y2 (not (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))))
% 1.40/2.19 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa2) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu) Uv))) (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 ((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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))))))))))))
% 1.40/2.19 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 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) TreeList2) Summary)) Deg4) (and (= Deg Deg4) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X2))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima2)))))))
% 1.40/2.19 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa2)) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu) Uv))) (= 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 ((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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))
% 1.40/2.19 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y2 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa2) Y2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X _let_1) (=> (= Y2 (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (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) (=> (= Y2 (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ 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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 1.40/2.19 (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 ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= 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 ((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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima)))))))))))))))
% 1.40/2.19 (assert (= tptp.complete_Sup_Sup_int (lambda ((X2 tptp.set_int)) (@ tptp.the_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) X2) (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) X2) (@ (@ tptp.ord_less_eq_int Y4) X4)))))))))
% 1.40/2.19 (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 ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= 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 ((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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X4) (and (@ (@ tptp.ord_less_nat Mi3) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma3)))))))))))))) Mima))))))))))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 1.40/2.19 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) (@ tptp.pred_numeral K))))))
% 1.40/2.19 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int) (R2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) R2) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N)) L2) R2)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I2)) (@ (@ tptp.minus_minus_nat N) I2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N)) I2))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N)) Q2) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q2)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) L2)))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M2 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M2) N)))) M))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M2 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M2)))) M))))
% 1.40/2.19 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (N2 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))))
% 1.40/2.19 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 1.40/2.19 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)))
% 1.40/2.19 (assert (forall ((X tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real))))
% 1.40/2.19 (assert (forall ((X tptp.real) (Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y2) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X) X5) (@ (@ tptp.ord_less_real X5) Y2))))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X5) X)))))
% 1.40/2.19 (assert (forall ((X tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X) X5)))))
% 1.40/2.19 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 1.40/2.19 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.one_one_int) (@ tptp.ring_1_of_int_rat K))))
% 1.40/2.19 (assert (= tptp.one_one_rat (@ (@ tptp.fract tptp.one_one_int) tptp.one_one_int)))
% 1.40/2.19 (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)))))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (assert (forall ((A tptp.int)) (= (@ (@ tptp.fract A) tptp.zero_zero_int) (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int))))
% 1.40/2.19 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.fract (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int) (@ tptp.semiri681578069525770553at_rat K))))
% 1.40/2.19 (assert (= tptp.zero_zero_rat (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int)))
% 1.40/2.19 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 1.40/2.19 (assert (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))
% 1.40/2.19 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 1.40/2.19 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 1.40/2.19 (assert (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 1.40/2.19 (assert (forall ((N tptp.int) (M tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ (@ tptp.plus_plus_int M) N)) N) (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract M) N)) tptp.one_one_rat)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (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))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.numeral_numeral_int Q4)))))) (@ (@ tptp.bit_take_bit_num _let_1) N))))))
% 1.40/2.19 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 1.40/2.19 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 1.40/2.19 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num tptp.one))) N))))
% 1.40/2.19 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ 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)))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 1.40/2.19 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N) M)))))
% 1.40/2.19 (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))))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N8 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N8)))) (@ (@ tptp.bit_and_not_num M) N)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N2) M)))) N))))
% 1.40/2.19 (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)))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 1.40/2.19 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 1.40/2.19 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) (@ tptp.some_num Q2)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int Q2)))))
% 1.40/2.19 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))) N))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N) M)))))
% 1.40/2.19 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B)))))
% 1.40/2.19 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y2) (@ tptp.positive (@ (@ tptp.plus_plus_rat X) Y2))))))
% 1.40/2.19 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y2) (@ tptp.positive (@ (@ tptp.times_times_rat X) Y2))))))
% 1.40/2.19 (assert (= tptp.positive (lambda ((X4 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X4))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa2) Y2) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N4 tptp.num)) (= Xa2 (@ tptp.bit0 N4))) (not (= Y2 (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N4 tptp.num)) (= Xa2 (@ tptp.bit1 N4))) _let_1)) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num _let_1))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N4)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N4)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N8 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N8)))) (@ (@ tptp.bit_and_not_num M5) N4)))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N4))))))))))))))))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num _let_1)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N8 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N8)))) (@ (@ tptp.bit_and_not_num M5) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (not (= Y2 (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa2 tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y2 tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa2) Y2) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N4 tptp.num)) (= Xa2 (@ tptp.bit0 N4))) _let_4)) (=> (=> _let_5 (=> (exists ((N4 tptp.num)) (= Xa2 (@ tptp.bit1 N4))) _let_1)) (=> (=> (exists ((M5 tptp.num)) (= X (@ tptp.bit0 M5))) (=> _let_2 _let_4)) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4)))))))) (=> (=> (exists ((M5 tptp.num)) (= X (@ tptp.bit1 M5))) _let_3) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4)))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N8 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N8)))) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4)))))))))))))))))))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 1.40/2.19 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num tptp.one))))
% 1.40/2.19 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)))
% 1.40/2.19 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N8 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N8)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa2 _let_1) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N8 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N8)))) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa2) Y2) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y2 tptp.none_num)))) (=> (=> _let_1 (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y2 (@ tptp.some_num (@ tptp.bit1 N4))))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 N4))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit1 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (=> (= Xa2 tptp.one) (not (= Y2 (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N4)) (not (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N4)) (not (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4)))))))))))))))))))))
% 1.40/2.19 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))))
% 1.40/2.19 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 1.40/2.19 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num (@ tptp.bit0 N)))))
% 1.40/2.19 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num (@ tptp.bit1 N)))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))))
% 1.40/2.19 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y2 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa2) Y2) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y2 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ tptp.bit1 N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit1 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y2 (@ tptp.some_num (@ tptp.bit0 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit0 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N4 tptp.num)) (let ((_let_1 (@ tptp.bit1 N4))) (=> (= Xa2 _let_1) (=> (= Y2 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 1.40/2.19 (assert (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))
% 1.40/2.19 (assert (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))
% 1.40/2.19 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 1.40/2.19 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 1.40/2.19 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M6 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A4 tptp.nat) (X4 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 ((P6 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) P6)))) (lambda ((P6 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P6))))) X4))) A4))) (@ (@ tptp.product_Pair_nat_num N2) M6)))))
% 1.40/2.19 (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))))))))
% 1.40/2.19 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J)) I2))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I2) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) M)) J))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I2) J)) (@ (@ tptp.minus_minus_nat J) I2))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) M))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 1.40/2.19 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.upt I2) J) tptp.nil_nat))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.upt M) N))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I2) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I2)))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I2) J)) K) _let_1)))))
% 1.40/2.19 (assert (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))
% 1.40/2.19 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I4) J3)))))
% 1.40/2.19 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M6))))))
% 1.40/2.19 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M6)))))
% 1.40/2.19 (assert (= tptp.set_ord_lessThan_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N2)))))
% 1.40/2.19 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M6))))))
% 1.40/2.19 (assert (forall ((M tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q2)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q2))))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat)) (= (@ (@ tptp.upt I2) tptp.zero_zero_nat) tptp.nil_nat)))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I2) J))))
% 1.40/2.19 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J))))))
% 1.40/2.20 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 1.40/2.20 (assert (forall ((I2 tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat X) Xs)) (and (@ (@ tptp.ord_less_nat I2) J) (= I2 X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat)) J) Xs)))))
% 1.40/2.20 (assert (= tptp.upt (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J3)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J3))) tptp.nil_nat))))
% 1.40/2.20 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 1.40/2.20 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 1.40/2.20 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))
% 1.40/2.20 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N)))))
% 1.40/2.20 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 1.40/2.20 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.upt M) N))))
% 1.40/2.20 (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))))))))
% 1.40/2.20 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N3))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L) N3)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L)) tptp.one_one_nat) N3))))))))))
% 1.40/2.20 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L) M) (= (@ tptp.groups4561878855575611511st_nat L) N3))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N3) M)) tptp.one_one_nat)) N3))))
% 1.40/2.20 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))))
% 1.40/2.20 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 1.40/2.20 (assert (forall ((Ns tptp.list_nat) (I2 tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.nth_nat Ns) I2))))))
% 1.40/2.20 (assert (forall ((M tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N))))
% 1.40/2.20 (assert (forall ((I2 tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I2) J))))
% 1.40/2.20 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) N))))
% 1.40/2.20 (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)))))
% 1.40/2.20 (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)))))
% 1.40/2.20 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))))
% 1.40/2.20 (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))))))
% 1.40/2.20 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 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) N2)) M6))))))))
% 1.40/2.20 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 1.40/2.20 (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))))
% 1.40/2.20 (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)))))
% 1.40/2.20 (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)))))
% 1.40/2.20 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N2))) M6)))))
% 1.40/2.20 (assert (forall ((X tptp.list_nat) (Y2 tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y2) (=> (=> (= X tptp.nil_nat) (not (= Y2 tptp.zero_zero_nat))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X5) Xs2)) (not (= Y2 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs2)))))))))))))
% 1.40/2.20 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs)))))))
% 1.40/2.20 (assert (forall ((X tptp.list_nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y2) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y2 tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X5) Xs2))) (=> (= X _let_1) (=> (= Y2 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs2))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 1.40/2.20 (assert (forall ((N3 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N3) (= (@ tptp.gcd_Gcd_nat N3) tptp.one_one_nat))))
% 1.40/2.20 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 1.40/2.20 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 1.40/2.20 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X4)) (@ tptp.product_snd_int_int X4)))))))
% 1.40/2.20 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X4 tptp.nat)) X4)) _let_1) _let_1))))
% 1.40/2.20 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X4 tptp.int)) X4)) _let_1) _let_1))))
% 1.40/2.20 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.int) (Y2 tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.nat) (Y2 tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.num) (Y2 tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.num) (Y2 tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.rat) (Y2 tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.real) (Y2 tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X2 tptp.real)) (@ P X2)))))
% 1.40/2.20 (assert (forall ((X tptp.code_integer) (Y2 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.code_integer) (Y2 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.set_int) (Y2 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.vEBT_VEBT) (Y2 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.vEBT_VEBT) (Y2 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.list_int) (Y2 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.list_int) (Y2 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.list_nat) (Y2 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.list_nat) (Y2 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.option_num) (Y2 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.option_num) (Y2 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.product_prod_int_int) (Y2 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.product_prod_int_int) (Y2 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y2 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y2) Y2)))
% 1.40/2.20 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y2 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y2) X)))
% 1.40/2.20 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 1.40/2.20 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y2 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) cvc5 interrupted by timeout.
% 300.17/290.86 /export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 20164 CPU time limit exceeded (core dumped) ( read result; case "$result" in
% 300.17/290.86 unsat)
% 300.17/290.86 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 300.17/290.86 ;;
% 300.17/290.86 sat)
% 300.17/290.86 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 300.17/290.86 ;;
% 300.17/290.86 esac; exit 1 )
% 300.17/290.87 Cputime limit exceeded (core dumped) (core dumped)
% 300.17/290.87 % cvc5---1.0.5 exiting
% 300.17/290.87 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------